摘要:

FARADAY SPECIAL DISCUSSIONS OF THE CHEMICAL SOCIETY NO. 2 1972 Solid/Solid Interfaces THE FARADAY DIVISION CHEMICAL SOCIETY LONDONFARADAY SPECIAL DISCUSSIONS OF THE CHEMICAL SOCIETY NO. 2 1972 Solid/Solid Interfaces THE FARADAY DIVISION CHEMICAL SOCIETY LONDONA SPECIAL DISCUSSION ON Solid/ Soli d Interfaces 18th, 19th and 20th September 1972 A SPECIAL DISCUSSION on Solid/Solid Interfaces was held at the University of Nottingham on the 18th, 19th and 20th September, 1972. It was the second in the series of Special Discussions on physico-chemical topics of particular significance in industrial and technological research, the first being that on Thin Liquid Films and Boundary Layers (September, 1970, at Cambridge University). The Chairman at the opening session was the President of the Faraday Division, Professor J.W. Linnett, F.R.S. who welcomed 112 Fellows and others. Among the visitors from overseas were: Dr. F. Jost, W. Germany, Mr. J. F. Mandell, U.S.A., Prof. 0. Ishai, Israel, Prof. R. Sh. Mikhail, Egypt, Dr. T. Murayama, U.S.A., Dr. R. J. Nash, U.S.A., Dr. R. N. Williams, U.S.A.0 The Chemical Society and Contributors 1973 Printed in Great Britain at the University Press, AberdeenCONTENTS Page 7 18 26 38 46 56 63 77 90 109 117 123 127 137 144 FRICTION AND ADHESION Surface Forces in Friction and Adhesion by B. J. Briscoe and D. Tabor Adhesion of Metals to Polymers by C. Weaver A Theoretical Explanation of the Lowering of Frictional Forces with Layer Height of Long Chain Polar Lubricants by M. J. Sutcliffe and A.Cameron Strength and Failure Patterns of Metal-Metal Adhesives by K. W. Allen, H. S. Alsalim and W. C. Wake Nature of the Deformation and Flow of Metals at and Near the Interface During Abrasion, and its Relation to the Friction by D. S . Lin and H. Wilman GENERAL DIscussxoN.-Dr. H. Wilman, Dr. B. J. Briscoe, Dr. D. Tabor, Prof. M. W. Roberts, Dr. R. G. Linford, Dr. J. R. Young, Prof. D. D. Eley, Prof. W. C. Wake COMPOSITE MATERIALS I Fibre Reinforced Composite Materials. by B. A. Proctor Static and Fatigue Failure of Glass Fibre Reinforced Polyester Resins under Complex Stress Conditions by M. J. Owen and M. S. Found Fracture Toughness Studies of Fibre Reinforced Plastic Laminates by F. J. McGarry and J. F. Mandell Transverse Crack Propagation in Fibre Reinforced Composites by J.G. Morley Some Problems of Design in Fibre Reinforced Materials by W. D. Biggs GENERAL DIscussIoN.-Prof. R. Sh. Mikhail, Dr. B. A. Proctor, Prof. W. C. Wake, Prof. D. D. Eley, Dr. M. J. Owen, Mr. P. T. Bishop An Introductory Review COMPOSITE MATERIALS I1 Morphology and Mechanical Properties of a Rubber Reinforced Composite by G. Allen, D. J. Blundell, M. J. Bowden, F. G. Hutchinson and G. M. Jeffs Interface Morphology and Mechanical Properties of Unidirectional Fibre Reinforced Nylon 6 by T. Bessell, D. Hull and J. B. Shortall Some Interfacial Problems in Metal Matrix- Carbon Fibre Composites by S. V. Barnett, S. J. Harris and J. V. Weaver 159 * Effect of Surface Treatment on the Interfacial Bond Strength in Glass Fibre- Polyester Resin Systems by J.B. Shortall and H. W. C. Yip 165 Reinforcement of Thermoplastics using Carbon Fibres by W. H. Bowyer and M. G. Bader 174 GENERAL DIscussroN.-Prof. W. C. Wake, Prof. M. W. Roberts, Dr. R. G. Linford, Dr. S . J. Harris, Prof. R. Sh. Mikhail, Mr. R. Leveson 56 CONTENTS 177 185 194 198 210 222 228 ELECTRODEPOSITED AND OTHER COATINGS SolidlSolid Interfaces-Electrodeposited and Dynamic Coatings by J. P. G. Farr and G. W. Rowe Epitaxy on Nickel Electrodeposits on a Copper (1 10) Face, from a Sulphamate Bath, in Relation to Rate of Deposition, Deposit Thickness, Degree of Stirring, and Bath Temperature by S. K. Verma and H. Wilman Interface Crystallography of Ion Group Metals and Alloys Electrodeposited on Copper by J. M. O’Sullivan and D. P. Oxley Mechanism of Formation and Some Surface Characteristics of Thin Polymer Films Formed on Metal Surfaces by Electron Bombardment by S. Frost, W. J. Murphy, M. W. Roberts, J. R. H. Ross and J. H. Wood Mechanical Degradation of Thin Polystyrene Films by Robert J. Nash and Darryl M. Jacobs GENERAL Drscuss1oN.-Dr. H. Wilman, Dr. J. P. G. Farr, Prof. M. W. Roberts, Dr. J. M. O’Sullivan, Prof. W. C. Wake, Prof. R. Sh. Mikhail AUTHOR INDEX

ISSN:0370-9302    

DOI:10.1039/S19720200001

出版商:RSC    

年代:1972

数据来源: RSC

摘要:

Friction and Adhesion Surface Forces in Friction and Adhesion B Y B. J. BRISCOE AND D. TABOR Surface Physics, Cavendish Laboratory, University of Cambridge Receiued 23rd June, 1972 Atomic forces at the interface constitute the major factor responsible for friction and adhesion between unlubricated surfaces. For non-metals these are basically the van der Waals dispersion forces, though in special cases electrostatic forces may be involved. Some recent work on van der Waals forces at very small separations will be described. These forces provide a fairly direct measure of the adhesion between soft rubber-like materials and between polymeric solids. With polymers, such interfacial forces are sufficient to transfer portions of the polymer from one surface to the other when they are placed in contact or slid over one another.Frictional transfer occurs even for mater- ials such as P.T.F.E. With metal surfaces, van der Waals forces are overtaken by metallic bonding when the regions of contact are separated by distances comparable with atomic dimensions. This leads to very strong adhesion between metals which are atomically clean. By contrast, very small quantities of active vapours adsorbed at the interface can produce a drastic reduction in adhesion. Another factor which greatly influences the adhesion of a metal is its ductility : metals which have a limited number of slip planes usually show smaller adhesion. The importance of ductility is also shown in the behaviour of very hard materials such as Tic or diamond in ultra high vacuum.Intimate contact is restricted to individual asperities, and the ad- hesion for very clean surfaces is far less than might be expected from calculations based on surface forces. This is partly because the area of real contact is very small ; partly because of the brittleness of these materials. If one of the surfaces is soft or ductile adhesion may be quite strong. For example the adhesion of clean Tic to Tic is extremely small ; of clean copper to Tic extremely large. Here again surface films can greatly reduce the adhesive strength, The force exerted by one solid surface on another in close proximity to it is the result of atomic interactions. To a first approximation, these surface atomic forces are similar to those which are responsible for the cohesive strength of the solid.Thus, adhesion between two clean solids should be as natural and as strong as the cohesion which occurs within the bulk and under certain favourable conditions this is so. For example, two pieces of clean gold placed in contact will form metallic bonds over the regions of atomic contact and the interface will have the strength of bulk gold. With materials such as diamond or titanium carbide, if thoroughly clean, the surface forces will resemble valency forces : with rock salt the surface forces will be partly ionic. All these are essentially short-range forces. In addition there are of course van der Waals forces which are exerted by all atoms. These are weaker than the other forces we have described but they operate over larger distances. Surface forces are capable of producing adhesion.Since friction is generally a measure of the force required to break adhesions at the regions of real contact, there should be a connection between surface forces and friction. In what follows we shall discuss this for certain specific systems and relate our conclusions to some of the other papers published in this session of the conference. For simplicity we begin with a description of recent work on van der Waals forces and their role in adhesion and friction. 78 SURFACE FORCES SURFACE FORCES IN ADHESlON THE DIRECT MEASUREMENT OF VAN DER WAALS FORCES All atoms and molecules attract one another. If they are polar this attraction is due either to dipole-dipole interactions or to dipole induced-dipole interactions.As London showed in 1930 similar attractions can occur between non polar molecules. This is because their non-polarity is a time-average. If examined over a very short time interval (ca 10-l6 s), the electronic distribution will not be symmetrical and the atom or molecule will possess an instantaneous dipole. This will interact with a neighbouring atom or molecule to give a resultant attractive force which varies as l/x7 where x is the distance between the atom and its neighbour. If, however, the atoms are far apart, the time taken for the electrostatic field created by one atom to reach a neighbouring atom may be comparable with the fluctuating period of its own dipole. In that case, the initial dipole and the induced dipole are no longer in phase : the interaction is known as retarded van der Waals forces and the attractive force falls off as 1/x8.If the period of the fluctuating dipole is ca. s there will be lack of correlation between neighbouring atoms when the separation is greater than 3 x 10-8m. The most direct way of studying these interactions is to measure the forces between two solid bodies when they are brought very close together. As a first approxima- tion it may be assumed that the van der WaaIs force between any pair of atoms (or molecules) is additive so that the total force may be calculated by summation for all pairs of atoms in the two bodies. This leads to the following result for a sphere of radius R at a distance of nearest approach D from a flat surface : non retarded forces F = (A/6)R/D2 (1) retarded forces F = (2nB/3)R/D3 (2) where A and B are the Hamaker constants for non-retarded and retarded forces respectively. Previous work which employed polished surfaces of quartz or glass was generally unable to operate at separations less than about 100 nm because of the problem of surface roughness.Such measurements confirmed the existence of retarded van der Waals force~.l-~ Clearly the forces involved in adhesion and friction must be those which operate when separations are far smaller. The only work which has carried the measurements down to separations of the order of a few atomic spacings is that involving the use of mica surfaces which can be cleaved to be molecularly smooth. In these experiments, the mica specimens were silvered on their back faces and glued on to cylindrical glass mountings. They were supported with their axes mutually at right angles so that the contact resembles that between a sphere and a flat.The separation could be determined using multiple beam interferometry to an accuracy of about 0.2 nm. In the fist series of experiment^,^ the lower surface was mounted on a stiff piezo-electric transducer so that it could be moved smoothly and contin- uously towards the upper surface. The latter was mounted at the end of a cantilever spring. As the lower surface was moved towards the upper, at some point depending on the stiffness of the spirng, the two would jump into contact. The stiffer the spring the shorter the jump distance so that small jump distances were less affected by external vibrations than large jump distances.If Do is the critical jump distance, R the radius of curvature of the cylinders and c is the force constant of the spring it is easy to show thatB . J . BRISCOE AND D. TABOR 9 Di = $/(;) for non-retarded forces D: = 2zl?/(;) for retarded forces. (3) (4) Thus, by measuring the jump distance for different values of the spring stiffness a relation between Do and c/R could be obtained. The results of a log-log plot due to Tabor and Winterton are shown in fig. 1 and it is seen that for Do below 10 nm the slope is one third, for Do above 15 nm it approaches one quarter. Further the calculated values of A and B agree well with theory. FIG. 1.-Data of Tabor and Winterton for opposed mica cylinders plotted according to eqn (3) and (4).Do is the critical jump distance, c the stiffness of the elastic beam and R the radius of curva- ture of the cylinders. The results show a transition from non-retarded to retarded van der Waals forces at a separation of approximately 15 nm. Above 20 nm the results are close to the calculated vaIues obtained from the Lifshitz theory using a theoretical value for the Hamaker constant, B, of 0.87 x J m. Below 10 nm the results are consistent with a calculated Hamaker constant, A, of 10-l9 J. A and B may be calculated from the optical properties of mica. These studies have recently been extended to a wider range of separation^.^^ ti The jump method has been extended down to a jump distance of 2 nm. For separa- tions above 20 to 30 nm the leaf spring is so weak that vibrations picked up from external sources makes measurements impossible. A new dynamic method was developed which covers the range from 10 to 130 nm.By feeding the piezo-electric transducer with an ax. voltage, the lower surface can be set vibrating in a vertical direction at very small amplitudes (ca. 0.1 nm) over a convenient range of frequencies The upper surface is supported on a stiff spring also made of piezo-electric material. Its natural frequency depends both on the spring stiffness and on the van der Waals10 SURFACE FORCES force exerted on it by the lower surface. By determining the resonant frequency of the upper surface as a function of separation, the law of force may be deduced. In the region where the two methods overlapped (that is between 10 and 20 nm) the results 10 * I 10-2 10-8 surface force parameter FIG. 2.-Transition from retarded to non-retarded forces as the separation of two mica cylinders is reduced from 100 nm to 2 nm.The transition occurs at about 20 nm. Data taken from Israel- achvili and Tabor.5 Between 10nm and 130nm, a new dynamic method was used. The jump method was used for separations between 20 and 2 nm. The data from the two methods are normal- ized such that the surface force parameter provides lines with gradients of IZ + 2 where n is the power law dependence of the force. The region enclosed by the broken lines corresponds to the experi- mental region covered by the work of Tabor and Winterton given in fig. 1. were in excellent agreement. If the results are expressed as though they had been obtained by a single method the whole of the data from 2 to 130 nm can be combined as in fig.2. Finally fig. 3 shows the transition from non-retarded to retarded van der Waals forces as the separation is increased from about 12 nm to 50 nm. We may conclude I 2 4 6 8 10 2 ; 4 0 00 ROlOG 2 0 0 separation /nm FIG. 3.-Power law dependence, n, plotted against separation for crossed mica cylinders. The data show the gradual transition from non-retarded forces, n = 2, to retarded forces, n = 3, over a region of separation between 10 nm and 100 n ~ . ~10 SURFACE FORCES force exerted on it by the lower surface. By determining the resonant frequency of the upper surface as a function of separation, the law of force may be deduced. In the region where the two methods overlapped (that is between 10 and 20 nm) the results 10 * I 10-2 10-8 surface force parameter FIG.2.-Transition from retarded to non-retarded forces as the separation of two mica cylinders is reduced from 100 nm to 2 nm. The transition occurs at about 20 nm. Data taken from Israel- achvili and Tabor.5 Between 10nm and 130nm, a new dynamic method was used. The jump method was used for separations between 20 and 2 nm. The data from the two methods are normal- ized such that the surface force parameter provides lines with gradients of IZ + 2 where n is the power law dependence of the force. The region enclosed by the broken lines corresponds to the experi- mental region covered by the work of Tabor and Winterton given in fig. 1. were in excellent agreement. If the results are expressed as though they had been obtained by a single method the whole of the data from 2 to 130 nm can be combined as in fig.2. Finally fig. 3 shows the transition from non-retarded to retarded van der Waals forces as the separation is increased from about 12 nm to 50 nm. We may conclude I 2 4 6 8 10 2 ; 4 0 00 ROlOG 2 0 0 separation /nm FIG. 3.-Power law dependence, n, plotted against separation for crossed mica cylinders. The data show the gradual transition from non-retarded forces, n = 2, to retarded forces, n = 3, over a region of separation between 10 nm and 100 n ~ . ~12 SURFACE FORCES VAN DER WAALS INTERACTIONS AND THE FRICTION OF POLYMERS When polymers slide over a clean glass surface, the adhesion at the polymer-glass interface is usually stronger than the cohesion within the polymer itself.This is partly because the Hamaker constant for glass is larger than for the polymer so that the van der Waals interaction alone is sufficient to make the interface stronger. This may well be augmented by electrostatic or other short range forces. The net result is that, during sliding, shearing occurs within the polymer rather than at the interface. The friction is determined by the strength properties of the polymer (representative values of p, the coefficient of friction, lying between 0.2 and 0.5) and fragments of polymer are transferred to the glass. Even with a PTFE slider on clean glass, the initial static friction is relatively high (p = 0.2 to 0.3) and there is lumpy transfer of polymer.However, as soon as sliding begins a new phenomenon is observed. The coefficient of friction rapidly falls to p = 0.06 and this is accom- panied by a complete change in the nature of the transfer : it now consists of a very thin rather tenuous film of polymer of thickness 2 to 10 nm. This film can, with care, be removed and examined by electron diffraction : such a study shows that the poly- mer chains are drawn and strongly oriented parallel to the sliding direction. If the slider is placed on a fresh part of the glass surface and sliding is commenced in the same direction, the static friction is almost equal to the kinetic (pu0.06) and there is no lumpy transfer. If, however, the slider is rotated through 90" about its axis and placed on a fresh part of the glass surface, the static friction is again high (,u,xO.2), there is again lumpy transfer, and this is followed by a low kinetic friction ( ~ ~ ~ ~ 0 .0 6 ) and a thin film of highly oriented polymer. Evidently the underface of the slider becomes oriented. This face adheres strongly to clean glass. If sliding is carried out at right angles to the orientation of the slider underface the force required to shear the polymer is large, the friction is high and transfer is lumpy. If, however, the sliding is in the same direction as the orientation of the slider underface, the sliding process involves the drawing out of molecular chains from the slider and their adhesion to the glass. There is a further point of interest. If the slider repeatedly traverses the same track on the glass surface the transferred film does not grow appreciably thicker and the friction remains constant at its low value of pk x 0.06.Apparently the sliding of the oriented slider over the oriented film involves shear stresses which are just about equal to the stress required to draw further material from the slider.ll* l2 If the PTFE molecule is modified to incorporate bulky side groups, it ceases to be a material which gives a low kinetic friction and light film-like transfer. It becomes a " normal " polymer giving a fairly high kinetic friction and lumpy transfer. Similar results are observed with polythene. Low density polythene, which contains numer- ous straggly side-groups, is a " normal " high friction material. By contrast, high density polythene which has practically no side groups behaves in a manner similar to PTFE.The exceptional frictional behaviour of PTFE and high density polythene is associated with their smooth molecular profile. The low friction of PTFE over an oriented transferred film of PTFE involves the sliding of polymer chains over one another. It provides a very good example of a frictional process in which the interaction is entirely due to van der Waals forces. Another example is provided in the sliding of solid surfaces lubricated by hydro- carbon films. Recently Scruton et aZ.l3. l4 have studied this process in the following way (see also Bowers and Zisman 15). A hemispherical slider of fired glass was slid over a flat surface which was also made of fired glass. These surfaces are not Most thermoplastic polymers behave in this way.B .J . BRISCOE A N D D. TABOR 13 molecularly smooth but they are smooth enough for us to assume that the area of true molecular contact is essentially the same as the macroscopic (Hertzian) area of contact. By varying the radius of curvature of the slider from 3.7 pm to 2.4 mm and the normal load from g to 20 g it was possible to obtain contact pressures ranging from lo7 N m-2 to 3 x lo9 N m-2. Monolayers and multilayers of calcium stearate were deposited on the glass from a Langmuir trough containing a 5 x M solution of CaCI, at pH = 9 so that the films were, in fact, almost 100 % anhydrous calcium stearate. The force to produce sliding at a specified speed was measured. If this is divided by the calculated area of contact, we obtain a value for the shear strength z of the film material.Such measurements showed that z was almost independent of film thickness, but the effect of contact pressure was very marked. Typical results are shown in fig. 4. On the same graph, experimental points are included for the bulk 1o61 ' I I 1 I o6 lo7 loB lo9 10'O contact pressure/N m-2 FIG. 4.-Comparison of shear strength data as a function of pressure for various paraffinic materials. It is seen that a wide range of substances of different structures and thicknesses manifest similar behaviour. 0, calcium stearate, five monolayers sheared between a glass flat and sphere l3 ; 0, calcium stearate+stearic acid, two monolayers sheared between mica surfaces l6 ; 0 , thin (ca.125 nm) film of paraffi wax (m.p. 65°C) sheared between a spherical and flat surface l5 ; 8 , a relatively thick initially unoriented layer of stearic acid sheared between platens l7 ; x , thick initially unoriented layer of sodium stearate sheared between platens ' and A, thick initially unoriented layer of ferric stearate sheared between platens.'' These data and other data 19> *O not recorded in the figure suggest that for all these materials the shear process involves the sliding of methylene groups or chain segments over each other. shear strength of copper stearate, ferric stearate, sodium stearate, stearic acid and paraffin wax (m.p. 65°C). It is seen that in spite of structural and chemical differences they all behave in a very similar way. The shear strength z for low contact pressures does not change markedly with contact pressure : but for contact pressures exceeding about lo8 N m-2 (10 kg mnr2), z increases almost linearly with pressure.This explains the general observation that the friction of surfaces lubricated with these materials does not depend very markedly on the hardness of the surfaces. Of greater relevance, in the context of the present paper, is the comparison between the shear strength of these hydrocarbon films and that of polythene and PTFE as described earlier. This is shown in fig. 5, which compares shear strength of 5 monolayers of stearic acid as a function of temperature with the interfacial shear strength of the polymers in the low-friction regime. The agreement is rather close.As mentioned above, electron-diffraction has shown that in the polymer experiments the molecular14 SURFACE FORCES chains in one surface slide over molecular chains oriented in the same direction in the other. This suggests that with all the hydrocarbon materials recorded in fig. 4 the sliding process distorts the molecules and orients them such that shearing, whether in thin films or in the bulk, involves essentially the sliding of chains, lengthways, over temperat ure/"C FIG. 5.-Temperature dependence of the shear strength of calcium stearate ( O),I4 of high density polythene (0) and P.T.F.E. (O)." The calcium stearate results are for 5 layers deposited on, and sheared between, glass surfaces, so that the contact pressure is substantially independent of temper- ature. The polymer results are from friction experiments in which the polymer is slid over a clean glass surface : the contact pressure falls somewhat because of softening. The results are therefore not strictly comparable but the overall pattern of behaviour is similar.In addition the shear pres- sures involve activation energies of similar magnitudes. one another. It is interesting in this connection to see the theoretical model which Sutcliffe and Cameron 21 have adopted in their theoretical treatment of this problem. One of the major difficulties here, as in all papers of this genre, is that the forces between atoms and molecules do not generally provide a direct measure of strength properties. The role of flaws and/or dislocations must always be considered : often they are the decisive factor.This has long been recognized in the field of metal physics. We may also note that even in the friction of metals there is a tendency for an orientation favouring easy glide to be generated by the sliding process itself. VAN DER WAALS FORCES AND NEGATIVE COEFFICIENTS OF FRICTION Skinner 22 has recently studied the sliding of metals such as lead or gold over a smooth diamond or graphite surface. The loads were very small, usually of order 100 dyn N) or less. The whole experiment was carried out in the field of view of a scanning electron microscope ; vibrations from external sources were almost entirely eliminated. The surfaces were probably slightly contaminated so that no perceptible transfer of metal to the other surface occurred.After repeated sliding had produced a flat on the metal slider (as a result of flow or creep), it was observed that a finite normal force was required to lift the slider away from the other surface. Simple calculation showed that this could be attributed to van der Waals forces operating over most of the contact region, assuming a gap of order 1 nm. This adhesion was retained even during sliding. Consequently a negative normal load could be applied and, provided it was less than the adhesional force, steady sliding could be achieved by the application of an appropriate tangential force. This implies6 0 - 1 5 2 c( 2 4 0 2 -2 20- dz .- + It is assumed that intimate contact occurs over a small portion of the worn flat. The rest of the flat is, on the average, about 1 nm distant from the lower surface and the van der Waals attraction imposes an augmented normal load on the regions of true contact where the frictional process takes place. The work suggests that such effects are not observed in large scale experiments because of the ease with which vibrations can separate the surfaces when negative normal loads are applied.It is possible that this is one of the factors responsible for the absence of adhesion between clean TIC surfaces as described below. I I - /*o* I /' / / / I I / I i / I' 0- - / * a - - - - - - - fAA - - - - 3 0 0 -200 - 100 0 t 5 0 THE ADHESION OF CLEAN METALS AND OTHER NON-VAN DER WAALS SOLIDS THE EFFECT OF DUCTILITY AND OF SURFACE FILMS If two clean metals are brought together, they will first experience an attractive force due to van der Waals interactions.When the separation is within two or three atomic spacings the van der Waals interaction will be weakened by the shielding action of the conduction electrons : at the same time a metallic-type bond will begin to form and when the separation is as small as an atomic specing the biondng will be wholly metallic. The bond is perhaps 50 or 100 times stronger than that which would be calculated on the assumption that van der Waals interactions operate in their normal way down to atomic separations. This corresponds to the fact that for clean metals the free surface energy is of order 1000 to 3000mJm-2 compared with 30mJm-2 for simple hydrocarbons or plastics. Consequently, for clean metals the adhesion is determined primarily by metallic bonds over the areas of atomic contact-all other regions of " near-contact " will contribute very little.16 SURFACE FORCES Pfaelzer 23 has recently studied the adhesion between metals thoroughly cleaned in a vacuum of lo-'' Torr.There are two new factors involved in these experiments. First, the surfaces are not atomically smooth so that the area of true contact is deter- mined by the deformation of the individual asperities. At the very small loads used in this work this is probably elastic. Secondly, if the adhesion is to be measured, the joining load must first be removed before we can apply a separating force. In the course of this process elastic stresses will be released, the shape of the interface will be slightly changed and the junctions will be subjected to strong tensile stresses.If the material is lacking in ductility this process may well break the junctions even before a separating force has been applied. Consequently, the ductility of the metal is of great importance in determining the observed adhesive strength : this in turn is closely connected with the number of independent slip-planes. Thus copper and gold show strong adhesion: cobalt which is hexagonal shows weak adhesion; titanium carbide (see below) which is brittle shows almost zero adhesion. The effect of ductility is well illustrated by considering the behaviour of TIC. We should expect strong short range bonding both against itself and against metals. Nevertheless, the observed adhesion of Tic against Tic is very small : for Tic against iron it is larger and for Tic against clean copper the adhesion is very strong indeed.Here the ductility of the metal is able to accommodate the elastic stresses released when the joining load is removed. The effect of surface films has also been studied. With pure iron specimens pressed against them~elves,~~ a fraction of a monolayer of oxygen is able to reduce the adhesion to negligible values. This is a chemisorbed film. With copper specimens, far more oxygen is required and the film is presumably chemically combined. The surface film probably acts in two ways. It interposes a layer between the metals and so reduces or eliminates true metal-metal bonding. Secondly, although the surface film itself may adhere strongly to the counter surface it may well lack ductility.Unfortunately there is little direct information concerning the mechanical properties of very thin adsorbed or chemically formed films. However there is a good deal of indirect evidence showing that many metal oxides are in fact relatively brittle. The critical influence of ductility is also apparent in the action of adhesives. In the first instance, adhesives must wet the surfaces, since this implies good contact and good interfacial adhesion strength. Secondly, they must not show marked volume changes on solidifying so that they do not produce localized regions of high stress concentrations. Finally, they must have some ductility in order to take up any dimensional changes which may occur either as a result of loading, or as a result of differential thermal expansion.Some of these, as well as other, issues are discussed in the paper by Allen, Alsalin and Wake (this Discussion). Recently, Barnes 2 5 has studied the friction of metals and their carbides in ultra high vacuum. He has shown that the friction depends upon the mechanical pro- perties and surface contamination in a similar manner to the adhesion. CONCLUSION It is evident that surface forces are of fundamental importance in the adhesion and friction of solid bodies. Of these, the forces that operate between all materials are the van der Waals interactions and for the first time a direct measurements has been made of these forces down to separations comparable with atomic dimensions. It is thus possible to calculate the part that non-retarded van der Wads forces play in the surface energy and adhesion of solids.With many organic substances such as polymers, these are the only forces which are involved and there is good agreementB . J . BRISCOE AND D . TABOR 17 between theory and experiment. With other materials such as inorganic solids and metals, van der Waals forces dominate down to separations of 1 to 2nm but are then swamped by shorter range forces corresponding to valence- or metallic- bonds. Although adhesion is essentially the result of interfacial forces, the observed adhesional force between solids is influenced by two additional factors. The first is the influence of elastic stresses released when the joining load is removed. These can peel junctions apart, particularly if the solids are lacking in ductility.The second is the presence of surface films which may reduce the adhesive forces: in addition, particularly with metals, the oxides which are normally present may provide an interlayer which is relatively brittle. Friction is mainly due to adhesion at the regions of real contact. The factors which influence adhesion, by and large, influence friction in the same way. The calculation of friction from surface forces is, however, more difficult since it involves not only the surface forces themselves but the possible role of flaws, defects and dislocations in the sliding process. B. V. Derjaguin, I. I. Abrikossova and E. M. Lifshitz, Quart. Rev., 1956, 10, 295. A. van Silfhout, Proc. Kon. Ned. Akad. Wet. B, 1966, 69, 501. G. C. J. Rouweler and J. Th. G. Overbeek, Trans. Faraday Sac., 1971, 67,2117. D. Tabor and R. H. S. Winterton, Proc. Roy. Soc. A, 1969,312,435. J. N. Israelachvili and D. Tabor, Proc. Roy. Soc. A , to be published. J. N. Israelachvili and D. Tabor, Nature, 1972, 237, 88. A. I. Bailey and S. M. Kay, Brit. J. Appl. Phys., 1965, 16, 39. K. L. Johnson, K. Kendall and A. D. Roberts, Proc. Roy. SOC. A, 1971,324,301. ' J. N. Israelachvili, Proc. Roy. Soc. A, to be published. lo C. Weaver, this Discussion, p. OOO. l 1 C. M. Pooley and D. Tabor, Proc. Roy. SOC. A, to be published. l 2 C. M. Pooley and D. Tabor, Nature, 1972, 236,106. l 3 B. Scruton, D. Tabor and R. F. Willis, Nature, 1972,236, 59. l4 B. Scruton, Ph.D. Thesis (University of Cambridge, 1971). R. C. Bowers and W. A. Zisman, J. Appl. Phys., 1968, 39, 5385. l6 A. I. Bailey and J. S. Courtney-Pratt, Proc. Roy. Soc. A, 1955, 227, 500. J. Boyd and P. B. Robertson, Trans. Amer. Soc. Mech. Eng., 1945, 67, 51. "J. R. White, Lubrication Eng., 1954, 10, 340. L. C. Towle, J. Appl. Phys., 1971,42,2368. 2o F. P. Bowden and D. Tabor, Friction and Lubrication of Solids, Pt. 2 (Clarendon Press, Oxford, 1964), 396. 21 A. Cameron and M. J. Sutcliffe, this Discussion, p. 0oO. 22 J. Skinner, Ph.D. Thesis (University of Cambridge, 1971). 23 P. Pfaelzer, Ph.D. Thesis (University of Cambridge, 1971). 24 N. Gane, private communication. *' D. J. Barnes, unpublished data.

ISSN:0370-9302    

DOI:10.1039/S19720200007

出版商:RSC    

年代:1972

数据来源: RSC

摘要:

Adhesion of Metals to Polymers BY C. WEAVER Department of Applied Physics, University of Strathclyde, Glasgow Received 19th June, 1972 Methods of measuring the adhesion of thin films to bulk substrates are critically reviewed, with particular emphasis on the value of scratch testing methods. Results obtained by this method for a range of metals and polymers show that in many cases there is a considerable electrostatic component of adhesion, which is both time and temperature dependent. An examination of electrical conduction in polyethylene shows space-charge-limited currents, due apparently to positive hole injection at the anode. It is suggested that a similar mechanisms is the cause of the adhesion results. Some of the major difficulties associated with any work on adhesion are experi- mental.In the first place, there is the difficulty of obtaining perfect contact between two surfaces, particularly in the case of bulk materials. The most careful preparation of any surface leaves minute irregularities which are still large compared with atomic dimensions even if adsorbed layers can be eliminated. Consequently, when two surfaces are brought together, contact occurs only at the high spots and even if extreme pressure is applied to force the surfaces into intimate contact, the elastic stresses which are released when the pressure is removed cause a partial separation of the surfaces. These effects can be reduced by using a soft, ductile material such as lead or indium for one surface and a ball-bearing or similar hard indenter for the other, as shown by Bowden and Tabor.’ Plastic flow occurs and the force of separation becomes equal to the original applied force.Similar results may be obtained by annealing two metals in contact under pressure. The cases where these methods may be used are obviously restricted and it is still difficult to ensure uniform contact and freedom from localized stresses over the entire interface. An alternative approach is to try to produce a layer in intimate contact with a solid surface by freezing a liquid in contact with the surface, allowing solvent to evaporate from a solution as in the case of many adhesives, or condensing material on the surface, but this raises problems in detachment. It has frequently been pointed out that the strength of adhesive joints may be explained quite adequately in terms of van der Waals forces alone, e.g., de Bruyne,’ and the universal nature of these forces would suggest this type of bonding should represent the lower limit of adhesion when a perfect interface is achieved.There are several factors which indicate that this lower limit should be of the order of lo9 dyn cm-2 (lo8 N m-’). Theoretically, calculations of London dispersion forces 3-6 give values from about lo9 dyn cm-’ (lo8 N m-’) upwards while Tabor has estimated the force required to strip a pure hydrocarbon liquid from a surface leaving an absorbed layer as 6 x lo8 dyn cm-2 (6 x lo7 N m-’), considerably greater force being required to leave a clean solid surface. Experimentally, shearing forces up to 4 x lo7 dyn cm-2 (4 x lo6 N m-’) were required to remove ice frozen in situ from a metal surface and failure invariably occurred in the ice itself,8 suggesting that the interface was considerably stronger and 18C.WEAVER 19 probably above the value of 1.2 x 10' dyn cm-2 (1.8 x lo7 N m-2) obtained in friction experiments with ice. Admittedly, lower values of the order lo7 dyn cm-2 (lo6 N m-2) were obtained for surfaces which were not perfectly wetted, but this suggests imperfect contact. In experiments on friction between solid surfaces it is generally found that fragments of material are transferred from one surface to the other. Since ultimate strengths of most mtaerials are of the order of lo9 dyn cm-2 (10' N m-2) the adhesion bonding must be of at least the same order.A more direct measure of adhesion was obtained by Beams who tried to measure the centrifugal force required to detach an electroplated film from the steel rotor of an ultra-centrifuge. In most cases the rotor disintegrated before detachment and successful results were obtained only when bonding was reduced to the van der Waals level by putting a layer of albumin or oil between the film and the rotor. Bond strengths of the order 1.1 x lo9 dyn cm-2 (1.1 x 10' N m-2) were then obtained. These arguments and facts lead inevitably to the conclusion that any adhesion experiments giving an ultimate strength significantly below the van der Waals level should be examined most carefully for possible explanations. Imperfect contact can easily occur and it is difficult to avoid stress concentrations which lead to pro- gressive separation or peeling.Where results show a wide scatter which cannot be explained by the normal experimental errors, it suggests that these factors occur and particular significance should be attached to the highest values rather than average values, as representing a closer approach to perfect conditions, even though the average (or even the lowest) values may have greater practical significance. Various attempts have been made to measure the adhesion of thin vacuum- deposited films on different substrates, partly because of the technological importance and partly because the deposition process produces almost perfect interfacial contact. The difficulties arise in trying to remove the film from the substrate in a manner which gives a reliable indication of the adhesion.The most direct approach is to stick, solder or cement to the film surface a probe, rod or block of material which may then be used to apply a force to the film. An extensive series of measurements was made by Belser lo using flat-headed pins or short aluminium cylinders to apply a pull normal to the substrate. Results showed a wide scatter and were consistently an order of magnitude or more below the value obtained by Beams for a poorly adherent film, i.e., below the van der Waals level. The method naturally raises questions of adhesive (or solvent) penetrating the film and reaching the film-substrate interface, stresses produced during setting of the adhesive causing partial detachment, and non- uniform stress distribution over the contact area during the pulling process, all of which would affect the final result.More recently Butler l1 has used a short rod of square section which was then toppled sideways about one edge of the square contact area, producing an effective tensile pull at the other side, and Lin l2 has bonded a flat glass plate onto the top surface of his films so as to produce a lap joint which was then pulled to produce a shear stress. Accurate calculation was difficult but Butler estimated tensile stresses up to 4 x lo7 N m-2 before failure of the adhesive. Lin l 2 obtained results showing scatter over more than an order of magnitude with average values of 3 x lo5 N m-2 for gold on glass, 8 x lo5 N for copper on glass, and 1.6 x lo6 N m-2 for aluminium on glass, and maximum values about five times greater (e.g., > 5 x lo6 N m-2 for A1 on glass).Electron diffraction could not detect any adhesive at the film-substrate interface, but the figures all appear low compared with -lo8 N m-2 for van der Waals bonding. It has long been known, however, that the stress distribution in a lap joint is quite complicated 14* l 5 and photo-elastic models of lap joints have shown concentrations which depend, amongst other factors, on the shape of the glue fillets at either end of the joint. Many workers 16-19 on the20 ADHESION OF METALS TO POLYMERS adhesion of thin films have used scratch testing, in which a smoothly rounded point or stylus is drawn across the surface of the film under a load applied normal to the sur- face.As the load is increased, a point is reached at which the film under the moving point is detached and the critical load above which a clear scratch is produced then forms a measure of the film-substrate adhesion. Experimental measurements and calculations have shown that the horizontal force required to move the point across the surface does not play a significant part in the process and there is a fundamental difficulty in explaining how a compressive force normal to the substrate produces detachment of the film from the substrate, but it was observed that the process always involved plastic deformation of the substrate by the point. In 1960, a theory was presented which showed that as a result of this deformation a shearing force was produced at the film-substrate interface around the rim of the indentation produced by the point and a relationship was developed between the applied load and the shearing force.The most convincing evidence that the critical load is determined primarily by the adhesion between the film and the substrate is provided by measurements of two- layer metal films on glass. Fig. 1, shows the variation of critical load with time for s a o l IOSOA I .1 / I 2 5 0 i ISSOi 0 9 18 2 7 36 45 54 time/h FIG. 1.-Adhesion changes during annealing of Au-A1 thin-film diffusion couples with gold under- layers. different thicknesses of gold film deposited on glass and then overlaid with aluminium. Gold has a relatively poor adhesion to glass and the measurements start at a low value. Aluminium has a much higher adhesion to glass and, as the two metals interdiffuse, an abrupt change in adhesion occurs at exactly the stage where some aluminium (in the form of an intermetallic compound with gold) appears at the metal-glass interface.This can easily be detected by observation through the glass substrate. There is an exact parabolic relationship between the gold thickness and the time as measured up to the break in the adhesion curve, in accordance with diffusion theory ; diffusion coefficients may be calculated from the measurements. If the same metals are used but deposited in reverse order with the aluminium in contact with the glass substrate, the same diffusion occurs but the results are completely different, being determined mainly by the aluminium underlayer as shown in fig.2, which shows adhesion meas- urements for the two-layer film and for the aluminium and gold films separately. The detailed reasons for the different adhesions in this diagram have been explained elsewhere. O During recent years, the development of scanning electron microscopy has allowed examination of the scratches in more detail than was previously possible. As aC. WEAVER 21 result, the method has been criticized 21* 22 primarily because the micrographs show film becoming detached a short distance ahead of the moving stylus, and to a certain extent along the sides of the track. It is difficult to reconcile this with the remarkable success which the method has had both in measuring adhesion and in detecting alloying effects in bimetallic films.23 It certainly indicates that the process is more complex than originally envisaged, but the explanation probably lies in the fact that vacuum-deposited metallic films are almost invariably in a state of tensile stress and for very thick films, which are poorly adherent, spontaneous detachment can occur wherein the film curls away from the substrate and peels under the action of the internal stress.This means that if film detachment occms under the stylus and particularly around the perimeter of the contact area where the interfacial shearing lo0l 8 0 I 6ot P 0 16 2 0 3 0 4 0 time/h FIG. 2.-Changes in the measured adhesion of an Au-Al thin film diffusion couple on glass with an aluminium underlayer, together with corresponding changes in adhesion of individual Au and A1 films to the glass substrate.force is a maximum, the intrinsic tensile stresses in the film immediately around the stylus tend to lift the loosened edge and peel the film away from the substrate. This may be expressed somewhat differently by saying that a Griffith’s crack extends away from the stylus along the interface, but the length of such cracks is limited. According to the theory of crack p r ~ g a g a t i o n , ~ ~ ~ 25 the smallest stress 0 capable of extending the crack is of the order 0 N, s(3a/Z)+ where s is the ultimate strength (in our case the adhesion), a is the lattice spacing, I is the crack length and Q would of course be given by the intrinsic film stress. Movement of the stylus would tend to push down the loosened edge, creating a loop or hillock of detached film immediately ahead of the stylus, but for a thin film the bending moment in this loop would be insufficient to produce further crack propaga- tion and the loose film would be pushed aside until the stylus reached the end of the Griffith’s crack.The shear stress under the stylus would then repeat the loosening process. The net result is very reminiscent of a stick-slip process and such rhythmic effects may be seen in micrographs of the 22 This explanation modifies and expands the detail of how a film is removed but the initial stage is still dependent on the shearing force under the point. Other complications may arise. Some degree of peeling can occur with very poorly adherent films and it may be difficult to obtain completely clear scratches with highly adherent films because maximum shearing22 ADHESION OF METALS TO POLYMERS effects occur at the edge of the scratch.In practice, it has been found that the best results are obtained with steel points, frequently renewed, rather than diamond or sapphire styli, which have failed to give consistent results according to our experience. It should be obvious that the model is a simplification of a complex situation but an important advantage is that it consistently leads to adhesive strengths which compare favourably with the best theoretical and experimental data. An entirely different approach to the measurement of adhesion is by peeling a film from a substrate. In an ideal case, e.g., splitting of mica sheet,26 this is a revers- ible process and in most cases it leads to an energy of adhesion rather than an ultimate force.Theoretically, the energy would be given by the sum of the surface energies of the new surfaces produced, less the original interfacial energy. Derjaguin 2 7 9 28 was probably the first to notice the discrepancies between the peeling energy and the theoretical values, and attributed the high peeling energy to the separation of charges in an electrical double layer at the interface. Energies of the order of lo5 erg cm-2 (100 J m-2) were obtained for stripping of a polymer film from a metal surface and evidence was presented of electrical discharges in the gap between the separating FIG. 3.-Changes in adhesion with time for metal films on a polypropylene substrate.x , copper ; 0, gold ; + , silver ; 0, aluminium. surfaces. The work has been strongly criticized by Huntsberger and by Gardon 29 on the grounds that most of the experimental work of peeling was dissipated in plastic deformation. Similar effects may be observed in cohesive failure, where there is no reason for postulating an electrical double layer. Any electrical effects observed could easily be attributed to the heavy deformation of the peeled layer since there is evidence of piezo-electric effects in The major criticisms would of course apply to the measured work in any peeling process and it is doubtful whether the peeling energy has any theoretical significance in adhesion. Some of the lowest peeling energies have been obtained by Chapman 31 who peeled gold film off glass substrates using a backing of adhesive tape.Energies of the order of 2000 erg cm-2 (2J m-2) were obtained, and when thicker gold films were used so that the backing tape could be discarded, the measured energies fell to about 500 erg cm-2 (0.5 J m-2). However, a rate dependence and a pressure dependence were still observed, which suggests that energy is being dissipated and the true adhesionC . WEAVER 23 energy might be much lower. Estimated values of van der Waals bonding energy for various metals on alkali halide faces 32 are of the order of 100-300 erg cm-2 (0.1- 0.3 J m-2). ADHESION OF METAL FILMS TO POLYMERS Scratch testing has been used to measure the adhesion of metal films to various polymer surfaces. The films were deposited by vacuum evaporation on smooth plastic surfaces.In some cases, a glow discharge was used to clean the surfaces of adsorbed layers, but in other cases the films were deposited on the surfaces as placed in the vacuum chamber. Most metals showed a change in adhesion with time after deposition but in many cases the change was small. The largest effects were con- sistently observed with copper silver and gold; fig. 3 shows the changes in adhesion with time for a polypropylene substrate which had been subjected to a cleaning discharge. Similar effects may be observed for many polymers. In some cases such as polymethylmethacrylate and polycarbonate, the effects are much greater and in other cases such as P.T.F.E. the effects are smaller, but the general trends remain the same and the same group of metals shows the greatest adhesion. The fact that gold is amongst the metals showing maximum adhesion makes any form of chemical reaction most unlikely.Tabulated work functions show too much scatter to form a reliable guide but comparisons of work functions by contact potential measurements has shown that copper, silver and gold have work functions which are almost identical. 902 Application of d i IC har 9 e I I c, tk - + -+ + *'- 0 2 0 0 4 0 0 600 800 time/h x , Cu on Perspex ; 0, Cu on NaCl ; + , Cu on glass. FIG. 4.-Adhesion of evaporated copper films on Perspex showing elimination of charged layers by an ionizing discharge. These facts in conjunction suggest the possibility of an electrical component of ad- hesion. Fig. 4 shows some results obtained for copper films which were first aged for 200 h to develop increased adhesion and then replaced in a vacuum chamber and subjected to a glow discharge for a few minutes.The glow discharge produced no effects for copper on sodium chloride, which shows van der Waals bonding only, or for copper on glass, which shows an initial increase in adhesion due to oxide formation, For copper on Perspex, the high adhesion which had built up with ageing was reduced to van der Waals level and started to build up again. The process could be repeated. The manner in which the increased adhesion may be wiped out by an ionizing24 ADHESION OF METALS TO POLYMERS discharge provides almost perfect confirmation of the electrical nature of the in- creased adhesion, but does not explain the mechanism of charge transfer between the metal and the polymer.Derjaguin assumed electron transfer from the metal to the polymer so as to equalize the Fermi levels but this should be a rapid process compared with the ageing periods involved here, if it occurs at all. The conduction band in most insulators is no more than 1-2 eV below the vacuum level so that an electron at the Fermi level in a typical metal with a work function of the order of 4-5 eV would be faced with a potential barrier of the order of 3 eV. The chance of a metal electron having excess energy in this range is negligible. Measurements in our laboratories of conduction in polyethylene have shown space-charge-limited currents with gold and aluminium electrode~,~~ with a carrier mobility of the order of 3 x lo-* cm2 V-1 s-l (3 x m2 V-I s-l) at room temperature. When two different electrodes, having different conduction characteristics, were used on the same specimen, the observed conduction was always typical of the positive electrode.In conjunction with the other features this indicated positive hole injection at the gold and aluminium elec- trodes. Similar effects have been observed in less detail with polypropylene. This suggests that the charge transfer in adhesion is due to positive hole injection, i.e., electron transfer from the valence band of the polymer to the metal with the injected charge causing band bending until the Fermi levels equalize. This would of course imply that the effective Fermi level in the polymer normally lies above the Fermi level in the metal when these adhesion effects are observed. Any reasonable estimate for the Fermi level in the polymer would still leave a large difference between the valence band and the Fermi level in the metal so that, even allowing for band bending, there would be a substantial barrier to hole injection if the holes are injected directly into the valency band, but the space-charge-limited current characteristics show a total trap density 4 x lo1* ~ m - ~ (4 x m-3) expo- nentially distributed and the low mobility is typical of a hopping mechanism between traps.There seems little doubt that these traps play a part in charge transfer and adhesion as well as conduction. When a positive hole is trapped the trapping centre releases an electron, normally into the valence band or to another trap, but a trap sufficiently close to the polymer surface could release an electron directly to the metal electrode by tunnelling.The trapped positive hole would subsequently migrate away from the interface under the space-charge field, leaving the original trap free to repeat the process. This would allow the transfer of an electron to the metal at an energy level somewhat below the Fermi level where there is a reasonable chance of finding a vacant energy state, and the rate of charge transfer would be governed by the density of available vacant energy states in the metal as well as the trap density and energy. The problem of why copper, silver, gold, and to lesser extent aluminium, should show these charging effects to a much greater degree than other metals is a more difficult question which has not been completely resolved but these are all metals with odd numbers of electrons/atom and half-filled energy bands.Most other metals, apart from the alkali metals, conduct because of band overlap and have one band almost completely filled, with a spill-over into the next higher band. An elementary argument based on possible wave-vectors towards the top of the energy distribution suggests that there could be momentum restrictions on possible transfers, particularly if the metal shows some orientation effects such as fibre orientation about an axis perpendicular to the substrate. In presenting this paper I have drawn together the work of several research students, which I should like to acknowledge and I should like to thank Dr.G. A. P. Wyllie of Glasgow University for some helpful discussions.C. WEAVER 25 The continued support of the Ministry of Defence for this work is gratefully acknowledged. F. P. Bowden and D. Tabor, Proc. 2nd Znt. Congr. Surface Activity (Butterworth, London, 1957), 3, 386. N. A. de Bruyne, J. Sci. Znstr., 1947, 24, 29. P. Benjamin and C. Weaver, Proc. Roy. Soc. A, 1960, 254, 163. D. Taylor, Jr and J. E. Rutzler, Jr, Znd. Eng. Chem., 1958, 50, 928. J. R. Hunstsberger, Treatise on Adhesion and Adhesives, Vol. 1, ed. R. L. Patrick (Arnold, London, 1967), p. 21. B. N. Chapman, Ph.D. Thesis (Imperial College, London). D. Tabor, Rep. Prog. Appl. Chem., 1951,36, 621. L. E. Raraty, Ph.D. Diss. (Cambridge, 1955).J . W. Beams, 43rd Ann. Proc. Amer. Electroplaters SOC., 1956. 42453, 1954. R. B. Belser and W. Hicklin, Rev. Sci. Znstr., 1956, 27, 293. lo R. B. Belser, Interim Rep. No. 7, Project 163-176, U.S. Ordnance Contract DA-36-039-Sc- l2 D. W. Butler, J. Phys. E, 1970, 3, 979. l3 D. S. Lin, J. Phys. D, 1971,4, 1977. l4 C. Mylonas and N. A. de Bruyne, Adhesion and Adhesives, ed. N. A. de Bruyne and R. Houwink (Elsevier, Amsterdam, 1951), p. 91. L. Greenwood, T. R. Boag and A. S. McLaren, Adhesion, Fundamentals and Practice (Ministry of Technology, McLaren and Sons Ltd., London, 1969), p. 273. l6 0. S. Heavens, J. Phys. Rad., 1950, 11, 355. l7 P. Benjamin and C. Weaver, Proc. Roy. SOC. A, 1960,254,177 ; 1961,261,516 ; 1963,274,267. l 8 M. M. Karnowsky and W. B. Estill, Rev. Sci. Znstr., 1964, 35, 1324. l9 D. M. Mattox, J. Appl. Phys., 1966, 37, 3613. zo C. Weaver and D. T. Parkinson, Phil. Mag., 1970, 22, 377. 21 D. W. Butler, C. T. H. Stoddart and P. R. Stuart, J. Phys. D, 1970,3,877. z 2 D. W. Butler, C. T. H. Stoddart and P. R. Stuart, Aspects of Adhesion, Vol. 6, ed. D. J. Alner 23 C. Weaver and R. H. Hill, Adv. Phys., 1959,8,375. 24 A. H. Cottrell, The Mechanical Properties of Matter (Wiley, London, 1964). 2 5 E. Orowan, Reports Prog. Phys., 1949, 12, 185. 26 A. I. Bailey, Proc. 2nd Int. Congr. Surface Activity (Butterworth, London, 1957), 3, 406. 27 B. V. Derjaguin, Research, 1955, 8, 70. z8 B. V. Derjaguin and V. P. Smilga, Proc. 3rd Znt. Congr. Surface Activity (Butterworth, London, 29 J. L. Gardon, Treatise on Adhesion and Adhesives, Vol. 1, ed. R. L. Patrick (Arnold, London, 30 Yu. N. Novikov and F. T. Polovikov, Soviet Phys.-Solid State, 1966, 8, 1240. 31 B. N. Chapman, Aspects ofAdhesion, Vol. 6, ed. D. J. Alner (Univ. Lond. Press, 1971), p. 43. 32 P. Benjamin and C. Weaver, Proc. Roy. SOC. A, 1963, 274,267. 33 T. McGrenary, unpublished work, University of Strathclyde. 34 D. T. Morrison, Ph.D. Thesis (University of Strathclyde 1970). (Univ. Lond. Press, 1971), p. 55. 1960), 2B, 349. 1967), p. 320.

ISSN:0370-9302    

DOI:10.1039/S19720200018

出版商:RSC    

年代:1972

数据来源: RSC

摘要:

A Theoretical Explanation of the Lowering of Frictional Forces with Layer Height of Long Chain Polar Lubricants BY M. J. SUTCLIFFE AND A. CAMERON Dept. of Mechanical Engineering, Imperial College, London, S. W.7. Received 23rd June, 1972 Assuming the anisotropic elastic constants of stearic acid as a function of layer height to be as determined by Akhmatov and Panova, the shear strengths of mono layers and multi layers are calculated. A computer programme describing the slip of a monolayer of an orthorhombic fatty acid crystal system about the methyl end groups is adapted to represent layer height by the use of a range of interaction potentials. Although the computed shear strengths are too high in magnitude compared with experimental results, as expected from strength calculations of an ideal crystal system, the correct trend of behaviour between multilayers and monolayers is shown.1. INTRODUCTION Various theories of one phase multimolecular film formation exist, physical and chemically based. Godrey considers a single chemisorbed layer as a basis, while Drauglis and Allen have put forward an ordered liquid model which, through a local short range force, produces long range order. Akhmatov cites long polar molecules having true elasticity of shape and places great importance on the elastic and mechanical properties of long chain hydrocarbon lubricants being decreasing func- tions of the layer thickness. has deter- mined elasticity constants of stearic acid from monolayers to 100 monolayers. In the literature, Denisov and Toporov,6 have shown multilayers to display a lower shear strength than monolayers.The purpose of this paper is to try and test some of the theories available in terms of a computer programme already in use to describe monolayers, assuming experi- mental constants available in the literature. As the programme describes shear between methyl planes of polar molecules in an orthorhombic crystal structure, the paper is most applicable to Akhmatov’s quasi solid theory and not to liquid ordered models, which require some order of randomness of the molecules. As in all inter- molecular theories which consider ideal and perfect systems, the actual magnitudes of derived forces are usually far too high compared with experimental results, but it is hoped to show a trend of behaviour between mono and multilayers.Using the “ layer stack ” method, Panova 2. FRICTIONAL MODEL The frictional model on which the theory is based is as follows. Firstly an orthorhombic crystal structure of long chain hydrocarbons is assumed, according to Muller and Smith.* When one surface is moved relative to the other, shear is assumed to take place between the terminal methyl groups. When multi- layers are considered, slip is assumed to take place at the mid-point between the two solid phases. Secondly, the assumption is made that all the energy needed for movement is dissipated and none is recovered ; clearly if some energy were recovered 26M. J . SUTCLIFFE AND A . CAMERON 27 Z AXIS t FIG. 1.-Arrangement of molecules in hydro- carbon crystal as determined by Miiller, where 0 represents methyl groups, 0 = methylene groups, a = 7.426 A, b = 4.956A (repeat dis- tance in z direction), d = 3.09 8, (gap distance), e = 0.94 A, (gap distance), k = 1.203 A, y setting angle, 8 = tetrahedral angle, - - - = top chains, - = bottom chains.I 2 . 1 1 ib $ INTERACTION ENERGY /CHAIN FIG. 2.-Compression diagram of interaction energy /chain against distance compressed ' GAP DISTANCE explaining the mode of energy dissipation. BETWEEN PLANES28 REDUCTION OF FRICTION the observed frictional force would be lower by that amount. Thirdly, during shear the terminal methyl groups are assumed to be capable of internal rotations. They are allowed to rotate about the C-C bond in the xy plane and to tilt in the z direction, which, when used simultaneously, gives a good model of pure axial rotation about the C-C bond.The potential barrier of the methyl group is taken as 3 kcal/mol for a 120" rotation about the C-C a ~ i s . ~ - l l For a deformation of 20°, if a sinusoidal potential curve is ass~med,~ the energy dissipated is of the order of 0.5 kcal/mol (the maximum potential is assumed to occur at 60"). The mode of energy dissipation used was first suggested in the discussion of Cameron's paper l2 by van Battun and Broeder, who pointed out that when the chains were moved under a load, the vertical distance between chains may change. The frictional work is then made up of two terms-see fig. 2. The load N is proportional to the gradient of the compression curve at El and gap distance d l , at point A .At some other point B the system is in the same state of compression, i.e., comparable gradients at energy E2 and gap distance d2. (1) The energy profile of the interaction forces The two terms then are AE = (El -EZ), (2) the work against the normal load N Ad where 2 Ad = (d2 - d l ) , as both planes move by opposite and equal reaction. The total energy dissipated is E = AE+N*Ad; the force is E AE = x=x+T- where X is the distance moved in the shearing action, i.e., the two compressed states at D(0) and D(X). Therefore the coefficient of friction p is F AE Ad p = - =-+- N N X 3. PROGRAMME A computer programme was developed which allowed the distances between the X-ray scattering centres of a long chain molecule at the origin of a given set of axes and all the other chains within a radius of 25 A to be determined under all conditions of movement (translation, rotation and deformation of the terminal methyl group).These were used to calculate the attractive potentials. There was a sub-routine to calculate all relevant H-H repulsive distances under all conditions of shear encountered. All distances were resolved along three orthogonal axes in terms of the tetrahedral angle 8 between the C-C chain bonds and CH2 groups, the setting angle y of the orthorhombic crystal system chosen. Provision was provided through the angle B for the chains to be oriented to the vertical and the terminal methyl group was allowed to rotate about the CC axis and to be deformed in the z axis. The periodicity of the interaction potentials of the source chain over the unit cell was shown and the setting angle of the system was calculated at 44" in excellent agreement with Smith's experimental results.*M. J . SUTCLIFFE AND A . CAMERON 29 4. P 0 TEN TI ALS AND COMPRESS I BI LI TY DIAGRAMS A Slater-Kirkwood attractive potential was used to describe the contribution from the C-C and C-H pairs to the dispersive van der Waal forces. The coeffi- cients used were 22.6 and 8.68 kcal/mol for CC and CH contributions respectively. The total interaction energy of the HH pairs were described by a Buckingham " 6-exp " potential of the form described by Coulson and Haig l 3 as U(R,) = - A/R: + B exp( - CR,) with R1 the distance in atomic units. The H-H potentials used are described in table 1. In addition, one Lennard- Jones potential (l/r12) was used with coefficient 1.35 x lo4 kcal/mol.Hirschfelder 2o has used an empirical curve fitting procedure to produce U(R,) = ART6+0.818 Rf exp( - 2R,). TABLE 1 Barton l4 3.397 13.207 2.434 Hendrickson 3.573 15.93 2.434 Hendrickson-Bartell l6 3.573 21.66 2.497 Bartell l7 3.573 10.51 2.160 Muller 4.496 100.9 2.645 Slater l9 3.573 16.8 2.43 t y p e A B C By assuming that a situation analogous to Hooke's law exists between the com- pressive deformation and external pressure, relationships connecting all parameters of energy in boundary layers can be derived, i.e., AA = AZ/Z,,= -PIEb (3) where AA = compressive strain ; AZ = change of distance (I- lo) ; lo = equilibrium distance ; Eb = elasticity modulus ; p = external pressure .'.(z-zo)/zo = -p/Eb. RSC HFE L DEH 8.0 - E - 2 6.0 a a .* .I 4.0 5 2 8 2.0 \ ;? a, a ._ u O O 4 4 6 .I - 2.0 E QU I L I BRI U M '0'51 TlON 3.09 EEN STROMS 0 FIG. 3.-Compression diagram for scattering centre interaction potentials.30 REDUCTION OF FRICTION Usingp = -a4/aZ, i.e., force is the negative gradient at any point on an (energy/cm2, distance) graph, it can be shown that where & is the interaction energy/cm2 at the equilibrium position lo, and by using eqn (3) it follows by introducing A , the area of cross section of the chain to give interaction energylchain, a, that 1 EbA (@--@o) = - -(Z-Z0)? 2 lo (5) Fig. 3 shows computed compression graphs using the potentials in table 1. For each potential, <Do is different; all the potentials except Hirschfelder’s display a potential minimum consistent with the crystal model.As lo and A are the same for each case, the only factor contributing to the different gradients will be the elasticity Eb. 5. ELASTICITY AS A FUNCTION OF LAYER HEIGHT Akhmatov considers that long chain polar molecules under bounda1.y lubrication conditions assume the properties of a “ quasi solid ”, or crystalline solid which display gradients of physical constants in the z direction. Hardy 21 attributes the anomalous compressive strain FIG. 4.-Compression diagram of normal stress against strain of stearic acid, as a function of layer height, from Panova’s results using layer stack method. nature to the influence of the field of the solid phase, and other authors to structural changes caused indirectly by the solid.Panova has managed to measure the elasticity of multilayers ranging from 100 layers to a monolayer using a “ layer stack method ”. The graphical relationship between these layers to each other is shown in fig. 4 for stearic acid. AkhmatovM. J . SUTCLIFFE AND A . CAMERON 31 cites these results and gives the absolute value of Young’s modulus of 100 molecular layers as 0.25 x lo6 kg/cm2 and of a monomolecular layer as 3.47 x lo6 k g / ~ m ~ . ~ Using these values and fig. 4, a graph of elasticity (log scale) against monolayers can be drawn as in fig. 5 ; from this graph the elasticity of any number of layers can be extrapolated. ELASTICITY IN X AND Y DIRECTIONS (105kg/cm2) OF ORTHORHOMBIC CELL. no. of monolayers FIG. 5.-Graph of elasticity (log scale) against number of monolayers from Panova’s results.It can also be seen that Akhmatov associates the value of the elasticity of the methyl gap in a monomolecular layer with the elasticity of the chain.” Cameron and Sutcliffe 22 showed that the gapcompressibilityshould be of the order of the values in the x and y direction of the unit cell; for the purposes of this paper Akhmatov’s assumption will be used for reasons given in the next section. 6. RELATIONSHIP BETWEEN LAYER HEIGHT AND POTENTIAL FUNCTIONS Using eqn (5), the theoretical compression curve formula, in conjunction with the information in fig. 5 ; the elasticity as a function of layer height and elasticity can be drawn, fig. 6, which shows a compression graph as a function of layer height and elasticity. By comparison with fig.3, the actual potential profiles obtained, it can be seen that a Barton potential function can be used to describe the effect across the methyl slip plane midway between two solid phases of five molecular layers of lubri- cant and Miiller and Lennard-Jones potentials used to represent three layers.32 REDUCTION OF FRICTION \@ No OF LAYERS 0 E = 981Nlm‘ ( lo6 kglcm’) EQUlLl BRIUM POSl T I ON 309 8 3 0 24 *‘ 6- E= 98.1 Nlrn’ \ .CI .U 4 = l . O kcal lmol - 2 L FIG. 6.-Compression graph of stearic acid as a function of layer height and elasticity. If the gap compressibilities were taken to be the same as the xy plane, the Slater and Bartell potentials describe a monolayer which implies that the softest potential available could only describe three layers at the most.Using Akhmatov’s assumption of the gap compressibility, Bartell’s potential describes three layers which meant that another suitable potential had to be developed to describe the slip plane character- istics of a monolayer. - 0 5 6 - Q) - 2 1 .5 FIG. 7.-Compression curves of fitted potential, representing a monolayer, as a function of ROT/ ROCK ratio and distance along the x-axis. This potential was developed using a polynomial fit employing a least squares method. A curve to the fourth power provided an adequate approximation of the exponential type 4(Rl) = Co+C,exp(-R,)+C2exp(-2Rl)+. . . +C,exp(-nR,) with the coefficients C, = 2.38 x lo4 ; C1 = -7.19 x lo5 ; C2 = 8.08 x lo6 ; C3 = -4.01 x 107 ; c4 = 7.39 x 107.This is shown in fig. 7 compressed at the equilibrium position D(O.0).M . J . SUTCLIFFE AND A . CAMERON 33 Thus every suitable potential can be used to represent the properties of the slip plane under compression, differing layer thicknesses represented by a different potential, i.e., Barton 5M Hendrickson-Bartell 5M Slater 3-5M Bartell 3M Muller 21 3M Lennard-Jones 3M Polyfit potential 1M where M = no. of monolayers 7. EFFECT OF LOAD AND METHOD OF CALCULATING RESULTS A consequence of having gradients of physical constants in the z direction is that a multilayer will shear about its weakest point, which will be the methyl plane midway between the two solid phases. This implies that when a load is applied to the multi- layer, the slip plane methyl gap compresses less than the others surrounding it.Again, an anisotropic law is taken to govern the gap compression as a function of height ; because the probable structural changes under compression are unknown, O I - \ D (2.4) D (2.4) U .- 4 2 0 9 2.0 I 2- - 2 / DISTANCE BETWEEN PLANES IN ANGSTROMS - FIG. 8.-Compression diagram for Barton's scattering centre potential (- - -) representing five layers and Miiller's scattering centre potential (--) representing three layers as a function of ROTIROCK ratio and distance along the x-axis. the model must cope with the anisotropy within its parameters-the mutual approach of CH3 groups. Akhmatov quotes an inverse law between layer thickness and yield strength implying shear across the slip plane, thus it seems reasonable to apply an inverse proportion law governing CH3-CH3 approach.All the results were cal- culated using these principles and any excessive decrease across the gaps is assumed to be taken up by the chain compressions. The basic model of shear across the unit cell was taken from the ideas expressed by van Battum and Broeder explained in the "friction model " (Section 2). 2-B34 REDUCTION OF FRICTION To do this, compression diagrams of all the potentials were needed as a function of internal rotation at the equilibrium point and at the maximum potential profile on the x-axis-which occurs at a point D = 2.4A from the origin. Fig. 7 and 8 show examples of these diagrams, viz the polyfit monomolecular potential ; Muller's 3M potential representation and Barton's 5M potential representation.Friction forces were calculated using the amount the gap between the planes lifts the load (the load is proportional to equal gradients on the two curves), the remaining interaction potential profile AE, and the energy dissipation required to rotate or deform the terminal groups. Programmes were run to obtain compression diagrams at all potential maximum profiles throughout the unit cell. It was found that values of AE were 60-80 % of AE, x-axis values-but Ad values were approximately constant. Pro- grammes were also run to give results for a 3 and 5 molecular layer at an angle of 20" to the vertical. The results were either interpreted as " kinetic friction "-taken as the statistical average of energy dissipated/cm of the shear path-(which was found to be the only way x-axis results could be combined with other orientations) and " static friction " of the x-axis which is taken as the maximum frictional force of the shear path, i.e., the force to initiate motion.8. RESULTS TABLE Z-RIGID MOLECULES-STATIC-X-AXIS potential layers FO PST Barton 5M 2.083 0.5 Hendrickson 5M 1.596 0.5 Slater 3-5M 0.965 0.49 Bartell 3M 1.74 0.4 Muller 3M 1.74 0.47 Lennard-Jones 3M 0.675 0.48 Where M represents no. of layers, Fo = intercept on specific force axis at zero normal stress kg/cm2 x lo3. N.B. 1 . 0 ~ lo3 kg/cm2 N 0.981 N/m2 (the graphs are presented in both units). Rotation = ROT/ROCK; ST = " static " coefficient of friction-taken as the slope on the (specific force, stress) graphs ; p~ = " kinetic coefficient " of friction-taken as the slope on the (specific force, stress) graphs.TABLE 3 .-ROTATION ~/O-KINETIC-X-AXIS Barton 5M 0.393 0.094 Hendrickson 5M 0.393 0.094 Slater 3-5M 0.180 0.10 Bartell 3M 0.326 0.08 MuIIer 3M 0.328 0.085 Lennard-Jones 3M 0.128 0.09 potential layers Fo PST TABLE 4 . 4 / 2 0 STATIC-X-aXIS potential Barton Hendrickson Slater Bartell Muller Lennard- Jones Polyfit layers 5M 5M 3-5M 3M 3M 3M 1M FO 2.22 2.22 2.22 2.02 2.7 2.02 2.41 PST 0.25 0.25 0.3 0.15 0.325 0.215 0.23M. J . SUTCLIFFE AND A . CAMERON 0) 2 2 o 2 0 3 O a 6 35 1.0 N / m 2 1 - EN€ RGY DISSIPATED KINETIC CASE -0.5 Nlm' TABLE 5.4120 KINETIC-X-AXIS 0.4 0.2 potential Barton Hendrickson Slater Bartell Muller Len nard-Jones Polyfit - MONOLAYER TILTED AT Zoo I ia - 5.0NIm2 TO THE VERTICAL 11.0 N l m 2 layers 5M 5M 3-5M 3M 3M 3M 1M FO 0.43 0.43 0.43 0.394 0.55 0.394 0.45 PK 0.047 0.047 0.055 0.03 0.04 0.04 0.044 Table 5 can be summarized as follows-by taking the average of the layer number and the average 70 % of Fo for a 360" average layers FO 70 % Fo 5M 0.43 0.305 3M 0.446 0.310 1M 0.45 0.3 15 See fig.9-the graphs have been extrapolated to enable the relationship to be seen Programmes were run to obtain compressive data on the x-axis with the chains more clearly. inclined at 20" to the vertical, compare table 6 and see fig. 10 for these data. 1 ENERGY DISSIPATED OVER 1.4 1 ON X-AXIS, STATIC CASE 5 .0N/m2 normal stress kg/cmZ x lo3 FIG. 9.-Graph of specific force against normal stress as a function of layer height, rotation 0/20, over the x-axis.TABLE 6 layers Fo PK 5M 0.058 3M 0.078 all in the range 1M 0.098 0.03-0.05REDUCTION OF FRICTION - FIG. 10.-Graph of specific force against normal stress as a function of layer height, rotation 0/20, and shift of chains to the vertical, over the x-axis. 9. DISCUSSION The coefficients of friction are of the correct order for fatty acid lubricated systems. The magnitude of the shear forces are generally too high by an order of magnitude, i.e., Godrey gives several values for the shear stress of stearic acid as a function of pressures ranging from 25 kg/cm2 at 250 kg/cm2 of pressure to 140 kg/cm2 at pres- sures of 1000 kg/cm2 and 440 kg/cm2 of pressure. Attempts have been made to calculate strength properties of solid materials from a knowledge of intermolecular forces, e.g.by De Boer 23 and Kemball 24 but in all cases the theoretical values are far greater than experimental values. The discrepancy is attributed to dislocations in the crystalline It is suggested that dislocations would affect the magnitude of the forces involved but not the coefficient of friction, as was found in the case of comparing x-axis values to other orientations of the crystal where AE was 60-80 % of x-axis values at zero load but Ad was constant. The correct relationship between layer height and shear forces has been shown ; dislocations should affect them all equally. If the layers are tilted 20" to the vertical the shear forces are less. D. Godrey, Symposium of Properties of Surfaces, A.S.T.M. Special Publication, 1962, NO. 340, 109. E.Drauglis and C. M. Allen, Wear, 1969,14, 363. A. S. Akhmatov, Molecular Physics of Boundary Friction (Israel Programme for Scientific Translation, 1966). Chapter 7. Panova, see ref. (3), p. 255-264. P. V. Denisov, Thesis (Moscow, 1954). Investigation of the Phenomena of Adhesion in Flat Steel Surfaces. Y . P. Toporov, Research in Surface Forces. Vol. 21 ; (Consultants Bureau, New York, 1966), p. 312. ' A. Muller, Proc. Roy. SOC. A, 1927, 114, 542. A. E. Smith, J. Chem. Phys., 1953, 21,2229. K. S . Pitzer, Disc. Faraday SOC., 1951, 10, oo00. lo J. Oosterhoff, Disc. Faraday Soc., 1951, 10, oo00. l 1 S. Mizushima, Structure of Molecules and Internal Rotations (Academic Press, New York, l 2 A. Cameron, Amer. SOC. Lubr. Engineers, 1960, 2, 195. l3 C. A. Coulson and Haig, Tetrahedron, 1963,19, 527. l4 D. H. R. Barton, J. Chem. SOC., 1948, 340. l6 J. B. Hendrickson and L. S. Bartell, J. Amer. Chem. Soc., 1961,83,4537. 1954. T. B. Hendrickson, J. Amer. Chem. Soc., 1961, 83,4537.M. J . SUTCLIFFE AND A . CAMERON 37 L. S. Bartell, J. Chem. Phys., 1960, 32, 831. l 8 A. Muller, Proc. Roy. SOC. A, 1936, 154, 624. l9 A. Muller, Proc. Roy. SOC. A, 1941, 178, 227. 2o J. 0. Hirschfelder, J. Chem. Phys., 1950, 00, 130. 21 W. B. Hardy, Proc. Roy. SOC. A, 1925,108,000. 22 M. J. SutclXe and A. Cameron, to be published. 23 J. H. de Boer, Trans. Faraday SOC., 1936, 22, 10. 24 C. Kemball, Adhesion and Adhesive-Fundunzentuls and Practice (Society of Chemical Industry, 2 5 C. A. Wert and R. M. Thomson, Physics of Solids (McGraw Hill, N.Y. 1969), p. 108-113. London), p. 69.

ISSN:0370-9302    

DOI:10.1039/S19720200026

出版商:RSC    

年代:1972

数据来源: RSC

摘要:

Strength and Failure Patterns of Metal-Metal Adhesives BY K. W. ALLEN, H. S. ALSALIM AND W. C. WAKE The City University, St John Street, London, EClV, 4PB Receiued 12th June, 1972 Torsional shear napkin-ring test-pieces have been used in adhesion studies with two titanium alloys, modified epoxy and epoxy-phenolic adhesives. The temperature profiles have been obtained and the failure surfaces studied. The metallography of the surfaces is recorded and the effect of a variety of preparative surface treatments. Most treatments lead to rutile, and in one case rutile needles bond to the adhesive more strongly than to the substrate. Surface roughness is shown to enhance bond strength. To achieve understanding about adhesives and to supply data for design purposes, stress rupture experiments have been used, most frequently based on a lap joint stressed in tensile shear.The stress distribution in this joint is complex, and torsional shear provides a simpler system and was advocated in 1951 by de Bruyne.l A torsional shear test associated with a cleavage test, such as peeling a flexible adherend, should enable adhesive design to be placed on a more rational basis. temperature/"C FIG. 1 .-(Strength, temperature) profile of Redux 775 adhesive. Two epoxy-based adhesives have been tested in torsional shear and their behaviour on two titanium alloys studied in detail. Napkin-ring test-pieces and apparatus for torsional shear testing are described el~ewhere,~-~ as also are the expressions used 38K . W. ALLEN, H. S . ALSALIM AND W . C .WAKE 39 for calculating the breaking stress from the observed t ~ r q u e . ~ In the present work, all calculations assumed elastic failures even though at elevated temperatures this is unlikely. The error is of no consequence as absolute stress values are not discussed. Previous work with torsional shear has shown that REDUX 775, a metal adhesive widely used in airframe manufacture and based on polyvinyl formal together with a phenol-formaldehyde resin, shows a breaking strength which varies in mechanism and magnitude with temperature. As shown in fig. 1, highest strengths are obtained at low temperatures where failure is by brittle fracture. Failure is wholly within the adhesive layer and, as would be expected from crack surface-energy considerations, strength does not vary much with temperature.Around room temperature, ductile failure is apparent in the adhesive and the temperature effect becomes more pronounced and typical of a flow process. Failure, although within the adhesive is, at this stage, characterized by clean areas on one of the adherends ; clean as far as can be seen by electron microscopy and ellipsometry. The (strength, temperature) curve was identical for aluminium, stainless steel and titanium alloy substrates, thus supporting the idea that failure is always within the adhesive. The surfaces of all three of metals were prepared by mechanical polishing and were not chemically etched. EXPERIMENTAL AND RESULTS BOND STRENGTH-TEMPERATURE PROFILES ADHESIVE BSL 308 ON TITANIUM ALLOY I M I 205 REDUX BSL 308, Ciba-Geigy Ltd.Duxford, is said to be a modified epoxy adhesive with a blend of resin based on bis-phenol A, together with a hardener, and is supplied as an unsupported film. Test pieces were ground flat and polished to 60 pm and were either used in this condition or were then subjected to one of several chemical etch treatments before bonding. Fig. 2 shows the temperature profiles of this ad- hesive with the various substrate treatments. At temperatures lower than 25"C, different levels of bond strength were obtained with different substrate treatments. Moreover, the (strength, temperature) curve was by no means level at these temper- atures although for some of the surface treatments there is less temperature dependence than for others. The highest strengths are given by treatment (.f), obtained with 2 h oxidation by 0.05 M hydrogen peroxide in 0.4 M sodium hydroxide at room temper- ature and the lowest strengths by treatment (e), aqueous hydrofluoric acid, 4 % w/v.Failure at these lower temperatures was not noticeably brittle in nature and apparently clean areas were seen on the adherend surface. At temperatures above 25°C there is no difference in bond strength between treatments. Neither does the broken surface suggest the ductile type failure expected at higher temperatures ; instead, the appearance of the broken test pieces remained unchanged over the entire temperature range and the adhesive appeared irregularly broken at the interface and across the thickness of the adhesive. However, careful examination of the apparently clean metal by phase contrast interference microscopy revealed the presence of a thin layer of transparent material.The position of the break is shown diagramatically in fig. 3 but the thin layer of adhesive on the substrate is not uniformly thin although, un- fortunately, it was not possible to measure its thickness. However, the ratio of areas of apparently bare metal and dark adhesive does vary. At the lower temperatures this ratio is greater than at higher temperatures when it becomes more nearly unity. BSL 308 is a dark material containing carbon black and aluminium powder, the Iatter being noticeably present in the surface as well as in the bulk of the film before bonding. After breaking the bond, the contact angles shown by water on the40 STRENGTH OF METAL ADHESIVES substrate and the matching adhesive surface were not significantly different.An attempt was also made to measure the refractive index of the thin transparent film mentioned above by flooding with liquids of different refractive indices. From this it I - 5 0 0 50 100 150 temperature/'% FIG. 2.-(Strength, temperature) profile of BSL 308 adhesive on titanium alloy IMI 205. (a) Plain wet polished surface, 0 ; (b) electrolytic oxidation in 0.1 N sulphuric acid, (first-order blue oxide) ; (c) electrolytic oxidation as (b), A (second-order yellow-oxide) ; (d) electrolytic oxidation as (b), 0 (second-order bronze oxide) ; (e) 4 % w/v aqueous hydrofluoric acid, x ; (f) sodium hydroxide+ hydrogen peroxide, + (black oxide region). appeared that the film was not entirely homogeneous as the reflection from some areas disappeared in a liquid of refractive index 1.598 and other areas in a liquid of 1.585.The refractive index of an epoxy resin is about 1.55 increasing with cross-linking and depending on the nature of the curing agent. The film was free from filler particles. I Adherznd FIG. 3.-Position of failure with BSL 308 adhesive on titanium alloy IMI 205. It appears therefore that some component of the adhesive migrates during curing to the interface and failure of the bond is close to, or at, the boundary of this migrated layer, although this should not be taken to imply that a sharp boundary exists.K . W . ALLEN, H . S . ALSALIM A N D W. C. WAKE 41 Material of low molecular weight would be expected to migrate preferentially from a broadly dispersed polymer.In some way the substrate surface is influencing the breaking of the bond at lower temperatures by initiating the failure process in different ways, although at higher temperatures this is not so and failure may be assumed to be wholly initiated by the adhesive. TITANIUM ALLOY IMI 205 This alloy, consisting of 85 % titanium and 15 % m~lybdenum,~ is classified as a p phase alloy and contains at the most about 5 % volume fraction of a phase. Molyb- denum stabilizes the /I phase and the electrolytic oxidation rate of the two phases is identical and hence with electrolytic oxidation there is no change in surface topography. In contrast, both hydrofluoric acid and sodium hydroxide preferentially attack one of the phases.With hydrofluoric acid, oxide formation occurs hydrolytically but with sodium hydroxide, hydrogen peroxide is included to bring about surface oxida- tion and its concentration limits the extent of surface dissolution. Alloy polished by a wet process has a surface consisting of a highly hydrated titanium oxide of unknown composition.6 Metal specimens prepared by polishing unfortunately acquired charge in the electron diffraction apparatus and hence the nature of the surface could not be identified in the present studies. The surface product from electrolytic oxidation is rutile, clearly identified by electron diffraction. Various oxide thicknesses, as judged by colour order, were produced by varying the voltage and the electrolyte. Attack by hydrofluoric acid produces a black oxide layer which was loosely adherent and patchy.When this alloy was dissolved in aqueous hydrofluoric acid, a molybdenum oxide (possibly Mo,O,) was precipitated. The black surface layer is due to molybdenum.’ The use of sodium hydroxide with hydrogen peroxide * produces a rough and porous surface due to preferential attack of one phase. The surface is a mixture of oxides with rutile predominating. Experiments, with a range of hydroxide/peroxide ratios and varying times of treatment, established that the strongest adhesive bonds were obtained with test pieces oxidized for short periods just long enough to form black oxide. If treatment is continued beyond this stage, one phase disappears from the surface leaving entrapped gases which appear as bubbles in the adhesive.The results used in fig. 2 were obtained with conditions to give optimum strength. Stereoscan and light microscopy of the adhesive surface after breaking showed evidence of substrate failure though whether oxide or metal was not ascertained but both a and B phases could be distinguished. ADHESIVE BSL 308 ON TITANIUM ALLOY I M I 318 Fig. 4 shows the temperature profiles of the same adhesive on this (Ti-Al-V) alloy, the results covering the same range as on the previous alloy. They show similar differences with the various surface treatments. The mode of failure, as shown by the appearance of the adhesive, was identical with that observed with IMI 205. TITANIUM ALLOY I M I 3 18 and is an a-P alloy which, in the samples obtained, had an alp ratio of about 70/30.As with IMI 205, the plain polished surface is presumed to be hydrated oxide,6 Electro- lytic treatment produces rutile with topography unchanged. Aqueous hydrofluoric acid attacks the a phase much faster than it attacks the p phase and TiO, (rutile) is formed on both phases but is precipitated as needles on the a phase. This, together This alloy consists of 90 % titanium, 6 % aluminium and 4 % vanadium- 5 0 0 5 0 100 I5 0 temperature/"C FIG. 4.-(Strength, temperature) profile of BSL 308 adhesive on titanium alloy IMI 318. (a) Plain wet polished surface, 0 ; (6) 4 % w/v aqueous hydrofluoric acid, + ; (c) electrolytic oxidation in 0.1 N sulphuric acid; 0, ( d ) sodium hydroxide+hydrogen peroxide, x (black oxide region).I . ' ' .- 5 0 100 150 2 0 0 250 300 - 5 0 0 temperature/"C FIG. 6.-(Strength, temperature) profile of Hidux 1197C adhesive on titanium alloy 318. (a) Plain wet polished, 0 ; (6) 4 % w/v aqueous hydrofluoric acid, x ; (c) as (6) but 10 % wlv nitric acid added, A.FIG. 5.-Titanium alloy IMI 318 after treatment with aqueous hydrofluoric acid. Electron micrograph ; carbon replica, platinum-shaded at 45". To face page 431K . W . ALLEN, H . S . ALSALIM A N D W. C. WAKE 43 with the shadow cast by the protruding, relatively unattacked p phase is the interpret- ation of the electronmicrograph shown as fig. 5. Sodium hydroxide preferentially dissolves material from the phase boundaries and the p phase, leaving a phase relatively untouched. A mixed oxide, containing rutile, is deposited on both phases but the surface is irregular and porous, much more so than with IMI 205.The conditions selected for surface treatment for the bonds included in fig. 4 were those giving optimum joint strength. ADHESIVE HIDUX 1197 c ON TITANIUM ALLOY IMI 318 This adhesive (Ciba-Geigy, Ltd., Duxford) is said to be a modified epoxy phenolic adhesive supplied as film on a glass cloth carrier. It also contains aluminium powder. Fig 6 shows the corresponding (strength, temperature) profiles for plain polished, and after etching with aqueous hydrofluoric acid, with and without the addition of nitric acid. The profiles are different in general form and, as might be expected from an adhesive reinforced by glass cloth, bond failure is apparently at the interface.The alloy appears superficially clean and the high finish of the metal is reflected in the surface appearance of the separated adhesive as if no true wetting had occurred. Electron micrography of a surface replica from broken joints made with polished adherends showed most of the adherend surface to be bare metal and this applied to joints over the whole temperature range at least to 250°C, after which decomposition of the adhesive is apparent. The apparently smooth surface of adhesive and adherend from joints made with etched surfaces were seen to be quite rough on microscopic examination at magnifications above 100, too rough for phase contrast or electron microscopy. A diagramatic view of the surface is shown in fig. 7 . The clear resin, completely free from aluminium has migrated to the interface and is more apparent at low temperatures whilst at higher temperature bare metal, or rather oxide, occupies more area.Where oxide or metal is apparent, it is as rough surface with bright spots of metal showed where protruding j? phase has been broken off. From areas of adhesive opposite to these bare patches, minute amounts of a black powder were recovered by layer I Ad he rend FIG. 7.-Position of failure with Hidux 1197C adhesive on titanium alloy IMI 138. treatment with dimethyl formamide and De-Solv.lo Microscopy showed there to be needle crystals together with small mauve irregular shapes typical of p phase. The needles were identified by X-ray analysis as ivtile. The addition of nitric acid inhibits the dissolution of the alloy by hydrofluoric acid by the formation of oxide and a smoother surface finish is produced with fewer but thicker needles on the a phase but the appearance after breaking the joint is similar.The proportions shown in fig. 7 are arbitrary and the damaged areas of the oxide substrate are, in fact, micro- scopic in area. DISCUSSION there seems to be a different mechanism for initiating failure at higher temperatures than at lower temperatures, though with the adhesives studied As with earlier44 STRENGTH OF METAL ADHESIVES it is not simply brittle fracture of the adhesive at low and ductile failure at higher temperatures. The appearance of the broken adhesive does not differ over the temperature range except insofar as with REDUX BSL308 there are more breaks through the adhesive from one metal interface to the other at lower temperatures, but there is no sign of drawn ductile edges at high temperatures as was reported4 for REDUX 775. Breaking through the adhesive suggests a form of brittle fracture which is prevented by the glass reinforcement of HIDUX 1197 C which throws the process to the interface with the metal, in fact, to the very thin adhesive layer between the glass cloth and the metal.This entails a higher rate of straining of adhesive near the interface than for unsupported adhesive where the shear is distributed across the total thickness, constant rate of loading being assumed. A further differentiation in the properties of the adhesive near to the metal is that caused by migration away from the filler present in both adhesives.Whether the migrated material is intrin- sically different in constitution or molecular weight or not, makes little difference to the argument since freedom from filler will alone suffice to change both molecular and fracture properties. There exists therefore an extreme case of the situation postulated by Good in which variation in these two properties is a function of distance from the interface and leads to failure close to, but not at, the interface. Where fracture occurs more easily through the bulk of the adhesive, there exists the tendency for the temperature profile to level off at lower temperatures (fig. 2 and 4) as was clearly demonstrated earlier (fig. l), but where reinforcement interferes with bulk fracture this feature of the (temperature, strength) profile is absent (fig.6). However, if fracture of the adhesive in one way or another were the sole determinant of strength, surface treatment of the adherend would not influence joint strength and it apparently does so at the lower temperatures. Polishing of the adherend with water-lubricated carborundum has in each series of experiments produced a greater scatter of results than most of the chemical treatments (fig. 2 and 4) and, for the supported adhesive has given the lowest bond strength over most of the temperature range. This may be the result of contamination as well as of a Bikerman weak boundary layer in the form of the hydrated oxide which has not been identified in this work for reasons stated. Electrolytically-produced oxide layers on IMI205 are very coherent rutile layers firmly secured to the substrate.The few data available suggest the thickness corresponding to a second-order yellow colour gives a significantly stronger bond than the thinner layer corresponding to first order blue. The loose molybdenum oxide surface produced by the action of hydrofluoric acid on IMI205 possibly accounts for the fact that this surface treatment gave the lowest results on this alloy, lower than simple wet polishing. On the other alloy, hydrofluoric acid gives a rough surface with the deposition of rutile needles and this gives bond strength in excess of polished metal (fig. 4 and 6). The roughest surfaces were produced by sodium hydroxide and hydrogen peroxide and these gave the strongest joints with REDUX BSL308.A feature of these joints was substrate failure. Previous work on the embrittlement of titanium alloys has always stressed the importance of hydrogen absorption as a cause, and with high concentrations, as might occur in acid etching, hydride formation would be expected. Examination of freshly etched specimens by optical and electron microscopy failed to reveal any hydride phase but there has been no attempt in the present work to investigate the effect of hydrogen. The indications so far in the present work are that a coherent, rough curface of rutile provides the best substrate for adhesives and this is best obtained by sodium hydroxide and hydrogen peroxide. This, coupled with information on the natureK . W. ALLEN, H .S . ALSALIM AND W. C . WAKE 45 of failure in the adherend suggests that at low temperatures there is a mechanical interaction which modifies adhesive behaviour. The authors thank their colleagues F. B. Elliot and M. Phillips for assistance with, and advice on, metallography, phase contrast interference and electron microscopy ; to D. F. Neale of Imperial Metal Industries (Kynoch) Ltd. for help with metallography and phase identification. This work has been made possible by a research agreement with the University by the Ministry of Defence Procurement Executive. Adhesion and Adhesives, N. A. de Bruyne and R. Houwink (Elsevier, Amsterdam, 1951), pp. 92 476. R. T. Humpidge and B. J. Taylor, J. Sci. Instr., 1967,44,457. Torsional Shear Adhesive Test Apparatus (H. W. Wallace and Co. Ltd., Croydon, 1969). H. Foulkes, J. Shields and W. C. Wake, J. Adh., 1970, 2, 254. IMI Titanium 205 (Imperial Metal Industries (Kynoch) Ltd., Birmingham, 1965), p. 3. S. H. Weiman, Corrosion, 1966, 22, 98. D. F. Neal, Imperial Metal Industries (Kynoch) Ltd., Birmingham, private communication. G. Bianchi, F. Mama and S. Trasatti, Proc. 2nd Int. Cong. Metallic Corrosion (National Assoc. Corrosion Eng., Houston, 1963), p. 905. ZMI Titanium 318 (Imperial Metal Industries (Kynoch) Ltd., Birmingham, 1969), p. 3. l o DE SOLV 8090 obtained from Oxley Developments Co Ltd., Ulverston. l 1 R. J. Good, (a) Aspects of Adhesion, 7, ed. D. J. Alner (Univ. of London Press., Ltd.), to be published ; (b) Amer. Chem. SOC. Div. of Organic Coatings and Plastics Chem. (Washington Meeting, 1971), 31, (2), 169.

ISSN:0370-9302    

DOI:10.1039/S19720200038

出版商:RSC    

年代:1972

数据来源: RSC

摘要:

Nature of the Deformation and Flow of Metals at and Near the Interface During Abrasion, and its Relation to the Friction BY D. S. LIN AND H. WILMAN Applied Physics and Chemistry of Surfaces Laboratory, Department of Chemical Engineering and Chemical Technology, Imperial College of Science and Technology, London, S. W.7. Received 12th June, 1972 The direction of flow of various metals (Pb, Al, Au, Ag, 62.1 At. % Au-Ag alloy, Cu, Ni, 25.7 At. % Ni-Cu, Mo, W, U, Ti, Mg, and Zn) past the faces of a ploughing Vickers diamond pyramid of dihedral angle 136" is shown in ploughing (a) parallel to the side of the initial square indentation, (b) parallel to the diagonal, (c) in an intermediate asymmetrical direction. In all these cases, with this obtuse indenter, the metal flow at the interface is close to the direction lying in a plane through the ploughing direction, normal to the surface of the specimen.Approximate theoretical expressions are derived for the friction coefficient p for such conditions. The form of the flow past an indenter is also indicated by observations on the ploughing of macro- scopic metal pyramids and cones in Plasticene built from superposed layers of different colours. Observations are also made on the widths of grooves ploughed by the diamond on various metals, compared with the width of the static indentation. These are considered in relation to the theoretical expressions and the factors which may affect the groove development. To elucidate the frictional behaviour of metals sliding against multi-asperity surfaces, as in typical abrasion, it is desirable to investigate the action of single indenters of known shape.The experiments below explore the flow of many metals at and near the interface with a ploughing Vickers diamond pyramid (cf. also Buttery and Archard for steels). only about 10 % of the total groove volume ploughed out is removed as wear (similarly for Sic papers 5 ; cf. also Stroud and Wilman 6), thus the friction coefficient p is more characteristic of the shape and orientation of the non-wear-producing asperities. Goddard and Wilmar~,~ in a theory of abrasive friction and wear, derived expressions for the p of not too obtuse cones and pyramids with axis vertical, assuming that flow of metal round the indenter is practically in a horizontal plane. However, for the other extreme of obtuse indenters, such as a Vickers diamond square pyramid of dihedral angle 136" between opposite faces, the experiments below show the flow past the front face(s) is in or near a vertical plane parallel to the sliding direction, and expressions for p for this case are derived.Emery particles appear to be mainly relatively o b t ~ s e , ~ * ~ * ~ * ~ thus a ploughing Vickers diamond gives a useful and relevant comparison. preferred " smooth-cut " steel files as a standard abrasive surface for quantitative studies ; these are coarse enough to avoid clogging, and on them metals give p values of a similar order to those on coarse emery papers, and thus seem to involve many obtuse asperities. p for metals in relation to hardness and structure were broadly similar to the p on emery papers, and remarkably similar to the adhesion-coefficient data of Sikorski.lo Studies were also made on the p, wear rate, hardness and surface 46 In abrasion of metals on bonded abrasives such as emery papers 3 9 To avoid clogging and abrasive-pick-up effects, Alison and WilmanD .S . LIN AND H . WILMAN 47 structure in abrasion of Zn-Cu alloys,l Ni-Cu 1 g and Au-Cu alloys,l and the age-hardening alloy A 1 4 wt. % Cu,14* l 5 and on the relation of p to the state of work-hardening of metals.16 EXPERIMENTAL The purity and sources of the metals and alloys used are given in table 1. Prior to measurement of the static microhardness and the groove widths, the specimen surfaces were first fully abraded unidirectionally to work-harden their surface region to the maximum extent, as in normal abrasion conditions.This was done by abrasion on carefully cleaned and dried “ smooth-cut ” steel files,g for about 400 cm under hand pressure N 1 kg load. They were then smoothed by about 1000 cm abrasion in the same direction on emery papers from grade 0 (35 pm particle dim.) to 0000 (5 pm). In both processes the surfaces were well wetted with propyl alcohol to minimize heating and oxidation and also pick-up of emery particles. The microhardness tests and experiments on groove formation in all cases followed immediately the above initial surface preparation. The Vickers diamond-indentation microhardness H of the surface region was measured using a load in grams equal to +H, TABLE 1 .-GROOVE WIDTHS (mm) AND HORIZONTAL PROJECTIONS OF CONTACT AREAS (mm2), AT x 610 MAGNIFICATION, FROM A VICKERS DIAMOND PYRAMID UNDER LOAD +H GRAMS, PLOUGHING AND INDENTING IN FULLY ABRADED METAL AND ALLOY SURFACES* metal/alloy W f structure b.c.c.H 509 bi bm (D)25.1 (S)16.3 (D)24.3 (S)16.6 (D)23.9 (S)16.7 (D)25.2 (S) 1 7.8 (D)26.3 (S)18.3 (D)27.3 (S)18.3 (D)26.5 (S)18.5 (D)27.3 (S)18.8 (D)18.4 (S) 1 5.1 b Astat. slp from eqn (3) 1.61 1.36 1.07 1.74 2.00 1.91 1.65 1.74 1.16 164 164 181 173 182 190 198 203 196 (D)20.3 (S)13.1 (D)20.6 (S) 13.8 (D)20.7 (S)13.6 (D)21.6 (S) 1 3.8 (D)21.7 (S) 1 3.6 (D)21.7 (S) 13.8 (D)22.1 (S)14.0 (D)23.1 (S)13.9 (D)22.1 (S)15.5 (D)24.8 (S)15.8 (D)24.1 (S)15.4 (D)25.0 (S)15.4 (D)24.8 (S)16.4 (D)27.2 (S)17.4 (D)27.4 (S) 1 7.3 (D)25.9 (S)17.4 (D)27.4 (S)18.0 (D)21 .O (S)16.5 (i)lll 164 ($237 (i)100 154 ($219 (i)103 148.5 (ii)227 (i)124 165 (ii)260 (i)159 193 (ii)3 1 1 (i)176 204 ($326 (i)138 190 (ii)290 (i)141 200 (ii)302 (i)109 115 (ii)247 U 2 b.c.c.390 MO Ni b.c.c. f.c.c. f.c.c. f.c.c. f.c.c. f.c.c. 267 182 132 cu5 Ag Au A1 112 101 36 5 Pb f.c.c. 62.1 At % Au/Ag lo f.c.c. 125 (D)20.9 (S) 1 3.7 (D)25.8 (S)16.7 (D)26.0 (S)15.6 (i)102 178 (ii)224 177 1.14 25.7 At % Ni/Cu l1 f.c.c. c.p.h. c.p.h. c.p.h. 166 233 52 46 (D)21.1 (S)13.9 (D)22.1 (S)13.4 (D)19.9 (S)13.6 (D)19.3 (S)13.4 (D)27.4 (S)16.7 (D)24.4 (S)15.4 (D)22.2 (S)15.6 (D)19.7 (S) 1 5.1 (D)28.1 (S)16.2 (D)29.0 (S)20.4 (D)22.6 (S) 1 5.1 (D)21.1 (S)15.0 (i)108 185 (ii)240 (i)232 368 (ii)442 (i) 84 139 (ii) 195 (i) 95 124 ($203 178 161 182 181 1.42 3 .O 0.38 0.55 Ti l2 Mg l3 Zn l4 [References to Table I overleaf48 FLOW OF METALS AT INTERFACES DURING ABRASION where His in kg/mm2 and using where possible values found by Alison and W i l r n a ~ ~ , ~ thus indentations of the same size were made in the different metals. The load used for the formation of the grooves by the diamond was then taken as, in grams, half the H value just measured.RESULTS 1. MICROSCOPIC OBSERVATIONS OF THE GROOVE MORPHOLOGY I N METALS AND ALLOYS THE INITIAL BROADENING OF THE GROOVE 1 . 1 Generally there is a very slight narrowing just ahead of the initial indentation, cf. fig. 1. On starting to slide, the diamond has to over-ride the initial adjacent piled-up metal (note slightly curving sides of the initial indentation) and becomes slightly lifted, and also there is less displaced metal at the corners of the initial indentation.The indenter loses contact at the back face(s) and the depth of indentation increases until the reaction of the metal on the remaining faces again balances the load. After moving about twice the diameter of the static indentation, a dynamic equilibrium is reached in which the pile-up of metal at the front face is displaced continuously round to the sides of the indenter, giving the well-known ridge of piled-up metal at the sides of the groove, and a constant maximum groove width. 1.2 THE TRANSVERSE VERTICAL CROSS-SECTION OF THE GROOVES By oblique illumination at 45", the groove profile in transverse section can be seen Fig. 1, 5(a) from the displacements of the shadow lines cast by fine graticule lines.and 6(a) show considerable pile-up of metal at the lateral groove edges. References to Table I ] * Purity 99.99 % except 99.98 for Pb, 99.95 for Mg and somewhat less for Au. H is the Vickers microhardness in kg/mm2 of the fully abraded metal surface measured at a load fi 3H (kg/mm2) in g. All subsequent grooves ploughed using a load = +H (kg/mm2) in g, bi, bm, bf are the the groove widths x 610 in inm at the initial indentation, halfway along the groove and at the front end of the groove respectively. (D), (S) denote ploughing direction of the diamond indenter along the square diagonal and parallel to the square side of the indeutation respectively. As is the projected horizontal contact area x 6102 in mm2 when the diamond indenter is ploughing in a direction parallel to the square side of the indentation.(i) A: denotes the projected contact area of the front face of the indentations including the contact with the pile-up in front of the diamond indenter. (ii) A: as (i) plus the projected contact area of the side faces. AD is the projected horizontal contact area x 6102 in mm2 when the diamond indenter is ploughing in a direction along a diagonal of the square indentation. Asat. is the projected horizontal contact area x 6102 in mm2 of a static square indentation made in the vicinity of the grooves at the same load and during the same period of time. l From Murex Ltd., - rod, From Metallography Division, A.E.R.E., Hanvell-commercial purity. From Murex Ltd.-rod. From The International Nickel Co.(Mond) Ltd.-cast from highest-purity nickel pellets in vacuo. From the British Aluminium Co. Ltd.-" super-purity " A1 rod. From Hopkin & Williams Ltd.-Analar. lo From Johnson, Matthey & Co Ltd.- From the International Nickel Co. l2 From Metallography Division, A.E.R.E., Harwell-commercial purity Ti. l3 From Magnesium Elektron Co. Ltd. l4 From Hopkin & Williams Ltd.-Analar, re-cast. 5-7 From Johnson, Matthey & Co. Ltd.-Spec pure.(b) FIG. 1.-Micrographs showing grooves made by Vickers diamond pyramid ploughing ]I to the square side of the indentation, and I/ to the initial fine surfacing grooves, on (a) Mo (x 425), H = 267 kg/ mm2; (b) Au (x S O ) , H = 101 kg/mm2. In (a) the vertical lines are oblique shadows of fine graticule lines.( a ) (b) FIG. 3.-(a) Front end of groove ploughed /I to square side, 1 to the initial surfacing giooves, in Mo (x 1450); (6) as (a) but 11 to initial surfacing grooves (x 1150)-note several initial surfacing fine grooves passing down the front face, approx. I1 to groove, in this plan view. (b) FIG. 4.-Micrographs showing profile of front end pile-up of (a) a groove in Ag ( x 500) ploughed 11 to square side ; (b) two grooves in 25.7 At. % Ni-Cu alloy ( x 215). [To face page 48(4 (6) FIG. 5.-Micrographs of front end of grooves in Mo, ploughed I/ to the square diagonal, (a) x 820, (b) x 610; note " twin " pile-ups ahead, and several initial fine surfacing grooves continuing down the front face at -10" to groove direction in this plan view. (6) (c) FIG.6.-Micrographs of grooves ploughed in Au in a direction at 25" to square diagonal, and /I to initial fine surfacing grooves : (a) x 590, (6) x 700, (c) x 680. Note asymmetric pile-up ahead, " chatter " marks in the groove, and oblique shadow lines showing groove profile in (a). (a) (6) FIG. 7.-Micrographs of front end of grooves ploughed /I to square side in (a) 25.7 At. % Ni-Cu ( x 1100), (b) 62.1 At. % Au-Ag ( x 1100). Note irregular shape of front face indicating strong adhesion to diamond.(a) (6) FIG. 8.-Micrographs of (a) front end of groove ploughed j / to the square diagonal, in Ti ( x 600). Note the two " chips " prqjecting from the surface ahead of the groove, (6) Ti adhering strongly to the diamond. FIG. 9.-Micrograph of front part of a groove ploughed 11 to the square side on U.Note cracks and fractures in the groove surface. FIG. lO(6) FIG. 10 (a) FIG. lO.-(a) Plan view ( x 1 .l) and (6) longitudinal median vertical section ( x 1.7) through the groove of (a), which was ploughed by a 90" square pyramid of brass, I1 to the square side, in a stratified Plasticene block. Note front pile-up and lateral " flaking " at edges of groove in (a) ; and initial forward and upward, then downward flow in (6).FIG. 11 (a) FIG. 11 (c) FIG. 11.-As fig. 10 but ploughed ll to square diagonal ; (a) plan ( x 1.0)-note forward flow in the twin pile-ups ahead of the front of the groove; (6) transverse vertical section ( x 1.7) through tip of indenter at front end of groove ; (c) longitudinal median vertical section ( x 1.7) showing profile of pile-up, and subsurface flow directions.FIG. 1 1 (b) FIG. 12 (a) FIG. 13.-Plan view of the front end o f a groove ploughed in stratified Plasticene by a cone. FIG. 12 (6) FIG. 12.-(a) Oblique view ( x 1.7) on to surface of a Plasticene block, showing chip formation by an acute- angled square pyramid indenter, ploughing /I to the square side. (6) plan view of a groove made by an acute-angled square pyramid plough- ing in Plasticene \ / to the square di- agonal ( x 0.2). Note twin " chips ", cf. fig. 8(a).FIG. 8.-Stereoscan micrograph showing a FIG. 9.-Stereoscan micrograph of the fracture sheath of nylon surrounding a pulled out fibre. surface of a 0.15 Vf surface treated carbon fibre showing little pull out of fibres. FIG. 10.-Stereoscan micrograph of fracture surfaces of a 0.15 Vf carbon fibre/nylon com- posite showing the effect of matrix morphology on fracture (note fibre, lower left).FIG. 11 .-Stereoscan micrograph of the fracture surface of a 0.1 5 Vf uncoated carbon fibre/nylon composite showing high degree of pull out.D. S . LIN AND H . WILMAN 49 The volume of metal displaced from below the original specimen surface level is seen to be approximately matched by the volume of metal left behind at the groove edges, as is also shown by the groove profiles recorded by the Rank-Taylor-Hobson " Talysurf " apparatus, as in fig. 2. FIG. 2.-" Talysurf " trace across the groove of fig. l(a). 1.3 THE LONGITUDINAL VERTICAL CROSS-SECTION OF THE FRONT END OF THE GROOVES Fig. 4 shows typical profiles of the pile-up of metal at the front end of the grooves, in Ag and in 25.7 At.% Ni-Cu alloy, with the indenter sliding parallel to the square side. Fig. 3(a) and (b) show the appearance of the front pile-up, in plan view, and indicate the tendency for some concentric wrinkling to occur. Fig. 5(a) and (b) show the groove form for the diamond sliding along the square diagonal direction-note less pile-up at the front edge than towards the sides; and fig. 6 shows the groove form for an indenter at an oblique angle of sliding, with the square diagonal at 25" to the direction of sliding, giving asymmetric pile-up. 1.4 OBSERVATIONS O N THE FLOW OF METAL DURING PLOUGHING The initial fine surfacing abrasion grooves give a useful indication of the direction of flow of the displaced surface metal during ploughing.A continuation of the surface abrasion grooves on to the front contact face is clearly visible in micrographs such as fig. 3(a), 3(b), 5(a) and 5(b). In fig. 3(a), the lines are curves concentric with the upper edge of the front pile-up; in fig. 3(b) the lines pass down the front face parallel to the sliding direction; and in fig. 5(a) and 5(b) the lines on the front faces are at about 10" diverging outwards from the sliding direction, then parallel to it at the side faces of the groove. 2. MACROSCOPIC OBSERVATIONS ON GROOVE FORMATION I N STRATIFIED PLASTICENE To examine the sub-surface flow, which is not revealed by the microscopic exam- ination of grooves on metals, experiments were made on stratified Plasticene blocks about 3 in.thick, the coloured strata being about 1/16 in. thick. Plasticene has a stress-strain relation resembling that of metals and has been used to investigate the flow in various types of def0rmation.l' Brass indenters were used, machined to a fine finish and polished smooth on emery to grade 4/0 followed by metal polish. The square pyramidal indenters were50 FLOW OF METALS AT INTERFACES D U R I N G ABRASION of dihedral angle 40" and 90" between opposite pyramid faces, and the cone had a semiapical angle of 30". These were clamped at a fixed level in a milling machine, and the Plasticene slabs, held between steel blocks on a steel base, were raised until the indenter penetrated about 5/16 in. and then traversed horizontally so as to plough a groove at about 3 in./s.Fig. lO(a) shows a plan view of a groove ploughed by the 90" square pyramid sliding parallel to the side of the initial square indentation (cf. fig. 1 and 3). Note the similarity between the " flaking " effect at the lateral sides of the groove with that in the grooves made by the diamond in metals like gold, fig. l(b). Fig. 10(b) shows a median longitudinal section of the groove of fig. lO(a). It is seen that some of the surface and sub-surface material is first pushed up and forward by the front indenter face before flowing down past the indenter and along the groove sides. Fig. 1 l(a), (b) and (c) similarly show a plan, a view of the front end (and transverse section through the apex) from along the groove, and a median longitudinal section, of a groove ploughed by the 90" square pyramid in a direction along a diagonal of the square indentation.Note in this case the lower pile-up at the front edge than towards the sides of the two front faces, as is seen in fig. 5(a), (b), and fig. 1 l(c). Fig. 12(a) is with the acute-angled square pyramid (dihedral angle 40") sliding along the square side, and fig. 12(b) along the square diagonal direction. Chip formation is seen (cf. Avient, Goddard and Wilman and Sedriks and Mulhearn 18), with two symmetrical chips in the case of sliding along the square diagonal (fig. 12(b)). Fig. 13 illustrates the flow pattern of the sub-surface material for ploughing by the cone of semiapical angle 30" (plan view). Note the practically horizontal flow round this acute cone.3. GROOVE MEASUREMENTS I N P U R E METALS A N D ALLOYS Table 1 shows the mean side of the square indentations measured at the beginning of the grooves made with the diamond pyramid sliding parallel to a square side. The initial indentations at the beginning of the groove agree satisfactorily with static indentations, such as those made during the microhardness measurements. The Vickers hardness is given by H = 1854 W/d2 (kg/mm2), where W is the load applied, in g, and d is the diagonal of the square indentation in pm. Thus when W = +H (Hin kg/mm2), in g, d = 0.030 45 mm. The diagonal length on the projected image, at the standard magnification used, x 610, should thus be 18.6 mm for all the metals, and the side of the square indentation 13.15 mm. It is seen from table 1 that apart from Pb, which is known to recrystallize at room temperature,lg the initial groove breadths bi(S) for all the other metals and the two alloys, agree to within 10 %.The slight discrepancies observed, especially in the case of the softer metals, may well be due to the initial vibrations on turning the micrometer screw to start the ploughing. For the diagonal ploughing direction, however, the initial groove breadths bi(D) are all high, ranging from 19.3 to 23.1 mm, instead of the calculated 18.6 mm in the image. This may be associated with the more uneven sliding in this direction; for example note the " chatter " marks in fig. 5 and 6. The median groove breadth b, and front-end breadth 6, show good agreement for all the metals and alloys except for a few metals such as Ti and Pb, where b, is notice- ably less than b,, probably associated with strong adhesion of metal to the indenter faces during ploughing (cf.fig. 8(b)), causing a large drag or tension on the metal behind the advancing indenter (cf. also fig. 10(a) at the edges of the groove). Under the heading of As in table 1, for the horizontal projected area of the frontD . S . LIN AND H . WILMAN 51 contact, when sliding is parallel to the square side, (i) A: is the area for the front face only, (ii) A: the area including also the two side faces, which is the expected operative area against which the metal flow pressure acts. It is seen that there is an appreciably wide spread of values of A,(i) and (ii) for the metals investigated.This spread is noticeably less for the projected contact area AD when the ploughing is along the square diagonal. It is also seen from table 1 that except for the softer metals the measured horizontal projected static-indentation areas A,,,,. are all in reasonable agreement with the calculated value of (13.15)2 = 173 mm2. All the projected horizontal areas were estimated by tracing on transparent mm-squared paper the curved periphery of the front contact area and that of the side faces, or the square indentation, as seen on the microscope projection screen. DISCUSSION 1. THE CONTACT AREAS AT THE FRONT OF THE GROOVES DURING PLOUGHING OF THE VICKERS DIAMOND When an abrasive asperity or an indenter such as a Vickers diamond pyramid is under load W against a metal, the area of the static indentation is given by W/p, where p is the maximum flow pressure of the metal.20* 21 When the loaded indenter is caused to plough by applying a sufficient force F to it parallel to the metal surface, there is loss of contact at the back face of the indenter, and the remaining faces must support the load, thus the indentation becomes deeper, and the groove width increases, as is observed, e.g., in fig.1. The estimates in table 1 of the horizontal projected areas of contact AD made by the indenter when sliding parallel to the square diagonal agree quite well with the pro- jected area Astat. of the static indentation, except for Pb and the hexagonal metals Zn, Mg, Ti. A$ is mostly considerably larger than Astat., by a factor too large to be explained by the presence of a few furrows passing down the interface, making the real area of contact less than the nominal apparent contact area (in any case this would also apply for AD which agrees well).Also, if the dynamic flow pressure p' during ploughing differs from the static flow pressure p , it would be expected to be larger thanp,20 and this wouldreduce the observed A? relative to Astat,, which is in the sense opposite to the observations in table 1. &T- PLAN P L A N FIG. 14. In the case of the relatively obtuse Vickers pyramid, as seen above from micro- graphs such as fig. 3, 5 and 6, the flow of metal down the front face of the indenter is practically in a vertical plane parallel to the sliding direction when this is along the square side, and not far from the sliding direction (only about 10" in the horizontal projection, i.e., plan view as in fig.5) when this is along the square diagonal, or at intermediate azimuths. For such flow, the vertical component (downwards in this52 FLOW OF METALS AT INTERFACES DURING ABRASION case) of the adhesive shear force (s/unit area) of the metal along the front face (see fig. 14) must be added to the load, and the total then balanced by the product of p and the horizontal projected area, in a way similar to that applied by Sedriks and Mulhearn l 8 in the case of a ploughing machine tool. We may consider the following directions of ploughing. (i) PLOUGHING PARALLEL TO THE SQUARE SIDE W = p(A, +2A2) sin 8’-sA, cos 8’ = pA;-sA; cot 8’ A; = w / { p - ~ ( A ; / A ; ) cot el) = ( w / p ) / { 1 - ( s / p ) ( ~ ; / A ; ) cot el] sip = (A;-- A,,,,.)/A; cot 81, (1) ( 2 ) (3) thus, where A , = area of contact on the front face, A2 = area of contact at each side face, A: = horizontal projected area of the whole area of contact = ( A , + 2A2) sin Of, A; = horizontal projection of Al, = A l sin Of, and 8’ is the angle between the pyra- mid axis and the bisecting line of a face.Thus, A{ involves not only (s/p) and 8’ but also the ratio (&/A;) which has a mean value of 0.47 from the data in table 1. Resolving the forces horizontally, and neglecting any slight deviation of the flow from a vertical plane, the coefficient of friction p is given as the resultant horizontal frictional force I: divided by W (given by eqn (1)) :- F = 2sA2 +sA, sin 8’ +PA1 cos 8’ (4) ( 5 ) = s(2A2 + A , ) +sAl(sin 8’ - 1) +PA1 cos 8’ Thus, p involves the ratio (s/p) and Of, and also the ratio &/A{.(ii) PLOUGHING PARALLEL TO THE SQUARE DIAGONAL W = 2pA, sin 8’ -2sA1 cos 8 = pAD-sAD cos O/sin 8’ A D = (W/P)/{l - (s/P)(cos 8/sin of)), (7) thus, (8) where 8 is the angle between the pyramid axis and an edge of the square pyramid, thus tan 8 = ,/?tan 8’. In this case, AD does not involve any ratio of front contact area to side contact area. Also, (9) which again only involves (s/p) and 8‘. p = (COS 8‘ cos 45” + (s/p) sin e]/(sin 8‘ - (s/p) cos el, (iii) PLOUGHING I N AN INTERMEDIATE DIRECTION AT ANGLE 4 TO THE SQUARE SIDE If the areas of contact on the two front faces are A , and A2, W = p(A1 +A2) sin 8’-s(A, cos <, +A2 cos c2) F = s(A, sin cl +A2 sin c2)+p sin 8’(A1 cos 4 + A 2 sin (6) = pAI-s(Al cos 5 1 +A2 cos 5 2 )D .S . LIN AND H . WILMAN 53 where c, and c, are given by tan rl = tan B'/cos 4 ; tan C2 = tan B'/sin 4, and A , = ( A , +A,) sin 8' = horizontal projected area of contact. In the above equations it might appear that (s/p)-O.4 to 0.6, since the friction coefficient of a smooth diamond surface on various metals at room temperature in air was found to be of this order.22* 23 However, if we use the data in table 1 for A:, A; and Astat. in eqn (3), we obtain values for s / p given in the last column of table 1, the mean being about 1.7 for the (fully-work-hardened) cubic metals, if we exclude Pb and U as being extremes of softness and brittleness, respectively.This high s / p may possibly indicate that shear occurs in the metal rather than at the true interface. Fig. 15 and 16 shows the p values as a function of 8, to be expected from eqn (6) and (9), for ploughing square pyramids, for various s / p values and taking &/A," = 0.47 as the average from the data of table 1. Since these equations only apply for sufficiently obtuse square pyramids, the curves calculated from the expressions of Goddard and Wilman for acute square pyramids for which practically horizontal flow round the indenter occurs (if there is no " chip " formation), are also shown in fig. 15 and 16. In the intermediate region of 8, transitional values can be expected as 8 FIG. 15.-The relation between p and the angle 8 between the square pyramid axis and an edge, for various s / p values and taking &/A; = 0.47 (cf.table 1) ; ploughing I[ to square side. The curves through points El are calculated from eqn (6) assuming flow in a vertical plane round the obtuse indenter ; the other curves are calculated from Goddard and Wilman's ' expression assuming hori- zontal flow for acute pyramids. Curves . . . . are the suggested transition.54 FLOW OF METALS AT INTERFACES DURING ABRASION indicated by the dotted curves, corresponding to more or less inclined flow. Although we have not as yet estimated the p experimentally, it appears that if s/p- 1.7 a value of -3-4 can be expected for the ploughing Vickers diamond.* 0 6 5 4 P 3 2 I I0 20 30 do ;o do Yo' 8'0 goo 0 . 5 There are, nevertheless, uncertainties such as whether the effective flow pressure may be less for the piled-up metal just ahead of the front face, than for deeper metal more surrounded by the mass of the specimen.If much temperature rise of the metal at and near the indenter surface occurs during ploughing, this could also result in a lower p for the metal there than that under static conditions, at room temperature. 2. GROOVE MORPHOLOGY I N RELATION TO HARDNESS AND CRYSTAL STRUCTURE Fig. 8(a) shows the front contact face of a groove ploughed in Ti. This is a hexagonal metal of quite high hardness, about 233 kg/mm2, so clean-cut grooves of the type seen in metals like Mo and Cu would be expected. In fact, the grooves show a considerable amount of adhesion effects, and fig. 8(6) also shows the strong adhesion of Ti to the diamond surface.Lead, an extremely soft rnetal, surprisingly did not show similar strong adhesion (cf. Sedriks and Mulhearn 18). * see Discussion, p. 60: p 2 0.45; contact area < apparent area.D . S . LIN AND H . WILMAN 55 The alloys investigated also showed some interesting features, particularly the uneven nature of the contact at the front face as seen in fig. 7(a) and (b). Metals harder than about 250 kg/mm2 show some cracks and fractures at the side of the grooves, as in uranium, fig. 9, such metals being increasingly brittle in nature. The above experimental work was carried out under a contract between the National Engineering Laboratory (Ministry of Technology) and the Imperial College of Science and Technology, London, SW.7. D. S. Lin, Ph.0. Thesis (University of London, 1967). T. C. Buttery and J. F. Archard, Proc. Inst. Mech. Eng., 1970-71, 185, 537. J. Goddard, H. J. Harker and H. Wilman, Nature, 1959, 184, 333. B. W. E. Avient, J. Goddard and H. Wilman, Proc. Roy. SOC. A, 1960, 258, 159. T. 0. Mulhearn and L. E. Samuels, Wear, 1962, 5,478. M. F. Stroud and H. Wilman, Brit. J. Appl. Phys., 1962, 13, 173. P. V. K. Porgess and H. Wilman, Proc. Roy. SOC. A, 1959, 252, 35. P. J. Alison and H. Wilman, Brit. J. Appl. Phys., 1964, 15, 281. P. J. Alison, M. F. Stroud and H. Wilman, Proc. Inst. Mech. Eng., 1964-5, 179, part 35, 246. H. Wilman, Metals and Materials, 1967, 1, 290. l3 D. S. Lin and H. Wilman, Brit. J. Appl. Phys., 1968, 1, 561. l4 D. S. Lin and H. Wilman, Wear, 1969, 14, 323. l5 D. S. Lin and H. Wilman, Wear, 1969, 14, 337. l 6 D. S. Lin, Wear, 1969, 13, 91. ’ J. Goddard and H. Wilman, Wear, 1962,5, 114. lo M. E. Sikorski, Wear, 1964, 7, 144. D. Baker and I. E. Bryan, Brit. J. Appl. Phys., 1965, 16, 865. A. J. Sedriks and T. 0. Mulhearn, Wear, 1963, 6,457 ; 1964, 7,451. l9 P. A. Beck, Trans. A.I.M.E., 1940, 137, 222. 2o F. P. Bowden and D. Tabor, Friction and Lubrication of Solids, part I (Clarendon Press, 21 D. Tabor, The Hardness of Metals (Clarendon Press, Oxford, 1951). 22 D. M. Kenyon, Ph. D. Thesis (University of Cambridge, 1956). 23 F. P. Bowden and D. Tabor, Friction and Lubrication of Solids, part I1 (Clarendon Press, Oxford, 1950). Oxford, 1964).

ISSN:0370-9302    

DOI:10.1039/S19720200046

出版商:RSC    

年代:1972

数据来源: RSC

摘要:

GENERAL DISCUSSION Dr. H. Wilman (Imperial College, London)said : May I ask Briscoe and Tabor whether the approximate agreement of the shear strength of 3 x lo6 N m-2 for the calcium stearate of their fig. 5 with the approx. 3 x lo6 N m-2 at a contact pressure of about 10' N m-2 in fig. 4 means that the results in fig. 5 correspond to this contact pressure? If so, can they indicate to what they ascribe the rise in shear strength to more than 10' N m-' at the higher contact pressures in fig. 4? Do they consider that no regions of direct contact (of higher shear strength) of the two underlying substrates (in general, atomically uneven) are involved, presumably increasingly the higher the pressure ? Can the rise in shear strength correspond at least partly to a breaking-up of the molecular layers into progressively smaller crystalline regions and thus increase the extent of the grain boundaries and associated dislocations, and so increase resistance to shear? Their conclusion, that at high contact pressures the shear of long-chain materials such as stearic acid involves sliding of the chains lengthwise over each other, is interesting.I recall that Schoon pointed out that the angle of tilt of the chains to the ab planes in crystals of the a, B and y forms of stearic acid are consistent with the chains cohering along their length, but with different longitudinal shifts; and he suggested that such a sliding of the chains along each other by a multiple of the C-C spacing might be possible, and correspond to a series of other possible poly- morphic forms or metastable equilibria of molecule coherence.It seems not necessary that the molecule chains should lie quite parallel to the shear direction, i.e., the substrate surfaces. Electron diffraction results which I obtained on stearic acid in 1937 showed that rubbing a thick layer of stearic acid ( N 1 cm2 area at a few kg load) in one direction, caused a strong 2-degree preferred crystal orientation, as shown by a pattern of diffraction spots and arcs. The long axes of the molecules were then oriented not parallel to the substrate interface, but at about 5" to it (in a vertical plane through the rubbing direction), instead of at the normal angle of about 55" to the substrate when in (001) orientation. (Rubbing a very thin layer of stearic acid on to polished copper resulted, however, in a strong orientation with the molecule chains tilted in the rubbing direction, at the usual angle of about 55" to the substrate; but this could correspond to chemisorbed copper stearate.) Brummage found that in some cases rubbed n-paraffin layers were in part in an orientation with the chains at about 3" to the substrate surface, analogous to my observations above on stearic acid.Dr. B. J. Briscoe and Dr. D. Tabor (Cambridge University) said: We are grateful to Wilman for the points he has raised. His surmisal concerning fig. 5 is perfectly correct. The results in this figure for the polymers are based on direct friction experi- ments between polymers and glass where the contact pressure is of the order of several kg mm-2 (or several lo7 N m-2).These results have been compared in this figure with results obtained on calcium stearate films at a known contact pressure of lo8 N m-2. Since then we have transferred thin films of polymer to the glass substrate and studied the shear properties of the film by exactly the same procedure as that T. H. Schoon, 2. phys. Chern. B, 1937, 39, 385. see fig. 40 of G. I. Finch, J. Chern. Soc., 1938, 1137. K. G. Brummage, Proc. Roy. SOC. A, 1947, 188,414. 56GENERAL DISCUSSION 57 described for calcium stearate. The shear strength of the polymer films turns out to be somewhat greater than that quoted in fig. 5 but the effect of contact pressure closely resembles that shown in fig. 4 for calcium stearate etc. In these experiments, examination of the substrate before and after sliding shows no evidence for glass-glass contact even at the heaviest pressures employed.If such interaction was to occur the damage to the glass would be severe and detectable. Further, the results are very similar to those obtained in the bulk shearing of metallic soaps (see ref. (1 7), (1 8) of our paper) and the bulk shearing of polymers between diamond platens recently carried out in our laboratory by Dr. H. D. Flack. The increase in shear strength with pressure may or may not be due to grain boundary effects analogous to the increased hardness of metallic specimens as the grain size is reduced. It may not, however, be necessary to invoke such a mechanism. The contact pressures are very large compared with the modulus of these materials so that the molecular components are pressed close together.In these circumstances the interaction energy must be increased whether grain boundary effects are involved or not. Further many of the soaps lack any clearly defined crystalline structure. One of the un- certainties involved in the experiments quoted by Wilman is that electron diffraction can show the structure only after sliding has occurred. We have looked at the struc- ture of polymer films sheared between diamond platens using X-ray diffraction during the shearing process itself. Here the evidence supports the view that there is con- siderable, if not complete, orientation of the chains in the direction of shear. The evidence quoted for chain orientation is of great interest. Prof.M. W. Roberts (University of Bradford) said : Briscoe’s reference to a fraction of a monolayer of chemisorbed oxygen present on an iron surface is puzzling in the sense that oxygen rearranges very readily on iron to give an oxide. For example many “ monolayers ” form at a Po, N Torr and 77 K, i.e., with close to zero activation energy. Dr. B. J. Briscoe and Dr. D. Tabor (Cambridge University) said: We are grateful to Roberts for his comments. It may well be that the films formed in our experiments on iron were thin oxide films rather than a chemisorbed film. The main point we wished to emphasise was that far more oxygen was required to produce a comparable reduction of adhesion with copper surfaces. Dr. R. G. Linford (Berkeley Nuclear Lab.) said: The transition from retarded to non-retarded forces is shown in fig.2 of the paper by Briscoe and Tabor as occurring in the same region as the change-over from the dynamic to the jump method. In view of the extreme experimental difficulties of these elegant experiments, are the authors convinced that there is a definite transition and that it has been correctly located ? Dr. B. J. Briscoe and Dr. D. Tabor (Cambridge University) said: In reply to Linford, the detailed results given in our paper show that both methods give self--consistent results. The jump method covers separations from 2 to 20nm and shows that as the separation is increased the transition from non-retarded to retarded forces begins for separations greater than 12 nm. The resonance method covers separations from 120 nm down to 10 nm and shows that the transition from retarded to non-retarded forces begins at a separation of 50 nm and is complete when the separation is 12 nm.Thus, both techniques are in complete accord as far as the transition is concerned and in the region of overlap the absolute agreement in the magnitude of the force is58 GENERAL DISCUSSION extremely close. For both techniques the accuracy of the power law index n in the two regions is better than f O . l as indicated in fig. 3. Dr. J. R. Young (Duckhams Oils) said: The observations of Briscoe and Tabor relating to PTFE sliders on clean glass are puzzling. The results show that the wear mode of the polymer changes once smooth sliding has commenced. A thin orientated polymer layer is then transferred to the glass, and the surface of the slider becomes similarly orientated in the direction of sliding.If the slider is now turned through 90" and again moved over the previous track " lumpy " transfer with high friction is again observed in the initial stages. It seems unlikely that the transferred layer is well ordered and, in so far as the individual chain groups are concerned, may be considered a random two-dimensional array. If this is true one must ask how does the slider surface distinguish between the two directions of motion relative to the transferred layer ? Dr. B. J. Briscoe and Dr. D. Tabor (Cambridge University) said: Young has raised an interesting point but it is based on a slight misunderstanding of the statements in our paper. The only results of repeated sliding over the same friction track refer to the behaviour of an oriented slider over an oriented film.Here the van der Waals interaction involves a shear strength just about equal to or slightly less than the forces required to draw further material from the slider. The friction is low and there is practically no further transfer of PTFE. The effect of rotating the slider through 90" was limited to sliding over a clean glass surface.The interaction between PTFE and glass is strong : the orientation of the slider is unfavourable for easy drawing : a lump of PTFE is plucked out of the slider and the initial friction is high. The behaviour when the slider is rotated through 90" and slid over an oriented PTFE film is more complicated and is not discussed in the present paper though it is dealt with in the fuller paper by Pooley and Tabor.In effect, it depends on whether the transferred film completely covers the glass substrate. If it is a " good " continuous film, the friction and transfer are both low. If the film is tenuous so that a fair amount of glass is exposed through the film, the friction may be high. In general, if the interfacial adhesion is strong, the friction and transfer are large unless the sliding surface is favourably oriented. If the interfacial adhesion is low the friction and transfer are both small. Prof. D. D. Eley (Nottingham University) said: In relation to Weaver's paper, it is interesting to note that McAloon and Perkins,l using SCF CNDO theory have calculated an electron energy band structure for polyethylene with a band gap of 13-19 eV depending on the approximation used.Dr. J. R. Young (Duckhams Oils) said: With reference to the postulate of Allen et al. that migration is the process accounting for the formation of a filler-free layer at the adherend surface, the observations of Griffin are relevant. Griffin was seeking an explanation for the wide variations in friction and wear properties reported for apparently similar mixtures of solid lubricants (e.g., graphite, and molybdenum disulphide) in thermoplastic supports (e.g., polypropylene and polystyrene). He examined the distribution and orientation of particles close to the surface of injection- moulded test pieces. He found that (i) the surface of the test piece which had con- ' B.J. McAloon and P. G. Perkins, J.C.S. Faruduy Trans. 11, 1972, 68, 1121. G. J. L. Griffin, A.S.L.E. Trans., 1972, 15, 171.GENERAL DISCUSSION 59 tacted the mould was totally free from solid particles for a depth of 20-30 pm; (ii) the plate-like particles deeper in the solid were oriented parallel to the surface. arising from his theoretical study of the viscous flow of lamellar solid suspensions. It may, therefore, be unnecessary to invoke diffusion to account for the surface effect presently reported. These observations were judged consistent with predictions made by Jeffery Dr. H. Wilman (Imperial College, London) said : Can Sutcliffe and Cameron clarify what they assumed about the direction of motion of the (001) molecular layers over each other, relative to the crystallographic axes a and b ? Was the direction of relative motion taken to be a particular lattice direction, e.g., parallel to the x axis, or were all possible azimuthal directions considered and an average taken ? Was the relative motion in a given direction taken to be unidirectional, or in a zig-zag such as occurs in slip of close-packed sheets of atoms in metal slip planes over each other ((0001) hexagonal or (1 11) f.c.c.metals)? The long-chain molecules here are in a pseudo- hexagonal lateral packing, and analogous zig-zag slip may be expected. In our recent results we have shown that elastic hysteresis losses associated with periodic motion normal to the sliding direction (the units of one sheet moving in and out of a sequence of potential troughs as they slide over the opposing sheet of close- packed units) can contribute appreciably to the friction.Would not such a contribu- tion be expected similarly for sliding of sheets of hydrocarbon molecules over each other, and did their calculations include such periodic normal components or com- pressions along the molecule chains or their methyl end groups? With respect to the experimental values being much lower than those calculated, and this being attributable to the presence of dislocations, it is indeed probable with these layer structures that rotational slip would occur to an appreciable extent, and result in easier slip thereafter, giving rise to a series of relative azimuthal rotations such as those observed by Wilman.2 Dr. B. J. Briscoe and Dr.D. Tabor (Cambridge University) said: Cameron and Sutcliffe have embarked on a difficult problem. We have two comments. Both are concerned with the models they have chosen for the mode of shear in these materials. First, they consider that shear in a multilayer occurs between methyl groups midway between the two substrates. We wonder if this is a reasonable assumption. Recently, Dr. Israelachvili has carried out a series of experiments in our laboratory which seem to indicate that this type of shear is rarely realized. In his experiments he used mica crossed cylinders, the surfaces of which were covered with Langmuir- Blodgett layers of stearic acid. He was able to subject these layers to compressive and shear forces while observing the total film thickness to f0.2 nm using multiple beam interferometry. With a monolayer on each mica surface he found that the total film thickness was about 5.5 nm and the layers were stable both in compression, and shear. However, when three layers of acid were deposited on the surfaces the situation was rather different.The layers were stable to compressive forces, but the structure of the layers was destroyed immediately a shear force was applied. In these experiments the contact pressures were comparatively low (about lo7 N m-2) and the sliding speeds were of the order of mm s-l. In engineering systems, both the G. B. Jeffery, Proc. Roy. SOC. A , 1923, 102, 161. H. Wilman, Nature, 1950, 165, 321 ; Proc. Phys. SOC. A , 1951, 64, 329; A. D. Whapham J. Inst. Metals, 1956, 84, 109; A. D.Whapham and H. Wilman, Nature, 1955, 176, 460; Proc. Roy. SOC. A , 1956, 237, 513. ' P. V. K. Porgess and H. Wilman, Proc. Roy. SOC. A , 1959,252,35.60 GENERAL DISCUSSION pressure and the sliding velocity will be generally much higher. Hence we would expect that the structure of multilayer films would always be destroyed in these cases. Further, the fact that all surfaces are significantly rougher than mica would enhance this re-ordering. Secondly, apart from the experiment described above, we wonder if one ever has the situation where one Langmuir-Blodgett layer slides over another. We have found that a Langmuir-Blodgett layer deposited on glass has similar shear properties to the bulk material. There are perhaps two reasons for this similarity. (i) During sliding, additional material on the surface finds its way into the zone of contact and one is then sliding not on a monolayer, but on a wedge of material.Within the wedge (if it is formed), the molecules appear to be orientated with their chains parallel to the direction of sliding (see arguments in our paper). We also recall the observations of Flack which we described in reply to the question from Wilman on our paper. Flack was able to study the orientation of long molecular chains in polymers during shear using X-ray techniques. He found that there was considerable orientation of the chains in the direction of shear. Where this material comes from is uncertain when initially only one monolayer is present, but since the area of contact is small, very little material (less than 1 pg) would be required to provide a surface separation of 100 nm.(ii) The energy required to move a series of methyl groups over one another (Cameron and Sutcliffe model) is similar to that required to move methylene groups in the form of extended chains over each other. In their paper the authors mention that they can adjust p, the angle between the normal to the surface and the axis of the hydrocarbon chain. Could be set at n/2, or would a new model be required? We raise this point because Flack carried out a theoretical calculation of the forces involved in sliding long-chain molecules over one another in a direction parallel to the chain axis. His calculated shear strengths turn out to be about 10 times bigger than the observed values and are thus comparable with the values quoted by the authors for a very different molecular arrangement.Prof. W. C. Wake (City University) said: In reply to Young, I accept that a flow process can give rise to boundary zones free from suspended particles but the extent of flow during compression moulding is very small particularly at very low shear rates. For the adhesive supported on glass cloth there will be no flow in the centre of the annulus of the test piece. Both film and coated adhesive show filler particles in their surface as supplied even though a flow process would be involved in manufacture. I think the shear rates are too low to show the effect found by Griffin. The particle size of the aluminium in the adhesive was larger than 30pm and the carbon black very considerably smaller.Prof. D. D. Eley (Nottingham University) said: The presence of surface OH on rutile has been established by i.-r. spectrometry and I wonder whether they play a role in adhesion by hydrogen-bonding to the epoxy resin considered by Allen et aZ. ? Dr. H. Wilman (Imperial CoZZege, London) said : In the paper by Lin and myself, we had hoped to include a measurement of the coefficient of friction p of the Vickers diamond pyramid during ploughing along the surface of metals work-hardened by abrasion. We have now made this determination and find that on both freshly abraded Mo and Ni, ,u is about 0.47 when the load is half the hardness of the surface region in grams, and ploughing is parallel to the side of the square indentation. To make this measurement we held the front section of the microscope objective (on the front face of which the very small diamond for micro-indentation tests is mountedGENERAL DISCUSSION 61 centrally) in a collar having on two opposite sides extensions to about 4 cm length horizontally then bent down vertically to about 4 cm length so that a weighted scale pan could be hung from these extensions so as to load the diamond in a stable manner.A horizontal force to overcome the friction was applied by weights on a second scale pan on a thread passing over a low-friction pulley and attached low down close to the diamond. This observation makes it clear that the conditions are more complex than was assumed tentatively in our paper, which led to the estimate of s / p e 1.7 and p expected to be 3-4.There are four main possibilities to account for the observed p e 0.47 : (1) the real area of interface contact on the diamond is appreciably less than the apparent area (and is x times this) ; (2) the interface is mainly between the surface metal oxide and the diamond, and must have a low mean s/p - 0.4 or less ; (3) the flow pressure p of the piled-up metal just ahead of the ploughing indenter may be less than for the bulk metal, since it is projecting and thus under less constraint from any surrounding metal; (4) p under the dynamic conditions of ploughing is higher than for static indentation. Consider the first possibility. If the true contact area is x times the apparent area, eqn (l), (2), (3) and (5) must be replaced by : (1') w = ~ X A ; - ~ ~ A I , cot 81, F = sx(2A, +A,) + sxA,(sin 8' - 1) + pxA, cos 6', (5') but eqn (6) for p remains unchanged, thus fig.15 still applies. If, therefore, we use fig. 15 to conclude that the observed p of 0.47 must correspond to s/p-0.3 (for 8' = 68", i.e., 8 = 74", and A;/A; 1 0 . 4 7 as observed), then from eqn (3') we find x e 0.84 for Mo and 0.71 for Ni. If s/p = 0.4, we obtain only slightly different values, x = 0.86 for Mo and 0.72.for Ni. Thus, it appears that the observed p can indeed be accounted for mainly by (1) the true contact area being only 0.7-0.85 of the apparent area, and (2) a low s/p - 0.3-0.4 for the metal at the interface, this presum- ably being thus really metal-oxide surface film contacting the diamond (cf. (metal+ oxide) contacting (metal + oxide) with p == 0.28 in the experiments of Goddard, Harker and Wilman,l and Avient, Goddard and Wilman).2 We have already drawn attention in the paper to the presence of some furrows at the interface in the grooves ploughed on these rough work-hardened metal surfaces, hence this seems a reasonable explanation for the p value.The third possibility is difficult to assess, and it may be of only minor importance ; and the fourth possibility seems unlikely to have much effect because, although early work of Bowden and Tabor (see ref. (20), part I, 1950, p. 93) suggestedp for indium is increased considerably under dynamic conditions, other results such as those from shock-wave experiments on metals indicate only very small increases in yield stress as compared with that at lower loading rates. Dr. R. G. Linford (Berkeley Nuclear Lab.) said: Fig. 2 of the paper of Lin and Wilman shows a Talysurf trace of the groove. This is perhaps misleading as the magnifications in the horizontal and in the vertical directions differ by a factor of three for this instrument and the groove is therefore considerably less acute than shown. J. Goddard, H. J. Harker and H. Wilman, Nature, 1959, 184, 333. B. W. E. Avient, J. Goddard and H. Wilman, Proc. Roy. Soc. A , 1960, 258, 159.62 GENERAL DISCUSSION Interpretation of Talysurf traces often leads to confusion : for example, metal sur- faces prepared by normal engineering techniques yield profiles looking as jagged as the Alps whereas such surfaces more closely resemble the rolling hills of the Lake District. Dr. H. Wiiman (Imperial College, London) said: I thank Linford for reminding me that we had omitted to state the scales for the Talysurf trace in fig. 2. In fact, the vertical magnification is x 5000, while the horizontal magnification is x 200. The angle contained by the sides of the groove is 136", in reality, like the dihedral angle of the diamond pyramid (cf. fig. 4).

ISSN:0370-9302    

DOI:10.1039/S19720200056

出版商:RSC    

年代:1972

数据来源: RSC

摘要:

Composite Materials I Fibre Reinforced Composite Materials An Introductory Review BY B. A. PROCTOR Pilkington Research and Development Laboratories, Lathom, Ormskirk, Lancashire Received 30th May, 1972 The principles of reinforcement and the properties of fibre reinforced composites are briefly out- lined and then discussed with particular regard to the role which the interface plays in controlling fibre strength and the utilization of fibre properties. The contradictory requirements for interfacial bond strength and the limitations of anisotropy are discussed, and the suggestion made that high performance composites may need to be designed with particular property requirements and com- ponent performance in mind. 1. INTRODUCTION In the design of structures the ratio of material strength (or stiffness) to specific gravity is often of more importance than the absolute value of strength or stiffness : this is particularly true in the field of aerospace but remains important in transporta- tion and for tall stationary structures such as towers.The specific strengths and stiffnesses of conventional " homogeneous " structural materials lie within a sur- prisingly narrow band (fig. 1) and in order to escape this limitation we have, over the last 10 years or so, turned increasingly to a range of high performance, fibre-reinforced, composite materials. r - I specific stiffness (E/s.g.) specific strength (o/s.g.) FIG. 1 .-Relative specific properties of conventional materials. For many years, brittle materials such as glasses and ceramics have offered attract- ive specific stiffnesses because of their high intrinsic bond strengths and somewhat open, low density structures.Often they had good high temperature properties too, but had the disadvantages of extreme brittleness and low strengths. Recently the 6364 FIBRE REINFORCED COMPOSITES problem of low strength has been largely solved and a number of high strength reinforcing fibres, which offer many-fold increases in specific strength and stiffness over the conventional " homogeneous '' structural materials, have become available (fig. 2). The problem of brittleness has been partially, but none the less usefully, solved by incorporating such fibres as reinforcement in relatively weak matrices to form " Fibre Reinforced Composite Materials '7.This has turned an interesting scientific curiosity into an important branch of materials technology and led to significant improvements in the specific properties of useable solids (fig. 3). t-L P- glass fibre boron fibre carbon fibre sappnire whiskrr graphite wl,'sker specific stiffness (E/s.g.) specific strength (0ls.g.) FIG. 2.-Relative specific properties of reinforcing fibres with background of conventional metal values. (* unidirectional) I - I I I I 1 t I I I L 1 2 3 4 5 4 3 2 1 specific stiffness (E/s.g.) specific strength (a/s.g.) FIG. 3.-Relative specific properties of unidirectional glass reinforced plastic and carbon fibre reinforced plastic compared with steel, aluminium and titanium (representative alloys). A true fibre reinforced material may be defined as one in which almost all of the load is carried by the fibres, so that the strength and stiffness are governed by the properties of the fibre.However, the surfaces of the reinforcing fibres and the inter- faces between fibres and matrices play important roles in controlling the properties of the composite. This paper attempts to outline these roles and (hopefully) to set the scene for subsequent papers within the context of a " Discussion Meeting on Surfaces and Solid-Solid Interfaces." 2. THE LAW OF MIXTURES AND THE STRENGTHS OF FIBRES The simplest fibre reinforced system is an array of unidirectional fibres set in a matrix and stretching continuously through its length ; the whole assembly being stressed along the fibre direction (fig. 4). If A,, Af and A , are the total cross sectionalB .A . PROCTOR 65 areas of composite, fibre and matrix respectively and E, 0, E (with similar subscripts) are the modulus, stress and strain respectively, then the total load F, borne by the composite will be shared between fibres and matrix according to, If we make the further assumption that the strain in the fibres is the same as that in the matrix (i.e., Ef = E, = E,) we have (2.2) This simple equation already indicates certain important requirements which are needed if the composite is to fulfil our definition of true reinforcement, i.e., AfEf must be significantly greater than A,&',, which means that the fibres must be very much stiffer than the matrix and must occupy a reasonable fraction of the composite cross section.F = AfQf$.AmQm. (2.1) I; = (AfEf + AmEm)Ec* F A f FIG. 4.--Idealized unidirectional continuous fibre composite. Since F = a,A, and A,/&, &/Ac represent the volume fractions (Vf and Vm) of fibres and matrix material respectively we can rewrite eqn (2.2) to express the com- posite modulus Ec = Ef Vf + Em V m which is well known as the " Law of mixtures ". derivations give very similar results and (2.3) is certainly valid within experimental error for a wide range of unidirectional composites (e.g., fig. 5 ref. (3)). Since we have already deduced that the fibre must be significantly stiffer than the matrix, and the fibre content should be fairly high, EfVfgE,V,, and (2.3) illustrates the important con- clusion that composite stiffness is governed by the stiffness and concentration of fibres.Eqn (2.2) may be rewritten to give the stress in the composite, Q,, in terms of stresses in the fibres and the matrix. Since most load is carried by the fibres we may assume that the composite fails when the fibres fail, hence composite strength 8, is : (2.3) More rigorous '* a, = a,v,+a:v, (2.4) where af = fibre strength and 02 = stress in matrix at the failure strain of the fibres. In practice, af Vf % 02 V, so that the strength of the composite (from eqn (2.4)) is seen to depend on the strength of the fibres which is, in its turn, governed by the condition of the fibre surface and hence of the fibre/matrix interface. This is the first way in which surfaces and interfaces are important to composite behaviour.2-c66 FIBRE REINFORCED COMPOSITES Recent papers 4-6 have stressed the importance of the " geometrical " perfection of fibre surfaces. Surface abrasion caused by quite normal handling techniques can easily introduce stress-raising cracks in the surfaces of brittle materials with consequent drastic strength loss. In the glass fibre field a considerable technology has been devoted to the development of surface coatings or " sizes " which lubricate and protect the fibre from the worst of the damage (fig. 6), but this factor should be borne in mind in the handling of all fibres prior to and during their incorporation in composites. fibre volume fraction/ Vf FIG. 5.-Young's Modulus plotted against fibre volume fraction for carbon fibre-resin composites. 5 = mean value k standard deviation.I000 2 0'00 3600 4000 breaking s trength/MNm-* FIG. 6.-Tensile strengths of single fibres extracted from a strand and compared with virgin fibre strengths (E-glass, 2 cm test length). Most strong solids lose strength as a result of heat treatment ; for glass silica * and sapphire at least, this has been shown to be due to the creation of local flaws at the fibre surface due to interaction between accidental dust contamination and theFIG. 7.-(Photograph). Heat treatment flaw on silica rod showing contamination core and surround- ing interacted and cracked region (ref. (9)). To face page 671B . A . PROCTOR 67 fibre material (fig. 7). In composites we deliberately place fibres in intimate contact with the matrix : for metal matrices, in particular, fabrication temperatures are often high and one motive for their use is a need for high temperature composites.Inter- facial reactions occur with drastic effects on composite strength in a number of fibre/ metal systems lo-' (Harris, this Discussion). Finally, the chemical environment at the fibre-matrix interface during stressing of the composite is important. Brittle solids are frequently subject to a type of stress- corrosion which leads to time-dependant strength effects, or static fatigue, in which the strength falls with longer times of stressing (fig. 8). Silica and glass interact with moisture in this way 4* * ; water diffuses through many resin matrices and may even collect as water at the interface.16* l7 Carbon fibres show this static fatigue behaviour at elevated temperatures in air and again oxygen may diffuse through plastic or metal matrices l8 (also Harris this Discussion w.r.t.nickel) to cause stress-rupture or stress activated corrosion type failure of the fibres. Thus by directly affecting fibre strengths, the condition of the fibre surface and fibre-matrix interface controls the load bearing ability of composites. I - range of -- failure times 1 I day I yeor I I 10-2 100 10 * 10 (0 time to fracture/min FIG. &--Static fatigue of undamaged silica fibres in air at room temperature. 3. DISCONTINUOUS FIBRES AND THE SHEAR STRENGTH OF THE INTERFACE These important conclusions regarding composite behaviour have been derived without specifying in any way the degree or type of bonding at the interface between fibre and matrix.In making the equal strain assumption, however, it had been implicit that fibres and matrix were held together sufficiently for their deformations to be equal. More detailed considerations of load transfer and of the behaviour of composites containing discontinuous fibres impose additional requirements on the interface. In some instances it is convenient to handle and incorporate reinforcing fibres in relatively short lengths, whilst other reinforcements (e.g., whisker crystals) are only available as short fibres. All brittle fibres contain flaws, and hence weak points, so will break up into discrete lengths under stress even if, as in many carbon and filament wound glass composites, they were originally incorporated as continuous fibres.In all these cases, the matrix must transfer load into the fibre by means of some gripping mechanism at the end region. Consider a fibre of length I embedded in and bonded to a matrix of much lower modulus (fig. 9), the whole being subject to a tensile strain in the direction of the fibre. It is clear that in the region of the fibre the matrix will be restrained and differential68 FIBRE REINFORCED COMPOSITES displacements near the fibre ends in particular will set up shear stresses in the matrix and at the matrix-fibre interface. This problem has been treated analytically by Cox l9 and others 20* on the assumption that fibre and matrix are elastic and re- main adhering. Cox showed that the tensile stress in the fibre rose rapidly from zero at the end ( x = 0) to a maximum (plateau) in the centre (x = 1/2) (fig.9) according to (Of), = EfEm{ l-(c*sh p(;-x))/cosh p i } where p = (2G,/(Efrf210g,(rl/rf)))~ and E, = matrix strain, rf = fibre radius, rl = interfibre spacing. Conversely, the shear stress at the interface was shown to be a maximum at the ends of the fibre, falling almost to zero in the centre (fig. 9) according to Eqn (3.1) and (3.2) and fig. 9 show quite clearly that there is a region at the end of each fibre which is lightly stressed and is thus ineffective in carrying load (the ‘‘ in- effective length ”, Rosen 21) : for this reason the average stress carried by a length I of discontinuous fibre is less than that which would be borne by an equivalent length of continuous fibre ; the shorter the fibre the less effective it is as reinforcement, a fact recognized by Cox.<Cf f o r frictional or yielding load transfer FIG. 9.-Diagrammatic illustration of matrix deformation around discontinuous fibre in a low modulus matrix and the rise in fibre stress and interface shear stress along the fibre length. Eqn (3.1) and (3.2) enable us to calculate the ratio of the maximum interface shear stress at the fibre end to the maximum tensile stress in the centre of the fibre. The values depend on matrix and fibre modulii and on length of fibre and fibre content : but for a long glass fibre in a typical resin matrix at V, = 50 %, the shear stress needed at the ends in order to realize a practical glass strength of -22000 MN/m2 would approach 280 MN/m2. This is clearly greater than the shear strength of anyB .A . PROCTOR 69 present resin or the bond strength between resin and fibre. The estimates of shear stress are in themselves conservative since stress concentration effects are neglected in the Cox type of shear-lag analysis. More recent treatments based on finite element techniques which take some account of stress concentrations 22-24 indicate that the actual interface shear stresses are at least twice those predicted by Cox. This must imply some form of failure in the matrix at the fibre end which was first recognized by Outwater 25 in 1956 who discussed bond failure at fibre-ends in a glass reinforced plastic material and postulated that load transfer was essentially achieved by a frictional gripping of the fibre due, in turn, to resin shrinkage during curing.Kelly 26 also tackled this problem with reference to the yielding in shear of a metal matrix near the ends of a discontinuous fibre : it is possible that localized yielding may also occur in some resin matrices. Both Outwater's and Kelly's treatments assume essen- tially a constant and limiting value of shear stress, z, around the fibre ends; the tensile stress (0) carried by the fibre then rises linearly from the end according to where rf = radius of fibres ; the rate of increase in (T being governed by z, the value of yield stress or frictional stress, but inevitably being lower than that in the " unfailed " elastic case (eqn (3.1) and fig. 9). Thus the bond strength and interfacial condition directly affect the " ineffective lengths " at fibre ends, hence the average load borne by discontinuous fibres, and thus both the modulus and strength of the composite in the fibre direction.In practice, the effect of this may be small since fibres are often and wisely used in lengths long compared with those theoretically required ; it may partly account, however, for the relatively low effective reinforcement of thermoplastics by short, chopped, high modulus fibres. As well as affecting the average utilization of a given fibre strength, the interfacial shear strength may also effect the actual he2 of fibre strength utilized in a composite. Flaw-free fibres such as the " virgin " glass fibres tested by Thomas 27 and Cameron 28 have consistent strengths which are independent of gauge length, but flawed fibres of boron, carbon, " handled " glass, etc., have variable strengths which, on average, decrease as the tested length increases (or as the probability of including a weak spot increases, fig.10 and, e.g., ref. (29), (30)). A lower value of interfacial shear strength or shear yield stress effectively spreads out the tensile stress distribution in the fibre as if a longer gauge length were being used, resulting in a lower available strength from flawed fibres. The strengths of fibres and bundles of fibres have been treated statistically by Daniels 31 and Coleman,32 whereas Rosen in particular has applied these treatments to composite strength predictions.21* 33* 34 The important point here is that in order to make maximum use of fibre strength (and to a lesser extent of modulus) in unidirectional composites reinforced with discontinuous or flawed continuous fibres, the interfacial bond strength and/or shear yield strength should be high.Finally in these types of composites, deterioration in the bond or yield strength as a result of ageing, stress-rupture, stress or temperature cycling, or creep relaxation will lead to a fall in unidirectional composite strength. 34-3 * mf" do = 27crfz dx. (3.3) 4. CRACK PROPAGATION AND TOUGHNESS Problems of low fracture toughness in unidirectional composites are associated with crack propagation perpendicular to the fibres by one, or a combination of more than one, of the mechanisms shown in fig. 11. In fig. 1 l(a) an advancing matrix crack which may have initiated at a broken or transverse fibre, at a void, pre-existing crack, or surface notch causes direct fracture70 FIBRE REINFORCED COMPOSITES of the reinforcing fibre.Clearly this is a very dangerous situation and such a com- posite will be extremely brittle and notch sensitive. The probability of this behaviour will be increased by high fibre-matrix adhesion, by a stiff and brittle matrix and by 6~ B 5 - 4 - 3 - 2- FIG. 1 - I I000 20bo 3600 strength/MN 10.-Tensile strengths of single E glass fibres extracted from a strand, B, 2 cm test length. A 3 A, 10 cm test length; high rates of loading since in these cases there will be little elastic or plastic relaxation locally and the extra load from the broken matrix will be transferred into a short length of fibre near the crack plane.Even if the matrix bond fails locally, by de- bonding or yield, a high remaining friction or yield stress will help to maintain the probability of fibre fracture as discussed by Cooper and Kelly.39 In practical composite materials, this behaviour is usually avoided, but in carbon fibre reinforced plastics, where the fibre-resin adhesion may be readily increased by surface treatments, the dangers are real as reported by Mallinder 40 and Daniels and H a r a k a ~ . ~ ~ Fig. 12 (ref. (40)) shows a dropin the flexural strength (tensile typefailures) of a carbon/epoxy composite as surface treatment (and interlaminar shear strength) increases. The more usual and desirable composite situation is indicated in fig. 1 lb where an advancing matrix crack does not immediately break the fibre, which may be left bridging the crack and give a pseudo-ductile behaviour to an all-brittle composite 43 Discontinuous fibres may subsequently pull out of one side of the matrix if the crack advances further, continuous fibres may break at a weak point away from the crack and then pull out.Outwater and Murphy44 discuss thisB . A . PROCTOR 71 behaviour in glass reinforced plastics and consider the possibility of fibres debonding at the interface for some distance back from the crack rather than fracturing at the crack plane. They derive a condition for debonding (i.e., desirable behaviour as in fig. l l b ) as where GI1 = interfacial bond energy, af = fibre strength, a = fibre diameter and Ef = fibre modulus. GII = (8:a)/8Ef (4.1) 0, U C FIG.11 break. .-Crack propagation and initiation mechanisms. (a) Advancing matrix crack initiates fibre (c) Fibre break initiates matrix crack. (6) Advancing matrix crack leaves bridging fibre. (d) Fibre break leaves matrix uncracked. The same authors then derive an expression for the work to fracture of a com- posite when the crack spreads through an array of bridging fibres and, emphasizing the contribution of the work needed to debond the interfaces for some distance back from the crack surface, they conclude that the work to fracture per unit area of composite (GI) increases as the interfacial bond energy (Gii) and the interfacial frictional shear strength (z) decrease, where bC = composite strength. GI = (a6:/4E VfT)((8c/Vf) - 2[2E,G, Ja] $} (4.2) Kelly45 points out that the contribution of work72 FIBRE REINFORCED COMPOSITES of pull out always exceeds that due to debonding.He derives expressions which lead to a work to fracture per unit area of composite of the form where z = interfacial shear yield strength or frictional shear strength. In contrast to the requirements of the previous section, eqn (4.1), (4.2) and (4.3) indicate that tough unidirectional composites having a high work to fracture normal to the fibre direction must have relatively low interfacial bond strengths. GI cc VJ&;a/z (4.3) '"""t N I E N I E z Y (d FIG. extent of surface treatment+ posite (mean strengths and total spread of results). 12.-Flexural strengths and short beam shear test results for a carbon fibre epoxy-resin com- The mechanisms shown in fig.l l c and 1 Id are really the inverse of l l a and llb respectively, 1 Id being generally desirable and 1 lc potentially hazardous. Both types of behaviour have been particularly with carbon-resin systems where the interfacial bond may be varied over a wide range. Mechanism 1 l c is more likely when both bond and fibre strengths are high and when fibre diameters are large ; it is particularly dangerous with brittle matrices when an overlap with the regime of mechanism l l a can lead to entirely brittle behaviour and the complete loss of the point of separating the reinforcement into separate fibrous elements ! 5. ANISOTROPY, TRANSVERSE PROPERTIES AND MULTI- DIRECTIONAL REINFORCEMENT If a simple unidirectional composite is stressed in tension at an angle 0 to the fibres (fig.13) the applied stress Q may be resolved into a uniaxial component (0,) along the fibres, a transverse component (or) and a shear stress ( T , , , ) . ~ ~ - ~ ~ The values of transverse stress (a,,) and shear stress (z,,) rise rapidly as 8 increases from zero and theB . A . PROCTOR 73 strength of the material, at an angle 8 to the fibres (&), may be considered in terms of 3 failure modes ; fibre breakage at very small 8, interfibre shear at intermediate values of 8 and transverse tensile failure at larger 8 (fig. 14, ref. (3)). This simple maximum stress failure criterion does in fact predict composite behaviour quite accurately, and agrees closely with more sophisticated theories.49 9 f i b r e I / direction .5 - m0 - FIG.13.-Resolution of applied stress along and perpendicular to fibre direction in a unidirectional composite ; U, = u cos2 8, uY = u sinz 8, T~~ = u sin 8 cos 8. In practice, the shear strength (.Zxy) and transverse strength (a,) are interface dominated and are very much less than the axial strength 6,; the composite is thus highly anisotropic, as indicated in fig. 14. Attempts to reduce this anisotropy by increasing the interfacial bond strength are limited by the strength of the matrix itself and by the need for toughness and resistance to crack propogation as discussed in the previous section. Morley 51* 52 (also this Discussion) has suggested a double interface system involving an outer surface which is strongly bonded to the matrix to provide transverse and shear strengths, and an inner surface of controlled and variable shear strength to prevent transverse crack propagation through the core part of the 2 0.05- E Y 0.02 - I / / /./ or / interface shear ' matrix shear si necos0 matrix or interlace transverse tensile failure 6 - .zL sin20 I I I I 30' 6r3' 9 0 angle 8 FIG. 14.-Tensile strength of unidirectional carbon-fibre epoxy-resin composite as a function of angle between fibres and test direction.74 FIBRE REINFORCED COMPOSITES reinforcing fibre. This novel approach separates the competing requirements of high and low interface strength but the shear and transverse strengths of a unidirectional composite are still limited by the matrix properties. An alternative approach is to arrange for the fibres to lie in more than one direction in order that some fibres will be able to act as " unidirectional " reinforcement against a stress applied in any direction.This also has limitations in that the fibre content and the effective fraction of fibres bearing the load, are both reduced as the degree of " multidirectionality " increases (fig. 15). Further, some fibres will always lie transverse to the applied stress when they will act as rigid inclusions 47* 53* 5 4 rather than reinforcement. They then magnify the stress at the interface and initiate debonding which can spread as a matrix crack. Precisely this failure mechanism has been observed by Owen 5 5 and McGarry 56 in studying the initiation of fatigue failure in multidirectional fibre composites.6 . CONCLUSIONS Interfacial properties are seen to control, very directly, the strength and toughness of composites via the initiation and propagation of failure, the efficiency of utilization of fibre strength, and the retention of fibre strength itself: to a smaller extent they affect elastic properties and utilization of fibre modulus. Creep, long term load bearing ability and weathering are also significantly affected. There are competing and contradictory requirements for interfacial properties. unidirec tiona I theoretical Vf(max) 91°f0 practical Vf (rnaxl- 80°/0 max i m urn composite properties in the fibre direct ion - 0.8 (0' or Ef) cross plied theoretical Vf(max) 79'/0 practical Vf(rnax) 70°/, maximum corn posite properties in any one fibre direction - 0.35 (Uor Ef) ordered 3 - D array t heo re t ica I practical Vf(maxl - 40% V' (ma x) 5 0 - 6 0% maximum composite properties in any one fibre direction "'0.13(0 or E$ FIG.15.-Fibre packing densities and utilization of fibre properties for unidirectional, cross-plied, and 3-dimensional composites. Initially, the properties of composites were seen as a relatively simple function of fibre properties and research was concentrated on new and improved fibres for reinforcement. Increasingly, in use, complex and transverse stress systems are encountered which lay emphasis on the important role of both interface and matrix. There will be a tendency and a need to develop more sophisticated composites, optimized for one or more aspects of performance and incorporating such features as controlled and multiple interfaces, flexible and elastic/plastic matrices, selected and mixed fibre lengths and distributions. In the long term however, the cost effectiveness of the property in operation in the component, covering, e.g., fabrication and design as well as material cost, will be important.Means of applying the required sophisti- cation to continuous large scale production will have to be found.B. A . PROCTOR 75 I am indebted to many present colleagues at Pilkington Brothers Research and Development, and former colleagues at Rolls Royce Old Hall Laboratories for helpful discussions and information : particularly to Dr. N. G. Nair. I also wish to thank the Directors of Pilkington Brothers and Dr. D. S . Oliver, Director of Group Research and Development for permission to publish this paper.l R. Hill, J. Mech. Phys. Solids, 1963,11, 357. M. D. Heaton, Brit. J. Appl. Phys. (J. Phys. D.), 1968, 1,1039. F. P. Mallinder, Znst. Rubber Industry Conf. on Advances in Polymer Reinforcement and Blends (Loughborough, September, 1969). B. A. Proctor, Composites, 1971, 2, 85. M. H. de Wad, Relations between the Mechanical Strength of Glass and its Surface State ; (Review of Two Year's Co-operation in Scientific Research on Glass, December, 1971, Organization for Economic Co-operation and Development, DAS/SPR/71.35), p. 128. R. L. Crane and R. E. Tressler, J. Comp. Mat., 1971, 5, 537. W. Brearley and D. G. Holloway, Phys. Chem. Glasses, 1963,4, 69. B. A. Proctor, I. Whitney and J. W. Johnson, Proc.Roy. Soc. A, 1967,297, 534. B. A. Proctor, The Physical Basis of Yield and Fracture (Institute of Physics Conference Series No. 1, 1966, 218. lo D. Cratchley and A. A. Baker, Compte Rendu Symposium sur le Contact du Verre avec le Metal, 1964, 671 (Union Scientifique Continentale du Verre). H. W. Rauch, Ceramic Fibres and Fibrous Composite Materials (Academic Press, New York, 1968). l2 E. H. Andrews, J. Mat. Sci., 1969, 4, 377. l3 P. W. Jackson and J. R. Marjoram, J. Mat. Sci., 1970,5,9. l4 R. B. Barclay and W. Bonfield, J. Mat. Sci., 1971, 6, 1076. l5 J. A. Snide, F. A. Ashdown and J. R. Myers, Fibre Science and Technology, 1972, 5, 61. l 6 D. I. James, R. H. Norman and M . H. Stone, Plastics and Polymers, 1968, 36, 21. l7 K. H. G. Ashbee and R. C. Wyatt, Proc.Roy. Soc. A, 1969,312, 553. l 8 F. S. Galasso and J. Pinto, Fibre Science and Technology, 1970,2, 303. l9 H. L. Cox, Brit. J. Appl. Phys., 1952, 3, 72. 2o N. F. Dow, General Electric Company Report R63SD61, 1963. 21 B. W. Rosen, A.Z.A.A. Journal, 1964, 2, 1985. 22 A. S. Carrara and F. J. McGarry, J. Comp. Mat., 1968,2,222. 23 H . D. Conway and C. I. Chang, Fibre Sci. Tech., 1971,3,249. 24 R. M. Barker and T. F. Maclaughlin, J. Comp. Mat., 1971, 5,492. 25 J. 0. 0. Outwater, Modern Plastics, 1956, 33, 156. 26 A. Kelly, Strong Solids (Oxford University Press, London 1966). 27 W. F. Thomas, Phys. Chem. Glasses, 1960, 1,4. 2 8 N. M. Cameron, J. Amer. Ceram. Soc., 1966, 49, 144. 29 D. J. Thorne, Carbon Fibre Strength-Eflect of Internalfluws (Soc. Chem. Ind., 3rd Carbon 30 A.G. Metcalfe and G. K. Schmitz, Materials Res. Stand. (ASTM), 1967, 7, 146. 31 H. E. Daniels, Proc. Roy. Soc. A, 1945, 183, 405. 32 B. D. Coleman, J, Mech. Phys. Solids, 1958, 7, 60. 33 B. W. Rosen, Strength of Uniaxial Fibrous Composites, Mechanics of Composite Materials, 34 B. W. Rosen, Proc. Roy. Soc. A, 1970, 319, 95. 35 J. M. Lifshitz and A. Roten, Fibre Sci. Techn., 1970, 3, 1. 36 N. Fried, The Degradation of Composite Materials. Conference, London, 1970). ed. F. W. Wendt, H. Liebowitz and N. Perrone (Pergamon Press, London 1970), 621. The Eflect of Water on Glass-reinforced Plastics in Mechanics of Composite Materials ed. by F. W. Wendt, H. Liebowitz and N. Perrone (Pergamon, London 1970), p. 813. 37 F. J. McGarry and M. Fujiwara, Modern Plastics, London 1968, p. 143. 38 C. A. Calow and A. Moore, Composites, 1971, 2, 231. jg G. A. Cooper and A. Kelly, Role of the Interface in the Fractwe of Fibre-Composite Materials in 40 F. P. Mallinder, private communication. 41 B. K. Daniels and N. K. Harakas, Nature Phys. Sci., 1971, 231,41. 42 H. G. Allen, J. Comp. Mat., 1971,5, 194. 43 A. J. Majumdar, Proc. Roy. Soc. A, 1970,319,69. Interfaces in Composites (ASTM Special Technical Publication 452, 1969), p. 90.76 FIBRE REINFORCED COMPOSITES 44 J. 0. Outwater and M. C. Murphy, On the Fracture Energy of Uni-directional Laminates. (Reinforced Plastics/Composites Division, Society of Plastics Industry, 24th Annual Conference 1969), Section 11-C. 45 A. Kelly, Proc. Roy. SOC. A, 1970,319,95. 46 J. Mullin, J. M. Berry and A. Gatti, General Electric Co. Space Sciences Laboratory Report 47 E. Z. Stowell and T. S. Liu, J. Mech. Phys. Solids, 1961, 9, 242. 48 A. Kelly and G. J. Davies, Met. Rev., 1965, 10, No. 37. 49 P. W. Jackson and D. Cratchley, J. Mech. Phys. Solids, 1966, 14,49. G. J. Schneider, Fibre Sci. Tech., 1972, 5, 29. 51 J. G. Morley, Proc. Roy. Soc. A, 1970, 319, 117. 52 J. G. Morley, Composites, 1971,2, 80. s3 H. Schuerch, Advanced Concepts for Composites in Mechanics of Composite Materials ed. 54 J. N. Goodier, Trans. Amer. Soc. Mech. Eng., 1933, 55, 39. 5 5 M. J. Owen and T. R. Smith, Plastics andPoZymers, Feb. 1968, p. 33. 5 6 F. J. McGarry, Crack Propagation in Fibre Reinforced Plastic Composites, in Fundamental Aspects of Fibre Reinforced Plastic Composites ed. R. T. Schwartz and H. S. Schwartz (Inter- science, New York, 1968), p. 63. R67 SD51, September, 1967. F. W. Wendt, H. Liebowitz and N. Perrone (Pergamon Press, London 1970), p. 583.

ISSN:0370-9302    

DOI:10.1039/S19720200063

出版商:RSC    

年代:1972

数据来源: RSC

摘要:

Static and Fatigue Failure of Glass Fibre Reinforced Polyester Resins under Complex Stress Conditions BY M. J. OWEN AND M. S . FOUND Department of Mechanical Engineering, University of Nottingham Received 1st June, 1972 Static and fatigue tests have been carried out at several principal stress ratios on thin-walled tubes fabricated from " E " glass chopped strand mat and a polyester resin. Corresponding data have been obtained from flat laminates under axial tension, axial compression, and in-plane shear loading. The onset of debonding, and resin cracking were observed as well as rupture. The results have been compared with predictions based on the theories of failure for anisotropic materials. Only those theories which include the results of a complex stress test gave safe predictions.The fatigue results for cylinders gave failures at much lower stresses than would have been expected from corresponding axial stress data and further work is required to explain the anomaly. NOMENCLATURE (a) Chopped Strand Mat Cylinders o,, hoop principal stress ; 02, axial principal stress; R, principal stress ratio, o2/oI. o,, 02, 0 6 , normal stresses and in-plane shear stress respectively parallel and per- pendicular to the fibre axes ; F,, F2, F6, strengths corresponding to ol, 02, 0 6 ; Flt, FZt, tensile values of Fl and F2 ; Flc, FZc, compressive values of Fl and F2 ; K2, H12, constants in failure theories. (6) Failure theories To use failure theories for chopped strand mat cylinders put 0 6 = 0, when or and o2 become principal stresses.When designing structures or components, the engineer is usually required to provide a finished product with a guaranteed working lifetime at minimum total cost. Safe-life design procedures for fatigue conditions are reasonably well understood for isotropic metals and have been developed particularly by aero-engine and airframe constructors. Design in glass reinforced plastics (GRP) is handicapped by the lack of proven safe-life design procedures. Most fatigue testing of GRP has been carried out on small laboratory samples subjected to repeated uniaxial stresses parallel to a principal material axis, treating the specimen as if it were homogeneous and isotropic with complete separation as the criterion of failure.2 A few attempts have been made 3-5 to observe the progressive damage which occurs in GRP under both static and fatigue loading.It has been established that the first sign of damage is usually separation at the glasslresin interface for fibres lying perpendicular to the line of load. This transverse fibre debonding occurs at an average strain of 0.3 % under static loading or as low as 0.14 % strain after lo6 cycle^.^ These strains correspond to only a small fraction of the conventional 77ref. Group 1 maximum stress ti maximum strain? Hill Azzi and Tsai Norris interaction lo Norris failure Hoffman l 2 Group 2 modified Marin (Franklin) l 3 Gol'denblat and Kopnov l 4 Tsai and Wu l5 TABLE 1 .-FAILURE CRITERIA WHICH HAVE BEEN SUGGESTED FOR ANISOTROPIC MATERIALS key to fig.* failure criterion B B F F F * A, B etc., are the key letters to fig.11 to 14M. J . OWEN AND M. S . FOUND 79 ultimate strength. The further progress of damage depends to some extent on the arrangement of the reinforcements, but in materials containing resin rich zones, the debonds progress outwards into the resin rich zones to form cracks. These cracks are more numerous under repeated loading than static loading and it has been shown that the development of cracking leads to a progressive loss of residual strength. Visible damage is not normally acceptable to designers and there is a tendency to over design in order to avoid it. Among the problems which anisotropy causes for the designer is the lack of a proven theory of failure for use as a predictive rule under combined stress conditions. Table 1 shows two groups of expressions which have been proposed for anisotropic materials.The first group are mainly extensions of isotropic theories and require only the use of two or three principal strengths and the in-plane shear strength. The second group require additional data from the results of a complex stress strength test. The expressions proposed by Franklin l3 and Gol’denblat and Kopnov l4 have been shown to give good predictions of failure for fibre reinforced materials subjected to static biaxial stress loading. Griffith and Baldwin l6 have tried to predict complex stress failures under static and fatigue loading, but their theory requires the use of compliances and assumes therefore that the material behaviour is linearly elastic to failure. The work reported in this paper represents the first stage of an investigation into fatigue under multiaxial stress conditions to establish the suitability of various theories of failure.The work takes into account not only complete rupture of the specimens but also the onset of transverse fibre debonding and resin cracking as definable states of damage. A full account of the work is given ref. (17). EXPERIMENTAL MATERIALS AND SPECIMENS Details of the materials and laminating procedures are given in table 2. Flat laminates (69x 53 cm) were prepared by the wet lay-up technique on a glass plate treated with release TABLE 2.-MATERIALS glass content reinforcement type lay-up thickness Imm % by weight Fibreglass Supremat 3 layers 3.2 34 or E-glass Mat 6 layers 6.4 polyester resin-Beetle L2615 BIP Chemicals, Ltd. maleic anhydride 1 mol phthdic anhydride 1 mol propylene glycol 3 mol alkyd/styrene ratio 65/35 hydroquinone 0.008 % on blended resin catalyst MEKP 1 % accelerator cobalt napthenate 4 % room temperature cure 18 h postcure 3 hr at 80°C agent and restrained by a steel picture frame mould.To ensure uniform thickness, the finished laminates were covered with release film and a second sheet of glass was placed on top and pressed down by weights. The properties of the laminates are given in table 3.80 FAILURE O F GLASS FIBRE COMPOSITES The flat laminates were cut into rectangular specimen blanks using a diamond-impregnated slitting wheel and were cut to shape using a pantograph type copying machine with a diamond- impregnated tool.Four specimen shapes were used for various types of test (fig. 1). TABLE 3.-LAMINATE PROPERTIES ultimate strength reinforcement tensile compressive in-plane shear glass content type MN/m2 lo3 Ibf/in* MN/m2 lo3 Ibf/in2 MN/m* 103 lbf/inZ % weight mat 119 17.2 228 33.0 64 9.3 34.0 Chopped strand mat reinforced thin-walled cylindrical tubes were also prepared. The method was essentially the same as for the flat laminates except that the reinforcement was wound on to a slowly rotating mandrel. The finished cylinders were wrapped with release film and were rotated continuously against a roller until gelling of the resin took place. This R76’ 32.0 all dimensions in millimetres FIG. 1 .-Flat laminate specimens : (a), static tensile specimen ; (b), static and fatigue compression specimen ; (c), tensile fatigue specimen ; (d), in-plane shear specimen.prevented resin drainage and ensured a uniform wall thickness. Cylinders which were to be subjected to compressive axial loads were overwound with glass fabric at the ends to prevent crushing. Cylinders which were to be subjected to tensile axial loads had coarse threads cast on to the ends in an epoxy casting resin. Cylinders which were required for tests to rupture were coated internally with silicone rubber liners. All the cylinders were 180 mm long and 65 mm internal diameter. Cylinders used for compressive axial stress were 72 mm outside diameter, whilst those for tensile axial stress were 70 mm outside diameter. EQUIPMENT Short term tensile tests were conducted in a modified type E Tensometer universal testing machine of 110 kN capacity at a crosshead speed 0.13 cm/min.All uniaxial stress fatigue tests were carried out in a set of fatigue machines specially constructed for testing GRP and described in ref. (18). The tests were conducted at 100 c/min. The machines are arranged so that cycle counting ceases when specimen rupture occurs. The onset of transverse fibre debonding and resin cracking was determined by observing the specimens through a travelling microscope. Biaxial stress fatigue tests were conducted using thin-walled tubes. The tubes wereM. J . OWEN AND M. S. FOUND 81 0 placed in a loading frame in tandem with a hydraulic jack. The same hydraulic oil supply was supplied to the jack and the specimen, ensuring that axial load and internal pressure were always in phase.Jacks of several different diameters were available and they could be arranged to provide tensile or compressive load. Thus a range of principal stress ratios in the cylinder walls could be obtained. Principal stress ratios, R, of 1 .O, 0.5,0, - 0.5 and - 1 .O were used in these tests although others are also available. A hydraulic oil supply under pulsating pressure at 100 c/min was provided by a pulsator pump of identical design to that described in ref. (18). The fatigue stress in the test cylinders was adjusted by controlling the volume of oil delivered by the pulsator pump into the closed elastic system consisting of the jack, specimen, and load cell. The five loading frames are equipped with strain gauge type proving rings to measure axial load and pressure pick-ups to measure oil pressure.Electrohydraulic circuits are arranged to divert the oil supply at specimen failure and to provide cycle counting. Although the pulsator pump has a common mechanical drive, the five cylinders are hydraulicaIly independent and there is no interaction between the five loading frames. Full details are given in ref. (17). o RUPTURE 0 RESIN CRACKING RESULTS Chopped strand mat reinforced cylinders were subjected to single applications of load to produce debonding, resin cracking, or rupture. Combined internal pressure and axial load were tested at were applied to produce five principal stress ratios. Three cylinders each stress condition. Silicone rubber-lined cylinders were used in FIG.2.-Static test results for chopped strand matlpolyester resin cylinders.M. J . OWEN AND M. S. FOUND 81 0 placed in a loading frame in tandem with a hydraulic jack. The same hydraulic oil supply was supplied to the jack and the specimen, ensuring that axial load and internal pressure were always in phase. Jacks of several different diameters were available and they could be arranged to provide tensile or compressive load. Thus a range of principal stress ratios in the cylinder walls could be obtained. Principal stress ratios, R, of 1 .O, 0.5,0, - 0.5 and - 1 .O were used in these tests although others are also available. A hydraulic oil supply under pulsating pressure at 100 c/min was provided by a pulsator pump of identical design to that described in ref.(18). The fatigue stress in the test cylinders was adjusted by controlling the volume of oil delivered by the pulsator pump into the closed elastic system consisting of the jack, specimen, and load cell. The five loading frames are equipped with strain gauge type proving rings to measure axial load and pressure pick-ups to measure oil pressure. Electrohydraulic circuits are arranged to divert the oil supply at specimen failure and to provide cycle counting. Although the pulsator pump has a common mechanical drive, the five cylinders are hydraulicaIly independent and there is no interaction between the five loading frames. Full details are given in ref. (17). o RUPTURE 0 RESIN CRACKING RESULTS Chopped strand mat reinforced cylinders were subjected to single applications of load to produce debonding, resin cracking, or rupture.Combined internal pressure and axial load were tested at were applied to produce five principal stress ratios. Three cylinders each stress condition. Silicone rubber-lined cylinders were used in FIG. 2.-Static test results for chopped strand matlpolyester resin cylinders.M . J . OWEN AND M . S. FOUND 83 l2C 8C 4c I E z E c c . d 2 Y - ._ X - 4 ( - 8( -12( hoop stress, al/MN m-' 0 2 0 40 I hoop stress, ul /MN m-2 FIG. 5.-Constant life curves for chopped strand mat/polyester resin cylinders at rupture. 3c 2( IC N I E s c 2 1 3 m" v) U - .- 2 -1c -2c -3 c 10 20 3 hoop stress, ol/MN m-2 FIG. 7.-Constant life curves for chopped strand mat /polyester resin cylinders at fibre debonding.FIG. 6.--Constant life curves for chopped strand mat /polyester resin cylinders at resin cracking.RESIN CRACKING + DEBONDING -UNBROKEN SPECIMEN endurance-cycles FIG. 10.-In-plane shear static strength and fatigue results for flat laminates. 160- E z 1 I2O- t : 80, 1 2 E 4 0 + + Y 0 o RUPTURE \ 0 0 U a -0-p- " I --0 I - -*-. cr -+.++-, -++5+ 32 0 7 240: E z E 2 - 160 3 v) 8 8 0 O-- o RUPTURE RESINCRACKING - U N BROKEN SPEC 1 MEN I IM . J . OWEN AND M. S. FOUND 85 FIG. 11 .-Comparison of static results with failure theories for chopped strand mat/polyester resin cylinders at rupture. Key letters refer to table 1. 12 i e ( 4( "; E \ s 2 - 4 c M 'j; - 8C rni Y v) - cd (d -12( - 16C -2oc 0 hoop stress, ul /MN m-2 FIG. 12.-Comparison of static results with failure theories for chopped strand matlpolyester resin cylinders at resin cracking.Key letters refer to table 1. 4 0 8 0 I 2 0 160 hoop stress, u,/MN m-'86 FAILURE OF GLASS FIBRE COMPOSITES 0 10 20 3 0 hoop stress, ai/MN m2 N E $ Y E 8 v; c( .r( cb 3 FIG. 14.-Comparison of lo6 cycle fatigue results with failure theories for chopped strand mat/ polyester resin cylinders at rupture. Key letters refer to table 1. FIG. 13.-Comparison of static results with failure theories for chopped strand matlpolyester resin cylinders at fibre debonding. Key letters refer to table 1. hoop stress, al /MN m-’M. J. OWEN AND M. S. FOUND 87 sections. The static and fatigue results are presented in fig. 10. With this method of test, it was found that the onset of damage was virtually coincident with complete rupture of the specimens.In fig. 11, 12, 13 and 14 the results obtained from cylinders are compared with curves based on the expressions in table 1 and uniaxial and in-plane shear strength data. Fig. 11, 12 and 13 show the comparisons for static strength at complete rupture, resin cracking, and debonding respectively. Fig. 14 shows the same com- parison for the lo6 cycle fatigue strength at specimen rupture. DISCUSSION The most significant feature of the biaxial stress results for rupture of chopped strand mat cylinders is that they all fall well inside the rectangular boundary which represents the maximum stress theory of failure (fig. 11 and 14) under both static and fatigue loading. In the tension/tension stress quadrant it is seen that the theories developed from conventional isotropic failure theories (group 1, table 1) are all inade- quate and that the more complicated theories of group 2 give a better correlation with the test results.This amounts to curve fitting because the theories of group 2 involve not only the tensile and compressive strength of the material (as does the Hoffman theory) but also an additional constant. These constants have to be evaluated from a complex stress test. If mat laminates are regarded as macroscopically plane iso- tropic then it is not possible to devise an " off-axis " tensile specimen and the complex stress test must involve externally applied complex stresses. Thus the authors have used the results for R = + 1.0 to evaluate the constants.The inadequacy of the group 1 theories, especially the maximum stress theory, is of great significance for designers who use theories of this type to design under complex stress conditions using simple uniaxial test data. It is possible that in the range R = + co through to R = - 1.0, in the absence of complex stress data, a simple approximation such as a circle of radius Ft, where Ft is the tensile strength at rupture, could be used. This might be a much better criterion of failure than for example the conventional maximum stress, maximum shear, or distortional energy criteria, which engineers use for isotropic materials and to which several of the group 1 theories simplify for plane isotropic material. The use of the circular failure boundary needs further investigation.In fig. 2 the static debonding and resin cracking behaviour appears to depend on stress ratio, R, in much the same manner as the rupture results. The comparison with the failure theories at debonding in fig. 13 is also very similar. It should be noted that debonding was detected at stress levels approximately one-fifth of the corres- ponding ultimate value. In fig. 11 and 13 the failure stress at R = 0 obtained from cylinders was virtually identical with the corresponding failure stress at R = +co based on flat laminate tensile specimens with a small correction for the difference in glass ~ 0 n t e n t . l ~ The corresponding stresses at the onset of resin cracking did not agree so closely, the stress value for cylinders being lower. Fig. 12 has been con- structed using the flat laminate results for the failure stress at both R = 0 and R = +a.Thus the cylinder results fall inside the failure curves. These results are undoubtedly anomalous and it is believed that the resin cracking behaviour may be affected by the hydraulic oil in the absence of silicone rubber liner. Fig. 5, 6 and 7 show the fatigue results for chopped strand mat cylinders as constant life curves. The results for rupture in fig. 5 indicate a slightly greater fatigue effect at R = 1 than at R = 0 when compared with the corresponding mean static failure curve. This effect is particularly marked in fig. 6 and 7 for the onset of88 FAILURE OF GLASS FIBRE COMPOSITES resin cracking and debonding respectively. It is known from the work of Howe and Owen that, under axial load conditions, the primary cause of fatigue damage is the development of resin cracking which reduces the residual static strength.It would appear from fig. 5 that biaxial tensile stress conditions produce more rapid develop- ment of resin cracking than axial stress conditions. The more marked effect of biaxial tensile stress at debonding and resin cracking (fig. 6 and 7) may be due to the effects of hydraulic oil in the absence of the rubber liner. Failure mechanism studies linked with an investigation of oil effects will be pursued in due course. In fig. 7 the fact that the constant life curve for lo3 cycles crosses outside the static boundary also calls for an explanation. No specific explanation has been found but it is known that the debonding properties are particularly sensitive to roll to roll variations in the mat.The fatigue results for chopped strand mat cylinders at R = 0 would be expected to correspond with the 0-tension axial load fatigue results of fig. 8 in the same way that the cylinder results correspond with the static strength. The 0-tension fatigue curve for rupture is also reproduced in fig. 4 where it is seen that the fatigue strength at lo6 cycles is almost twice that for the cylinders at R = 0. This difference is difficult to explain. The static strength of the flat laminates was slightly higher than the cylinders due to a higher glass content but a straightforward linear correction can be a~p1ied.l~ The axial load fatigue results are consistent with other work done in the lab~ratory.~.However, previous work has also shown that quite wide variations in glass content of chopped strand mat laminates do not have a significant effect on the 0-tension fatigue strength at lo6 cycles. Other possible explanations are that there may be a size effect (the circumference of the cylindrical specimens is approximately 200 mm com- pared with 12 mm for the flat laminate specimen), that the silicone rubber liner may not be completely satisfactory under fatigue loading and that the oil influences the failures, that the radial stress (pressure) at the inner surface of the cylinder may be significant, etc. Complete evaluation of these possibilities will take some time. The failure curves in fig. 14 have been fitted to the results obtained from cylinders only, that is to say that the value of o2 at R = + co is the same value as o1 at R = 0.Under these circumstances it is seen once again that only the group 2 theories give a satisfactory fit. 0-compression fatigue data are given in fig. 9 for the sake of com- pleteness but have not been inserted in fig. 5 (at R = - co) because of the unresolved difficulties over the cylinder results. A thin walled cylinder subjected to internal pressure can be regarded as a simple component. The anomalies in the observed results reveal some of the difficulties which face the designer and confirm that much more work is necessary to develop safe life design procedures. CONCLUSIONS 1. Although chopped strand mat laminates are usually regarded as plane isotropic under complex stress conditions the failure behaviour is best described by anisotropic failure theories.2. Only failure theories which incorporate the results of complex stress tests provide a satisfactory fit to all the test data at all principal stress ratios and damage states. 3. There is a serious discrepancy between the thin walled cylinder and flat laminate fatigue results for chopped strand mat laminates. This may be due to several possible effects which have still to be evaluated. The work reported in this paper forms part of a project supported by means of a generous grant from the Science Research Council. It also forms part of a Ph.D. thesis submitted to the University of Nottingham by M. S . F.17M. J . OWEN AND M . S . FOUND 89 K. D. Raithby, J. Roy. Aero. SOC., 1961, 65, 729. M. J. Owen, Glass Reinforced Plastics, ed. B. Parkyn (Iliffe Books, London, 1st ed. 1970), chap. 18, p, 253. T. R. Smith and M. J. Owen, paper 27. 6th Int. Reinf. Plastics Conf. (Brit. Plastics Fedn. 1968). L. J. Broutman and S. Sahu, Section 11-D, 24th Ann. Tech & Man Conf., S.P.I. 1969. R. J. Howe and M. J. Owen, to be published. 8th Int. Reinf. Plastics Conf. Brit. Plastics Fedn, 1972. E. Z. Stowell and T. S. Liu, J. Mech. Phys. Solids, 1961, 9,242. R. Hill, Proc. Roy. SOC. A, 1948, 193, 281. V. D. Azzi and S. W. Tsai, Expt. Mech. 1965,5,283. 'I M. E. Waddoups, General Dynamics, Fort Worth Div., Report FZM 4763, 1967. lo C. B. Norris and P. F. McKinnon, 1956, U.S. For. Prod. Lab Rep, 1328. l1 C. B. Noriis, 1962, U.S. For. Prod. Lab Rep. 1816. l2 0. Hoffman, J. Conzp. Mat., 1967, 1,200. l 3 H. G. Franklin, Fibre Sci. Tech., 1968, 1, 137. l4 I. I. Gol'denblat and V. A. Kopnov, Polymer Mechanics, 1965, 1, 54. l5 S. W. Tsai and E. M. Wu. J. Cornp. Mat., 1971,5, 58. l6 J. E. Griffith and W. M. Baldwin, Proc. 1st Southeastern Conf. Theor. Appl. Mechs. (Gatlinburg, l8 M. J. Owen, J. Trans Plastics Inst., 1967, 35, 353. Tenn., 1962). M. S. Found, Ph.D. Thesis (University of Nottingham, 1972).

ISSN:0370-9302    

DOI:10.1039/S19720200077

出版商:RSC    

年代:1972

数据来源: RSC

摘要:

Fracture Toughness Studies of Fibre Reinforced Plastic Laminates BY F. J. MCGARRY AND J. F. MANDELL Dept. of Civil Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, U.S.A. Received 7th August, 1972 The mode of fracture and the origins of fracture work have been investigated for several fibreglass laminate constructions. Crack propagation in woven fabric and cross-plied unidirectional ply laminates with fibres parallel and perpendicular to the load direction was resisted by splitting between the fibres in the load direction at the crack tip. Crack propagation occurred by successive split formation and failure of the region of fibres adjacent to the split. Although crack tip damage was often extensive, fracture was governed by the classical crack tip stress singularity in all cases.The fracture work determined from notched tension tests was quantitatively associated with the elastic strain energy decrease in the region of fibres adjacent to the split at the crack tip when the crack advanced. Variations of up to a factor of fifteen in longitudinal ply fracture work were realized by varying the ply configuration of Scotchply laminates. Predictable increases in fracture work with fibre volume fraction and woven fabric ply orientation were also achieved. Crack propagation in the absence of general yielding has been studied extensively in isotropic materials, and recent advances have been made in the area of fibrous composite materials. Fracture toughness studies typically involve the determination of either the intensity of the crack tip stress field, K,, or the rate of elastic strain energy release with crack growth, G,, necessary for crack extension.' G, is also recognized to be twice the work of forming a unit area of new crack surface, here denoted as y.The quantities G and K are related by GI = K:/E (1) for isotropic materials under plane stress conditions and or G I = K:C (3) for orthotropic material^,^ where the subscript I indicates the opening, or cleavage, mode of fracture and the Aij's are from the stress-strain relations [El = [Al[oI. (4) Once the validity of fracture toughness measurements has been established for a particular material, the fracture surface work can be determined from the results of standard tests such as that described in fig.1. Solutions for K exist for many geometries including those of standard test specimens,1 and G, can be determined from eqn (1) or ( 2 ) when K , , is known. G, can also be determined directly for specimens where the change in elastic energy with crack growth can be mea~ured.~ 90F . J . MCGARRY AND J . F . MANDELL 91 Since G, represents the amount of irreversible work per unit area necessary to separate the material at the crack tip, the results of fracture tests can be used to check the validity of hypothesized mechanisms of toughening. FIG. 1 .-Double edge notched tension specimen. The applicability of the fracture mechanics approach has been established for several fibrous glass reinforced plastics composite systems ; woven fabric reinforced laminate^,^ “ isotropic ” Scotchply,6 and unidirectional Scotchply with the crack in the fibre direction ’ all displayed a constant K,, value for different specimen geometries and crack lengths, thus indicating that the fracture toughness is a true material property. Hiatt, however, has found that K,, is not a constant for unidirectional Scotchply with the original crack perpendicular to the fibres and the load in the fibre direction.* In this case the crack propagated parallel to the fibres, perpendicular to the original crack direction.Several theories have been presented to explain the origins of the fracture work in those fibrous composites which display little inherent ductility in either the fibres or the matrix, such as the case with glass fibre reinforced plastics.The theories may be divided into two groups : In systems with fibres which may fail at a weak point away from the crack surface, a section of the fibre must be extracted from the surrounding matrix as the crack surfaces separate. The work done against friction in pulling out these fibres will dominate the apparent fracture work.g. lo Considerable interfibre splitting and fibre-matrix debonding may occur at the tip of a propagating crack. The work of forming these new surfaces directly controls the fracture work of the primary crack.ll Kelly l2 has combined these theories in order to view a crack in graphite fibre reinforced plastic as working against the debonding work at the very tip of the crack and the pullout work in the region behind the crack tip where the crack surfaces separate significantly. The pullout work is concluded to be the dominant term unless the crack is short compared with the debonded length.To the authors’ knowledge, 1. 2.92 FRACTURE TOUGHNESS OF LAMINATES however, little direct evidence is available to support these theories for the general class of laminates considered in this paper. The work reported in this paper represents the initial findings of a continuing effort to establish the basic characteristics of fracture toughness in common types of fibre reinforced plastics. A model composite system was first used to investigate possible toughening mechanisms and the parameters important to toughness. The results of the model study were then used as a basis for the study of several relatively simple laminates : woven fabric, crossplied constructions with unidirectional plies oriented at 0" (0 rad) and 90" (1.57 rad) to the load direction, and randomly oriented chopped fibres.In each case, the validity of the fracture mechanics approach was investigated, and hypothesized toughening mechanisms were compared with the measured toughness. MODEL RESULTS A complete description of the model study has been presented elsewhere,13* l4 and only a brief summary will be given here. The model specimen is shown in fig. 2 : the cantilever-beam cleavage specimen l5 is altered by placing yarns of various fibres perpendicular to the direction of crack propagation. The specimen configura- tion and low fibre volume fraction ( N 1 %) ensure that the crack will propagate in the desired direction, rather than deflect parallel to the fibres.The stable nature of crack growth in this specimen permits convenient observations of the mechanism of toughening at the crack tip. P t 7r 0.25 in. (6.35 mm) T (30.48 mml P FIBRES' 0.006 in. (0.152 mm) WIDE SLOT' FIG. 2.-Cleavage specimen. The following sequence of events is characteristic of crack growth in the model system : (1) as the matrix crack approaches a yarn, the yarn begins to debond from the matrix; (2) the debonding continues as the matrix crack passes by the yarn and eventually the matrix crack is spanned by many locally debonded but unbroken yarns which constrain the crack advance; (3) further crack growth occurs only by tensile failure of the outermost yarn somewhere along its debonded length; (4) the matrix crack then advances by one yarn spacing, and the process repeats as the crack continues down the length of the specimen.This mode of crack resistance, which has also been reported by Outwater for a single-filament mode1,16 is clearly evident in the cross-polarized light view of the crack tip in fig. 3. Observation of this fracture mode led to the hypothesis that the fracture work derives from the work of debonding and elastically deforming the debonded portionFIG. 3.-Crack tip region in cross-polarized light showing matrix crack tip at extreme right, five stressed yarns and then two broken yarns to the left of the matrix crack tip. 0.02 in. (0.51 mm) - FIG. 4.-Growing crack in crossplied laboratory-constructed laminate showing splitting (vertical) at the crack tip.[To face D a m 92(a) As fractured. (b) Outside plies removed after fracture. FIG. 6.-Fractured Scotchply specimens with ply configuration 90" (1.57 rad), 0" (0 rad), 0" (0 rad), 90" (1.57 rad). Crack propagated left to right.[90"(1.57 rad), O o ( O rad), O c ( O rad), gO"(1.57 rad)] 0.1 in. (2.54 mm) H [90"(1.57 rad), 0"(0rad), Oo(O rad), 0"(0rad), gO"(1.57 rad)] 0.1 in. (2.54mm) H FIG. 7.-Cross sections through longitudinal splits in Scotchply specimens.FIG. 9.-Fractured 181-glass yarn-epoxy specimen. Crack propagated left to right. T t 1 0.02 in. (0.51 mml * FIG. 10.-Cross section close to the fracture surface in 12-ply, 181-style fabric-polyester laminate. 0.2 in. (5.08 mm) c-------1 FIG. 11 .-Crack growing from a notch in randomly oriented chopped fibre mat reinforced polyester laminate.(Crack tip is near the end of the severely damaged region).F. J . MCGARRY AND J . F. MANDELL 93 of the yarn until the yarn fails at its ultimate strength. The toughness of the matrix materials (polyester and epoxy) was relatively low compared to the yarn contribution even for the low fibre volume fractions studied. The hypothesized origin of the toughness was verified directly by removing slightly debonded but unbroken yarns from the crack tip and measuring the work necessary to fully debond and fail them. A procedure was also developed to simulate the situation at the crack tip so the work to debond and fail the yarns could be measured conveniently. Table 1 indicates good agreement between the toughness predicted from these tests and the actual toughness measured for the model.The majority of the fracture work is derived from elastically deforming the yarns in the local region at the crack tip though a finite amount of work is also dissipated as the yarns debond. Friction from fibre pullout was observed only with one group of graphite fibres and was not significant even in this case. (Any frictional work is usually satisfied by the elastic energy stored in the debonded region of the yarn, and is performed as the yarn retracts in the debonded region after failure. This elastic energy would be lost to the system whether dissipated through pullout friction or by other mechanical damping means.) TABLE l.-PREDICTED MODEL FRACTURE ENERGY FROM TENSILE TESTS ON YARN DEBONDED REGION y* at 10 yarns per inch (25.4 mm) lo5 erg/cmz (102 N/m) yarn matrix in.Ib (Nm) predicted cleavage results av. work per yarn 18 1 -glass polyester 0.0312 (0.0035) 3.41 (3.41) 3.14-3.70 (3.14-3.70) 181-glass epoxy 0.252 (0.0028) 2.75 (2.75) 1.85-3.34 (1.85-3.34) Thornel 50 epoxy 0.0644 (0.0072) 7.05 (7.05) 5.95-6.35 (5.95-6.35) Knowledge of the toughening mechanism enabled the improvement of toughness in the model by several variations in the composite parameters. Increases in the volume fraction of fibres resulted in the expected proportional increase in fracture surface work for all fibre-matrix combinations. An increase in fibre-matrix bond strength, either by fibre-surface treatments or the use of different matrices, resulted in a decrease in debonding length and, consequently, a decrease in toughness. A microscopic study of debonding characteristics suggested that a tightly twisted yarn would debond more readily than a loose yarn ; in subsequent experiments an increase of sevenfold in fracture surface work proportional to the increase in debonding length, was realized by moderate twisting of glass yarns. The fracture surface work also increased in a predictable manner when yarns were placed in small groups rather than spaced evenly in the matrix.Finally, the work to fail individual yarns was found to be independent of the orientation of the yarn to the crack direction over a range of k60" (k 1.05 rad) ; debonding length was also observed to be constant in this range.LAMINATE STUDIES Several varieties of glass fibre reinforced laminates were investigated : 1. Laboratory-constructed model lamintes with one ply of yarns in the load direction and one transverse ply on each side of the longitudinal ply [designated 90" (1.57 rad), 0" (0 rad), 90" (1.57 rad)]. The yarn spacing in each ply was varied; Epon 828 epoxy (Shell Chemical Company) with Curing Agent D was used as the matrix. Scotchply Type 1002 with unidirectional plies oriented both in the load direction (longitudinal) and perpendicular to the load direction (transverse). The stacking sequence and number of plies were varied. 2.94 FRACTURE TOUGHNESS OF LAMINATES 3. 4. Single ply, 18 1 -style balanced weave glass fabric reinforced epoxy and polyester (Laminac 4172, American Cyanamid Co.).Randomly oriented chopped fibre mat reinforced polyester. A detailed account of fabricating and curing procedures can be found in ref. (13). Rectangular test specimens were machined from the cured plates and notches were cut in the specimen edges perpendicular to the load direction as indicated in fig. 1. The specimens were loaded in an Instron testing machine using fixed grips ; the load and displacement to failure were recorded. Crack growth in most cases was catastrophic and the fracture load used in calculating K,, was clearly defined. CHARACTERISTICS OF CRACK GROWTH The laminates differ from the model system primarily in that the fibre volume fraction is much higher and fibres are aligned in more than one direction in the laminates. The low fibre volume fraction was necessary in the model to keep the crack from deflecting parallel to the fibres ; in the laminates, crack deflection is resisted 4 r-- 4 4 (a) Low load (b) (4 Incipient failure Propagating crack FIG.5-Schematic diagrams of crack tip splitting in longitudinal ply. by the fibres in the transverse direction. Fig. 4 shows the tip of a crack in a laboratory- constructed laminate and fig. 5 shows schematically the sequence of events associated with crack growth in the longitudinal plies : At relatively low stress level, a split forms in the load direction between the cut and load-bearing fibres of the longitudinal ply at the crack tip. The split propagates with increasing load, and the transverse fibres are dis- torted by relative movement of the two sides of the split.The transverse fibres may delaminate slightly from the longitudinal fibres along the split (fig. 4). The load-bearing fibres in the crack tip region reach their ultimate strength and fail. The main crack then extends in its original direction for a short distance until another longitudinal split forms. The crack propagates across the speci- ment in this fashion, hesitating briefly at each longitudinal split. 1. 2. 3.F . J . MCGARRY AND J . F . MANDELL 95 The transverse plies also form cracks between the fibres at relatively low stress level as they do in simple tension tests.17 Fig. 6 shows failed Scotchply specimens with the outside plies transverse and the two inside plies longitudinal [designated 90" (1.57 rad), 0" (0 rad), 0" (0 rad) 90" (1.57 rad)] ; the initial stages of crack growth are well-behaved, with fracture of the material along each split occurring at mid-length of the split near the tip of the original crack. After the crack has propagated for a short distance, the split length and ply delamination increase markedly, probably due to bending of the specimen. Fig.7 indicates that the longitudinal splits are simply cracks penetrating through the longitudinal plies. The split also may deflect along the interface with the transverse ply causing local delamination. The length to which the slit extended was very sensitive to the ply stacking sequence, as will be illustrated later. Fig. 8 indicates that a close relation- ship exists between the split length and the distance between splits for the first several increments of crack growth.Specimens with the longitudinal plies adjacent, and the transverse plies on the outside, fractured in a more regular fashion than specimens with the longitudinal plies on the outside. This latter specimen configuration showed a less regular pattern of crack growth; discussion in this paper will be restricted to specimens with the transverse plies on the outside. Most of the laminates tested were observed to fail in this manner. 0 . 1 I I I 1 I l I I I I I I I -.- 0.01 0,05 0.1 0.5 distance between splits, Aclin. ( x 25.4 mm) FIG. 8.-Log-log plot of longitudinal split length against distance between splits for Scotchply of various constructions. Woven glass fabric and laboratory-constructed laminates failed in the same sequence as described for Scotchply. The longitudinal splits in these laminates were much shorter and usually occurred at each yarn.Fig. 9 shows the fracture region for a laboratory-constructed laminate consisting of three unidirectional plies [go" (1.57 rad), 0" (0 rad), 90" (1.57 rad)] of yarn taken from the 181-style fabric. The split first forms along the yarn when the crack approaches and then debonding occurs around the rest of the yarn as it fails. The cross section of a 12-ply, 181-style fabric reinforced polyester specimen is given in fig. 10. The splits appear similar in cross section to those found in Scotchply (fig. 7).96 FRACTURE TOUGHNESS OF LAMINATES Only the randomly oriented, chopped fibre mat reinforced polyester laminates displayed a fundamentally different type of fracture.As fig. 11 indicates, these laminates fractured in a manner similar to the model, with locally debonded yarns bridging the crack tip. Although these laminates were not studied in detail, it is postulated that the findings of the model study regarding the effect of such parameters as yarn geometry may apply directly to this case, due to the similarity in fracture modes. 10 QUANTITATIVE RESULTS VALIDITY OF THE FRACTURE MECHANICS APPROACH The variability of K,, with crack length and other specimen dimensions was tested for the Scotchply, woven fabric, and chopped fibre laminates and will be discussed for each in a later section. A more thorough investigation was made of the Scotchply system, in which the length of the longitudinal split at the crack tip and the crack opening displacement were measured as functions of nominal stress (load divided by unnotched cross-sectional area).Since fracture mechanics is based on a stress distribution in which the local stresses at the crack tip vary inversely - - - a e I A I I I l l 1 1 I I I I l l l l U 50 1 n / x 09 W 1 2 - crack opening displacement, S/in. ( x 25.4 mm) I A a 1 I I I I l l 1 I I I I I I l l U - 0.1 0.5 1 5 10 longitudinal split length, //in. ( x 25.4 mm) FIG. 12.-Log-log plots of nominal stress against crack opening displacement, and nominal stress against longitudinal split length for Scotchply construction [go" (1.57 rad), 0" (0 rad), 0" (0 rad), 0" (0 rad), 90" (1.57 rad)]. Specimen crack length in. (mm) 0 , S4-1.5-2, 0.375, (9.52) ; 0, S4-1.5-3, 0.375, (9.52); A, S4-1.5-5, 0.25, (6.35); 0, S4-1.5-6, 0.25, (6.35).F.J . MCGARRY AND J . F. MANDELL 97 with the square root of the distance from the crack tip, any stress sensitive phenomenon such as yielding or, in this case, splitting, is expected to vary in extent approximately with the square of the nominal stress.ls Furthermore, the crack opening displace- ment is also expected to vary with the square of the nominal stress in the presence of a yield zone in homogeneous material^,'^ and this relationship has also been extended to unidirectional composites.20 Hiatt observed that the crack opening displacement does increase with the square of the nominal stress during longitudinal split growth in unidirectional Scotchply with the fibres in the load direction.Scotchply specimens with three adjacent longitudinal plies on the inside and transverse plies on the outside [90° (1.57 rad), 0" (0 rad), 0" (0 rad), 0" (0 rad), 90" (1.57 rad)] displayed the greatest longitudinal split length and the greatest toughness of the various stacking sequences tested. Since deviations from fracture mechanics theory are usually associated with large plastic zones which alter the nature of the crack tip stress singularity, Scotchply specimens of this stacking sequence were chosen as the most severe case for measurements of split length and crack opening displacement. The results presented in fig. 12 for two initial notch sizes indicate good agreement with theory over the complete range of split lengths encountered.These results are particularly significant because they indicate that the longitudinal split type of crack tip damage, even when considerably more extensive than the main crack length itself, does not change the nature of the stress singularity. The growth of the split, even when far removed from the crack tip, appears to be controlled by the crack tip singularity in the classical way. ESTIMATING THE FRACTURE WORK The origin of the fracture work for laminates with a longitudinal split at the crack tip is not so evident as for the model, where debonded yarns bridge the crack tip and must be extended to failure before the crack can propagate. It is apparent from fig. 5, however, that a region of the longitudinal ply along the split must be stressed to failure for crack propagation to occur.When this region does fail, a second split is formed after a short distance of relatively brittle crack growth and the entire segment of longitudinal ply between the two splits partially unloads and retracts. In the process of retracting, the elastic energy stored in this segment apparently dissipates : (1) in forming the new split, (2) in satisfying any fibre pullout friction work for the region of failed material where crack extension occurred, (3) in spreading the zone of delamination between the longitudinal and transverse plies, and (4) any remaining energy may dissipate into heat or sound. The transverse plies, which are distorted across the split as the crack opens, transfer load from one side of the split to the other.Thus, the segment of longitudinal ply between splits does not retract to a completely unloaded state, but retains part of its original energy. This portion of the energy cannot be considered as lost to the system during crack growth. It is now possible to obtain an estimate of the energy lost from the system as the crack grows from one split to the next. Let the change in energy of the segment between splits as the crack passes be represented by where L\a is the average decrease in stress along the split, is the corresponding average decrease in strain, Z is the measured split length, and Yeq is an equivalent length of load transfer region which extends beyond the ends of the split and will be estimated later. The average decrease in strain is also approximately equal to the average difference in strain between the two sides of the split just prior to crack 2-D98 FRACTURE TOUGHNESS OF LAMINATES extension if the new split is assumed to be identical to the original one.From geo- metrical considerations, the average difference in strain across the split is where 6 is the measured crack tip opening displacement. Fig. 13 gives the relation- ship between 6 and I for the four Scotchply specimens discussed previously. The value of from this data is approximately 0.015 for all specimens, roughly half of the ultimate strain of the longitudinal plies.'l Since the material along the split can be taken as elastic, will be approximately half of the ultimate strength expected for the longitudinal ply material.If it is assumed that the value of & is approximately the same for the other ply stacking sequences and laminate materials, then, by estimating the ultimate strength of the material along the split, measuring 2, and estimating Yes, the fracture work of the laminates which exhibited the longitudinal splitting type of crack propagation can be estimated. - A& = 6/(I+ Yeq) (6) 0 0.005 0.010 0.015 0.020 0.025 crack opening displacement, 6/in. ( x 25.4 mm) FIG. 13- Longitudinal split length against crack opening displacement for Scotchply construction [90° (1.57 rad), 0" (0 rad), 0" (0 rad), 0" (0 rad), 90" (1.57 rad)]. Specimen crack length in. (mm). 0, S4-1.5-2, 0.375, (9.52); 0, S4-1.5-3, 0.375, (9.52); A, S4-1.5-5, 0.25, (6.35); 0, S4-1.5-6, 0.25, (6.3 5).TEST DATA REDUCTION The critical stress intensity factor, K,,, was calculated from the load, P, on the specimen when the crack extension occurred by the relationship (6) where c is the crack length for edge-notched specimens or half the crack length for centrally notched specimens, B is the specimen thickness, W is the specimen width K,, = YPC+/BW = oYc+F . J . MCGARRY A N D J . F . MANDELL 99 and Y is a function of c/W available in the literature for each type of specimen.' The results were normalized to the constant ply thickness for each type of laminate by using an average value of thickness in eqn (6), ignoring slight variations. (This procedure was found to yield consistent results in a previous study because the amount of fibre per ply is the same in each case and only the amount of matrix removed during fabrication varies.) The elastic constants of each laminate must be known before eqn (2) can be used to calculate G, from KIc.The best available data were used to obtain the elastic constants, which are given for each laminate in table 2. The initial longitudinal and transverse ply moduli given by the 3M Company 21 and the shear modulus given by Wu ' were used for the Scotchply specimens. Laminate moduli were obtained from the ply moduli by the relationship 1 n where n is the number of plies. The use of initial moduli may result in significant error since the laminates are generally in the secondary modulus region at failure. TABLE 2.-ELASnC CONSTANTS FOR LAMINATES elastic moduli, 106 psi (103 MN/m2) ~~ ~~~ material EL ET GLT SCOTCHPLY [go", 0", 90'1 [go", 0", 0", 90'1 [go", 0", 0", 0", 90'1 (1.57, 0, 1.57) 2.7 (18.614) 4.0 (27.576) 0.7 (4.826) (1.57, 0, 0, 1.57) 3.35 (23.095) 3.35 (23.095) 0.7 (4.825) (1.57, 0, 0, 0, 1.57) 4.0 (27.576) 3.1 (21.371) 0.7 (4.826) (1.57, 1.57, 0, 1.57, 1.57) 2.18 (15.029) 4.52 (31.161) 0.7 (4.826) (1.57, 0, 1.57, 0, 1.57) 2.96 (20.406) 3.74 (25.784) 0.7 (4.826) [go", go", O", go", 90"l [go", 0", go", 0", 90'1 specimen compliance C* (10-6 inl/lb) (10-10 m2/N) 0.343 (0.497) 0.357 (0.518) 0.408 (0.592) 0.305 (0.442) 0.352, (0.510) LABORATORY CONSTRUCTED LAMINATES 20 yarns/in. (25.4 mm) 0.88 (6.067) 0.505 (3.481) 0.24 (1.655) 2.01 (2.914) 40 yarns/in. (25.4 mm) 1.38 (9.514) 0.605 (4.171) 0.33 (2.275) 1.61 (2.334) 60 yarns/in. (25.4 mm) 1.88 (12.961) 0.705 (4.860) 0.43 (2.964) 1.36 (1.972) 181-style fabric laminates 2.06 (14.202) 2.06 (14.202) 0.7 (4.826) 0.535 (0.776) * Determined from eqn (2) using the compliances A l l = 1/EL, A 2 2 = 1/ET, A 6 6 = ~/GLT, A12 = -vLT/EL- Alz was not used in the calculation because it is much smaller than A66 for bidirectional, unoriented laminates.The extensive debonding of the transverse yarns in the laboratory-constructed laminates made the choice of moduli for the transverse plies difficult, and the matrix modulus alone was used in this case. The rule of mixtures was used to estimate the longitudinal ply moduli, and the shear modulus was estimated by linear extrapolation between the matrix modulus and the modulus of woven fabric composites using these yarns.22 The secondary longitudinal and transverse moduli 23 and the initial shear moduli 22 were used for the woven fabric laminates, and the final compliance was adjusted linearly to account for a difference in fibre volume fraction from the published data.A more detailed account of the choice of moduli can be found in ref. (13).1 00 FRACTURE TOUGHNESS OF LAMINATES The difficulty enountered in choosing elastic constants for use in obtaining G, from K,, may have a significant effect on the final results. A more definitive investi- gation of the proper elastic constants for such use would enable a more precise definition of the toughness of composites whose moduli may vary with stress level. SCOTCHPLY LAMINATES The range of ply configurations listed in table 2 for the Scotchply laminates provided sufficient variation in fracture behaviour for a meaningful study of the toughening mechanism.Initially, however, it was necessary to establish the validity of the fracture toughness values obtained from the tests; table 3 indicates that the fracture toughness for the two ply configurations with the greatest amount of crack tip splitting was not sensitive to changes in specimen geometry. These data, coupled with the previous work on longitudinal split length and crack opening displacement, indicate that the fracture toughness values measured from standard test specimens are a valid respresentation of the inherent toughness of the material. TABLE 3 .-EFFECT OF SPECIMEN GEOMETRY ON KIC FOR SCOTCHPLY LAMINATES width/ length / crack length/ KIc/(ksi dz) ply configuration/deg (rad) in.(mm) in. (mm) (in. mm)* (MN .\/m/mz) go", O", 0", 90" (1.57, 0, 0, 1.57) 1.0 (25.4) 6 (152.4) 0.10 (2.54) 22.0 (25.10) 1.0 (25.4) 6 (152.4) 0.10 (2.54) 26.4 (28.93) 1.0 (25.4) 6 (152.4) 0.10 (2.54) 25.5 (27.95) 1.25 (31.7) 9 (228.6) 0.09 (2.29) 24.3 (26.63) 1.25 (31.7) 9 (228.6) 0.20 (5.08) 20.0 (21.92) 1.25 (31.7) 9 (228.6) 0.20 (5.08) 25.0 (27.40) 1.25 (31.7) 9 (228.6) 0.20 (5.08) 26.4 (28.93) 1.25 (31.7) 9 (228.6) 0.30 (7.62) 23.4 (25.65) 1.25 (31.7) 9 (228.6) 0.30 (7.62) 24.2 (26.52) 1.25 (31.7) 9 (228.6) 0.30 (7.62) 21.7 (23.78) 1.25 (31.7) 9 (228.6) 0.31 (7.87) 24.7 (27.07) W", O", 0", 0", 90" (1.57, 0, 0, 0, 1.57) 1.5 (38.1) 11 (279.4) 0.25 (6.35) 45.8 (50.20) 1.5 (38.1) 11 (279.4) 0.265 (6.73) 39.5 (43.29) 1.5 (38.1) 11 (279.4) 0.375 (9.52) 40.3 (44.17) 1.5 (38.1) 11 (279.4) 0.375 (9.52) 38.9 (42.63) 1.5 (38.1) 11 (279.4) 0.391 (9.93) 39.5 (43.29) 1.5 (38.1) 11 (279.4) 0.420 (10.67) 45.6 (49.89) 2.0 (50.8) 8.5 (215.9) 0.20 (5.08) 37.7 (41.32) 2.0 (50.8) 8.5 (215.9) 0.25 (6.35) 36.2 (39.68) 2.0 (50.8) 8.5 (215.9) 0.36 (9.14) 42.7 (46.80) * notches in Scotchply specimens were cut with a jeweller's saw. The estimated and measured toughness data for all Scotchply specimens are given in fig.14. The critical strain energy release rate, Gc, has been modified to include only the longitudinal plies which are reponsible for the toughness by using the relation- ship number of plies number of longitudinal plies GcL = Gc where L stands for longitudinal ply. In this way, the effect of each longitudinal ply can be compared for different ply configurations.The line predicted by eqn (5) assumes an ultimate strength for the longitudinal ply in situ of 140 000 psi (965.1 MN/m2) which was obtained from tensile tests,13 so eqn (5) now becomes GcL = 27 = (525 lb/in2)(Z+ Yeq) = (3.62 MN/m2)(Z+ Yes).F. J . MCGARRY AND J . F . MANDELL 101 The value of Yes was estimated by back-extrapolation of the data in fig. 14 to zero toughness. The value thus obtained, 0.30 in. (7.62 mm) is apparently a measure of the effective crack blunting due to shearing of the matrix with no splitting. 0 k 0 0.5 1 .o 1.5 2.0 2.5; 1400 1200 n E 1000 z 2 . 4 v; x 800 d 2 $ 600 W W .- \ \ w .“ I (d 2 4G0 a 200 The two major findings of the Scotchply study are : (1) Toughness estimates based on the proposed toughening mechanism are in good agreement with experimental data. (2) A variation in longitudinal ply toughness up to a factor of fifteen can be realized by varying the ply configuration.Low toughness values [ 100-300 lb/in. (17 500- 52 530 N/m)] are from laminates with each longitudinal ply separated by a transverse ply, intermediate values [300-600 lb/in. (52 530-105 060 N/m)] are from laminates with two adjacent longitudinal plies, and high values [above 600 lb/in. (105 060 N/m)] are from laminates with three adjacent longitudinal plies. It is also interesting to note that the ultimate tensile strength, when normalized to the longitudinal ply strength in this fashion, would not be expected to vary significantly with ply c~nfiguration.~’ The many approximations such as estimates of do and & estimates of the elastic constants, and the use of the same value of Yeq for all ply configurations should be considered in assessing the accuracy of these results.More precise estimates require additional data not now available.102 FRACTURE TOUGHNESS OF LAMINATES LABORATORY-CONSTRUCTED LAMINATES These laminates were cut into specimens 7 in. (177.8 mm) long by 1.5 in. (38.10 mm) wide, and were nominally 0.015 in. (0.38 mm) thick. Notches were cut approxi- mately 0.25 in. (6.35 mm) deep with a 0.006 in. (0.15 mm) thick saw blade. Each specimen consisted of three plies : two transverse plies on the outside surfaces and one longitudinal ply in the centre plane. Yarns taken from 181-style woven glass fabric (yarn designation ECE 225/13, 4.4s twist) were used to make up the unidirec- tional plies of the variable fibre content.Fig. 15 indicates an approximately linear increase in KI, with fibre volume fraction of the longitudinal ply; the fibre volume fraction in the transverse plies had negligible effect on the toughness. The values of strength measured in yarn tension tests, with the measured average value of I of n 0 0 a I t I L 1 I I I 20 30 40 50 60 0 % ’ yarns per inch (25.4 mm), longitudinal yarn-epoxy laminates. Transverse Vf/longitudinal Vf: A, 0.5; 0, 1.0; 0, 2.0. FIG. 15.-Fracture toughness against longitudinal yarn spacing for laboratory-constructed 18 1 - glass 0.10 in. (2.54 mm) and a value of Yes of 0.025 in (0.63 mm) estimated from the model test data and confirmed photoela~tically,~~ yield a prediction of fracture work from eqn ( 5 ) of G, = 2y = 618 Vf (lb/in.) = 108 400 Vf(N/m) where Vf is the fibre volume fraction in the longitudinal plies.Fig. 16 indicates qualitative and quantitative agreement of this prediction with the experimentalF . J . MCGARRY AND J . F . MANDELL 103 data. The significant experimental scatter is due to washing of the yarns into regions of higher and lower density, which could not be prevented. These results are also in agreement with the results of the model study using the same yarns. - t 200 t 0 PREDICTED FROM / X t Y WOVEN FABRIC REINFORCED POLYESTER LAMINATES The effects of crack size and shape were studied in detail for single ply, 181-style balanced weave specimens.Previous work had indicated a constant value of K,, for laminates of this type, regardless of specimen geometry or the number of plies over a range of 3-50 plies. The value of K,, obtained for single ply laminates was also in agreement with the multiple ply laminate data. All specimens tested were 1.5 in. (38.10mm) wide, 12 in. (304.8 mm) long, and approximately 0.01 in. (0.25 mm) thick. Three methods were used to introduce cracks into the specimens : (1) A central circular hole was drilled. (2) Edge cracks were initiated with scissors. (3) A central crack was initiated by cutting the fabric with a razor blade prior to matrix impregnation. Upon slight loading, a sharp crack formed naturally in the matrix where the yarns were cut. Fig.17 indicates little difference in the K,, value determined for each type of crack. The crack tip blunting which results from the observed longitudinal split (debonding) length of approximately 0.125 in. (3.17 mm) in addition to the transfer length is104 FRACTURE TOUGHNESS OF LAMINATES sufficient to render even a circular hole effectively equal to the sharpest crack in this small crack size domain. Thus, the jeweller's saw and the 0.006 in. (0.15 mm) thick circular saw blade used to initiate notches in the various laminate specimens result in sufficiently sharp notches for valid K,, measurements. - NET STRENGTH 0 FIG. 17.-Predicted and experimental fracture toughness for various crack geometries and lengths (181-style fabric-polyster). 0, central circular hole ; A , centre crack, length 2 c ; 0, double edge crack.0 n b 0 : FROM PREDICTED G, US I NG EX PER I M EN TAL DEBONDED LENGTH - - - - O * ~ ' , ~ ' ~ ' ~ ~ ' ~ l l r ' r ' ~ ~ ' ~ The value of K,, is predicted to be the lower of the two curves in fig. 17, represent- ing two distinct types of fracture behaviour : (1) Complete notch insensitivity with failure occurring when the net section stress between notches reaches the ultimate tensile strength of the material, and (2) classical brittle failure controlled by the fracture toughness. The former case, expected to hold for short crack lengths, can be expressed quantitatively by substituting the relationship for the net section stress C,et = .( &J (9) into eqn (6). ultimate tensile strength : Failure will then occur at the value of K,, for which onet equals theF .J . MCGARRY AND J . F . MANDELL 105 The ultimate tensile strength of these specimens was taken as 41 500 psi (286.1 MN/m2) for the average fibre volume fraction of 41.5 %.’ Using the specimen width of 1.50 in. (38.10 mm) in eqn (lo), the steep curve in fig. 17 was obtained. The constant K,, line in this figure was obtained in the usual way from eqn (5) using the measured average longitudinal split length of 0.125 in (3.17 mm) and an equivalent transfer length of 0.025 in. (0.63 mm) as in the previous section. The ultimate tensile strength of 41 500 psi (286.1 MN/m2) and resulting ultimate strain of 0.0241 from the secondary modulus yield a value for G, of 187 lb/in. (32 744 N/m) for the woven fabric laminates. Substitution of G, into eqn (3) results in the predic- tion of 17.2 ksi Jiz(18.85 MN d a m 2 ) for K,, as indicated in fig.17. The experimental results for K,, as plotted against crack length in fig. 17 for the woven fabric laminates are in good agreement with the predicted values. As was the case with Scotchply laminates, the fracture mechanics approach is valid even when the split length at the crack tip exceeds the main crack length. It is also interesting to note that the value of K,, does not vary appreciably between a single ply laminate with a crack length of 0.05 in. (1.27 mm) and a fifty ply laminate with a crack length of 0.75 in. (10.05 mm).5 EFFECTS OF PLY ORIENTATION The results of the model study indicate that individual yarns supply the same amount of fracture work regardless of orientation.If this situation is also realized for a woven fabric ply, then the fracture work along any path through the ply should I I I I I I 1 1 1 ~~ 0 10 20 30 40 50 ply orientation, O/deg. ( x 0.017 45 rad) (Modified cleavage test.) FIG. 18. Effect of ply orientation on fracture energy for 1-ply, 181-style fabricepoxy laminate.106 FRACTURE TOUGHNESS OF LAMINATES be proportional to the number of yarns per unit length in that direction. The number of yarns per inch for a crack propagating at an angle, 6, to the warp direction in a 181-style balanced * weave ply is (1 1) where (N)oo is the number of yarns per inch in the wrap direction. Assuming a constant fracture work requirement per yarn, the fracture surface work at an angle 8 to the warp direction should be (12) This hypothesis was tested on single ply 181-style fabric reinforced epoxy speci- mens using a double cantilever arrangement similar to the model.The crack was constrained to propagate in the desired direction by bonding two adjacent aluminum beams to each face of the specimen. (See ref. (13) for a more complete description of this specimen.) The strain energy release rate was then measured directly from the load-deflection curve as the crack propagated down the length of the specimen. Fig. 18 indicates good agreement between the prediction of eqn (12) and the experimental data. The fracture surface work increases with fabric orientation despite a sharp reduction in ultimate tensile strength. The nature of the crack growth and the longitudinal split length were similar for all orientations, and no qualitative difference was observable between crack growth in the cantilever specimens and the standard fracture specimens.(N)e = (N)oo (sin 6 + cos 6) ye = yo. (sin O+cos 6). RANDOMLY ORIENTED CHOPPED FIBRE LAMINATES A brief study was made of the applicability of fracture mechanics to randomly oriented chopped fibre mat reinforced polyester laminates. The specimens were six plies, one inch (25.4 mm) wide by six inches (152.4 mm) long, 0.07 in. (1.78 mm) thick, with a fibre volume fraction of approximately 30 %. K,, was measured for various crack lengths using the double edge notched specimen. Results are given in table 4 for the standard K,, calculation and for K,, calculated using a crack length TABLE 4.-EFFECT OF CRACK LENGTH ON KI, FOR RANDOMLY ORIENTED DISCONTINUOUS FIBRE MAT REINFORCED POLYESTER LAMINATES crack length/ KIC I damage zone/ KI, adjusted for in.(mm) ksi 4' (MN 4'/m2) ksi t/iy(MN v'm/m2) 0.09 (2.29) 0.1 1 (2.79) 0.14 (3.56) 0.13 (3.30) 0.14 (3.56) 0.21 (5.33) 0.18 (4.57) 0.20 (5.01) 6.35 (6.96) 7.35 (8.06) 7.68 (8.42) 6.86 (7.52) 7.74 (8.48) 7.62 (8.35) 8.68 (9.51) 8.46 (9.27) 8.77 (9.61) 9.72 (10.65) 9.82 (10.76) 8.70 (9.54) 9.60 (10.52) 8.86 (9.71) 10.76 (11.79) 10.49 (11.40) of (c+rd), where rd is the radius of the debonding zone at the crack tip, measured as approximately 0.08 in. (2.03 mm) for these laminates. The results indicate that the damage zone must be added to the crack length in the K,, calculation to obtain an approximately constant fracture toughness.This condition, similar to that * 181-style fabric actually has ayarn count of 57/54 per in. (2.24/2.13 yarns/mm) in the two weave directions, but is considered here to be a balanced weave for convenience.F . J . MCGARRY AND J . F . MANDELL 107 observed with metals l8 distinguishes this type of laminate from those in which the damage zone consisted of a single longitudinal split parallel to the load direction. The ratio of net section stress to ultimate tensile strength was less than 0.67 in all cases. These results should be considered tentative due to the limited amount of data available at this time. SUMMARY Crack propagation in a model composite system was characterized by locally debonded yarns bridging the crack tip and resisting crack growth. The fracture work of the model derived primarily from the work necessary elastically to deform to failure the debonded region of the yarns.Effects of fibre volume fraction, fibre and matrix material, adhesion, orientation and yarn geometry were studied. Using the model study as a basis, crack propagation was investigated for several fibreglass laminate constructions. Crack resistance in Scotchply, woven fabric, and laboratory-constructed model laminates with fibres parallel and perpendicular to the load direction was characterized by crack blunting due to splitting between the longitudinal fibres at the crack tip. The growth of the longitudinal split was resisted by the transverse fibres which were sheared by relative movement of the two sides of the split as the crack opened.Crack propagation occurred by failure of the ligament of longitudinal ply material along the split and was terminated by a new split which then resisted further crack growth. The fracture work was estimated as the loss in elastic energy of the ligament of material along the split when the crack advanced. This energy was dissipated in the formation of a new split, delamination of the longitudinal and transverse plies, and possible fibre pullout friction; any additional energy would be dissipated into heat and sound. Estimates of fracture work based on this toughening mechanism were in good agreement with experimental data for each type of laminate. Variations in longitu- dinal splitting due to ply arrangement had a significant and quantitatively predictable effect on the toughness of Scotchply laminates.Increases in fibre volume fraction produced the predicted proportional increase in toughness for laboratory-constructed laminates. Variations in crack length resulted in a predictable shift from notch- insensitive to notch-sensitive behaviour for woven fabric laminates. Ply orientation produced a predictable increase in fracture surface work as measured in a double- cantilever test for the woven fabric laminates. Finally, randomly oriented chopped fibre laminates required a correction for debonding zone size before the fracture toughness behaved as a material property. This research was sponsored by the Advanced Research Projects Agency, Center for Materials Science and Engineering.The Dow Chemical Company and the Manu- facturing Chemists Association. P. C. Paris and G. C. Sih, Stress Anlaysis of Cracks, Fracture Toughness Testing and Its Applications, ASTM STP 381, American Society for Testing and Materials (1965). G. R. Irwin, Analysis of Stresses and Strains Near the End of a Crack Traversing a Plate, Trans. Amer. SOC. Mech. Eng., J . Appl. Mech., 1957 G. R. Irwin, Analytical Aspects of Crack Stress Field Problems, TAM Report No. 213, (Univ. of Illinois, 1962). G . R. Irwin, Fracture Testing of Hi-strength Sheet Materials Under Conditions Appropriate for Stress Analysis, U.S. Naval Laboratory, Washington, D.C., NLR Report 5486 (1960). W. J. Schulz, et al., Fracture Toughness of FRP LaminatedPlates, MIT Civil Engineering Report R70-10 (1970).108 FRACTURE TOUGHNESS OF LAMINATES R. G. Hamilton, The Eflect of Couple-Stress on the Initiation of Fracture in Composite Materials (MIT M.S. Thesis, 1970). ’ E. M. Wu and R. C. Reuter, Jr., Crack Extension in Fiber-glass Reinforced Plastics (Univ. of Illinois, TAM Report 275, 1965). D. B. Hiatt, Fracture of Prenotched Unidirectional Glass Fiber Reinforced Composites (MIT M.S. Thesis, 1969). A. H. Cottrell, Proc. Roy. Soc. A, 1965, 285. J. 0. Outwater and W. 0. Carnes, Fracture Mechanics of Composite Materials, Contract, No. DAAA 21-67-C-0041, U.S. Army Munitions Command, Picatinny Arsenal (1967). lo G. A. Cooper, J. Mat. Sci., 1970,5,645. l 2 A. Kelly, Proc. Roy. Soc. A, 1970,319,95. l3 J. F. Mandell, Fracture Toughness of Fibre Reinforced Plastics (MIT Ph.D. Thesis, 1971). l4 F. J. McGarry and J. F. Mandell, Fracture Toughness of Fibrous Glass Reinforced Plastic Composites, Proc. 27th Reinforced Plastics/Composites Div., SPI, (1972) Section 9-A. l 5 J. P. Berry, J. Appl. Phys., 1963, 34, 62. l6 J. 0. Outwater and M. C. Murphy, On the Fracture Energy of Unidirectional Laminates Pro- ceedings 24th Reinforced Plastics/Composites Div., SPI (1969) Section 11C. L. J. Broutman and R. H. Krock, Modern Composite Materials, (Addison-Wesley, Reading, Mass, 1967), p. 371. Fracture Testing of High Strength Sheet Materials, ASTM Bull, (January 1960). 1967), p. 67. l9 A. S. Tetelman and A. J. McEvily, Jr., Fracture of Structural Materials, (Wiley, New York, 2o F. A. McClintock, private communication. 21 3M Co., Technical Data Sheet for Type 1002 Scotchply (1963). 22 Plastics for Flight Vechicles, Part 11, Reinforced Plastics, MIL-HDBK-17 (U.S. Government 23 F. Werren and C. B. Norris, Directional Properties of Glass-Fiber-Base Plastic Laminate Panels Printing Office, Washington, D.C., 1959). of Sizes That do nor Buckle (Forest Products Laboratory, Madison, Wisconsin 1956).

ISSN:0370-9302    

DOI:10.1039/S19720200090

出版商:RSC    

年代:1972

数据来源: RSC