L Mingshuang et aL. Materials Science and Engineering A 489(2008)120-126 150y:2 Fig 9. SEM micrographs of the 2D-C/SiC composite ruptured surface under static and dynamic compression. which shown as: Xu et al. [17] presented the parameter n was relative to strain rate. Therefore, a new constitutive model was proposed E(l-D)E J=EE(I-D) where D is the damage parameter, assumed to follow a Weibull distribution where E, D, e and eo have the same meaning as before, while q is a rate-dependent parameter. For the 2D-C/SiC composites, the elastic modulus is linear to the logarithm of strain rate, which is defined as Eq. (3). Thus, where e.s and y are the elastic modulus. failure strain and Eq. (8)can be expressed as strength of the material associated with the damage mod respectively. e is the base of the natural logarithm and the param =E(-D\(a eter n defines the shape of the damage growth curve. However, the meaning of n is not illuminated For 2D-C/SiC composites D=1-exp (-m(y) in the paper, n can be defined as ed= es A ln n=a1+ a2 exp +a2 exp where aj=2.59, a2=13.93, a3=4. 15, as shown in Fig 10 The parameters of the constitutive model are shown Table 1 Fig. 1l compares the constitutive model with experimental data of 2D-C/SiC composites at different strain rate. It is shown 16A hat, the constitutive model agrees with the experimental data very well 3.5. Discussion For 2D-C/SiC composites, most of cracks initiate in the stress concentration center and the pore largely exists in the com- Fitted curve posites. Many microcracks exist due to the different thermal expansion coefficients of the base phase and reinforced pha These cracks will spread and induce brittle failure. Under 8 10 12 14 16 18 he parameters of the 2D-C/SiC composite dynamical constitutive mode Es(GPa) 7.6 360 0.0001 0.31 Fig. 10. The curve of the n vs logarithm strain rate124 L. Mingshuang et al. / Materials Science and Engineering A 489 (2008) 120–126 Fig. 9. SEM micrographs of the 2D-C/SiC composite ruptured surface under static and dynamic compression. which was shown as: σ = E(1 − D)ε (5) where D is the damage parameter, assumed to follow a Weibull distribution: D = 1 − exp  − 1 neEε Y n (6) where E, ε and Y are the elastic modulus, failure strain and strength of the material associated with the damage model, respectively. e is the base of the natural logarithm and the param￾eter n defines the shape of the damage growth curve. However, the meaning of n is not illuminated. For 2D-C/SiC composites in the paper, n can be defined as: n = a1 + a2 exp  −ln(ε/˙ ε˙0) a3  (7) where a1 = 2.59, a2 = 13.93, a3 = 4.15, as shown in Fig. 10. Fig. 10. The curve of the n vs. logarithm strain rate. Xu et al. [17] presented the parameter n was relative to strain rate. Therefore, a new constitutive model was proposed: σ = Eε(1 − D)  ε˙ ε˙0 q (8) where E, D, ε˙ and ε˙0 have the same meaning as before, while q is a rate-dependent parameter. For the 2D-C/SiC composites, the elastic modulus is linear to the logarithm of strain rate, which is defined as Eq. (3). Thus, Eq. (8) can be expressed as: ⎧ ⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨ ⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩ σ = Edε(1 − D)  ε˙ ε˙0 q D = 1 − exp  − 1 neEdε Y n Ed = ES + A ln  ε˙ ε˙0  n = a1 + a2 exp  −ln(ε/˙ ε˙0) a3  (9) The parameters of the constitutive model are shown in Table 1. Fig. 11 compares the constitutive model with experimental data of 2D-C/SiC composites at different strain rate. It is shown that, the constitutive model agrees with the experimental data very well. 3.5. Discussion For 2D-C/SiC composites, most of cracks initiate in the stress concentration center and the pore largely exists in the com￾posites. Many microcracks exist due to the different thermal expansion coefficients of the base phase and reinforced phase. These cracks will spread and induce brittle failure. Under high Table 1 The parameters of the 2D-C/SiC composite dynamical constitutive model Es (GPa) Y (MPa) ε˙0 (s−1) q A 7.6 360 0.0001 0.01 0.31