Failure Analysis of Woven Hybrid Composite Using a Finite Element Method
Y. Li, C. Ruiz and J. Harding
ABSTRACT: A finite element method is used to determine the stress and strain distributions around a failure link in a carbonreinforced ply in a woven carbon/glass laminate under tensile loading. On the assumption that delamination follows this initial tensile failure in a carbon link, the new stress and strain distribution is determined. Finally, the effect of stacking sequence on the failure of a woven hybrid laminate is discussed.
1. Introduction
Hybrid composites have many advantages, for example, they offer an effective way of increasing the impact strength and reducing the cost of an advanced composite material. In addition, the crack arresting properties and the fracture toughness of the composite can be improved due to the ‘hybrid effect’ in fibre fracture strain.
In the general case, a hybrid composite consists of two kinds of fibres. One fibre has a lower critical fracture strain, i.e., the low elongation (LE) phase, the other fibre has a high critical fracture strain, i.e., the high elongation (HE) phase. In this model, the LE phase is the carbon ply and the HE phase is the glass ply. If the bond between the fibre and the resin is perfect, the strain in the model is compatible, i.e., the HE phase and the LE phase have the same tensile strain provided that a uniform strain is applied to the specimen. The LE phase is first broken when the uniform strain is larger than the critical fracture strain of the LE phase. After, the LE phase breaks a tensile strain concentration and a shear stress concentration is produced around the position of the breakage. The tensile strain concentration may lead to the failure of neighbouring plies. On the other hand, the shear stress concentration may result in a delamination between the failure ply and neighbouring plies of the HE phase. Which type of failure occurs following the break of the LE ply depends on the ratio of maximum tensile strain to the ultimate tensile strain and the ratio of the maximum shear stress to the ultimate interlaminar shear stress.
In this report, the initial strain and stress redistribution and strain concentration factor around the failed carbon ply are calculated, using ABAQUS, for an interply woven hybrid laminate of carbon and glass introducing a discontinuity in the modulus to model failure. Assuming delamination follows the break of this ply, the strain redistribution is also determined. Finally, the effect of stacking sequence of carbon and glass plies on the fracture process is discussed.
 2. Experimental and Numerical Techniques
 2.1 The Finite Element Method
The finite element method has found wide application in composite material research since Puppo and Evensen [1] first used it for studying the interlaminar shear in laminated composites in 1970. Typical applications include the “boundary effect problem’ in laminated composites [24] and modelling the fracture process in unidirectional fibre composites [5]. Generally speaking, both the micromechanical approach and the macromechanical approach can be used for calculating the stress or strain distribution.
In the micromechanical approach, the fibres and resin are treated independently and the geometry of the fibre and the interaction between fibre and resin, and fibre and fibre can be considered. This means that the model has to be divided into a large number of elements and a computer with high speed and large storage is needed. In the macromechanical approach, the microstructure of the material is not considered, and the composite materia! is treated as orthotropic [6]. In view of the particularly complicated structure of the woven reinforcement geometry we use the macromechanical approach as a first attempt to obtain a numerical analysis solution of this problem.
2.2 Experimental Detail
Tensile specimens, as shown in Figure 1, have been tested in a split Hopkinsonbar device as described in [7]. The quasistatic elastic constants
FIGURE 1. General arrangement of tensile specimen.
for nonhybrid specimen reinforced with the same glass or the same carbon plies were measured by K. Saka [8]. The mean values were:
Allglass 
16.6 
13.8 
0.17 
0.14 
0.14 
Allcarbon 
45.3 
43.3 
0.14 
0.09 
0.13 
The Poisson’s ratio vf, determined from symmetry hypothesis of an orthotropic laminate, i.e., , = E_{3}v_{3l}, is also shown. The subscripts 1, 3
correspond to the longitudinal direction and to the transversal direction respectively (See Figure 2).
A detailed description of the experimental work is contained in [810].
2.3 Finite Element Analysis of Hybrid Specimen
The stress distribution in the standard design of tensile specimen has been determined using the PAFEC finite element package for both an allglass and a hybrid carbon/glass layup. In each case the tensile stress in the specimen gauge region was significantly higher than the tensile or shear stresses elsewhere in the specimen leading to the conclusion that the specimen design is satisfactory and that an initial tensile failure, as normally obtained in practice, is what would be expected. The use of the ABAQUS finite element package with triangular elements made possible a more accurate modelling of the waisted geometry of the specimen and, for an allglass layup, confirmed the above conclusion regarding the specimen design. Since then the ABAQUS analysis has been extended to allow a study of the stress distribution in a hybrid specimen with the particular aim of estimating the magnitude of any stress concentrations arising at points on the interface between the carbon and the glassreinforced plies where they intersect the free surface in the waisted region of the specimen.
The finite element mesh used for the analysis of the type 2b hybrid specimen, including the loading bar to which it is attached, is shown in Figure 2. The hybrid layup consists of alternating carbon and glassreinforced plies with a total of two glass and three carbon plies in the cross section of the central parallel region, where the stress is assumed to be uniform. The main purpose of the stress analysis was to check the validity of this assumption rather than to obtain accurate value of the stresses. To this end, approximate value of the elastic constants were taken, as shown in Figure 2. The material was treated as orthotropic, with
FIGURE 2. Finite element mesh for hybrid carbon/glass tensile specimen
The value taken for the tensile modulus in direction 2 is based on the rule of mixture, assuming a fibre volume fraction of 50%. v_{l2} was taken to be equal to 0.15. In the absence of any experimental data, it is not possible to provide precise value to the elastic properties in the throughthickness direction but this is unlikely to have much significant effect on the conclusion. The longitudinal tensile stresses (direction 1) in the parallel gauge section of the specimen were found to exceed the normal stresses (direction 2) and the interfacial shear stresses (on the 13 plane) by some five orders of magnitude, confirming that this part of the specimen is effectively in a state of uniaxial tension.
The corresponding stress states in the tapered region of the specimen, along the interface between the carbon and the glassreinforced plies where they intersect the free surface, positions ABC and DEF in Figure 3, are shown in Figure 4. Stresses are determined at the Gauss integration points close to the nodes. Along the interface ABC the normal stresses are three or more orders of magnitude less and the shear stresses two orders of magnitude less than the local longitudinal stresses while along the interface DEF this difference is reduced to about two orders of magnitude for the normal stresses and one order of magnitude for the shear stresses. Close to point D, however, discrepancies are apparent in the value of the normal stress and the shear stress when determined on opposite sides of the interface, suggesting that for these stresses the calculation is not very accurate. In contrast, at both interfaces a good agreement is obtained between the value of longitudinal stress measured on either side of the interface when the difference in elastic moduli in direction 1 for the two types of reinforcing ply is taken into account.
These results confirm, for the hybrid layup, the previous conclusion for the allglass layup that the design of specimen is satisfactory and that an initial tensile failure determined by the magnitude of the ruling longitudinal stresses in the parallel gauge section, as is observed in practice, is the expected failure mode. In addition, for the hybrid layup, where there are distinct differences in the elastic properties of the two types of reinforcing ply, it is now shown that stress concentration at the free surface remains relatively small.
2.4 Finite Element Analysis of a Specimen with a Failed Link
The specimen type 2(a) in Figure 1 has been selected for detailed analysis. In order to ascertain the effect of the stacking sequence on the failure process, several stacking sequences have been analysed:
 1. GCGCGCG (Basic alternating sequence)
 2. CGGCGGC
 3. GGCCCGG
FIGURE 3. Waisted region of hybrid tensile specimen.
FIGURE 4. Stress near free surface in waisted region of hybrid tensile specimen
Since the stresses away from the central reduced thickness region of the specimen are relatively small and the stress concentration over the tapered transition are negligible, it is possible to simplify the numerical analysis by considering the central region. Figure 5 shows the general dimensions of mathematical model. A state of plane strain is assumed and a mesh consisting of 210 elements is used as shown in Figure b Each element has a length of 0.2 mm. Assuming that the first stage in the fracture process is the tensile failure of one of the carbon fibre tows, as is observed in the practice, then to determine whether the next stage is also controlled by the longitudinal stresses or whether a delamination mechanism related to the local shear stresses or a deplying mechanism under the local normal stresses becomes the controlling process, it is necessary to determine the redistributed stress system in the vicinity of first failure. The carbon and the glassreinforced plies are divided into a number of elements, or links, and first failure is assumed to occur in an arbitrarily chosen link in one of the carbon reinforced plies.
To model the tensile failure of the link the longitudinal modulus is reduced by a factor of 0.001. This leads to a singularity at each node of the failed link and high shear stresses on the interface with the neighbouring plies at points close to these nodes. However, discontinuities in the normal and shear stresses across the interface close to the singularity indicate that here again the analysis has become inaccurate and the stress levels determined cannot be relied upon. This makes difficult the identification of the next stage in the failure process from a comparison of those stresses with the critical stresses for a tensile, a normal or a shear failure at the given strain rate.
Figure 7(a) shows a section of the specimen, comparing elements in two adjacent plies, one reinforced with carbon, the other with glass. When a uniform strain is applied to the specimen, the gauge lines AB and CD that define the two sections, move to A' В' and C' D'. If one of the plies breaks in the specimen, the specimen will respond by deforming in a nonuniform manner, so that the gauge lines will distort as shown in Figure 7(b). The interface of two adjacent plies are still subjected to the same tensile strain but the shear strains are different, being in the ratio of the shear moduli. The finite element analysis provides values of the stress and strain at points such as P and Q by extrapolation from the Gauss points. To characterize the state of strain in each ply and the shear stress at the interface, we note that: ^{[1]}
FIGURE 5. The mathematical model
FIGURE 6. The mesh of finite element and the definition of layers.
FIGURE 7. The state of strain in neighbouring carbon and glassreinforced plies.
The tensile strain and the shear stress between adjacent plies are calculated in the report.
 3. Results
 3.1 Failure of a Central Carbon Ply in the Basic Alternating Stacking Sequence (Figures 8, 9 and 10)
In the experimental work, it was found [9] that at a quasistatic rate, the mean failure strain for the allcarbon layup was 1.35% ± 0.3% and for allglass layup 2.52% ± 0.2%. In the analysis, therefore, it was assumed that the first carbon ply failed when an overall strain of 1.35% was applied.
In this stress analysis a perfect bond between neighbouring plies, i.e., compatibility of strain between the two types of ply, has been assumed. The corresponding distorted mesh for the failure of a link in the central carbon ply when an overall strain of 1.35% is applied to the parallel gauge region of specimen is shown in Figure 8(c). If the resulting tensile strain concentration in the neighbouring glass or carbonreinforced plies [Figure 8(a)], is sufficiently high their tensile failure may be the next stage in the failure process. Alternatively the shear concentration on the interlaminar plane between the failed ply and the neighbouring reinforced plies [Figure 8(b)], could lead to delamination as the next stage in the failure process. Which type of failure follows is determined, therefore, by the relative values of the critical tensile strain to the critical shear stress. Estimates of the former are available from the tensile tests on the nonhybrid carbon and glass reinforced laminates. The methods of determining the critical condition for interlaminar shear strength are still being investigated.
Experimental evidence suggests that, for woven reinforced laminates, a limited delamination follows tensile failure of a given fibre tow, the extent of delamination being greater under impact loading. In the model being considered, if delamination is represented simply as a crack between two frictionless surfaces the shear stress concentration at the singularity is not reduced very much by the delamination process but merely moves with the delamination crack tip, i.e., the delamination extends catastrophically through to the ends of the specimen. While such behaviour is sometimes observed, particularly in tests on unidirectionallyreinforced specimens, it does not describe the response seen in the present woven hybrid composites. Here, therefore, a friction coefficient of 0.5 is assumed on the delamination crack surfaces between which slip is allowed to occur. The delamination crack is modelled using the ABAQUS interface element for which, since there should be no relative movement until slip occurs, a modulus of 1000 GPa is assumed.
The resulting distorted mesh shapes, for delamination extending over either two or five links on either side of the initially failed link, and the relative tensile strain and shear stress distributions are shown in Figures 9 and 10. On the basis of these calculations delamination does lead to a reduction in the peak shear stress on the interlaminar surface at or near the delamination crack tip, by about 25.5% for a 2link delamination [Figure 9(b)] and by about 31.1% for a 5link delamination [Figure 10(b)], This is not a large reduction. Whether it is significant or not may depend on the balance of probability between tensile and shear failure in any given case and on how sensitive shear failure is to the very localised shear concentration. As shown in Figure 8(b), even without delamination the shear stress at the interface has fallen by more than an order of magnitude within 5 links, i.e., within 1 mm, of the singularity.
FIGURE 8.
3.2 Failure of a Lateral Carbon Link in the Basic Alternating Sequence (Figures 11,12, and 13)
The same technique has been followed to model this type of failure. Dae to the lack of symmetry, bending occurs in the specimen and the peak tensile strain and shear stress are slightly higher than before. Delamination is particularly noticeable in Figure 13.
3.3 Failure of a Glass Link in the Basic Alternating Sequence (Figures 14 and 15)
Although this is a very implausible situation, it could occur if, for example, one of the glassreinforced plies is defective. Figure 14 shows the results of a failure in one of the innermost glass plies. It is obvious that the tensile strain is very much smaller than that found when the carbon ply fails and that the shear stress is also very small. The same conclusion is reached when it is the outermost glass ply that fails as shown in Figure 15.
3.4 Failure of all Carbon Plies in the Basic Alternating Sequence (Figures 16 and 17)
If failure of central carbon ply at an average strain of 13.5 % is followed by failure of the neighbouring outer carbon plies at the same strain without any delamination, apeak tensile strain is reached in the remaining glass plies of about 10%, see Figure 16. These plies may then break in tension. On the other hand, very high shear stresses are also present, which may cause delamination between the failed links and the glass plies. If this happens, the tensile strain in the glass plies is then relieved, dropping from 10% to 5.5%. The interlaminar shear stresses are also reduced, from 250 MPa to 130 MPa, as shown in Figure 17. It follows that the final failure could be either fracture across the whole specimen with or without limited pullout (delamination) or by tensile failure of the carbon plies and pull out of the glass plies, depending on the relative tensile strength and failure strain of the glass plies and the interlaminar shear strength of carbon/glass interface.
3.5 Other Stacking Sequences (Figures 1825)
For comparison with the basic stacking sequence, the following stacking sequences and failures have also been analysed. The results are shown in the figures indicated. Each layup has the same overall proportion of carbon to glass (3 carbon plies to 4 glass plies).
Sequence 
Failure 
Figure No. 
GGCCCGG 
Central C 
18 
GGCCCGG 
Central C + delamination 
19 
GGCCCGG 
All C 
20 
GGCCCGG 
All C + delamination 
21 
CGGCGGC 
Central C 
22 
CGGCGGC 
Central C + delamination 
23 
CGGCGGC 
All C 
24 
CGGCGGC 
All C + delamination 
25 
 4. Summary of Results and Discussion
 4.1 Failure Process
It follows from these results that the strain and stress fields will vary throughout the volume of the tensile specimen following the initial (primary) failure. The shear stress is produced by the fibre failure. Both tensile strain and shear stress concentrations occur in the ply adjacent to the breakage. Which kind of failure (ply fracture or delamination) follows the initial failure depends on the critical value of shear stress and tensile strain. It is important, therefore, to obtain an estimate of the interlaminar shear strength experimentally before the present study can be taken much further.
In practice, experimental results show that the critical tensile fracture strain of the LE (carbon) phase is governed by a statistical distribution and so all the fibres of the LE phase will not fail at the same level of strain although with the present woven reinforcement configuration, the statistical variation in LE ply failure strain is likely to be much less significant. A region of pseudoyield behaviour is observed in which the specimens are slowly damaged provided the volume of HE fibre (glass) is enough to support the increased loading. This means that the fibres do not fail in the specimen one after another in catastrophic succession. The tensile strain concentration may be reduced during this process as a result of delamination, since, if delamination occurs, the strain concentration will be relaxed. This, therefore, will be considered in the next section. Otherwise, if the failure is still by ply fracture, final catastrophic failure will follow very quickly, and the pseudoyield behaviour will not he observed in the experiment.
If shear stress is the limiting parameter, delamination will occur after the first ply lailure. As a result of the delamination, fast fracture of all the plies will be prevented because delamination will reduce the tensile strain concentration in the ply adjacent to the first break. Tabic 1 shows the maximum
FIGURE 23.
TABLE 1.
Stacking Sequence 
Failure Form 
Climax (%) 
Concentration Factor on e„ 
Reduced Percentage Of („ 
^i2max (MPa) 
Reduced Percentage of Т,г 
*9 No. 
F 
6.78 
5.02 
152.6 
8 

GCGCGCG 
F + D 
4.01 
2.96 
40.4 
113.63 
25.5 
9 
F + LD 
3.71 
2.75 
45.1 
105.1 
31.1 
10 

F 
8.20 
6.07 
170.3 
II 

GCGCGCG 
F + D 
4.81 
3.57 
41.2 
122.46 
28.1 
12 
F + LD 
3.69 
2.73 
55.0 
101.01 
40.7 
13 

GCGCGCG 
F 
1.84 
1.37 
46.3 
14 

GCGCGCG 
F 
2.29 
1.70 
48.4 
15 
C. G: indicates that the failure occurs in this ply.
F: one ply only breaks.
D: the length of delamination is 0.4 mm at each side of broken link. LD: the length of delamination is 1.0 mm at each side of broken link.
value of tensile strain and shear stress in the adjacent ply after delamination. Note that in Figure 9, the delamination length is 0.4 mm, i.e., 2 elements at each side of the broken link, and in Figure 10 it is 1 mm, i.e., 5 elements.
Comparing Figure 8 to Figures 9 and 10, it is found that delamination reduces the tensile strain concentration by 41% while the shear stress concentration is reduced by about 25.5%. This implies that tensile fibre fracture may be avoided once delamination takes place. If delamination propagates further, the maximum tensile strain and shear stress change only a little. This shows that the tensile strain concentration will be relaxed mainly at the early stage of delamination. Similarly Figures 12 and 13 can be compared to Figure 11. From Figures 8 to 13, it can also be seen that, when the initial failure occurs in a carbon ply, the tensile strain concentration in the nearest carbon ply after delamination, about 2.74%, is the same whichever carbon ply fails. So the nearest carbon ply is also likely to break if the loading increases continuously.
Following the initial carbon ply failure, delamination takes place. Then, the nearest carbon ply fails, repeating this process until all the carbon plies break provided that the glass plies are still able to stand the increased loading. Finally, there is fast fracture of all glass plies once the tensile strain exceeds their critical fracture strain. Delamination in the failed specimens has been observed most markedly in tests on unidirectionallyreinforced composites and, to a lesser extent, in experimental results on woven hybrid composites of carbon and glass to which this report refers. Although the tensile strain concentration in Figure II is larger than that in Figure 9, the maximum value of the tensile strain after deiamination, about 3.7%, is nearly the same, as shown in Figures 10 and 13. Again, the tensile strain concentration is reduced quickly during the early stages as delamination propagates. The tensile strain concentration finally disappears if delamination propagates through the whole length of the specimen. The reduction of tensile strain in the ply adjacent to the failed ply is related to the length of delamination and also to the maximum value before delamination.
4.2 Stacking Sequence
In terms of the laminate theory, the stacking sequence does not affect the initial elastic constants which only depend on the total fibre volume and on the volume fraction of the two types of fibre. The elastic constants can be predicted by the rule of mixtures (ROM). This is verified by the experimental results of many investigators [10]. For strength, an extension of the laminate theory approach in an attempt to predict the strength properties of fabricreinforced hybrids has been made by Saka [8]. He used the TsaiWu criterion and laminate theory to predict the strength of hybrid carbon/glass laminates with different volume fractions. The results of his analytical predictions were in slightly better agreement with experimental results than those given by the ROM. Unlike the elastic constants, the strength of the hybrid composite material depends on many factors of which stacking sequence is one of the most important. It is difficult, therefore, to predict the strength of the hybrid composite only using the volume fraction of the constituents.
Following the principles of fracture mechanics, it may be accepted that crack growth occurs when the amount of strain energy released per unit area equals the energy absorbed in the creation of free surfaces. If the potential energy is U, the principle is expressed in the form,
where G is taken to be a property of the material. In the specimen that has been studied, the potential energy corresponding to an overall strain of 1.35% over a gauge length of 6 mm is 24.7 J for the unit width, regardless of the stacking sequence. The energy released when the first carbon ply breaks, depends on the stacking sequence, as shown below:
Type 
Stacking sequence 
AU(J) for first carbon ply failure 
1 
GCGCGCG 

2 
GGCCCGG 

3 
CGGCGGC 
1.2 (no delamination) 2.8 (delamination) 
The higher the amount of energy released, the easier it will be to satisfy the condition for crack growth [Equation (1)]. From those results it follows that the stacking sequence type 1 is more likely to exhibit a break in the central carbon ply than the other two although it is less likely to delaminate than type 3.
Extending this analysis to the case of a failure in all the carbon plies, the results obtained are:
Type 
Stacking sequence 
AU(J) for failure of all carbon plies 
1 
GCGCGCG 
6.6 (no delamination) 12.0 (delamination) 
Type 
Stacking sequence 
AU(J) for failure of all carbon plies 
2 
GGCCCGG 
11.4 (no delamination) 12.9 (delamination) 
3 
CGGCGGC 
8.3 (no delamination) 2.8 (delamination) 
Ignoring the possibility of delamination, it is now seen that type 1 can only release 6.6 J of potential energy while type 2 releases 11.4 J, making it the most likely to fail through crack growth in the carbon plies. Type 3 is intermediate between the two, at 8.3 J. The same conclusion is reached if the delamination is considered. It is worth noting that the number of delaminations is 6 in type 1, 2 in type 2 and 4 in type 3. The energy released per delamination is comparatively small.
The conclusion is that the alternating stacking sequence (type 1) will tend to start breaking before the other two, but because the total amount of potential energy that it can release is so low when more carbon plies fail, it will need more external work to produce the final failure.
The preceding treatment does not pretend to model the exact process of failure, but it still serves to highlight the difference between the three stacking sequences. Further development is obviously needed.
It is also interesting to apply the same approach to the alternating sequence in order to assess the most likely position of the first failure. The energy released for the failure of the central carbon ply, as we have seen, is 1.6 J (no delamination) and 2.7 J (delamination). If the outer carbon ply breaks, the corresponding values are 1.8 J and 4.1 J. It follows that an outer ply failure is the most likely with a relatively large amount of energy being released for the delamination process.
5. Conclusions
It is quite clear that the failure of the specimen may be initiated by the tensile fracture of a carbon ply. Whether this is in the centre or towards the surface, depends on statistical considerations since all plies are subjected to the same nominal strain. If the central ply breaks, the tensile strain in the adjacent glass ply increases by a factor of 5.02 and a maximum shear stress equal to 152.6 MPa appears between the broken ply and the adjacent glass plies. The maximum tensile strain in the carbonreinforced plies also increases but by a small amount. What happens next depends on the shear strength of the interply surface and on the tensile strength of the neighbouring glass ply. If delamination follows the first break, the tensile strain falls and so, to a lower extent, does the shear stress. This implies that delamination does not necessarily extend over the whole specimen. If the glass ply breaks following the fracture of the carbon, a fast tensile fracture results. Experimental observations tend to support the view that delamination plays an important role in determining the mode of failure.
When an outer carbon ply breaks, the situation is very similar except that the maximum tensile strain in the glass increases now by a factor of 6.07 and the maximum shear stress becomes 170.3 MPa. This means that, if a discontinuity is unavoidable in the manufacturing process, it is better to put it in the centre. Delamination has the same effect as before.
The hybrid effect not only depends on the volume fraction of two types of fibres, but also on the stacking sequence. If the volume fraction of two fibres is constant, the stacking sequence should affect the amount of energy released for carbon plies failure of laminate. The initial stiffness is not related to the stacking sequence.
The finite element method has been shown to highlight the features found in the experimental work. Further work is needed to characterize the in terply shear strength before a full numerical analysis can be developed to model the actual failure of specimen. The importance of the stacking sequence on the hybrid effect is also clear from the variation in strain concentration and shear strain values depending on the order in which tensile fracture and delamination occur.
 6. References
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 2. Reddy, J. N. and D. Sandidge. 1978. "Mixed Finite Element Models for Laminated Composite Plates", Trans. ASME, J. of Engineering for Industry, 109:3945.
 3. Pipes, R. B. and N. J. Pagano. 1933. “Interlaminar Stress in Composite Laminated under Uniform Axial Extension", J. of Composite Materials, 4:538548.
 4. Wong, С. M. S. and F. L. Matthews. 1981. “A Finite Element Analysis of Single and TwoHole Bolted Joints in Fiber Reinforced Plastic”, J. of Composite Materials, 15:481.
 5. Mandel. J. M., S. C. Pack and S. Tarazi. 1982. "Micromechanical Study of Crack Growth in Fiber Reinforced Material”, Engineering Fracture Mechanics, 16(5):741754.
 6. Shah, S., R. K. Y. Li and J. Harding. 1987. “Modelling of the Impact Response of FiberReinforced Composite”, O.U.E.L. Report, No. 1706/87.
 7. Harding, J. and L. M. Welsh. 1983. “A Tensile Testing Technique for Fiber Reinforced Composites at Impact Rates of Strain”, J. of Mater. Sci., 18:18101826.
 8. Saka, K. 1987. "Dynamic Mechanical Properties of FiberReinforced Plastics”, D. Phil. Thesis, Department of Engineering Science, Oxford University.
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 10. Harding, J. and K. Saka. 1988. “The Effect of Strain Rate on the Tensile Failure of WovenReinforced Carbon/Glass Hybrid Composites’, in Proc. IMPACT '87 (DGM Informationsgesellschafft mbh, Oberursel), 1:515522.
 [1] The tensile strain is the same either of the interface between adjacentplies. • The shear stress is continuous across the interface between adjacentplies.