SCIENCE CHINA Physics, Mechanics & Astronomy

SCIENCE CHINA Physics, Mechanics & Astronomy Article March 2014 Vol.57 No.3: 501 511 doi: 10.1007/s11433-013-5197-z Structural effects of three-dimensional angle-interlock woven composite undergoing bending cyclic loading JIN LiMin, YAO Yao, YU YiMin, ROTICH Gideon, SUN BaoZhong & GU BoHong * College of Textiles, Key Laboratory of High-performance Fibers & Products, Ministry of Education, Donghua University, Shanghai 201620, China Received May 6, 2012; accepted September 5, 2012; published online October 29, 2013 This paper reports the structural effects of three-dimensional (3-D) angle-interlock woven composite (3DAWC) undergoing three-point bending cyclic loading from experimental and finite element analysis (FEA) approaches. In experiment, the fatigue tests were conducted to measure the bending deflection and to observe the damage morphologies. By the FEA approach, a micro-structural unit-cell model of the 3DAWC was established at the yarn level to simulate the fatigue damage. The stress degradation at the loading condition of constant deformation amplitude was calculated to show the degradation of mechanical properties. In addition, the stress distribution, fatigue damage evolution and critical damage regions were also obtained to qualitatively reveal the structural effects and damage mechanisms of the 3DAWC subjected to three-point bending cyclic loading. three-dimensional angle-interlock woven composite (3DAWC), three-point bending fatigue, microstructure model, finite element analysis (FEA) PACS number(s): 46.50.+a, 81.05.Ni, 02.70.Dh Citation: Jin L M, Yao Y, Yu Y M, et al. Structural effects of three-dimensional angle-interlock woven composite undergoing bending cyclic loading. Sci China-Phys Mech Astron, 2014, 57: 501 511, doi: 10.1007/s11433-013-5197-z 1 Introduction *Corresponding author (email: gubh@dhu.edu.cn) Due to the high inter-layer strength and fracture toughness, three-dimensional (3-D) textile structural composites (3DTSCs) have been widely applied for structural engineering in recent years [1 3]. As one type of fabric reinforcement for the 3DTSCs, 3-D angle-interlock woven fabrics (3DAWFs) are manufactured with angle interlock weaving technique in which yarns are placed at an angle to the thickness direction to resist de-lamination. The 3-D angle-interlock woven composites (3DAWCs) which are reinforced with the 3DAWFs, have attracted growing interest in engineering applications. This is due to their easy and efficient processing in the traditional looms, high de-lamination resistance along the through-thickness direction owing to the special interlaced structure of the warp and weft yarns between adjacent layers [4]. As one of the important issues for composite materials in structural applications, the analysis of fatigue resistance is widely employed because of the requirement for safe applications. Due to the excellent performance and wide range of potential applications of the 3DTSCs such as 3DAWCs, it is valuable to study the fatigue behavior of such types of engineering materials. However, most research has been conducted on the 2D textile composite materials so far. Van Paepegem et al. [5] presented a phenomenological residual stiffness model to predict both the stiffness degradation and the failure of plain-weave glass/epoxy specimens. Huang et al. [6] established a bridging micromechanics model to simulate the ultimate failure strengths of different textile composite laminates subjected to fatigue loads. Hochard et al. [7] developed a non-linear cumulative damage model for woven ply laminates under static and fatigue loads based on Science China Press and Springer-Verlag Berlin Heidelberg 2013 phys.scichina.com link.springer.com

502 Jin L M, et al. Sci China-Phys Mech Astron March (2014) Vol. 57 No. 3 a continuum damage approach (CDA) and a non-local fiber rupture criterion. More recently, Hochard et al. [8] developed a generalized non-linear cumulative damage model for woven ply laminates subjected to static and fatigue loads. The damage, consisting of cracks running parallel to the fibers, leads to a loss of stiffness in the warp, weft and shear directions. As for the 3DAWCs, Gowayed et al. [9] developed a model which was established from a mathematical model to analyze the fatigue behavior and life of angle-interlock carbon fiber/epoxy composites and the obtained results were in good agreement with experimental data. Tsai et al. [10] conducted a comparative study on the fatigue properties and damage processes between untouched three-layer and five-layer of 3DAWC plates under tensile cyclic loading. The fatigue damage mechanisms primarily involved transverse cracks in the warp yarns, debonding between the warp and weft yarns, debonding extension and deflection into the matrix, and weft fiber breakages. However, the bending fatigue behavior of the 3DAWCs has not been well investigated so far. Moreover, for the 3DTSCs undergoing fatigue cases such as the cyclic loading modes of tension-tension, compression-compression, bending and tension-compression, it is worth mentioning that all the 3DTSCs have a normal series of fatigue damage behavior, including the damage of yarns, matrix and yarns-matrix interface debonding. However, considering the 3DTSCs can be divided into 3D woven, braided and knitted composites according to the categories of reinforcements, each of them will show the distinctive damage behavior in the cases of long-term cyclic loading. This is mainly determined by their distinct structural characteristics. In other words, the fatigue damage behavior of one specific type of 3DTSCs is mainly dominated by its structure. It is very important to know how the structure of composite affects its mechanical responses under cyclic loading, i.e., structural effects. The purpose of this paper is to qualitatively investigate the structural effects of the 3DAWC under three-point bending cyclic loading condition. The study was presented by fatigue tests and finite element analysis (FEA). A micro-structural unit-cell model at yarn level of the 3DAWC has been established to qualitatively analyze the fatigue damage. The stress degradation and damage morphologies were calculated and compared with those in experiments. In addition, the stress distribution, fatigue damage of yarns and resin, debonding propagation of yarns-resin interface, and the critical damage regions in the 3DAWC structure have also been discussed. woven in high-silica glass filaments. Its specifications are listed in Table 1. The sketch diagram of the 3DAWF structure is shown in Figure 2. It indicates that the 3DAWF construction is composed of two kinds of yarn systems, i.e., warp and weft yarns. It presents a layer-to-layer angle-interlocking structure where the weft yarns are almost straight. The two adjacent undulated warp yarns in a single layer display a converse undulation form to ensure the two adjacent layers of non-crimp weft yarns are held together to form a stable and integrated woven construction. Such a structure imparts both the higher stiffness and strength along the thickness direction and in-plane direction for the 3DAWF reinforced composites. Energy will propagate to the large area of the composite plates with high stress wave velocity in the cases of high strain rates or impact loading conditions [11,12]. Vacuum assisted resin transfer molding technique (VARTM) was employed to manufacture the 3DAWC plate. The applied resin and curing agent were AROPOL TM INF 80501-50 polyester resin manufactured by Ashland Composite Polymers China and AKZO M-50, respectively. Their proportion was 100:1.5 by weight. After that, the 3DAWC coupon presented in Figure 3 was cut with high-pressure water jet along the longitudinal and transverse directions of the composite plate. The longitudinal direction of each coupon was aligned with the weft yarns. The size (length width Figure 1 (Color online) Photographs of the 3DAWF. (a) Surface; (b) cross section. Table 1 Specifications of the 3DAWF Yarns Warp Weft Fiber type silicon dioxide fiber tows silicon dioxide fiber tows Linear density (Tex) Density (ends/cm) layers 440 1 10 10 440 2 4 11 2 Materials and bending fatigue tests 2.1 Materials Figure 1 shows the surface and cross-section of the 3DAWF Figure 2 (Color online) Sketch of the 3DAWF construction.

Jin L M, et al. Sci China-Phys Mech Astron March (2014) Vol. 57 No. 3 503 thickness) of each coupon was 200 mm 20 mm 8.4 mm. And the fiber volume fraction was approximately 54%. The material parameters of the glass-fiber tows and resin are listed in Table 2. 2.2 Quasi-static and bending fatigue tests The quasi-static three-point bending tests were performed on a MTS 810.23 material tester at the speed of 5 mm/min. As shown in Figure 4, one indenting roller and two supporting rollers with the same size of 20 mm 70 mm (diameter length) were employed for testing. The indenting roller was located at the centre of the top surface of the tested coupon. Three specimens were tested to obtain average results. The obtained average bending modulus (E f ), ultimate stress ( ult ) and deflection (D) of the 3DAWC were 19.51 GPa, 160.75 MPa and 8.89 mm, respectively. The three-point bending fatigue tests were also conducted on the MTS 810.23 system. A sinusoidal wave form cyclic loading of 2 Hz corresponds to a stress ratio R (the ratio of the minimum stress S min to the maximum stress S max in one cycle) of 0.1 was applied on the coupons. The tests were performed under two stress levels S max / ult (the ratio of the applied maximum stress S max in one cycle to the ultimate static bending stress ult of the composite coupon), i.e., 70% and 60%. 3.1 Microstructure model of the 3DAWC As the paper aims to obtain the critical damage regions in the 3DAWC structure to qualitatively summarize the structural effects and fatigue damage propagation of the 3DAWC structure under three-point bending cyclic loading, and simultaneously to save FEA computational time, one basic micro-structural unit-cell model of the 3DAWC was created, which will give the representative mechanical responses of the 3DAWC structure subjected to the three-point bending cyclic loading. As shown in Figures 5(a) (c), the microstructure models for the resin, warp and weft yarns were established. The entire geometrical microstructure model of the 3DAWC is shown in Figure 6. 3.2 Finite element model of the 3DAWC under bending cyclic loading The finite element model of the 3DAWC under three-point bending fatigue cyclic loading was established and shown in Figure 7. The detailed information on construction of the model is as follows: 3 Finite element analyses (FEA) FEA was conducted on the commercial available finite element software package ABAQUS/Standard (Ver. 6.10), module of Direct Cyclic. The OS platform was Windows XP. Figure 4 (Color online) Three-point bending fatigue testing (unit: mm). Figure 3 (Color online) 3DAWC coupon for testing. (a) Surface; (b) cross section Table 2 Material constants of glass-fiber and resin Material E Density Yield stress Plastic ν (GPa) (g/cm 3 ) (MPa) strain (%) Glass-fiber 70 0.20 1.44 2200 2.1 Resin 3.65 0.35 1.36 146 3.2 Figure 5 (Color online) Microstructure model of each system in the 3DAWC. (a) Resin; (b) warp yarns; (c) weft yarns.

504 Jin L M, et al. Sci China-Phys Mech Astron March (2014) Vol. 57 No. 3 surfaces. The contact between the roller surface and the bottom surface of resin was defined as TIE CONTACT. (3) Boundary and loading conditions. The rollers were treated as RIGID bodies with no freedom degree of displacement and rotation. As for the loading conditions, as presented in Figure 8, the displacement loading condition in the form of eq. (1) was applied at the central part of the top surface of the 3DAWC. f 0.5 0.1sin8 t (1) where f is the displacement boundary condition, t is the time, and f is in the range from 0.4 to 0.6. (4) Mesh. As shown in Figure 9, the rollers and each component of the 3DAWC were meshed with the technique of coincidence of nodes. The element numbers of the rollers, resin, warp yarns and weft yarns were 1536, 38566, 5760 and 8960, respectively. 3.3 Fatigue damage criteria 3.3.1 Damage initiation and evolution of material [13] For the micro-structure model of the 3DAWC, the yarns were glass fiber tows, and the matrix was polyester resin. Both of them were assumed as elastic-plastic materials. For the elastic-plastic materials under cyclic bending loading condition, as shown in Figure 10, the curve of bending load Figure 6 (Color online) Microstructure model of the 3DAWC. (a) Front view; (b) back view; (c) cross-section. Table 3 Specifications of roller E (GPa) ν Density (g/cm 3 ) 200 0.30 7.81 Figure 7 (Color online) Finite element model for the 3DAWC undergoing bending cyclic loading. (1) Specifications of materials. The specifications of glass-fiber and resin are listed in Table 2. The constants of roller are presented in Table 3. (2) Interaction condition. By the definition of materials contact, the interaction between the resin and the yarns was defined as SURFACE TO SURFACE CONTACT with the BONDING condition of limit bonding to slave nodes set in yarns, where the surface of resin was the master surface and the surfaces of warp and weft yarns were the slave Figure 8 Figure 9 nodes). Loading condition with constant displacement amplitude. (Color online) Mesh scheme of the model (coincidence of the

Jin L M, et al. Sci China-Phys Mech Astron March (2014) Vol. 57 No. 3 505 Figure 11 Three types of modes for the inter-laminar fracture. Figure 10 Typical hysteresis loop for material under bending loading. versus deflection per cycle is a closure loop, whose area W represents the inelastic hysteresis energy as presented as: W Pds, (2) where P is the applied cyclic load to the tested specimen, and s is the corresponding deflection. Herein, the damage initiation criterion for the material undergoing fatigue loading is characterized by the accumulated inelastic hysteresis energy per cycle W which is presented as: N k W (3) m1 0 1, where N 0 is the number of cycles in which damage is initiated, and k 1 and m 1 are material constants. Once the damage initiation criterion is satisfied for the material under fatigue cyclic loading condition, the damage state is calculated and updated based on the inelastic hysteresis energy for the stabilized cycle. As presented in eq. (4), the degradation of the elastic stiffness can be modeled using the scalar damage variable, D. Therefore, the rate of the damage in a material per cycle d D is also calculated dn based on the accumulated inelastic hysteresis energy W: d D k W m2 2 / L dn (4) where k 2 and m 2 are material constants, L is the characteristic length, and D is in the range of 0 to1. Typically, a material has completely lost its load carrying capacity when D=1. 3.3.2 Initiation and evolution of interface debonding (1) The yarns-resin interface fracture mode for the 3DAWC. As shown in Figure 11, according to the different loading conditions, there are three types of basic modes for the material inter-laminar fracture/debonding, which are in terms of mode 1 (open mode), mode 2 (slide mode) and mode 3 (twist mode), respectively. Among them, modes 1 and 2 belong to in-plane fracture/debonding, and mode 3 belongs to out-of-plane fracture. Given the structure of the 3DAWC (see Figure 7) and the loading condition of three-point bending into account, the layers near the top surface of the 3DAWC coupon are mainly subjected to the compression loading, while those near the bottom surface mainly undergo the tensile loading condition. The different loading magnitudes among different layers along the thickness direction result in the difference in interlayer stress, incorporated with the breaking strain of yarns being smaller than that of the resin. All of these factors may cause the resin-yarns interface debonding. Therefore, it can be concluded that debonding modes at the warp/weft yarns-resin interface belong to the mixed mode, including modes 1 and 2. (2) Onset and growth of interface debonding [13 15]. As presented in eqs. (5) and (6) respectively, the onset and growth of interface debonding under fatigue loading are both characterized by using the Paris-law [14], which relates the relative fracture energy release rate G in eq. (7), to d a interface debonding growth rates. dn N 1.0, c2 c G (5) 1 da c4 c3 G, dn (6) 2 max min max (1 ), G G G G R (7) where N is the number of cycles to initialize the debonding, C 1, C 2, C 3, C 4 are the Paris-law coefficients, a is the debonding length, N is the number of cycles, G max and G min correspond to the strain energy release rates when the structure is loaded up to the maximum load P max and minimum load P min within each fatigue cycle, respectively. R is defined as the ratio of minimum load P min to maximum load P max. For the debonding initiation and propagation under fatigue loading conditions, the corresponding curve of d a dn versus G is shown in Figure 12. Wherein the Paris regime is bounded by the energy re-

506 Jin L M, et al. Sci China-Phys Mech Astron March (2014) Vol. 57 No. 3 Table 4 Parameters for material damage simulation Material k 1 k 2 m 1 m 2 L(mm) Glass-fiber tow 0.02 1.67 10 4 1.14 0.15 0.125 Resin 0.01 2.97 10 5 2.24 0.20 0.125 Table 5 Cohesive parameters for the interface between fiber tows and resin C 1 C 2 C 3 C 4 G Ic (N/mm) G IIc (N/mm) 0.02 1.25 0.08 6.82 0.2 1.0 1.2 during bending fatigue testing, the Deflection Index versus Number of Cycles (F-N) curve of the 3DAWC during the test under the stress level of 70% (number of cycles at the ultimate failure: 90771) is shown in Figure 13. The Deflection Index (F) is defined in terms of the deflection of tested sample as presented follow: Figure 12 Fatigue crack growth governed by Paris law [14,15]. lease rate threshold G thresh and the energy release rate upper limit G pl. Below G thresh, there is no fatigue debonding initiation or growth. And above G pl, the fatigue debonding will grow at an accelerated rate. G equivc is the critical equivalent fracture energy release rate calculated based on the mixed mode criterion and the bond strength of the interface. The B-K law presented by Benzeggagh and Kenane was utilized to obtain G equivc as shown follow [15]: GII GIII GequivC GIC ( GIIC GIC ) GI GII G (8) III where G IC and G IIC are the critical fracture energy release rates under mode 1 and mode 2, respectively. G I, G II and G III are the fracture energy release rates under mode 1, mode 2 and mode 3, respectively. And is B-K law parameter. 3.3.3 Basic assumptions The objective of this paper is to understand the locations of critical damage regions in the 3DAWC structure, to qualitatively characterize the structural effects. Moreover, the parameters mentioned in sects. 3.3.1 and 3.3.2 just affect the speed of damage/de-bonding initiation and propagation according to eqs. (3) (8), i.e., their main functions are supposed to show the specific locations of damage regions by the FEA calculation procedure. Therefore, these parameters were assumed and listed in Tables 4 and 5, which will not affect the qualitative characterization results. And the values of G thresh /G equivc and G pl /G equivc were set to 0.02 and 0.80, respectively. F f d, (9) fu where f d is the deflection of the material during fatigue test, f u is the ultimate deflection of the material after fatigue test. F is in the range between 0 and 1. It is observed in Figure 13 that the sharp increase in F during a few testing cycles corresponds to the cycle intervals of 0 2500 and 85000 90771, while a slow continuous increase in F during a large number of cycles corresponds to the cycle intervals of 2500 85000. This is due to the cumulative fatigue damage and special damage mechanisms (see sect. 4.5) of the 3DAWC during the above three cycle intervals. For the calculation results from the finite element model, the Stress-N curve of one node located at the loading region is shown in Figure 14. It is found that the stress decreases with the increase of the number of cycles. And significantly, there is a sharp decrease in stress during a few number of testing cycles corresponding to the cycle intervals of 0 10. This indicates a slow continuous decrease in stress during a large number of cycles corresponding to the cycle interval 4 Results and discussions 4.1 Stress degradation In order to describe the deformation process of the 3DAWC Figure 13 Deflection index of the 3DAWC during fatigue loading under stress level of 70% (numbers of cycles to failure: 90771).

Jin L M, et al. Sci China-Phys Mech Astron 4.2 Figure 14 loading. Stress degradation for the 3DAWC under bending cyclic of 10 100. The variation of F for the specimen during testing is based on the constant stress level, amplitude, and the variation of stress for the model which is on the basis of constant deformation amplitude. Although they are different loading modes, both of them are the characterization of results for the cumulative damage of 3DAWC under the three-point bending cyclic loading, i.e., a severe degradation of mechanical properties of the composite is generated during the initial and final several cycles but a slow continuous degradation during the large number of mid-term cycles. Therefore, there is a qualitative agreement between the experiment and calculation results. Figure 16 March (2014) Vol. 57 No. 3 507 Stress distribution in the 3DAWC structure In order to obtain the stress distribution and to illustrate the structural functions of the 3DAWC undergoing three-point bending cyclic loading, several specific nodes as presented in Figure 15 were selected and their Stress-N curves are shown in Figure 16. At the right half side region of the model, there are 4 (T-wf-A, B, C and D) and 3 (H-wf-A, B and C) nodes belonging to the weft (wf) yarns along the thickness (T) and horizontal (H) directions, respectively. In order to illustrate the distribution of load-carrying magnitude in different layers of the 3DAWC, the stress variation in nodes T-wf-A, B, C and D are compared and presented in Figure 16(a). The depicted mean peak stress values in the 4 nodes are in the form: ST-wf-A >ST-wf-D >ST-wf-B >ST-wf-C. This indicates that the top and bottom layers bear most of the applied load during the bending cyclic loading, while the second and third layers bear the minimum amount of loads. As for the horizontal (H) direction, the comparison of stress among the 3 nodes H-wf-A, B and C is presented in Figure 15 (Color online) Specific nodes located in the model of 3DAWC. (Color online) Stress variation comparison in the specific nodes ((a) (d)).

508 Jin L M, et al. Sci China-Phys Mech Astron March (2014) Vol. 57 No. 3 Figure 16(b). It depicts the mean peak stress values in the 3 nodes in the form: S H-wf-A >S H-wf-B >S H-wf-C. This indicates that the central part of the composite bears more loads than the other regions during the three-point bending cyclic loading. In addition, in order to obtain the stress distribution in different components of the 3DAWC, i.e., resin, weft yarns and warp yarns, the comparison of stress variation in those nodes wp-1, 2, wf-1,2 and re-1, 2 respectively belonging to warp (wp) yarn, weft (wf) yarn and resin (re), at different regions along the horizontal direction are shown in Figures 16(c) and (d), respectively. Both of them depict the mean peak stress values in the 3 nodes in the form: S wp >S wf >S re. It indicates that the yarns system bears the maximum amount of load, while the warp yarns bear more loads than the weft yarns, and the resin bears the minimum amount of loads. Therefore, for the structure of the 3DAWC, the reinforcement system of the 3DAWF is the main load-carrying part, and since the warp yarns run through the thickness direction, they carry a large percentage of loads. 4.3 Damage evolution Considering the different fluctuating modes of warp yarns existing between the front and back surfaces of the 3DAWC, the fatigue damage evolution on the front and back surfaces of the 3DAWC model under bending cyclic loading are shown in Figures 17(a) and (b), respectively. For the front surface, it can be shown that the damage began to occur at the time of 1.25 s when the number of cycles was 5. The damage was dominated by the breakage of the warp yarn near the top surface of the 3DAWC and resin damage at the yarns-resin interfaces. Then, the damages continued to propagate at the critical regions of high stress concentration where they bear the most amounts of loads. For the back surface, it is found that the breakages of weft yarns and resin damage at the layers near the top and bottom surfaces of the 3DAWC dominate the damage mode. More importantly, the interface debonding between the resin and warp yarn near bottom surface occurred after the time of 5 s while the number of cycles was 20. After that, this type of interface cracking dominated the damage at the back surface of the 3DAWC structure. According to the phenomena mentioned above, it is found that there is a difference on the dominant damage modes between the front and back surfaces, i.e., the yarn breakages and resin damage on the front surface and the warp yarn-resin interface debonding and resin damage on the back surface. It is also found that the debonding does not easily occur at the weft yarns-resin interface because of the special structure of the 3DAWC and loading mode. 4.4 Critical damage regions Figure 18 shows the damage of the 3DAWC coupon under the stress levels of 60% and 70%. It is found that the yarns transversing breakages at specific locations dominate the damage of the 3DAWC under bending fatigue loading. The simulated result is presented in Figure 19. Good agreement is obtained. It is found that the above mentioned specific locations belong to the warp yarn near the top surface of the 3DAWC, and near the applied load area, i.e., the central part of the top surface in the 3DAWC. In order to find the critical damage regions for the structure of the 3DAWC under bending fatigue loading condition, the final damage status of the model is shown in Figure 20. Owing to the consideration of symmetry, the damaged regions in the half part of the model are presented here. For the front view of the model shown in Figure 20(a), 10 damaged regions signed as wp-1, 2, 3, 4, 5 in warp yarns and Figure 17 (Color online) Damage evolution of the 3DAWC. (a) Front surface; (b) back surface.

Jin L M, et al. Sci China-Phys Mech Astron March (2014) Vol. 57 No. 3 509 Figure 18 (Color online) Damaged 3DAWC coupons under bending fatigue tests. (a) Stress level of 60%; (b) stress level of 70%. Figure 19 (Color online) Simulated damage of yarns in the 3DAWC. wf-1, 2, 3, 4, 5 in weft yarns are taken into account. It is found that all the damaged regions are located at the corners of warp yarn-resin-weft yarn interfaces, and the number of damaged regions in the different layers along the thickness direction is different, where 4 damaged regions (wp-1, 2, 3 and wf-1), 2 damaged regions (wp-4 and wf-2), 1 damaged region (wf-3) and 3 damaged regions (wp-5 and wf-4, 5) belong to layer 1, 2, 3 and 4, respectively. This phenomenon is consistent with the result indicated in Figure 16, i.e., the mean stress values in layers of 1, 2, 3 and 4 meet the relationship below: S 1 >S 4 >S 2 >S 3. As for the back view of the model presented in Figure 20(b), 3 damaged regions shown as wp-6 in warp yarns and wf-6, 7 in weft yarns are taken into account. It is found that the damaged regions mainly are located at the weft yarns in layers of 1 and 4. Together with the interface debonding occurring at the region which is near the bottom surface of the 3DAWC (see Figure 17(b)), they compose the main damage mode in the back surface. In addition, as shown in Figure 20(c), 8 damaged regions in the resin shown as re-1, 2, 3, 4, 5, 6, 7, 8 are taken into account. It is found that these damaged regions mainly are located at the interfaces between the resin and yarns, indicating that the stress concentration is easily generated at these regions. All of these regions in warp, weft yarns and

510 Jin L M, et al. Sci China-Phys Mech Astron March (2014) Vol. 57 No. 3 Figure 20 (Color online) Critical regions for the 3DAWC under bending cyclic loading. (a) Front view; (b) back view; (c) resin; (d) experimental results. resin are the main critical regions for the structure of the 3DAWC under three-point bending fatigue loading. The phenomena mentioned in Figures 20(a), (b) and (c) is consistent with the experimental investigation which is presented in Figure 20(d). All of these are due to the three-point bending cyclic loading condition and the special structure of the 3DAWC. Taking these factors into consideration, the layers near the top surface of the 3DAWC mainly are subjected to compression loading, while those near the bottom surface mainly experienced tensile loads under the bending testing condition. Besides, the difference of the loading magnitudes in different layers along the thickness direction has resulted in different interlayer stresses, which may cause the debonding between the resin and yarns on their interface, and such cracks easily initiate and propagate at the regions of maximum load-carrying. 4.5 Fatigue damage mechanisms According to the testing and simulation results and taking the structure of the 3DAWC into account, the three-point bending fatigue damage mechanisms of the 3DAWC can be summarized into 3 steps below. Stage 1, as the bending cyclic load was applied on the top surface of the 3DAWC, simultaneously, the top surface and bottom surface of the 3DAWC experienced the compressive and tensile loads, respectively. The cracking of warp yarns and resin damage were generated at the critical damage regions after a small number of testing cycles. This process resulted in a sharp degradation of mechanical load-carrying performance of the composite and therefore a sharp increase of deformation. The above mentioned damages continued to propagate slowly into the inner layers of the composite due to the stress concentration when the damage process entered Stage 2. At this stage, with the increase of testing cycles and due to the different interlayer stress, the debonding on the resin-warp yarn interface near the bottom surface of the 3DAWC which is subjected to the maximum interface stress initiated and propagated. Such interface cracks and the slow damage growth of the resin and yarns dominated the cumulative fatigue damage at Stage 2. This stage involved more

Jin L M, et al. Sci China-Phys Mech Astron March (2014) Vol. 57 No. 3 511 cycles, which led to the progressive tiny degradation of mechanical properties of the 3DAWC and a small continuous increase of deformation. With further testing cycles, Stage 3 occurred. It corresponded to the progressive breakages of yarns until the ultimate failure at the outer surface layers of the 3DAWC. The ultimate fatigue failure of the composite may have taken place at this stage with a small increase in the number of cycles. This stage took a short period of testing time and corresponded to a sharp increase of deformation. 5 Conclusions The structural effects of the 3DAWC undergoing threepoint bending cyclic loading were qualitatively studied in experiments and FEA approaches. In experimental approach, the fatigue tests were conducted to measure the deflection variation of the composite during the testing process and to observe the damage morphologies. In the FEA approach, a micro-structure unit-cell model of the 3DAWC under threepoint bending fatigue loading was established to simulate the damage process. From the comparisons of the degradation of mechanical parameters and damage morphologies between experiment and FEA results, good agreements were obtained. The cumulative fatigue damage of the 3DAWC under three- point bending cyclic loading can be divided into 3 distinct stages, i.e., a severe degradation of mechanical properties of the composite is generated during the initial and final several cycles but a slow continuous degradation during the large number of mid-term testing cycles. The special structure of the 3DAWC and three-point bending cyclic loading conditions induce the characteristic stress distributions along the thickness and horizontal directions. The yarn system carries the maximum amount of loads. Therefore, for the structure of the 3DAWC, the reinforcement system of the 3DAWF is the main load-carrying part, and since the warp yarns run through the thickness direction, they carry a large percentage of loads. In addition, the special structure of the 3DAWC also leads to the critical damage regions of stress concentration. The transverse breakages of yarns at specific locations dominate the damage of the 3DAWC under bending fatigue loading. All the damaged regions are located at the corners of warp yarn-resin-weft yarn interfaces, indicating that the stress concentration is easily generated at these regions. All of these regions in warp, weft yarns and resin are the main critical damage regions for the structure of the 3DAWC under three-point bending cyclic loading. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11072058 and 11272087), the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 201056), Shanghai Rising-Star Program (Grant No. 11QH1400100), the Fundamental Research Funds for the Central Universities of China and Special Excellent Ph.D International Visit Program by Donghua University (Grant No. 102552011003). 1 Hu H, Zhang M X, Fangueiro R, et al. Mechanical properties of composite materials made of 3D stitched woven-knitted preforms. J Comp Mater, 2010, 44(14): 1753 1767 2 Ding Y Q, Yan Y, McIlhagger R, et al. Comparison of the fatigue behavior of 2-D and 3-D woven fabric reinforced composites. J Mater Process Tech, 1995, 55: 171 177 3 Hu J. 3-D Fibrous Assemblies: Properties, Applications and Modelling of Three-Dimensional Textile Structures. Woodhead Publishing Limited, 2008. 1 32 4 Bigaud D, Dreano L, Hamelin P. 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