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. 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