Composites

PII: S1359-8368(98)00008-0

Composites Part B 29B (1998) 521–533 1359-8368/98/$ - see front matter q 1998 Published by Elsevier Science Ltd. All rights reserved

Strain rate behavior of composite materials H. M. Hsiao a and I. M. Daniel b ,*

a Materials Science Department, Research and Technology, Hexcel Composites, Dublin, CA 94568, USA b Robert R. McCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL 60208-3020, USA

The effect of strain rate on the compressive and shear behavior of carbon/epoxy composite materials was investigated. Strain rate behavior of composites with fiber waviness was also studied. Falling weight impact system and servohydraulic testing machine were used for dynamic characterisation of composite materials in compression at strain rates up to several hundred per second. Strain rates below 10 s ¹1 were generated using a hydraulic testing machine. Strain rates above 10 s ¹1 were generated using the drop tower apparatus developed. Seventy-two-ply unidirectional carbon/epoxy laminates (IM6G/3501-6) loaded in the longitudinal and transverse directions and [(0 8/90 8) 2/0¯ 8] s crossply laminates were characterised. Off-axis (30 and 458) compression tests of the same unidirectional material were also conducted to obtain the in-plane shear stress–strain behavior. The 908 properties, which are governed by the matrix, show an increase in modulus and strength over the static values but no significant change in ultimate strain. The shear stress–strain behavior, which is also matrix-dominated, shows high nonlinearity with a plateau region at a stress level that increases significantly with increasing strain rate. The 08 and crossply laminates show higher strength and strain values as the strain rate increases, whereas the modulus increases only slightly over the static value. The increase in strength and ultimate strain observed may be related to the shear behavior of the composite and the change in failure modes. In all cases the dynamic stress–strain curves stiffen as the strain rate increases. The stiffening is lowest in the longitudinal case and highest in the transverse and shear cases. Unidirectional and crossply specimens with fiber waviness were fabricated and tested. It is shown that, with severe fiber waviness, strong nonlinearity occurs in the stress–strain curves due to fiber waviness with significant stiffening as the strain rate increases. q 1998 Published by Elsevier Science Ltd. All rights reserved (Keywords: strain rate effects; dynamic response; compressive testing of composites; falling weight impact)

INTRODUCTION Some applications of composite materials involve dynamically loaded components and structures. The analysis and design of such structures subjected to dynamic loadings, ranging from low-velocity impact to high-energy shock loadings, requires the input of high strain rate properties. Numerical simulations, such as finite element analysis, need an accurate description of such effects as strain rate, loading history, deformation, internal damage, and wave propagation. Related work on dynamic characterisation of composite materials has been relatively limited compared to quasistatic tests due to the difficulty of high strain rate testing and data interpretation. Most of the dynamic work conducted so far has involved lateral impact testing of composite laminates, but with less emphasis on constitutive properties characterisation. In order to develop more sophisticated constitutive models and failure criteria under dynamic * Corresponding author. Tel: +1 847 4915649; fax: +1 847 4915227; e-mail: [email protected]

loading and to assess their adequacy, experiments conducted over a wide range of strain rates, in which a single dominant stress component can be extracted, are very important. The various dynamic test methods used to date have different advantages and limitations. The use of a servohydraulic machine is common and convenient. However, the conventional hydraulic machine is limited to lower strain rates, below 10 s ¹1, because of inertial effects of the load cell and grips. Chou et al. 1 designed a special open/ closed loop hydraulic machine to study the dynamic compressive behaviour of neat resins over a range from 10 ¹4 to 10 3 s ¹1. The data presented show approximately three times increase in strength and are twice higher in initial modulus over static values for PMMA resin. The drop weight impact test has many advantages, it is inexpensive, can accommodate different specimen geometries and allows easy variation of strain rate. However, the system is very sensitive to the contact conditions between the impactor and specimen and to spurious noise from ringing and vibrations. Dynamic tests using such a device on composite materials were first conducted by Lifshitz 2 in 1976. He observed a

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Strain rate behavior of composite materials: H. M. Hsiao and I. M. Daniel significant strength increase under impact on balanced angle-ply laminates. Montiel and Williams 3 used an instrumented drop tower to determine compressive properties of 48-ply graphite/PEEK [0 2/90] 8s composites for strain rates up to 8 s ¹1. The results indicate that at high strain rate loading, the strength increases by 42% and the ultimate strain increases by 25%. There only appears to be a small strain rate effect on the initial modulus. Groves et al. 4 also developed a drop tower system to generate strain rates from 10 to 1000 s ¹1. The split Hopkinson pressure bar (SHPB) technique permits testing at higher strain rates exceeding 1000 s ¹1. Contact surface conditions are very critical as in the drop weight testing. Specimens must be short to minimize wave propagation effects. However, this raises questions on the homogeneity and uniaxiality of the induced stress in the specimen. Most of the high strain rate compressive properties reported to date have been obtained by this technique, e.g., Sierakowski et al., El-Habak, Harding, Lifshitz and Leber, Weeks and Sun, and Powers et al. 5–10. Sierakowski et al. 5 investigated steel/epoxy composites in compression up to 1000 s ¹1. They observed very different failure modes in static and dynamic compressive tests on cylindrical specimens. The initial modulus remains unchanged but the strength increases by 100% in the dynamic tests. Harding 7 studied two woven glass/epoxy material systems in compression up to 860 s ¹1 using cylindrical and thin strip specimens. He concluded that there is a significant increase in the initial modulus, strength and ultimate strain with increasing strain rate for woven glass/epoxy composites. Amijima and Fujii 11 studied glass/polyester plain woven and unidirectional composites in compressive tests of cylindrical specimens. The increase in strength is shown to be higher for the woven composites than for the unidirectional ones. Tests using thin ring specimens under dynamic internal or external pressure

Figure 1

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can minimize the wave propagation effects, but they are expensive and complex and cannot be used for thick composites. Daniel and LaBedz 12 developed a test method utilizing a thin graphite/epoxy ring (six to eight plies thick) composite specimen loaded by an external pressure pulse applied explosively through a liquid. They obtained compressive properties at strain rates up to 500 s ¹1. The 08 properties show some increase in initial modulus over the static values but no change in strength. The 908 properties show much higher than static modulus and strength. Reviews on high strain rate studies for composite materials can be found from the articles and books by Greszczuk and Sierakowski 13–15. This paper discusses the application of a drop weight system and a servohydraulic testing machine for dynamic characterisation of carbon/epoxy composites. Strain rate behavior of composites with fiber waviness was also studied. The results presented cover strain rates from quasi-static to several hundred per second. Strain rates above 10 s ¹1 were generated using a drop tower apparatus.

EXPERIMENTAL PROCEDURES Material selection and specimen fabrication Seventy-two-ply thick unidirectional and crossply laminates were selected to investigate the strain rate effect in this study. The material used was IM6G/3501-6 carbon/epoxy composite (Hexcel Corp.). The prepreg layup was cured in a press/autoclave by a three-step curing cycle especially developed for thick composites 16. The void content, as determined by digital image analysis of photomicrographs, was less than 1% in all panels tested.

(a) Impact specimen configurations; (b) specimen holding and guide fixture

Strain rate behavior of composite materials: H. M. Hsiao and I. M. Daniel Drop tower apparatus A drop tower was designed and built for dynamic compressive testing of thick composites at strain rates ranging from 10 to several hundred per second 17. It consists of two 2.54 cm (1 in) diameter and 3 m (10 ft) long guide rods which are 17.8 cm (7 in) apart. The drop weight is guided along the rods through two bearing assemblies. It is raised and released using an electromagnet connected to a cable. A 5000 g quartz accelerometer (Kistler Instr. Corp.) is mounted at the center of the drop weight on the top surface. Figure 1a shows the dynamic compression test specimen configuration for the drop tower. A 72-ply composite specimen 2.54 cm (1 in) long and 1.27 cm (0.50 in) wide was bonded to a similar high-strength steel specimen. The latter was made of 4140 steel with a yield stress of 1660 MPa (240 ksi) under quasi-static loading. Steel end caps were bonded at the outer ends. Each end cap consisted of a 51 3 51 3 6.4 mm (2 3 2 3 0.25 in) plate with a 8.7 3 12.7 mm (0.35 3 0.50 in) rectangular cutout at the center bonded to a similar 1.27 cm (0.50 in) thick plate without a cutout. Curing of the adhesive in the end caps was done by placing the specimen between the impactor and the base plate, which increased the uniformity of surface contact during impact. Close tolerances were achieved for flatness and perpendicularity on the contact faces to minimise outof-plane specimen bending. In all cases the specimens were end-loaded. A fixture was designed to hold and guide the specimen during impact (Figure 1b). Uniform end loading was accomplished through the use of this guide system to constrain all but the vertical motion of the specimen. The specimen with the end caps was mounted in such a way that the top of the end caps protruded by 6 mm (0.25 in) above the top of the guide system. Axial strain gages were mounted on both sides of

the composite and steel specimens, connected to a bridge conditioner, amplified by an HP amplifier and recorded by a four-channel digital processing oscilloscope (Norland 3001) at sampling intervals of 1–10 ms. For strain rates below 10 s ¹1 the servohydraulic testing machine was used, along with the specimen, guide fixture and data acquisition system described here. The dynamic impact force was measured in two different ways. Initially, it was measured with an accelerometer mounted on the top of the drop weight. The dynamic force and hence applied stress was obtained from the accelerometer reading multiplied by the mass of the impactor assembly, which included the drop weight, bearing assembly, and top end cap. This was checked against the value obtained more directly from strain readings on the steel portion of the specimen. The axial strain in the steel specimen (load cell), mounted in series with the composite specimen, was multiplied by its modulus (207 GPa; 30 Msi) for more accurate determination of the dynamic force. For the specimen dimensions used, the time required for a stress wave to travel the length of the steel specimen is approximately 5 ms and that for the composite specimen varies between 3 (08 specimen) and 11 ms (908 specimen). Valid results were obtained since the test durations in the drop tower tests, usually on the order of several hundred to 1000 ms, were much longer than the above stress wave travel times. In most cases the force results obtained from the accelerometer reading were in agreement with those obtained from strain readings in the steel specimen. Discrepancies occurred near the end of the stress–strain curve, with the accelerometer reading giving a lower force value. This was attributed to wave propagation effects inside the impactor and vibrations of the entire system. Because of the signal noise from the accelerometer, force determinations based on steel strain readings were judged to be more reliable and thus used in all cases.

Figure 2 Acceleration of 4.66 kg (10.27 lb) mass impacting a unidirectional IM6G/3501-6 carbon/epoxy specimen in the transverse direction and measured axial strains in composite and calibration steel specimens (height of drop, 2.44 m (8 ft))

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Strain rate behavior of composite materials: H. M. Hsiao and I. M. Daniel The major problem in the use of a drop tower apparatus is the presence of vibration stress waves superimposed on the stress–strain curves. In this study rubber sheets, from 2.54 mm (0.1 in) to 7.62 mm (0.3 in.) thick, were placed over the top end cap to minimise ringing due to impact. This absorber dampened the spurious noise in the acceleration and strain histories caused by apparatus vibrations and steelto-steel contact. It also served to distribute the load on the specimen more uniformly. Fiber-cork vibration damping pads were placed between the floor and the entire drop tower apparatus to reduce the undesirable wave reflections. It is noted that, without damping the system, the acceleration, load and strain measurements are distorted through oscillations, which include rigid body accelerations of the system and shock waves resulting from impact. To separate these two sources, a fast Fourier transform (FFT) analysis can be applied to decompose the frequency of the raw data 18,19. The lower frequency data are attributable to rigid body acceleration, whereas the higher frequency data result from acoustic waves. The high frequency data can then be culled from the raw data, resulting in a smooth stress–strain curve which contains rigid body acceleration only.

RESULTS AND DISCUSSION Transverse compressive behavior of unidirectional composite Strain rate tests were performed on the drop tower and the hydraulic testing machine. Tests conducted on the drop tower used a mass of 4.66 kg (10.27 lb) falling from a height of 2.44 m (8 ft), producing strain rates from 10 to several hundred per second. The impactor acceleration and the specimen strains (steel and composite) were recorded. Typical acceleration versus time and specimen strain versus

time plots are shown in Figure 2. Dynamic stress–strain curves of such a test are shown in Figure 3, where they are plotted based on both acceleration and steel calibration strain measurements. The two curves agree for the most part, except near the end where the acceleration measurements tend to underestimate the force (stress). Force determinations based on steel strain readings were judged to be more reliable and thus were used in all cases. Specimen strains versus time plots, such as the one shown in Figure 2, were used to determine the strain rate. Because of the absorbers used in dynamic testing, the initial part of the strain–time curve was not truly indicative of the effective strain rate experienced by the specimen. However, the strain rate seemed to reach a nearly constant value at a strain level of approximately 10%–20% of the ultimate strain in all cases. The strain rates were thus determined by differentiating the strain–time curve at strain readings above 20% of the ultimate rain. The strain rate obtained by this method for the case shown in Figure 2 was approximately 60 s ¹1. Transverse stress–strain curves to failure under quasistatic and high strain rates are shown in Figure 4. This comparison shows a significant strain rate effect. The transverse strength, which is a matrix-dominated property, shows nearly a two-fold increase from the quasi-static value. The initial modulus follows a similar trend, although not as pronounced, with an increase of up to 37%. The ultimate strain shows no strain rate effect at all, which implies that it can be used as a failure criterion in analysis under dynamic loading. Figure 4 also shows that the stress– strain behavior is a function of strain rate. The material stiffens (with a reduction in matrix ductility) as the strain rate increases. This stiffening behavior is very significant in the nonlinear region. Two possible reasons for this phenomenon are proposed. The first one is the viscoelastic nature of the polymeric matrix itself and the second one is

Figure 3 Transverse compressive stress–strain curves for unidirectional IM6G/3501-6 carbon/epoxy at a strain rate of 60 s ¹1 (the curves were based on both acceleration and steel calibration strain measurements)

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Strain rate behavior of composite materials: H. M. Hsiao and I. M. Daniel the time-dependent nature of accumulating damage. At slower rates damage accumulates more gradually, such that a well-defined nonlinear region occurs near the end of the stress–strain curve. At higher rates, however, damage does not have enough time to develop and thus the damage accumulation process has a diminishing effect on the stress– strain curve as the strain rate increases. A similar phenomenon was also observed on the transverse compressive behavior of AS4/APC2 carbon/PEEK under quasistatic and high strain rates of loading (Figure 5). However, PEEK-based resin is more ductile in the nonlinear region of the stress–strain curves compared to the 3501-6 epoxybased resin.

Figure 4

In-plane shear behavior of unidirectional composite The off-axis compression test was used to obtain the inplane shear behavior of the unidirectional composite. A 108 off-axis specimen is usually chosen to minimize the effects of longitudinal and transverse stress components, j 1 and j 2, on the shear response. However, under compressive loading, it is not practical to employ the 108 off-axis test since a long specimen is required. Therefore, off-axis specimens of 15, 30, 45 and 608 were first tested under quasi-static compressive loading to check the consistency of shear stress–strain curves obtained from different off-axis angles. These results, shown in Figure 6, reveal that the

Transverse compressive stress–strain curves for unidirectional IM6G/3501-6 carbon/epoxy under quasi-static and high strain rate loading

Figure 5 Comparison of transverse compressive stress–strain curves between AS4/APC2 carbon/PEEK and IM6G/3501-6 carbon/epoxy under quasi-static and high strain rate loading

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Strain rate behavior of composite materials: H. M. Hsiao and I. M. Daniel shear stress–strain curves obtained from different off-axis specimens agree well within both the linear and nonlinear ranges. This implies that the superposition principle still holds and the shear component can thus be decoupled from the applied uniaxial stress. It should be noted that the experimental results tend to overestimate the ultimate properties due to interaction of the transverse compressive stress across the fibers; nevertheless the elastic properties and overall shear stress–strain curve can be obtained from the off-axis test accurately. In this study, 30 and 458 off-axis specimens were used to investigate the strain rate effect on the in-plane shear behavior of the unidirectional composite. Shear property characterisation conducted on the drop tower used the mass of 4.66 kg (10.27 lb) falling from a

height of 2.44 m (8 ft). Figure 7 shows the shear stress– strain curves obtained from 30 and 458 off-axis specimens under quasi-static and high strain rates of loading for comparison. It appears that the shear stress–strain curves obtained from these two different angles agree well for the similar strain rate in either the static or dynamic domain. This characterisation also reveals a strong strain rate effect. The shear stress–strain behaviour, which is also matrix dominated, shows high nonlinearity with a plateau region at a stress level that increases significantly as the strain rate increases. The yield point of the curve also increases with increasing strain rate. The strength increases sharply with strain rate from the quasi-static value by up to 80%. The initial modulus follows a similar trend, although not as pronounced, with an increase up to 18%.

Figure 6

Comparison of in-plane shear stress–strain curves obtained from different off-axis tests under quasi-static compression

Figure 7

Comparison of shear stress–strain curves obtained from 308 and 458 off-axis tests under quasi-static and high strain rate compressive loading

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Strain rate behavior of composite materials: H. M. Hsiao and I. M. Daniel Longitudinal compressive behavior of unidirectional composite In this study the end loading principle was adopted to testing thick composites since it is widely accepted and, more importantly, easy to use for dynamic compressive testing. Test methods based on the end loading principle include the ASTM D695 test (SACMA SRM 1-88), the European version ICSTM test 20, and the DTRC test 21. Recently a new compression test method for thick composites (NU method), based on the concept of combined shear loading and end loading, was developed 22. It was found that the pure end loading method tends to

underestimate the longitudinal compressive strength and strain values of thick composites due to premature endcrushing failure (Figure 8). By using the NU test method, longitudinal compressive strengths of 1660 MPa (240 ksi), which are significantly higher than those measured by the end loading methods, are obtainable experimentally for thick composites under quasi-static loading. Therefore, experimental results from compression tests have to be interpreted with extra care. Longitudinal compressive strengths obtained at different strain rates can only be compared when the same loading method is used. Unidirectional specimens were loaded in the fiber direction with a mass of 17.31 kg (38.16 lb) falling from a

Figure 8 Comparison of compressive stress–strain curves between combined shear/end loading (NU test method) and pure end loading under quasi-static loading

Figure 9

Longitudinal compressive stress–strain curves for unidirectional IM6G/3501-6 carbon/epoxy under quasi-static and high strain rate loading

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Strain rate behavior of composite materials: H. M. Hsiao and I. M. Daniel height of 2.44 m (8 ft) on the drop tower. Figure 9 displays the longitudinal stress–strain curves to failure under quasistatic and high strain rates of loading. It clearly shows the stiffening behavior in the nonlinear range that is not observable from the end loading results alone. The stress– strain curve stiffens as the strain rate increases, although the magnitude of the change is much smaller compared to the transverse and shear behavior. The initial modulus shows only a slight increase with strain rate. The strength and ultimate strain are significantly higher than the static values by up to 79% and 74%, respectively. The increase in strength and ultimate strain observed may be related to the shear behavior of the composite and the change in failure

modes. It is known that longitudinal compressive failure is intimately related to, and governed by, the in-plane shear response of the composite, even in the presence of the slightest initial fiber misalignment 23–25. Any compressive failure observed follows some form of initial shear failure of the composite. The longitudinal compressive strength is expressed as F1c ¼ (jx )max ¼

tp f þ gp

where f is the initial fiber misalignment; and t*, g* are values of shear stress and strain as defined in Figure 10. Figure 10 shows a measured shear stress–strain curve for

Figure 10 Graphical determination of longitudinal compressive strength (f ¼ initial fiber misalignment)

Figure 11 Compressive stress–strain curves for [(0 8/90 8) 2/0¯ 8] s crossply IM6G/3501-6 carbon/epoxy under quasi-static and high strain rate loading

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Strain rate behavior of composite materials: H. M. Hsiao and I. M. Daniel an IM6G/3501-6 carbon/epoxy composite with an illustration of a graphical determination of t* and g*. The compressive strength corresponds to the values t* and g*, where the tangent to the shear stress–strain curve equals the slope t*/(f þ g*). It is apparent from Figure 10 that, if the in-plane shear behavior stiffens substantially with increasing strain rate, then this would lead to the increase in longitudinal compressive strength. Figures 7 and 10 combined give a good explanation of the increase in longitudinal strength and ultimate strain observed during the tests. This relationship can also be used to explain the significant increase in the compressive strength of woven composites under impact. It is found that a woven composite is more sensitive to strain rate than a unidirectional one, and that different woven composites have different strain rate effects due to the reinforcement structure 11,26. Plain-weave composites show a higher strain rate effect than satinweave, unidirectional or multidirectional ones. This is attributed to the higher shear-dependence in the plain-weave case than in the other cases. In addition, for high strain rate testing, the duration of loading is short enough that material failure occurs prior to the onset of fiber microbuckling. This suggests that a change in failure modes occurs as the strain rate increases. The microstructure change during the high rate testing should be studied in depth to elucidate the contribution of different damage mechanisms to the dynamic behavior of composite materials.

specimens with different types of controlled waviness 31. One hundred and fifty-ply unidirectional specimens with uniform through-the-thickness sinusoidal waviness (Figure 12a) and 72-ply [(0 8/90 8) 2/0¯ 8w] s crossply specimens with central layer waviness (Figure 12b) were fabricated to study their strain rate behavior. A and L in Figure 12 represent the amplitude and period of the wavy fiber, respectively. The degree of waviness is characterised by the amplitude to period ratio, A/L. The A/L ratio of unidirectional and crossply specimens studied here is 0.0425 and 0.02, respectively. The presence of fiber waviness can significantly degrade the compressive properties of composite materials. Figure 13 illustrates the predicted stiffness and strength reduction as a function of waviness parameter A/L along with the experimental result for unidirectional composites with uniform fiber waviness (quasi-static case) 29. It appears that both major Young’s modulus and compressive strength degrade seriously as the fiber waviness increases. Compressive strength is much more sensitive to fiber waviness than the major Young’s modulus, especially when A/L is small. Figure 14 illustrates the predicted stress–strain curves under uniaxial static compressive loading as a function of A/L for the same wave pattern 30. It demonstrates how material nonlinearity increases with increasing fiber

Compressive behavior of crossply composite Crossply specimens of [(0 8/90 8) 2/0¯ 8] s layup were loaded with a mass of 11.34 kg (25 lb) falling from a height of 2.44 m (8 ft). Stress–strain curves to failure under quasistatic and high strain rates of loading are shown in Figure 11 for comparison. It shows that the material stiffens as the strain rate increases, and the magnitude of the change is slightly higher than in the longitudinal case. The initial modulus shows only a slight increase with strain rate. The strength and ultimate strain are significantly higher than the static values by up to 67% and 57%, respectively. The strain rate sensitivity of the strength, initial modulus and ultimate strain of the crossply composite follow similar trends as the ones observed under longitudinal compression. Therefore, compressive behavior of a crossply composite is dominated by the 08 layers. Compressive behavior of composite with fiber waviness Fiber waviness is a type of manufacturing defect occurring during processing. It results from wet hoopwound filament strands under the pressure exerted by the overwrapped layers during the filament winding process. It occurs also in the manufacture of the fiber tows, in the prepreg tape impregnation process, or in the subsequent layup and curing process. Fiber waviness has been shown to affect significantly the compressive behavior of composite materials 27–30. Techniques were developed for fabrication of composite

Figure 12 (a) Representative volume and coordinates for a unidirectional composite with uniform fiber waviness. (b) Representative volume and coordinates for a [(0 8/90 8) 2/0¯ 8w] s crossply composite with central layer waviness

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Strain rate behavior of composite materials: H. M. Hsiao and I. M. Daniel waviness. Since it is shown that the stress–strain curve stiffens with increasing strain rate and decreasing fiber waviness, it is interesting to understand the combined effects of fiber waviness and strain rate on the compressive behavior of composite materials. Unidirectional and crossply specimens with fiber waviness were loaded with a mass of 11.34 kg (25 lb) falling from a height of 2.44 m (8 ft). Figure 15 shows the compressive stress–strain curves for unidirectional specimens with uniform fiber waviness (A/L ¼ 0.0425) under quasi-static and high strain rates of loading. The specimens tested failed prematurely due to the fiber discontinuities on the specimen surfaces (Figure 12a), and thus the strength

and ultimate strain cannot be compared in this particular case. The dynamic stress–strain curves stiffen slightly over the static ones up to the load level applied. This result agrees well with the predictions based on the numerical incremental analysis by the authors 32. However, it was suggested from the same analysis that the strain rate effect becomes significant at higher loads due to larger shear component involved (Figure 16). Figure 16 is the replot of Figure 15 along with the predictions made by the incremental analysis. It is shown that, with this type of severe fiber waviness (A/L ¼ 0.0425), strong nonlinearity occurs in the stress–strain curves due to fiber waviness with significant stiffening as the strain rate increases.

Figure 13 Predicted stiffness and strength reduction of unidirectional IM6G/3501-6 carbon/epoxy under quasi-static compressive loading as a function of waviness parameter A/L for uniform-waviness model

Figure 14 Predicted stress–strain curves as a function of waviness parameter A/L for unidirectional IM6G/3501-6 carbon/epoxy with uniform fiber waviness under quasi-static compressive loading

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Strain rate behavior of composite materials: H. M. Hsiao and I. M. Daniel

Figure 15 Compressive stress–strain curves for unidirectional IM6G/3501-6 carbon/epoxy with uniform fiber waviness (A/L ¼ 0.0425) under quasi-static and high strain rate loading

Figure 16 Predicted compressive stress–strain curves by incremental analysis and experimental results for unidirectional IM6G/3501-6 carbon/epoxy with uniform fiber waviness (A/L ¼ 0.0425) under quasi-static and high strain rate loading

Figure 17 shows the compressive stress–strain curves for crossply specimens with and without central layer waviness (maximum A/L ¼ 0.02) under quasi-static and high strain rates of loading. The waviness in this case is localised and much milder compared to the previous case (Figure 12). Therefore, the strain rate sensitivity of the strength, ultimate strain, initial modulus, and stress–strain behavior of this wavy crossply composite follows similar trends as its nonwavy counterpart with slightly higher magnitude.

SUMMARY AND CONCLUSIONS A systematic investigation was conducted of the effect of strain rate on the compressive and shear behavior of composite materials. Unidirectional carbon/epoxy laminates (IM6G/3501-6) with fibers at 0, 30, 45 and 908 with loading direction and [(0 8/90 8) 2/0¯ 8] s crossply laminates were characterised at strain rates up to several hundred per second. Unidirectional specimens with uniform fiber waviness and [(0 8/90 8) 2/0¯ 8w] s crossply specimens with

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Strain rate behavior of composite materials: H. M. Hsiao and I. M. Daniel

Figure 17 Compressive stress–strain curves for crossply IM6G/3501-6 carbon/epoxy with and without central layer waviness (maximum A/L ¼ 0.02) under quasi-static and high strain rate loading

central layer waviness were fabricated to study their strain rate behavior. The transverse compressive strength increases sharply with strain rate to nearly double the quasi-static value at the highest rate. The initial modulus follows a similar trend, although not as pronounced, with an increase up to 37%. The ultimate strain shows no strain rate effect at all, which implies that it can be used as a failure criterion for analysis under dynamic loading. The stress–strain behavior is also a strong function of strain rate. The material stiffens significantly as the strain rate increases. The 30 and 458 off-axis compression tests were conducted to investigate the strain rate effect on the in-plane shear behavior of unidirectional composites. Shear stress– strain curves obtained from these two different angles agree well for the similar strain rates in either the static or dynamic domain. The shear stress–strain behavior shows high nonlinearity with a plateau region at a stress level that increases significantly as the strain rate increases. The yield point of the curve also increases with increasing strain rate. The shear strength increases sharply with strain rate from the quasi-static value by up to 80%. Longitudinal compressive properties were obtained for strain rates up to 110 s ¹1. The initial modulus increases only slightly with strain rate over the static value. The strength and ultimate strain are significantly higher than the static values by up to 79% and 74%, respectively. The increase in strength and ultimate strain observed may be related to the stiffening of the composite in-plane shear behavior under dynamic loading and the change in failure modes. The stress–strain curve stiffens slightly as the strain rate increases. Compressive properties of a crossply composite were also obtained. The results show increases in strength and ultimate strain but only a slight increase in initial modulus. The stress–strain curve stiffens as the strain rate increases and the magnitude of the change is slightly higher than in the longitudinal case. The strain rate sensitivity of

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the strength, initial modulus and ultimate strain of the crossply composite follow similar trends as the ones observed under longitudinal compression. Therefore, compressive behavior of crossply composite is dominated by the 08 layers. Unidirectional and crossply specimens with fiber waviness were fabricated and tested. The dynamic stress–strain curves of unidirectional specimens stiffen slightly over the static ones up to the load level applied. This result agrees well with the predictions based on the numerical incremental analysis. However, it was suggested from the same analysis that the strain rate effect becomes significant at higher loads due to larger shear component involved. It is shown that, with this type of severe fiber waviness, strong nonlinearity occurs in the stress–strain curves due to fiber waviness with significant stiffening as the strain rate increases. The waviness in crossply specimens is localised and much milder compared to the unidirectional ones. The obtained strain rate sensitivity of this wavy crossply composite follows similar trends as its nonwavy counterpart with slightly higher magnitude.

ACKNOWLEDGEMENTS The work described in this paper was sponsored by the Office of Naval Research. We are grateful to Dr. Y. D. S. Rajapakse of ONR for his encouragement and cooperation.

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