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).