Compressive response and failure of braided textile composites: Part 1 experiments

Available online at www.sciencedirect.com International Journal of Non-Linear Mechanics 39 (2004) 635 648 Compressive response and failure of braided textile composites: Part 1 experiments Shu Ching Quek a, Anthony M. Waas a;, Khaled W. Shahwan b, Venkatesh Agaram b a Aerospace Engineering Department, Composite Structures Laboratory, University of Michigan, Ann Arbor, MI 48109-2118, USA b Experimental and Computational Mechanics Group, DaimlerChrysler Corporation, Auburn Hills, MI 48326, USA Received 10 September 2002; accepted 2 January 2003 Abstract Experimental results obtained by examining the planar biaxial compression/tension response of carbon 2D triaxial braided composites (2DTBC) are reported in this paper. These experiments were motivated by a need to examine the failure of 2DTBC in a state of stress that would be similar to what is experienced by the walls of a tubular member under compressive crush loads. Results obtained froma series of biaxial tests that were conducted with dierent proportional displacement loading ratio combinations of compression and tension are reported. In all cases, the dominant failure mechanism under such a stress state is the buckling of the bias and axial tows within the composite. Full eld surface displacement data is acquired concurrently during all biaxial and some uniaxial tests using the technique of digital speckle photography. Digital images of the specimen surface that is illuminated with a He Ne laser are acquired at discrete time intervals during the loading history using a high-resolution digital camera. These images are stored and analyzed to obtain the incremental inplane surface displacement eld, u(x; y) and v(x; y). Fromthese, the incremental inplane surface strains x, y and xy are obtained by numerical dierentiation. The present paper, which is the rst in a two part series, is devoted to the biaxial experimental results pertaining to 2DTBC failure.? 2003 Elsevier Ltd. All rights reserved. 1. Introduction Although organic matrix composites are superior to metals in specic stiness and specic strength, significant weight savings in applications are only possible with either thin or moderately thick walls for the composite body. In a crash or impact situation of a moderately thick-walled composite body, typical structural members will be subjected to membrane, bending and through the thickness (interlaminar shear and normal Corresponding author. Tel.: +1-734-764-8227; fax: +1-734- 763-0578. E-mail address: dcw@umich.edu (A.M. Waas). stresses) stresses. Thus, the state of stress in a typical member will, in general, be strictly three-dimensional (3D) with the magnitude of the out-of-plane stresses largely controlled by the relative thickness and the number of plies making the thickness. On the other hand, for thin-walled structural members, the stress state can be approximated to be two-dimensional (2D) dominated by the in-plane stresses developed during deformation. The deformation response and subsequent failure of composite structures under planar multiaxial load situations are areas of research that have seen signicant growth in the recent past. Much of this activity is related to the increased engineering applications of composite structures. In such cases, design engineers resort to nite element stress and 0020-7462/04/$ - see front matter? 2003 Elsevier Ltd. All rights reserved. doi:10.1016/s0020-7462(03)00018-0

636 S. Ching Quek et al. / International Journal of Non-Linear Mechanics 39 (2004) 635 648 Fig. 1. (a) Dimensions of biaxial cruciform specimen and (b) loading directions on specimen. Fig. 2. 3-strain-gage rosette pattern on biaxial cruciformspecimen. failure analysis of composite structures. One aspect of such analyses requires the choice of a suitable failure criterion and its implementation in a multi-axial stress setting. In this, the rst in a two part paper, we report experimental results pertaining to the failure mechanisms of 2D triaxial braided composites (2DTBC) in a biaxial planar setting, so that a mechanism based failure predictive methodology could be developed to analyze and design safe 2DTBC structures. The biaxial setting is representative of what is encountered in the wall of a structural member, such as that in a tube subjected to crushing under axial compression with an initiator plug, where the tube wall material is in a state of biaxial stress [1 3]. Towards reaching this goal, a number of planar biaxial tests with cruciformshaped specimens (Fig. 1) were conducted. Strains in the center of the specimen were measured via strain gages placed on the surface in a rosette conguration on the backside together with the use of DSP [4] on the other side of the specimen (Fig. 2). In DSP, the incremental displacement eld froma reference state to the current state is measured. Thus, if the load at the reference state and the current state are recorded, then using DSP, it is possible to measure the full eld incremental displacement eld (and thus the strains) corresponding to an incremental load.

S. Ching Quek et al. / International Journal of Non-Linear Mechanics 39 (2004) 635 648 637 In a biaxial test, the global stress eld (on the remote boundaries) and the local strain elds are measured as in Khamesh and Waas s [5,6] work. Thus, the biaxial test data oers a means to assess the validity of constitutive equations and numerical schemes that have been proposed to handle strain softening in 2DTBC. In addition, the eect of the biaxial stress or strain elds on the nature of damage evolution in composites with triaxially at braided architectures, must be characterized quantitatively (i.e. via measurement) in order to understand the dierent mechanisms of failure that are operative in a biaxial stress state of compression/tension. This would ultimately help to develop micromechanics based models that are re- ective of the failure mechanism present. Since the cruciformconguration provides a means to contain damaged material in a well-dened region, it allows one to obtain local strain eld information that will be reported in the following sections. 2. Test specimens, biaxial loading frame, data acquisition and test procedure 2.1. Test specimens Achieving failure within the gage section of the cruciformspecimen is a diculty that several papers have addressed before, see for example, Makinde et al. [7,8], Demmerle and Boehler [9], Khamesh and Waas [10] and Welsh et al. [11]. In order to select a desirable design of the specimen, a complete nite element model of the specimen with the loading end tabs was created to investigate the stress state involved for a compression/tension type of biaxial test. Unlike Demmerle and Boehler s [9] work, where they studied the optimal design of a tension/tension type biaxial cruciformshaped specimen, it is not possible to reduce the thickness of the specimen gage section (the test region) because that would alter the microarchitecture of the braided composite. Further, with a thinned out specimen, out of plane buckling of the thinned out section is likely to occur and this would detract from the main goal of achieving failure within the gage section under a planar stress state. As such, specimen congurations of several radii, R (Fig. 1a) was investigated using the nite element package SDRC-IDEAS as the pre-processor and the ABAQUS nite element analysis (FEA) software package, for the stress analysis. Stress analyses were performed where displacement boundary loading was applied at the boundary (Fig. 1b). Plate material and steel loading tabs were modeled using eight-noded parabolic plane stress elements. Material architecture descriptions and macroscopic orthotropic elastic properties are shown in Tables 1 and 2, respectively. With the guidance of previous work by Khamesh and Waas [10], a nal specimen geometry was achieved with dimensions given in Fig. 1. The working area of the specimen measures 50:80 mm 50:80 mm (2 in 2in)as shown in the braided portion of Fig. 1a. 2.2. Biaxial loading apparatus The biaxial tests were carried out in a special customdesigned load frame capable of exerting tension/compression loads of 222 kn (50; 000 lbf ) along two perpendicular planar axes. Each actuator of the frame (four of them) can be independently programmed either in load or displacement control via a feedback loop fromload cells or linear variable dierential transformer (LVDT) as shown in Fig. 3. There are 2 load cells indicated as A and B in Fig. 3 mated to 2 of the 4 actuators. Each load cell is rated for a magnitude of 222 kn (50; 000 lbf ) in tension and compression. A typical test would use proportional loading, whereby the loads (or displacements) increase in the same proportion along the two axes. 2.3. Data acquisition The objective of the biaxial tests was to measure the response of the material as it progressively fails. For this purpose, the applied load resultants, the strain state at the center of the specimen (via strain gages) and the entire biaxial strain eld ( x ; y and xy ) within the area of the specimen surface that is illuminated, via DSP, were measured during the entire loading process (from inception to nal catastrophic failure). The DSP leads to large amounts of image data, typically 500 MB to 1 GB amount of data per test. In early stages (linear response) of loading, these image data shed no new light on the specimen response, when compared to the data fromstrain gages. But consequently, as the testing progressed, data fromselected images corresponding to stages of damage initiation, localization and damage

638 S. Ching Quek et al. / International Journal of Non-Linear Mechanics 39 (2004) 635 648 Table 1 Material descriptions of carbon braided composites Braided 45 =0 = +45 Carbon ber composite (8:6 mm thick) Fiber Resin No. of plies Thickness Volume fraction Fortal Fibers 556 Epoxy 8 0:339 in 55% (axial tow) (513) 80 K vinyl ester Tensile modulus 231 GPa (Ashland Tensile strength 3800 MPa Hetron 922) X -sectional area (3:3 10 5 mm 2 ) 3:72 GPa Gral 12 K (Bias tow) Tensile modulus 234 GPa Tesile strength 4:5 GPa X -sectional area (3:7 10 5 mm 2 ) Table 2 Material properties of carbon braided composites Braided 45 =0 = +45 Carbon ber composite (8:6 mm thick) Properties Experiment data Computational data (GPa) (GPa) E x 68.53 68.70 E y 10.78 11.81 G xy 7.52 7.67 v xy 0.36 NA propagation provided much more information, since at this stage the strain gages have exceeded their capacity and are rendered inaccurate. Strain gages are placed in a rosette pattern as shown in Fig. 2. The 3-gage rosette pattern is used in the back surface of the specimen and a single gage is placed on the specimen front surface in the direction of the compressive load. In this manner, the front surface of the specimen can be used to obtain full eld strain data via the DSP procedure. The back-to-back gages, in the compressive loading direction, provide the average compressive axial strains and bending strains. In this case, bending strains are expected to be near zero, which is the case during the tests, as will be evident later. With the 3-gage rosette pattern, all strain components are determined through the small strain transformation relationships below. 1 ( 1 )=m 2 ( 1 ) x + n 2 ( 1 ) y + m( 1 )n( 1 ) xy =2; Fig. 3. Descriptions of parts of biaxial loading frame. 1,2,3,4: Left, top, right, and bottomhydraulic cylinders, respectively. Note: Each cylinder can be driven with a load or displacement feed-back, independent of the other three cylinders, A,B: left and top load cells, D: right and bottom ball joints, for specimen alignment, and a,b,c,d: Specimen xtures. 3 ( 2 )=m 2 ( 2 ) x + n 2 ( 2 ) y + m( 2 )n( 2 ) xy =2; 2 ( 3 )=m 2 ( 3 ) x + n 2 ( 3 ) y + m( 3 )n( 3 ) xy =2; (1) where, m( i ) = cos and n( i ) = sin. In these tests, 1 =0, 2 =45, 3 =90. Angles are measured with respect to the horizontal axis and

S. Ching Quek et al. / International Journal of Non-Linear Mechanics 39 (2004) 635 648 639 these angles indicate that the 1 2 coordinate system corresponds to the x y coordinate system, as indicated in Fig. 2. Dog-bone type uniaxial test specimens were used to obtain the orthotropic moduli, and the major Poisson s ratio. The values so obtained that are reported here are reective of at least three tests per each type of moduli reported. Both, strain gage readings and DSP were used to measure the average gage section strains in all of the uniaxial tests. 2.4. Test procedure In a typical biaxial test, the specimen is placed within the wedge grips and all strain gages are balanced and initialized to zero prior to commencement of loading. The digital camera that is positioned to acquire images is pre-programmed to capture images of the specimen front surface (an area of 10 mm 10 mm) at a frequency of 1 frame=s, throughout the loading history. The schematic drawing of the test setup and experimental setup is shown in Fig. 4. The setup to use DSP in the experiments is shown in Fig. 5. The strain gage readings and the load cell readings are acquired at 4 Hz, while the actuator movement rate (the displacement control loading) is carried out at 0:0005 in=s for the uniaxial tests and for a 1:1.5 compression-tension test, the compression direction actuator moves at 0:0005 in=s while the tension direction actuator moves at 0:00075 in=s. 3. Results and discussion of failure mechanisms for uniaxial and biaxial tests of carbon ( 45 =0= +45 ) 2DTBCs Fig. 6 shows the incremental (snap shot) shear strain, xy, contour plots for a typical 2DTBC specimen undergoing a displacement-control loading ratio of 1:1.5 (see Fig. 7 for loading ratios). All notations, as in 1:1.5, indicate that the rst number of the ratio refers to compression and the second number refers to tension. Sample DSP calculation in Fig. 6 is done with reference time at t1 as indicated in Fig. 8. This gure shows or locates the reference times, t1 t8 corresponding to each image from frame 76 to frame 83 (F76 F83), respectively. These master plots (Figs. 7 9) show the actuator displacements, loads and strains gage readings, respectively, as functions of time. Fig. 6 also shows the planar area that is in view in each contour plot, outlined in the upper left corner image. For example, the incremental strain contour plot for x for this test of loading ratio 1:1.5 in Fig. 11, are the incremental strains at time t2 with respect to the deformation state at time t1. The current time t2 and the reference time t1 are indicated at the top of each contour plot and the corresponding frame number F76 F77 is indicated at the bottom. These reference times in turn can be used for locating the corresponding load cell and strain gage data from the other graphs or master plots. A series of speckle images corresponding to the times indicated in Fig. 8 are shown in Fig. 10. In this manner, a sequence of incremental strain plots for x, y and xy as indicated in Figs. 11 13 are obtained. No incremental strain plots were made between times t7 and t8 because the material has completely ruptured at this point and thus no correlation can be found in the DSP method. These plots provide non-linear (with respect to load) pointwise values of strains in the regions of damaging material. In this particular specimen, distributed matrix cracking (DMC) that start at very low tensile loads progressively accumulate leading to ber tows locally loosing their support, which in the case of local compression leads to tow buckling/tow kinking. This type of damage is as shown in Fig. 14. The distributed matrix cracks are caused by the large tensile stresses that develop in the matrix situated between ber tows. Within a tow, individual bers undergo dierent deformation and rotation; consequently the matrix layers in between are subjected to shear. This shear generates substantial tensile stresses at large values (a shear can be decomposed into diagonal tension/compression). The large incremental shear strains just prior to failure are clearly visible in the speckle strain maps shown in Fig. 13. Notice that the maximum xy, within the imaged area is indicated on top of each specklegram, and as seen in Fig. 13, the total accumulated xy, is on the order of 1:41E 2. Similarly, the maximum accumulated tensile strains and compressive strains are on the order of 9:00E 3 and 9:65E 3, respectively. Furthermore, notice in Fig. 13 (compared to the last specklegramin Fig. 10, which shows the failed bias tow) that the maximum incremental shear strains are occurring parallel to the bias tows

640 S. Ching Quek et al. / International Journal of Non-Linear Mechanics 39 (2004) 635 648 Fig. 4. A schematic of the biaxial test set-up.

S. Ching Quek et al. / International Journal of Non-Linear Mechanics 39 (2004) 635 648 641 biaxial loading frame side actuator specimen control tower load cell & LVDT box Desktop computer Data acquisition system 5mW He-Ne laser High resolution Kodak digital camera Digital camera Acquisition system 1 frame/sec Fig. 5. Schematic of the biaxial using the DSP method. Fig. 6. DSP method and procedure of obtaining strain plots prior to failure point. indicative of the large deformation preceding the buckling event. Notice that the incremental shear strains are relatively large compared to the other strain values and progressing to dierent areas between the matrix and bias or angle tows. These large strains lead to progressive matrix cracking indicating strain softening induced by the damaging material. With a view to understanding the eects of dierent biaxial stress and strain ratios, 10 types of tests were performed on the braided composite, including uniaxial tension tests and uniaxial compression tests. In each test, the specimen was subjected to biaxial tension and compression displacement loading, but each type of test was done with a dierent loading ratio. The loading ratios used are presented in Fig. 15. The main mechanisms of failure for all the braided composite samples loaded biaxially is braid (tow)/matrix interfacial failure along the tows and tow buckling. Moreover, there are also many visible distributed cracks perpendicular to the tensioned direction. This distributed cracking occurs prior to the catastrophic failure event and is the mechanism by which the entire specimen undergoes strain softening. The culmination of this event is the growth of damage along the braid/matrix interface, and in the case

642 S. Ching Quek et al. / International Journal of Non-Linear Mechanics 39 (2004) 635 648 0.08 2.00 0.07 1.75 Displacement (inches) 0.06 0.05 0.04 0.03 compression tension 1.50 1.25 1.00 0.75 Displacement (mm) 0.02 0.50 0.01 0.25 0 0 20 0.00 40 60 80 100 120 Time (seconds) Fig. 7. Plot of actuator displacement versus time for a compression/tension ratio of 1:1.5. 20000 t1 t2 t3 t4 t5 t6 t7 t8 18000 16000 compression tension 80000 70000 14000 60000 Load (lbf) 12000 10000 8000 50000 40000 Load (N) 6000 30000 4000 20000 2000 10000 0 0 20 40 60 80 100 120 Time (seconds) 0 Fig. 8. Plot of compressive load and tensile load versus time for a ratio of 1:1.5.

S. Ching Quek et al. / International Journal of Non-Linear Mechanics 39 (2004) 635 648 643 8000 6000 4000 Microstrains, µε 2000 0 0 10 20 30 40 50 60 70 80 90 100-2000 110-4000 -6000 ex ec ey Axial SR Bending SR -8000 Time (seconds) Fig. 9. Strains versus time for displacement ratio of 1:1.5. Fig. 10. Speckle images at the times indicated for each load point as shown in the Fig. 8. of large compression, tow buckling and tow kinking. In the pure compression case, distributed cracks were not present in the failed specimen. In compression, the damage localizes into a band of about 8 12 mm in width, which is approximately the size of the representative unit cell (RUC) for the braided composite (the RUC is also termed the repeat unit ). This implies that the failure mechanism, and thus the physics that limit the compressive strength of 2DTBC is tow buckling in the presence of a matrix that is continually

644 S. Ching Quek et al. / International Journal of Non-Linear Mechanics 39 (2004) 635 648 Fig. 11. Compressive strain plots for 1:1.5 loading ratio for load increments (and corresponding time increments) indicated in Fig. 8. Fig. 12. Tensile strain plots for 1:1.5 loading ratio for load increments (and corresponding time increments) indicated in Fig. 8.

S. Ching Quek et al. / International Journal of Non-Linear Mechanics 39 (2004) 635 648 645 Fig. 13. Shear strain plots for 1:1.5 loading ratio for load increments (and corresponding time increments) indicated in Fig. 8. Fig. 14. Damaged area of a typical compressively loaded braided composite where tow buckling phenomenon is observed. being sheared (between tows) and plastically deforming, oering less and less resistance with continued loading. Here, we are collectively referring to all the mechanisms that cause softening of the matrix as plastically deforming. During this process some of the angled tows have also popped out fromthe surface. This mechanism persists for the biaxial compression dominated tests as well. However, the band of failed material becomes rotated (with respect to the loading directions) for dierent loadings ratios as seen in Fig. 15. For the uniaxial tension test, catastrophic failure is associated with matrix cracking and subsequent rupture of the bias tows. The failing material, as in the uniaxial compression case, forms a damage zone that is perpendicular to the direction of applied load. The complete compression/tension failure envelope, which is the locus of points in stress space corresponding to catastrophic failure (indicated by a large drop in load carrying capacity (see Fig. 8), is given in Fig. 16. These points can be connected by a representative curve, as indicated, that is parabolic, although careful observation reveals that there seems to be a compressive load limit and a tensile load limit. This implies that there exists a small range of

646 S. Ching Quek et al. / International Journal of Non-Linear Mechanics 39 (2004) 635 648 2.50 x (inches) vs y (inches) 2.25 c/t = 5.0 c/t = 4.0 c/t = 2.0 2.00 x / compression (mm) 1.75 1.50 1.25 1.00 0.75 c/t = 1.0 c/t = 0.91 c/t = 0.83 c/t = 0.67 c/t = 0.59 0.50 0.25 0.00 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 y / tension (mm) Fig. 15. Displacement ratios used in biaxial test matrix and corresponding failure points in displacement space. 4.0E +08 3.5E +08 A Compressive Load Limit e Stress, σ x (N /m 2 ) Compressiv 3.0E +08 2.5E +08 2.0E +08 1.5E +08 1.0E +08 B Pre-failure region Interaction Regime Post failure region C D Tensile Load Limit 5.0E +07 E 0.0E +00 0.0E+00 2.0E+07 4.0E+07 6.0E+07 8.0E+07 1.0E+08 1.2E+08 Tensile Stress, σ y (N/m 2 ) Fig. 16. Failure envelope of biaxial tests for 45 =0 = +45 CTBC in stress space.

S. Ching Quek et al. / International Journal of Non-Linear Mechanics 39 (2004) 635 648 647 Fig. 17. Failure patterns in specimens observed at dierent load type as indicated in Fig. 16. compressive/tensile load combinations that are not aected by load biaxiality. Instead, there is an upper bound for the compressive strength controlled by tow buckling and a lower bound for the tensile strength that is limited by the critical matrix tensile cracking strain. Typical failure patterns for dierent loading ratios are shown in Fig. 17 (images a e). 4. Concluding remarks The experimental results that we have presented clearly identify the failure mechanisms and how remote loads inuence these mechanisms. In particular, the mode of failure for braided composites (under biaxial stress states) involve distributed matrix cracking (DMC), and local loss of stability due to tow buckling, which precipitates braid/matrix interfacial failure (BMI). These mechanisms cause the release of internal strain energy. The damage zone is usually localized and causes the specimen to loose structural integrity. For compression-dominated situations, there is an upper bound on the compressive strength and this can be obtained by a uniaxial compression test. For pure tension loading, the matrix cracking strain limits the tensile strength. DMC leads to gradual softening, which ultimately leads to catastrophic failure. For DMC, the relevant quantities that are important for characterizing the energy released are the matrix tensile cracking strain and the matrix fracture energy, while for BMI, the relevant quantities are local stability of the microstructure and the interfacial ber/matrix fracture energy. In the case of pure compression, DMC is absent, instead tow buckling and tow kinking along with matrix inelasticity are the dominant modes of failure. When the tows buckle, the tow/interface fails (BMI) and this mechanism releases energy. A micromechanics based nite element model is developed in the second part of this two part paper. This model, which is a mechanism based approach to predicting failure, will be shown to predict the failure initiation envelope quite well.

648 S. Ching Quek et al. / International Journal of Non-Linear Mechanics 39 (2004) 635 648 Acknowledgements SQ and AMW are grateful for the nancial sponsorship of the Automotive Composites Consortium, Energy Management Working Group, and the Department of Aerospace Engineering, University of Michigan. The authors acknowledge that this research was supported, in whole or in part, by Department of Energy cooperative agreement no. DE-FC05-95OR22363. Such support does not constitute an endorsement by the Department of Energy of the views expressed herein. References [1] P.H. Thornton, R. Jeryan, Crash energy management in composite automotive structures, Int. J. Impact Eng. 7 (1988) 167 180. [2] D. Hull, A unied approach to progressive crushing of bre-reinforced composite tubes, Comput. Sci. Technol. 40 (1991) 377 421. [3] S.C. Quek, A.M. Waas, J. Homan, V. Agaram, The crushing response of braided and CSM glass reinforced composite tubes, J. Composite Struct. 52 (2001) 103 112. [4] F. Chen, Waas, H.K. Plummer, Jr., A.M. Waas, Computer generated Youngs fringe phase shift microscopic digital speckle photography, Proceedings of the Society Experimental Mechanics Summer Meeting, Seattle, WA, 1996 (see also US Patent #5,920,383 and #6,189,386). [5] A.R. Khamseh, A.M. Waas, Failure mechanisms of uniply composite plates with a circular hole under static compressive loading, ASME Trans. J. Eng. Mater. Technol. 114 (1992) 304 310. [6] A.R. Khamseh, A.M. Waas, Failure mechanisms of graphite/epoxy laminated composites under biaxial planar compression, ASME Trans. J. Eng. Mater. Technol. 119 (1996) 56 64. [7] A. Makinde, L. Thibodeau, K.W. Neale, Development of an apparatus for biaxial testing using cruciformspecimens, Experimental Mech. 32 (2) (1992) 138 144. [8] A. Makinde, K.W. Neale, Z. Sacharuk, A strain-based parametric biaxial failure criterion for ber-reinforced composites, Polym. Composites 13 (4) (1992) 263 272. [9] S. Demmerle, J.P. Boehler, Optimal design of biaxial tensile cruciformspecimens, J. Mech. Phys. Solids 41 (1) (1993) 143 181. [10] A.R. Khamseh, A.M. Waas, Failure mechanisms of composite plates with a circular hole under remote biaxial planar compressive loads, J. Eng. Mater. Technol. 119 (1997) 56 64. [11] J.S. Welsh, J.S. Mayes, C.T. Key, Damage initiation in glass fabric composites Proceedings of the 43rd AIAA 2002 SDM Conference, AIAA 2002, Washington, D.C., 1742.