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Measurement of the in-plane shear strengths of unidirectional composites with the Iosipescu test
PII: S0266-3538(97)00099-7
Composites Science and Technology 57 (1997) 1653±1660 # 1998 Elsevier Science Ltd. All rights reserved Printed in Northern Ireland 0266-3538/98 $19.00
MEASUREMENT OF THE IN-PLANE SHEAR STRENGTHS OF UNIDIRECTIONAL COMPOSITES WITH THE IOSIPESCU TEST Fabrice Pierron & Alain Vautrin DeÂpartement MeÂcanique et MateÂriaux, Centre Science des MateÂriaux et des Structures, Ecole des Mines de Saint-Etienne, 158 cours Fauriel, 42023 Saint-Etienne Cedex 2, France (Received 27 September 1996; revised 10 May 1997; accepted 13 June 1997)
can be established in order to produce reliable lamina strengths. Only then will it really be possible to validate failure criteria. Among the important design parameters for laminated composite materials is the in-plane shear strength. If measurement of the in-plane shear modulus of such composites is more or less a solved problem,6 that of the in-plane shear strength is far from being solved. Few papers focus on this problem and it is not uncommon to ®nd contradictory results.7,8 This lack of a reliable method for measuring the in-plane shear strength results in poor con®dence in the design allowables, and hence in overdesign of the composites structures as far as in-plane shear is concerned. The purpose of this paper is to present new ideas on the failure of samples tested with the Iosipescu shear test, also called the V-notch beam method (ASTM Standard D5379M-93), with a view to better measurement of the in-plane shear strength of unidirectional composites. In the present paper, test results as well as ®nite-element analyses will be presented for a carbon/ epoxy T300/914 unidirectional laminate.
Abstract This paper addresses the issue of the measurement of the in-plane shear strengths of unidirectional carbon/epoxy composites from Iosipescu specimens. A description of the failure of the samples is presented together with ®niteelement calculations that con®rm the observations. This leads to a discussion of the in¯uence of the boundary conditions on failure, supported by both experimental and ®nite-element analyses. Eventually, it is shown that failure under a homogeneous stress state is achieved, although the presence of parasitic transverse compressive stress complicates the interpretation in terms of in-plane shear strength. It is shown that the use of a quadratic failure criterion leads to the determination of the in-plane shear strength. # 1998 Elsevier Science Ltd. All rights reserved Keywords: unidirectional composites, in-plane shear, Iosipescu test, shear strength, shear failure 1 INTRODUCTION The prediction of the strength of laminated composite structures is of primary importance when designing with ®bre-reinforced plastics. Many attempts have been made by researchers to develop failure criteria that can predict the failure of complex laminates from the properties of the basic element, i.e. the unidirectional lamina (see Refs 1 and 2 among others). However, this topic is still extremely controversial3 as a consequence of heterogeneity and anisotropy. The impression that arises from the literature is that past work focuses on modelling, i.e. the failure criteria, and that the correct measurement of the basic input parameters of these models, i.e. the strengths of the lamina, is neglected. Yet, even for the simplest 0 tensile test on a unidirectional laminate, work on the design of specimens and tabs4,5 has demonstrated how the uniaxial 0 tensile strength of unidirectional laminates could be grossly underestimated. This is an indication that more work is needed on `basic' tests for lamina characterization so that relevant experimental procedures
2 THE IN-PLANE SHEAR STRENGTH A certain confusion arises from the literature as to the de®nition of shear strength. Indeed, for the same material, i.e. AS4/3501-6 0 carbon/epoxy, Broughton et al.9 report a `failure stress' of 58 MPa, the term `failure stress' implying the value to be ®xture-dependent and not an intrinsic material property, which is reasonable. However, Morton et al.10 report a `shear strength' of 68 MPa, from the same test, material and de®nition of failure point as Broughton et al. Finally, in a very recent paper, Adams and Lewis11 report a shear strength of 115 MPa, again using the same material and test, but not the same de®nition of the failure point. The purpose of the analysis in the present paper is the measurement of the in-plane shear strength, S, which is an input value for most of the failure criteria for composites widely used by designers. The de®nition of S is 1653
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the maximum shear stress that the material can sustain when submitted to an ideal state of pure and homogeneous stress, to be distinguished from a failure stress, the maximum stress that a specimen can sustain when tested in a particular ®xture. At present, very few tests can achieve a state of pure and homogeneous shear stress. The only one which can is the torsion tube test, but it is useless for panel characterization. The Iosipescu shear test and the 10 o-axis tests are two candidates for strength measurement. The 10 o-axis test has been studied separately12 and it was shown that, provided that a new testing methodology based on oblique tabs was used, failure under a state of homogeneous shear stress was achieved. However, the stress state in the o-axis coupon is not pure and it was shown that the presence of a very small amount of transverse tension resulted in premature failure of the specimen. Hence the necessity of using a failure criterion that takes the coupling between shear and transverse stresses into account in order to derive S. It is important to note that the most important feature to achieve is homogeneity since the interpretation of failure under a state of stress concentrations is still an unsolved problem. 3 THE IOSIPESCU SHEAR TEST The Iosipescu shear test has been studied extensively within the last 10 years, starting with the work by Walrath and Adams26 in the early 1980s. Since then, it has raised constant interest from the composites research community, leading to a recent ASTM Standard (D5379M-93). Most of the eort from researchers has focused on the measurement of the in-plane and sometimes out-of-plane shear moduli, which is now more or less a solved problem for classical prepreg materials.6,10,13 The ®xture developed by Adams and Walrath,8 known as the `modi®ed Wyoming ®xture', is used most often in the literature and is the one recommended by the standard. The idea is to apply predominant shear to a V-notched specimen by means of imposed vertical Uy displacements (Fig. 1). However, extensive work on the test by the present authors has led to the pointing out of a certain number
Fig. 1. Classical Iosipescu specimen (dimensions in mm).
of drawbacks of the ®xture14,15 and has resulted in the design of a new rig, the EMSE (Ecole des Mines de Saint-Etienne) ®xture, based on the same sample geometry but with a dierent load-introduction system. To avoid preload on the sample owing to the weight of the mobile part, the ®xture has been inverted, in comparison to the Wyoming ®xture (Fig. 2). Wedges of dierent thicknesses ensure that the load is applied in the middle plane of the sample. The result is the suppression of the parasitic twisting mentioned by Morton et al.10 This ®xture together with a careful experimental procedure has led to very good shear modulus data obtained from a carbon/epoxy unidirectional laminate with dierent Iosipescu con®gurations and 45 o-axis tests.6 These are the procedure and ®xture (Fig. 2) that will be used in this study. A description of the procedure together with plans of the ®xture are available from the authors.16 4 FAILURE OF THE IOSIPESCU SPECIMENS The material used for this study is a unidirectional carbon/epoxy T300/914 [0]24 laminate. Six 0 samples have been cut from a panel with a diamond-coated blade and machined down to the required dimensions with a diamond-tipped mill. The notches were then cut with a diamond-coated axisymmetrical tool. More details on the procedure can be found in Ref. 6. The samples were dried out in a ventilated oven at 60 C prior to testing. The crosshead speed was 0.5 mm minÿ1. A typical stress/time curve is shown in Fig. 3, together with the load drops associated with the dierent cracks. Basically, three families of cracks can be identi®ed. Cracks 1 and 2 are initiated near to the notch root (Fig. 4), early in the life of the specimen (at points 1 and 2 in Fig. 1). Their propagation is instantaneous and is stopped only in the region of high compressive stresses below the loading surfaces. The stress values at which cracks 1 and 2 occur are very sensitive to the amount of in-plane bending that the rig induces. Indeed, as shown by the following ®nite-element analysis, important
Fig. 2. New Iosipescu ®xture (Pierron14).
In-plane shear strengths and the Iosipescu test
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5 FINITE-ELEMENT MODEL
Fig. 3. Typical stress/time curve with associated load drops and cracks.
In order to evaluate the stress state at points 1 and 2, a ®rst ®nite-element model was set up.6 The model, developed on the ANSYS ®nite-element package, consisted of 952 two-dimensional (2D) plane-stress quadratic triangles and quadrangles and 2749 nodes. It was a static linear elastic analysis, in spite of the well-known non-linear behaviour of such composites in shear. Nevertheless, the results will give a ®rst insight into the stress and strain ®elds. The dimensions are that of Fig. 1 and the mesh is drawn in Fig. 6. The elastic constants were taken as those measured in Ref. 6: Exx 1350 GPa; Eyy 92 GPa;
Fig. 4. Cracks 1 (right) and 4 (left).
tensile transverse stresses exist at points 1 and 2. Any parasitic clockwise in-plane bending moment will increase the transverse tensile stress at point 1 and superimpose a compressive transverse stress at point 2, thus decreasing the total transverse tensile stress at this point. This will result in crack 1 appearing much earlier than crack 2. This was observed by the present authors when using the Wyoming ®xture as described in Ref. 8. For the revised ®xture in Fig. 2, crack 1 appeared systematically before crack 2, but the dierence between the stress values at which cracks 1 and 2 appeared is much smaller than for the Wyoming ®xture. This con®rms that the replacement of the guiding rod of the Wyoming ®xture by a very sti rail has been successful. Cracks 3 and 4 also grow from the notch, but closer to the root, as can be seen in Fig. 4. Their propagation is much slower and they cannot always be associated with load drops. Cracks 5 and beyond mark the end of the specimen life. They are associated with very large load drops and appear very quickly one after the other, propagating instantaneously, like cracks 1 and 2 (Fig. 5). Some authors have suggested that this ®nal fracture occurred under a state of homogeneous shear stress, but no demonstration has been given.8,9,17 It has even been proposed by previous authors to interpret the shear stress at the appearance of the ®nal cracks as the inplane shear strength. In order to ®nd out what the stress state is at the different points where fracture occurs, ®nite-element modelling was used.
Gxy 50 GPa xy 037
The initial boundary conditions were taken as those represented in Fig. 1. However, as shown by Ho et al.,18 any reaction force at a constrained node showing that the rig `pulls' the specimen leads to the constraint on this particular node to be released. After a few iterations, the ®nal model is reached. All details can be found in Refs 14 and 18. The main result is that the maximum tensile transverse stress occurs at the intersection of the circular and straight parts of the notch (Fig. 7), with an important gradient of both shear and transverse stresses. This can be visually related to the fracture points observed on the samples (Fig. 4). Fracture is the result of combined shear and transverse tensile stresses, as already mentioned by dierent authors.9,19,25 Therefore,19 the interpretation of the stress values at which cracks 1 and 2 are created in terms of shear strength is not possible, as the shear stress state is neither homogeneous nor pure. The statement from Ref. 7 that the average shear stress at which the ®rst load drop occurs is the shear strength of the material cannot be supported by the above results and remarks.
Fig. 5. Final cracks (5 and more) in a failed Iosipescu specimen.
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Fig. 6. Meshed Iosipescu specimen.
In order to assess the stress state in the gauge section of the Iosipescu specimen after the appearance of cracks 1 and 2, a ®nite-element model has been developed to take these cracks into account. This second model is based on the previous one, but the presence of cracks 1 and 2 is simulated by creating extra nodes along the crack lines and separating the elements on these lines. The sets of two nodes initially superimposed on the crack lines are free to move independently from one another. However, this can only work if the cracks tend to open, which is the case here. Although it may appear to the reader that such a linear elastic approach is not suitable for a specimen that has already failed, it has to be said that damage remains local and that the two cracks only represent a change in specimen geometry. A deformed view of the model is given in Fig. 8. The ®rst result is that stress concentrations can be detected near the notch root again, con®rming the creation of cracks 3 and 4. However, these concentrations are much smaller than that leading to cracks 1 and 2, and now, the transverse stress is compressive. So, as well as for points 1 and 2, the stress state is neither homogeneous nor pure, resulting in no possible interpretation of the stresses in terms of strength. In order to carry on with the model, cracks 3 and 4 should now be introduced. However, as the cracks remain closed because of the compressive stresses, the previous approach is no longer valid and contact elements should be introduced together with a contact law and friction coecients in order to simulate the presence of these cracks. This is far beyond the scope of the present paper. This is the reason why cracks 3 and 4 will not be simulated and their in¯uence on the resulting stress state between the notches will be neglected. So, the same model is kept for the interpretation of the ®nal cracks. If the stresses along the middle line between the notches are drawn for the two models, i.e. with and without cracks 1 and 2 (Fig. 9), then it can clearly be seen that the shear stress is much more homogeneous, which con®rms the statements found in Refs 8, 9, 17 and 18. Nevertheless, the transverse compressive stress, y, increases after the appearance of cracks 1 and 2, so
the stress state is homogeneous but not pure shear. The consequence of this will be discussed later. Although, for the sake of simplicity, the model uses only linear elastic behaviour for the material and cracks 3 and 4 are not simulated, the present results are useful to explain the trend to get a more homogeneous shear stress because of the change of geometry caused by cracks 1 and 2. This also suggests that if an easy cutting device could be used to create cracks 1 and 2 prior to testing, then the measurement of the shear modulus would be much easier as no correction factors would be required. This idea has already led to some very promising results.11,20 Experimental results are now presented in order to validate the above. 6 EXPERIMENTAL RESULTS By using the Iosipescu rig previously described, the ®rst set of six 0 T300/914 Iosipescu samples were tested. A typical stress/time curve is given in Fig. 3. The values of the average shear stress at the appearance of the dierent cracks are given in Table 1.
Fig. 7. Transverse tensile stress concentration near the notch root (for unit average shear stress).
In-plane shear strengths and the Iosipescu test
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Fig. 8. Deformed Iosipescu specimen after the appearance of cracks 1 and 2.
For the six samples, crack 1 appeared consistently before crack 2, suggesting the occurrence of some inplane bending. However, the high value at which cracks 1 occurred together with the closeness of the values at which cracks 2 took place indicate that bending is kept to a minimum, as explained before. Previous testing with the modi®ed Wyoming ®xture resulted in premature appearance of cracks 1 at about 50 to 60 MPa, suggesting that our rig is far less prone to bending, principally because of the nature of the guiding rail and the position of the loading point.16 The asterisks after certain values of the ultimate shear stress (crack 5) denote compressive failure at the upper right inner loading point, before the appearance of the central cracks. This was due to high compressive stresses at this point. The fact that it always happened at the upper right inner loading point resulted from the presence of some inevitable in-plane bending. However, the sharp loading wedges (Fig. 10), made from non-hardened steel, crushed locally at the inner loading points, and particularly at the upper right point, as shown in Fig. 10, where compressive failure occurred for samples 1 to 3. Each test resulted in more and more crushing of the wedges so that, after the three ®rst tests, the wedge looked like that in Fig. 10, and shear failure occurred as the inner loading points were moved away from the notch. It is important to note that this crushing generates a geometrical non-linearity. One conclusion from the above was that hardened steel was to be used for the loading wedges if repro-
ducible results were to be obtained. Preliminary testing using sharp wedges as shown in Fig. 10 resulted in systematic compressive failure at the upper right loading point, so that a smooth hardened steel wedge was designed (Fig. 10). Now, the high compressive stresses are relieved as the contact surface increases with load, as it was ®rst designed on the Wyoming ®xture, although not with hardened steel, hence the possibility of local damage of the ®xture. The negative aspect is that a geometrical non-linearity is now created at this contact point, so that the distance between the inner loading points, nominally 14 mm (Fig. 1), is reduced when failure occurs. In order to evaluate the in¯uence of the position of the inner loading points on the ®nal stress state, the previous ®nite-element model was used again with dierent inner loading point distances. The normalized shear and compressive stresses are given in Fig. 11(a) and (b). It clearly appears from the above that when the inner loading points are moved away from the notches, the transverse compressive stress decreases, as expected, and that, below 16 mm, the maximum lies in the centre of the notch line. For the shear stress, the pro®le moves from maximum shear stress near the notch, for 7.6 mm, to maximum shear stress in the centre, for 18.2 mm. In between, for about 14 mm, there is a position where the pro®le is ¯at, as shown in Fig. 9, i.e. the shear stress is homogeneous. In order to validate the above, a new set of samples was tested, in the same conditions as described before.
Table 1. Average shear stress at the appearance of the dierent cracks Specimen
1 2 3 4 5 6
Average shear stress (MPa) Crack 1
Crack 2
Crack 5
76 82 75 78 87 83
81 77 82 84 86 84
103* 104* 106* 108 109 109
Fig. 9. Stresses along the notch line, with and without cracks 1 and 2, for unit average shear stress.
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Fig. 10. Schematic views of the loading wedges.
The advantage of the ®xture shown in Fig. 2 is that the right-hand side can slide to adjust the distance L between the inner loading points. For two samples, L was set to 14 mm with the new wedges of Fig. 10. When the ®nal central cracks occurred, L was estimated to be only about 10 or 11 mm. Interestingly, for the two samples, cracks 5 and 6 occurred symmetrically near the notch root, the bottom before the top, which con®rms the shear stress pro®le of Fig. 11(b). The fact that the bottom crack appeared before the top one also con®rms the presence of bending that tends to relieve some of the compressive transverse stress at the bottom of the specimen. For two other samples, L was set to 17 mm, hence about 14 mm when fracture occurred. This time also the central cracks occurred near the notches, in contrast to what was expected from Fig. 11(b), probably a parasitic eect owing to in-plane bending. Three samples were ®nally tested with L set to 20 mm, hence about 16 mm when fracture occurred. However, two out of three failed in compression at the upper right point. This time, for sample 6, the ®nal cracks did occur further from the notch, as expected. The results are reported in Table 2. For cracks 1 and 2, no trend can be detected. The rather high scatter on these values is expected because of the local defects and the high stress concentrations. A trend can be suspected for crack 3, but the number of samples is much to low to conclude. For crack 5, one would have expected a sharper decrease of the ®nal stress value when L increases, because of the important diminution of the transverse compressive stress. However, the decrease is only moderate and this suggests that a linear elastic model is not sucient. Ideally, material and geometrical non-linearities should be taken into account, together with bending.
Fig. 11. (a) Normalized transverse compressive stress along the notch line as a function of inner loading point distance, for the cracked specimen. (b) Normalized shear stress along the notch line as a function of inner loading point distance, for the cracked specimen.
Nevertheless, important conclusions can be drawn from the above as to the determination of the in-plane shear strength, and this is the point of the following section. 7 INTERPRETATION AND DISCUSSION The value usually accepted for the in-plane shear strength of T300/914 pressed from prepreg, i.e. with a ®bre volume fraction around 0.6, is about 60 to 70 MPa. Some authors7 consider that the average shear stress value at the appearance of crack 1 can be considered as the shear strength. However, because of the mixed stress concentrations, this approach must be rejected. Even if ®nite-element analyses could predict the stress state near the notch, the interpretation of fracture under high stress concentrations is extremely dicult.21 Moreover, because of the presence of in-plane bending, the stress values at the appearance of cracks 1 and 2 are very
Table 2. Average shear stress at the appearance of the dierent cracks, when L varies Specimen
1 2 3 4 5 6 7
L (mm)
Average shear stress (MPa)
initial
®nal
Crack 1
Crack 2
Crack 3
Crack 5
14 14 17 17 20 20 20
11 11 14 14 16 16 16
81 88 73 84 89 88 90
85 92 90 89 89 86 85
114 116 112 112 112 109 108
125 126 122 121 110* 118 112*
In-plane shear strengths and the Iosipescu test sensitive to the ®xture con®guration, as experienced by the authors. Some other authors10 have suggested this value to be a lower bound of the shear strength. This statement is correct as premature failure is to be expected for the above reasons. It is interesting to note that, in the case of the values reported in Tables 1 and 2, it is systematically above the generally admitted shear strength value of 60 to 70 MPa. This suggests that the actual shear strength is at least 90 MPa. The present authors are of the opinion that only the ®nal central cracks can be successfully interpreted in term of shear strength, as already suggested by Broughton et al.9 and Adams and Walrath.8 As guessed by the previous authors, the existence of a state of homogeneous shear stress for a well chosen distance between the inner loading point is demonstrated, supported by experimental results. However, the previous authors suggest to take the maximum average shear stress value as the shear strength. The ®nite-element analysis presented here clearly shows that the presence of transverse compressive stress cannot be overlooked, and a mixed-mode failure must be considered. Taking the maximum shear stress as the shear strength results in important overestimation of this parameter. It can therefore be considered as an upper bound of the inplane shear strength. In order to derive the in-plane shear strength, S, interaction between shear and transverse compression is taken into account by using the Tsai±Wu quadratic failure criterion:1 Fxx x2 Fx x Fyy y2 Fy y Fxy x y Fss s2 1 1 If X+ and Xÿ are the strengths in tension and compression along the ®bre direction, Y+ and Yÿ perpendicular to the ®bre direction and S the in-plane shear strength, then the coecients of the criterion can be expressed as: Fxx
Fyy
Fss
1 ; X Xÿ 1 Y Yÿ 1 ; S2
;
Fx
Fy
1 1 ÿ X Xÿ 1 1 ÿ ÿ Y Y
Fxy Fxy p X Xÿ Y Yÿ
is the interaction term. where Fxy For T300/914, typical strength values, measured at the laboratory, are:
X 1400 MPa; Y 40 MPa;
Xÿ 1100 MPa Yÿ 180 MPa
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The interaction term, Fxy , is dicult to measure. It is . often taken as ÿ0 5 (generalized Von Mises criterion), which will be the case here. The values of the dierent stress components are derived from the ®nite-element model (Fig. 9) and from the failure stress of 120 MPa (Table 2), which gives:
y ÿ36 MPa;
s ÿ122 MPa
The terms containing x can be neglected with respect to the other terms. So, from eqn (1), S can be identi®ed and is found to be: S 98 MPa As expected, this value is between 90 MPa (shear stress at ®rst crack) and 120 MPa (ultimate shear stress). The compressive transverse stress is shown to increase the failure stress. It is also important to note that this value of 98 MPa is much higher than the generally accepted value of the shear strength for unidirectional T300/914, i.e. 60±70 MPa. The present analysis on its own could be controversial. However, recent work on the 10 o-axis tensile test12,22,23 has shown that the use of oblique tabs resulted in a homogeneous state of stress. However, in that case, the stress state is not pure shear either. There is a small amount of transverse tensile stress and since the transverse strength in tension is very small, it is suf®cient to cause premature failure. The failure stress, for the same material, was found to lie around 78 MPa, but if the in¯uence of the transverse stress is accounted for by using the same failure criterion, then S is found to be 95 MPa, which compares very well with the 98 MPa found with the Iosipescu test.24 This result gives us con®dence in the fact that what is measured here can be regarded as an intrinsic material property, which is what was aimed at. 8 CONCLUSION The ®rst important conclusion that can be drawn from the present paper is that, provided that careful attention is given to Iosipescu ®xture design, failure under a homogeneous stress state can be achieved. This happens for the ®nal failure of the Iosipescu samples as a set of central cracks running parallel to the ®bres. If the ®nal cracks appear under a homogeneous stress state, it is not pure shear. The presence of important transverse compressive stress tends to increase the failure stress. If the in¯uence of this transverse compressive stress is taken into account by using a quadratic failure criterion, then the shear strength, S, is found to be 98 MPa, which compares very well with the value of 95 MPa found with the 10 o-axis tensile test, using the same analysis with transverse tensile stress instead of compressive.
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The important conclusion suggested by the present paper is that, to date, the in-plane shear strength of unidirectional composites may have been rather grossly underestimated by inappropriate mechanical testing.
14.
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1. Tsai, S. W. and Wu, E. M., A general theory of strength for anisotropic materials. J. Compos. Mater., 1971, 5, 58± 80. 2. Hashin, Z., Failure criteria for unidirectional ®bre composites. J. Appl. Mech., 1980, 47, 329±334. 3. Hart-Smith, L. J., The role of biaxial stresses in discriminating between meaningful and illusory composite failure theories. Compos. Struct., 1993, 25, 3±20. 4. Wisnom, M. R. and Maheri, M. R., Tensile strength of unidirectional carbon ®bre±epoxy from tapered specimens. In Proc. ECCM-CTS 2, Hamburg, 13±15 September 1994, pp. 239±247. 5. Hart-Smith, L. J., Making better coupons. Aerospace Compos. Mater., 1991, part I: 3(3), 26±30 and 58; 1991, part II: 3(4), 13±17. 6. Pierron, F. and Vautrin, A., Accurate comparative determination of the in-plane shear modulus of T300/914 by the Iosipescu and 45 o-axis tests. Compos. Sci. Technol., 1994, 52(1), 61±72. 7. Swanson, S. R., Messick, M. and Toombes, G. R., Comparison of torsion tube and Iosipescu in-plane shear test results for a carbon ®bre-reinforced epoxy composite. Composites, 1985, 16(3), 220±224. 8. Adams, D. F. and Walrath, D. E., Current status of the Iosipescu shear test. J. Compos. Mater., 1987, 21, 494± 506. 9. Broughton, W., Kumosa, M. and Hull, D., Analysis of the Iosipescu shear test as applied to unidirectional carbon-®bre reinforced composites. Compos. Sci. Technol., 1990, 38, 299±325. 10. Morton, J., Ho, H., Tsai, M. Y. and Farley, G., An evaluation of the Iosipescu specimen for composite materials shear property measurement. J. Compos. Mater., 1992, 26, 708±750. 11. Adams, D. F. and Lewis, E. Q., Experimental strain analysis of the Iosipescu shear test specimen. Exp. Mech., 1995, 35(4), 352±360. 12. Pierron, F. and Vautrin, A., The 10 o-axis tensile test: a critical approach. Compos. Sci. Technol., 1996, 56(4), 483±488. 13. Gipple, K. L. and Hoyns, D., Measurement of the out-of-plane shear response of thick section composite
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Composites Science and Technology 57 (1997) 1653±1660 # 1998 Elsevier Science Ltd. All rights reserved Printed in Northern Ireland 0266-3538/98 $19.00
MEASUREMENT OF THE IN-PLANE SHEAR STRENGTHS OF UNIDIRECTIONAL COMPOSITES WITH THE IOSIPESCU TEST Fabrice Pierron & Alain Vautrin DeÂpartement MeÂcanique et MateÂriaux, Centre Science des MateÂriaux et des Structures, Ecole des Mines de Saint-Etienne, 158 cours Fauriel, 42023 Saint-Etienne Cedex 2, France (Received 27 September 1996; revised 10 May 1997; accepted 13 June 1997)
can be established in order to produce reliable lamina strengths. Only then will it really be possible to validate failure criteria. Among the important design parameters for laminated composite materials is the in-plane shear strength. If measurement of the in-plane shear modulus of such composites is more or less a solved problem,6 that of the in-plane shear strength is far from being solved. Few papers focus on this problem and it is not uncommon to ®nd contradictory results.7,8 This lack of a reliable method for measuring the in-plane shear strength results in poor con®dence in the design allowables, and hence in overdesign of the composites structures as far as in-plane shear is concerned. The purpose of this paper is to present new ideas on the failure of samples tested with the Iosipescu shear test, also called the V-notch beam method (ASTM Standard D5379M-93), with a view to better measurement of the in-plane shear strength of unidirectional composites. In the present paper, test results as well as ®nite-element analyses will be presented for a carbon/ epoxy T300/914 unidirectional laminate.
Abstract This paper addresses the issue of the measurement of the in-plane shear strengths of unidirectional carbon/epoxy composites from Iosipescu specimens. A description of the failure of the samples is presented together with ®niteelement calculations that con®rm the observations. This leads to a discussion of the in¯uence of the boundary conditions on failure, supported by both experimental and ®nite-element analyses. Eventually, it is shown that failure under a homogeneous stress state is achieved, although the presence of parasitic transverse compressive stress complicates the interpretation in terms of in-plane shear strength. It is shown that the use of a quadratic failure criterion leads to the determination of the in-plane shear strength. # 1998 Elsevier Science Ltd. All rights reserved Keywords: unidirectional composites, in-plane shear, Iosipescu test, shear strength, shear failure 1 INTRODUCTION The prediction of the strength of laminated composite structures is of primary importance when designing with ®bre-reinforced plastics. Many attempts have been made by researchers to develop failure criteria that can predict the failure of complex laminates from the properties of the basic element, i.e. the unidirectional lamina (see Refs 1 and 2 among others). However, this topic is still extremely controversial3 as a consequence of heterogeneity and anisotropy. The impression that arises from the literature is that past work focuses on modelling, i.e. the failure criteria, and that the correct measurement of the basic input parameters of these models, i.e. the strengths of the lamina, is neglected. Yet, even for the simplest 0 tensile test on a unidirectional laminate, work on the design of specimens and tabs4,5 has demonstrated how the uniaxial 0 tensile strength of unidirectional laminates could be grossly underestimated. This is an indication that more work is needed on `basic' tests for lamina characterization so that relevant experimental procedures
2 THE IN-PLANE SHEAR STRENGTH A certain confusion arises from the literature as to the de®nition of shear strength. Indeed, for the same material, i.e. AS4/3501-6 0 carbon/epoxy, Broughton et al.9 report a `failure stress' of 58 MPa, the term `failure stress' implying the value to be ®xture-dependent and not an intrinsic material property, which is reasonable. However, Morton et al.10 report a `shear strength' of 68 MPa, from the same test, material and de®nition of failure point as Broughton et al. Finally, in a very recent paper, Adams and Lewis11 report a shear strength of 115 MPa, again using the same material and test, but not the same de®nition of the failure point. The purpose of the analysis in the present paper is the measurement of the in-plane shear strength, S, which is an input value for most of the failure criteria for composites widely used by designers. The de®nition of S is 1653
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the maximum shear stress that the material can sustain when submitted to an ideal state of pure and homogeneous stress, to be distinguished from a failure stress, the maximum stress that a specimen can sustain when tested in a particular ®xture. At present, very few tests can achieve a state of pure and homogeneous shear stress. The only one which can is the torsion tube test, but it is useless for panel characterization. The Iosipescu shear test and the 10 o-axis tests are two candidates for strength measurement. The 10 o-axis test has been studied separately12 and it was shown that, provided that a new testing methodology based on oblique tabs was used, failure under a state of homogeneous shear stress was achieved. However, the stress state in the o-axis coupon is not pure and it was shown that the presence of a very small amount of transverse tension resulted in premature failure of the specimen. Hence the necessity of using a failure criterion that takes the coupling between shear and transverse stresses into account in order to derive S. It is important to note that the most important feature to achieve is homogeneity since the interpretation of failure under a state of stress concentrations is still an unsolved problem. 3 THE IOSIPESCU SHEAR TEST The Iosipescu shear test has been studied extensively within the last 10 years, starting with the work by Walrath and Adams26 in the early 1980s. Since then, it has raised constant interest from the composites research community, leading to a recent ASTM Standard (D5379M-93). Most of the eort from researchers has focused on the measurement of the in-plane and sometimes out-of-plane shear moduli, which is now more or less a solved problem for classical prepreg materials.6,10,13 The ®xture developed by Adams and Walrath,8 known as the `modi®ed Wyoming ®xture', is used most often in the literature and is the one recommended by the standard. The idea is to apply predominant shear to a V-notched specimen by means of imposed vertical Uy displacements (Fig. 1). However, extensive work on the test by the present authors has led to the pointing out of a certain number
Fig. 1. Classical Iosipescu specimen (dimensions in mm).
of drawbacks of the ®xture14,15 and has resulted in the design of a new rig, the EMSE (Ecole des Mines de Saint-Etienne) ®xture, based on the same sample geometry but with a dierent load-introduction system. To avoid preload on the sample owing to the weight of the mobile part, the ®xture has been inverted, in comparison to the Wyoming ®xture (Fig. 2). Wedges of dierent thicknesses ensure that the load is applied in the middle plane of the sample. The result is the suppression of the parasitic twisting mentioned by Morton et al.10 This ®xture together with a careful experimental procedure has led to very good shear modulus data obtained from a carbon/epoxy unidirectional laminate with dierent Iosipescu con®gurations and 45 o-axis tests.6 These are the procedure and ®xture (Fig. 2) that will be used in this study. A description of the procedure together with plans of the ®xture are available from the authors.16 4 FAILURE OF THE IOSIPESCU SPECIMENS The material used for this study is a unidirectional carbon/epoxy T300/914 [0]24 laminate. Six 0 samples have been cut from a panel with a diamond-coated blade and machined down to the required dimensions with a diamond-tipped mill. The notches were then cut with a diamond-coated axisymmetrical tool. More details on the procedure can be found in Ref. 6. The samples were dried out in a ventilated oven at 60 C prior to testing. The crosshead speed was 0.5 mm minÿ1. A typical stress/time curve is shown in Fig. 3, together with the load drops associated with the dierent cracks. Basically, three families of cracks can be identi®ed. Cracks 1 and 2 are initiated near to the notch root (Fig. 4), early in the life of the specimen (at points 1 and 2 in Fig. 1). Their propagation is instantaneous and is stopped only in the region of high compressive stresses below the loading surfaces. The stress values at which cracks 1 and 2 occur are very sensitive to the amount of in-plane bending that the rig induces. Indeed, as shown by the following ®nite-element analysis, important
Fig. 2. New Iosipescu ®xture (Pierron14).
In-plane shear strengths and the Iosipescu test
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5 FINITE-ELEMENT MODEL
Fig. 3. Typical stress/time curve with associated load drops and cracks.
In order to evaluate the stress state at points 1 and 2, a ®rst ®nite-element model was set up.6 The model, developed on the ANSYS ®nite-element package, consisted of 952 two-dimensional (2D) plane-stress quadratic triangles and quadrangles and 2749 nodes. It was a static linear elastic analysis, in spite of the well-known non-linear behaviour of such composites in shear. Nevertheless, the results will give a ®rst insight into the stress and strain ®elds. The dimensions are that of Fig. 1 and the mesh is drawn in Fig. 6. The elastic constants were taken as those measured in Ref. 6: Exx 1350 GPa; Eyy 92 GPa;
Fig. 4. Cracks 1 (right) and 4 (left).
tensile transverse stresses exist at points 1 and 2. Any parasitic clockwise in-plane bending moment will increase the transverse tensile stress at point 1 and superimpose a compressive transverse stress at point 2, thus decreasing the total transverse tensile stress at this point. This will result in crack 1 appearing much earlier than crack 2. This was observed by the present authors when using the Wyoming ®xture as described in Ref. 8. For the revised ®xture in Fig. 2, crack 1 appeared systematically before crack 2, but the dierence between the stress values at which cracks 1 and 2 appeared is much smaller than for the Wyoming ®xture. This con®rms that the replacement of the guiding rod of the Wyoming ®xture by a very sti rail has been successful. Cracks 3 and 4 also grow from the notch, but closer to the root, as can be seen in Fig. 4. Their propagation is much slower and they cannot always be associated with load drops. Cracks 5 and beyond mark the end of the specimen life. They are associated with very large load drops and appear very quickly one after the other, propagating instantaneously, like cracks 1 and 2 (Fig. 5). Some authors have suggested that this ®nal fracture occurred under a state of homogeneous shear stress, but no demonstration has been given.8,9,17 It has even been proposed by previous authors to interpret the shear stress at the appearance of the ®nal cracks as the inplane shear strength. In order to ®nd out what the stress state is at the different points where fracture occurs, ®nite-element modelling was used.
Gxy 50 GPa xy 037
The initial boundary conditions were taken as those represented in Fig. 1. However, as shown by Ho et al.,18 any reaction force at a constrained node showing that the rig `pulls' the specimen leads to the constraint on this particular node to be released. After a few iterations, the ®nal model is reached. All details can be found in Refs 14 and 18. The main result is that the maximum tensile transverse stress occurs at the intersection of the circular and straight parts of the notch (Fig. 7), with an important gradient of both shear and transverse stresses. This can be visually related to the fracture points observed on the samples (Fig. 4). Fracture is the result of combined shear and transverse tensile stresses, as already mentioned by dierent authors.9,19,25 Therefore,19 the interpretation of the stress values at which cracks 1 and 2 are created in terms of shear strength is not possible, as the shear stress state is neither homogeneous nor pure. The statement from Ref. 7 that the average shear stress at which the ®rst load drop occurs is the shear strength of the material cannot be supported by the above results and remarks.
Fig. 5. Final cracks (5 and more) in a failed Iosipescu specimen.
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Fig. 6. Meshed Iosipescu specimen.
In order to assess the stress state in the gauge section of the Iosipescu specimen after the appearance of cracks 1 and 2, a ®nite-element model has been developed to take these cracks into account. This second model is based on the previous one, but the presence of cracks 1 and 2 is simulated by creating extra nodes along the crack lines and separating the elements on these lines. The sets of two nodes initially superimposed on the crack lines are free to move independently from one another. However, this can only work if the cracks tend to open, which is the case here. Although it may appear to the reader that such a linear elastic approach is not suitable for a specimen that has already failed, it has to be said that damage remains local and that the two cracks only represent a change in specimen geometry. A deformed view of the model is given in Fig. 8. The ®rst result is that stress concentrations can be detected near the notch root again, con®rming the creation of cracks 3 and 4. However, these concentrations are much smaller than that leading to cracks 1 and 2, and now, the transverse stress is compressive. So, as well as for points 1 and 2, the stress state is neither homogeneous nor pure, resulting in no possible interpretation of the stresses in terms of strength. In order to carry on with the model, cracks 3 and 4 should now be introduced. However, as the cracks remain closed because of the compressive stresses, the previous approach is no longer valid and contact elements should be introduced together with a contact law and friction coecients in order to simulate the presence of these cracks. This is far beyond the scope of the present paper. This is the reason why cracks 3 and 4 will not be simulated and their in¯uence on the resulting stress state between the notches will be neglected. So, the same model is kept for the interpretation of the ®nal cracks. If the stresses along the middle line between the notches are drawn for the two models, i.e. with and without cracks 1 and 2 (Fig. 9), then it can clearly be seen that the shear stress is much more homogeneous, which con®rms the statements found in Refs 8, 9, 17 and 18. Nevertheless, the transverse compressive stress, y, increases after the appearance of cracks 1 and 2, so
the stress state is homogeneous but not pure shear. The consequence of this will be discussed later. Although, for the sake of simplicity, the model uses only linear elastic behaviour for the material and cracks 3 and 4 are not simulated, the present results are useful to explain the trend to get a more homogeneous shear stress because of the change of geometry caused by cracks 1 and 2. This also suggests that if an easy cutting device could be used to create cracks 1 and 2 prior to testing, then the measurement of the shear modulus would be much easier as no correction factors would be required. This idea has already led to some very promising results.11,20 Experimental results are now presented in order to validate the above. 6 EXPERIMENTAL RESULTS By using the Iosipescu rig previously described, the ®rst set of six 0 T300/914 Iosipescu samples were tested. A typical stress/time curve is given in Fig. 3. The values of the average shear stress at the appearance of the dierent cracks are given in Table 1.
Fig. 7. Transverse tensile stress concentration near the notch root (for unit average shear stress).
In-plane shear strengths and the Iosipescu test
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Fig. 8. Deformed Iosipescu specimen after the appearance of cracks 1 and 2.
For the six samples, crack 1 appeared consistently before crack 2, suggesting the occurrence of some inplane bending. However, the high value at which cracks 1 occurred together with the closeness of the values at which cracks 2 took place indicate that bending is kept to a minimum, as explained before. Previous testing with the modi®ed Wyoming ®xture resulted in premature appearance of cracks 1 at about 50 to 60 MPa, suggesting that our rig is far less prone to bending, principally because of the nature of the guiding rail and the position of the loading point.16 The asterisks after certain values of the ultimate shear stress (crack 5) denote compressive failure at the upper right inner loading point, before the appearance of the central cracks. This was due to high compressive stresses at this point. The fact that it always happened at the upper right inner loading point resulted from the presence of some inevitable in-plane bending. However, the sharp loading wedges (Fig. 10), made from non-hardened steel, crushed locally at the inner loading points, and particularly at the upper right point, as shown in Fig. 10, where compressive failure occurred for samples 1 to 3. Each test resulted in more and more crushing of the wedges so that, after the three ®rst tests, the wedge looked like that in Fig. 10, and shear failure occurred as the inner loading points were moved away from the notch. It is important to note that this crushing generates a geometrical non-linearity. One conclusion from the above was that hardened steel was to be used for the loading wedges if repro-
ducible results were to be obtained. Preliminary testing using sharp wedges as shown in Fig. 10 resulted in systematic compressive failure at the upper right loading point, so that a smooth hardened steel wedge was designed (Fig. 10). Now, the high compressive stresses are relieved as the contact surface increases with load, as it was ®rst designed on the Wyoming ®xture, although not with hardened steel, hence the possibility of local damage of the ®xture. The negative aspect is that a geometrical non-linearity is now created at this contact point, so that the distance between the inner loading points, nominally 14 mm (Fig. 1), is reduced when failure occurs. In order to evaluate the in¯uence of the position of the inner loading points on the ®nal stress state, the previous ®nite-element model was used again with dierent inner loading point distances. The normalized shear and compressive stresses are given in Fig. 11(a) and (b). It clearly appears from the above that when the inner loading points are moved away from the notches, the transverse compressive stress decreases, as expected, and that, below 16 mm, the maximum lies in the centre of the notch line. For the shear stress, the pro®le moves from maximum shear stress near the notch, for 7.6 mm, to maximum shear stress in the centre, for 18.2 mm. In between, for about 14 mm, there is a position where the pro®le is ¯at, as shown in Fig. 9, i.e. the shear stress is homogeneous. In order to validate the above, a new set of samples was tested, in the same conditions as described before.
Table 1. Average shear stress at the appearance of the dierent cracks Specimen
1 2 3 4 5 6
Average shear stress (MPa) Crack 1
Crack 2
Crack 5
76 82 75 78 87 83
81 77 82 84 86 84
103* 104* 106* 108 109 109
Fig. 9. Stresses along the notch line, with and without cracks 1 and 2, for unit average shear stress.
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Fig. 10. Schematic views of the loading wedges.
The advantage of the ®xture shown in Fig. 2 is that the right-hand side can slide to adjust the distance L between the inner loading points. For two samples, L was set to 14 mm with the new wedges of Fig. 10. When the ®nal central cracks occurred, L was estimated to be only about 10 or 11 mm. Interestingly, for the two samples, cracks 5 and 6 occurred symmetrically near the notch root, the bottom before the top, which con®rms the shear stress pro®le of Fig. 11(b). The fact that the bottom crack appeared before the top one also con®rms the presence of bending that tends to relieve some of the compressive transverse stress at the bottom of the specimen. For two other samples, L was set to 17 mm, hence about 14 mm when fracture occurred. This time also the central cracks occurred near the notches, in contrast to what was expected from Fig. 11(b), probably a parasitic eect owing to in-plane bending. Three samples were ®nally tested with L set to 20 mm, hence about 16 mm when fracture occurred. However, two out of three failed in compression at the upper right point. This time, for sample 6, the ®nal cracks did occur further from the notch, as expected. The results are reported in Table 2. For cracks 1 and 2, no trend can be detected. The rather high scatter on these values is expected because of the local defects and the high stress concentrations. A trend can be suspected for crack 3, but the number of samples is much to low to conclude. For crack 5, one would have expected a sharper decrease of the ®nal stress value when L increases, because of the important diminution of the transverse compressive stress. However, the decrease is only moderate and this suggests that a linear elastic model is not sucient. Ideally, material and geometrical non-linearities should be taken into account, together with bending.
Fig. 11. (a) Normalized transverse compressive stress along the notch line as a function of inner loading point distance, for the cracked specimen. (b) Normalized shear stress along the notch line as a function of inner loading point distance, for the cracked specimen.
Nevertheless, important conclusions can be drawn from the above as to the determination of the in-plane shear strength, and this is the point of the following section. 7 INTERPRETATION AND DISCUSSION The value usually accepted for the in-plane shear strength of T300/914 pressed from prepreg, i.e. with a ®bre volume fraction around 0.6, is about 60 to 70 MPa. Some authors7 consider that the average shear stress value at the appearance of crack 1 can be considered as the shear strength. However, because of the mixed stress concentrations, this approach must be rejected. Even if ®nite-element analyses could predict the stress state near the notch, the interpretation of fracture under high stress concentrations is extremely dicult.21 Moreover, because of the presence of in-plane bending, the stress values at the appearance of cracks 1 and 2 are very
Table 2. Average shear stress at the appearance of the dierent cracks, when L varies Specimen
1 2 3 4 5 6 7
L (mm)
Average shear stress (MPa)
initial
®nal
Crack 1
Crack 2
Crack 3
Crack 5
14 14 17 17 20 20 20
11 11 14 14 16 16 16
81 88 73 84 89 88 90
85 92 90 89 89 86 85
114 116 112 112 112 109 108
125 126 122 121 110* 118 112*
In-plane shear strengths and the Iosipescu test sensitive to the ®xture con®guration, as experienced by the authors. Some other authors10 have suggested this value to be a lower bound of the shear strength. This statement is correct as premature failure is to be expected for the above reasons. It is interesting to note that, in the case of the values reported in Tables 1 and 2, it is systematically above the generally admitted shear strength value of 60 to 70 MPa. This suggests that the actual shear strength is at least 90 MPa. The present authors are of the opinion that only the ®nal central cracks can be successfully interpreted in term of shear strength, as already suggested by Broughton et al.9 and Adams and Walrath.8 As guessed by the previous authors, the existence of a state of homogeneous shear stress for a well chosen distance between the inner loading point is demonstrated, supported by experimental results. However, the previous authors suggest to take the maximum average shear stress value as the shear strength. The ®nite-element analysis presented here clearly shows that the presence of transverse compressive stress cannot be overlooked, and a mixed-mode failure must be considered. Taking the maximum shear stress as the shear strength results in important overestimation of this parameter. It can therefore be considered as an upper bound of the inplane shear strength. In order to derive the in-plane shear strength, S, interaction between shear and transverse compression is taken into account by using the Tsai±Wu quadratic failure criterion:1 Fxx x2 Fx x Fyy y2 Fy y Fxy x y Fss s2 1 1 If X+ and Xÿ are the strengths in tension and compression along the ®bre direction, Y+ and Yÿ perpendicular to the ®bre direction and S the in-plane shear strength, then the coecients of the criterion can be expressed as: Fxx
Fyy
Fss
1 ; X Xÿ 1 Y Yÿ 1 ; S2
;
Fx
Fy
1 1 ÿ X Xÿ 1 1 ÿ ÿ Y Y
Fxy Fxy p X Xÿ Y Yÿ
is the interaction term. where Fxy For T300/914, typical strength values, measured at the laboratory, are:
X 1400 MPa; Y 40 MPa;
Xÿ 1100 MPa Yÿ 180 MPa
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The interaction term, Fxy , is dicult to measure. It is . often taken as ÿ0 5 (generalized Von Mises criterion), which will be the case here. The values of the dierent stress components are derived from the ®nite-element model (Fig. 9) and from the failure stress of 120 MPa (Table 2), which gives:
y ÿ36 MPa;
s ÿ122 MPa
The terms containing x can be neglected with respect to the other terms. So, from eqn (1), S can be identi®ed and is found to be: S 98 MPa As expected, this value is between 90 MPa (shear stress at ®rst crack) and 120 MPa (ultimate shear stress). The compressive transverse stress is shown to increase the failure stress. It is also important to note that this value of 98 MPa is much higher than the generally accepted value of the shear strength for unidirectional T300/914, i.e. 60±70 MPa. The present analysis on its own could be controversial. However, recent work on the 10 o-axis tensile test12,22,23 has shown that the use of oblique tabs resulted in a homogeneous state of stress. However, in that case, the stress state is not pure shear either. There is a small amount of transverse tensile stress and since the transverse strength in tension is very small, it is suf®cient to cause premature failure. The failure stress, for the same material, was found to lie around 78 MPa, but if the in¯uence of the transverse stress is accounted for by using the same failure criterion, then S is found to be 95 MPa, which compares very well with the 98 MPa found with the Iosipescu test.24 This result gives us con®dence in the fact that what is measured here can be regarded as an intrinsic material property, which is what was aimed at. 8 CONCLUSION The ®rst important conclusion that can be drawn from the present paper is that, provided that careful attention is given to Iosipescu ®xture design, failure under a homogeneous stress state can be achieved. This happens for the ®nal failure of the Iosipescu samples as a set of central cracks running parallel to the ®bres. If the ®nal cracks appear under a homogeneous stress state, it is not pure shear. The presence of important transverse compressive stress tends to increase the failure stress. If the in¯uence of this transverse compressive stress is taken into account by using a quadratic failure criterion, then the shear strength, S, is found to be 98 MPa, which compares very well with the value of 95 MPa found with the 10 o-axis tensile test, using the same analysis with transverse tensile stress instead of compressive.
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The important conclusion suggested by the present paper is that, to date, the in-plane shear strength of unidirectional composites may have been rather grossly underestimated by inappropriate mechanical testing.
14.
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