L Mingshuang et al. /Materials Science and Engineering A 489(2008)120-126 +l# sampl -3# sample 47# sample Fig. 8. The ruptured scratch of the 2D-C/SiC composites under static and 20 10 33. fracture observation 000010020030.040.05006007008 The specimens fail by shearing under static loading while True strain they are shattered to more fragments under dynamic conditions which indicated a multiple fracture mode. Therefore, a pad was ag o. in true suess yvs. stran curves or te -usl composites win the used to limit the compressive strain to about 6%(as shown in Fig. 1). The pictures of the ruptured 2D-C/SiC specimens under stituents(fiber, interphase, and matrix) are essentially brittle and static and dynamic compression are shown in Fig. 8. It can the cracking involves defect-induced random failures. There- be seen that shear fracture angles of the failed specimens are fore, statistical distribution of the strengths for the 2D- C/Sic approximately 500 at the strain rate of 10-4s-, and 550 at the composites can be described by Weibull equation, strain rate of 850s-, respectively. Garland et al. [13]investi gated the development of compressive damage zones in fibrous (4) composites, and the results showed that the magnitude of frac- interface would result in a large shear fracture angle, and weak where F(o)is a probability function; o is the applied stress m, interface induces a small fracture angle. Therefore, it seems that the Weibull modulus, is the most important parameter that char- the increase of fracture angle at the strain rate of 850s-could be acterizes the scatter of the material. The larger the value of m, contributed to the strain rate effect of interface strength, which the better the scatter of the material oo is the scale parameter or has been identified by the experiments made by Bi et al. [14] characteristic strength and the maximum density of the Weibull The observation that larger fracture angle corresponds to ahigher distribution is located at the position of o=oo. It could be found from Fig. 7 that the dynamIc compressive failure strength of 2D. compressive strength in the present study is also consistent with C/SiC composites also obeys Weibull distribution. The slope of the work of Narayanan and Schadler [15], who found a simi- the solid line, corresponding to the Weibull modulus m, and the lar relationship between the fracture angle and the compressive strength. Moreover, it can be clearly seen in Fig. that more shear haracteristic strength oo are 5.27 and 454.6 MPa, respectively. bands exist in the failed composite specimen tested under the The result is consistent with those of 3 D-C/SiC [11]and SiC/Sic strain rate of 850s-l. Obviously, the multiple shear bands could composites [12] improve the toughness of the composites through the forma tion of new failure surfaces under dynamic compressive loading Hence the fracture angle increased at a higher loading rate 1.0 Fig 9 shows the SEM micrographs of the 2D-C/SiC com- posites under static and dynamic compression, which were taken parallel with the loading direction. Compared with the clear rup- tured surface formed at the strain rate of 10-4s-I. the rough ruptured surface at the strain rate of 850s- indicates that more small cracked fiber and matrix fragments generates with the increase of strain rate, which further identified the multiple frac ture characteristic for the 2D-C/SiC composites under higher 2D.C/SiC 3.4. Constitutive model of 2D-C/SiC composites with a strain rate-dependent In(dynamic failure strength) A new continuum damage-mechanics-based constituti model for composite materials was implemented by Nandlall Fig. 7. The Weibull distribution of the 2D-C/SiC composites. et al. [16] in the ballistic response simulation of grP plates,L. Mingshuang et al. / Materials Science and Engineering A 489 (2008) 120–126 123 Fig. 6. The true stress vs. strain curves of the 2D-C/SiC composites with the same strain rate under dynamic compression. stituents (fiber, interphase, and matrix) are essentially brittle and the cracking involves defect-induced random failures. There￾fore, statistical distribution of the strengths for the 2D-C/SiC composites can be described by Weibull equation, F(σ) = 1 − exp −  σ σ0 m (4) where F(σ) is a probability function; σ is the applied stress; m, the Weibull modulus, is the most important parameter that char￾acterizes the scatter of the material. The larger the value of m, the better the scatter of the material. σ0 is the scale parameter or characteristic strength and the maximum density of the Weibull distribution is located at the position of σ = σ0. It could be found from Fig. 7 that the dynamic compressive failure strength of 2D￾C/SiC composites also obeys Weibull distribution. The slope of the solid line, corresponding to the Weibull modulus m, and the characteristic strength σ0 are 5.27 and 454.6 MPa, respectively. The result is consistent with those of 3D-C/SiC[11] and SiC/SiC composites [12]. Fig. 7. The Weibull distribution of the 2D-C/SiC composites. Fig. 8. The ruptured scratch of the 2D-C/SiC composites under static and dynamic compression. 3.3. Fracture observation The specimens fail by shearing under static loading while they are shattered to more fragments under dynamic conditions which indicated a multiple fracture mode. Therefore, a pad was used to limit the compressive strain to about 6% (as shown in Fig. 1). The pictures of the ruptured 2D-C/SiC specimens under static and dynamic compression are shown in Fig. 8. It can be seen that shear fracture angles of the failed specimens are approximately 50◦ at the strain rate of 10−4 s−1, and 55◦ at the strain rate of 850 s−1, respectively. Garland et al. [13] investi￾gated the development of compressive damage zones in fibrous composites, and the results showed that the magnitude of frac￾ture angles depends on the bonding strength of interface. Strong interface would result in a large shear fracture angle, and weak interface induces a small fracture angle. Therefore, it seems that the increase of fracture angle at the strain rate of 850 s−1 could be contributed to the strain rate effect of interface strength, which has been identified by the experiments made by Bi et al. [14]. The observation that larger fracture angle corresponds to a higher compressive strength in the present study is also consistent with the work of Narayanan and Schadler [15], who found a simi￾lar relationship between the fracture angle and the compressive strength. Moreover, it can be clearly seen in Fig. 8 that more shear bands exist in the failed composite specimen tested under the strain rate of 850 s−1. Obviously, the multiple shear bands could improve the toughness of the composites through the forma￾tion of new failure surfaces under dynamic compressive loading. Hence the fracture angle increased at a higher loading rate. Fig. 9 shows the SEM micrographs of the 2D-C/SiC com￾posites under static and dynamic compression, which were taken parallel with the loading direction. Compared with the clear rup￾tured surface formed at the strain rate of 10−4 s−1, the rough ruptured surface at the strain rate of 850 s−1 indicates that more small cracked fiber and matrix fragments generates with the increase of strain rate, which further identified the multiple frac￾ture characteristic for the 2D-C/SiC composites under higher strain rate. 3.4. Constitutive model of 2D-C/SiC composites with a strain rate-dependent A new continuum damage-mechanics-based constitutive model for composite materials was implemented by Nandlall et al. [16] in the ballistic response simulation of GRP plates