L Mingshuang et al. / Materials Science and Engineering A 489(2008)120-126 250 三 2D-C/Sic Fig 4. The typical true stress vs time curve of the 2D-C/SiC composites under Fig. 2. The failure strength vs. logarithm strain rate curve of 2D-C/SiC com- dynamic compression. that the stress state In the deons of the suss yokgjque is the logarithm of strain rate. Therefore, it can be defined in the As shown in Fig. 5, the elastic modulus varies linearly with following equation neous Clearly some time is needed for the specimen to achieve a homogeneous stress state after first loading. According to Ravichandran and Subhash [9], the homogeneity factor a(t)is Ed= es A ln defined where Ed and es are the elastic modulus at different strain rate a(D)、|o1(t)-02( (2) and referenced elastic modulus, respectively. e and Eo are the a1(t)+a2(1)/2 strain rate and referenced strain rate, respectively. A is a param- where o(t)and o(t) are the mean axial stresses on the inter- eter to be ascertained faces between the specimen and the incident bar as well as the specimen and the transmission bar, respectively. From Fig 3. it 3.2. The Weibull distribution of the dynamic failure strength is clear that the homogeneity factor falls down to 5% when the loading time is 9 us. The stress vs time curve of this specimen The dynamic failure strengths of the 2D-C/SiC compos ites are also scattered at the strain rate of 2800s(as shown 9 us). the stress is about 60 MPa and the strain is about 0. 01. in Fig. 6). The average strength and mean squared error are It accords with the investigation of Sharpe and Hoge [10] 427.5 and 56.7 MPa, respectively. As well be known, the The elastic modulus of the 2D-C/SiC composites under strength of brittle materials tallies with Weibull distribution. For dynamic loading can be calculated from the experimental data. fiber-reinforced ceramic matrix composites, the three basic con- 642 10 8642 Elastic modulus -a % Time /us Fig. 5. The elastic modular vs logarithm strain rate curve of 2D-C/SiC com- Fig3. The typical curve of a-i in the 2D-C/SiC composite sample. posites.122 L. Mingshuang et al. / Materials Science and Engineering A 489 (2008) 120–126 Fig. 2. The failure strength vs. logarithm strain rate curve of 2D-C/SiC com￾posites. One of the basic assumptions of the SHPB technique is that the stress state in the deforming specimen is homoge￾neous. Clearly some time is needed for the specimen to achieve a homogeneous stress state after first loading. According to Ravichandran and Subhash [9], the homogeneity factor α(t) is defined as: α(t) = |σ1(t) − σ2(t)| [σ1(t) + σ2(t)]/2 (2) where σ1(t) and σ2(t) are the mean axial stresses on the inter￾faces between the specimen and the incident bar as well as the specimen and the transmission bar, respectively. From Fig. 3, it is clear that the homogeneity factor falls down to 5% when the loading time is 9 s. The stress vs. time curve of this specimen is shown in Fig. 4. When the stress state reaches homogeneous (t = 9s), the stress is about 60 MPa and the strain is about 0.01. It accords with the investigation of Sharpe and Hoge [10]. The elastic modulus of the 2D-C/SiC composites under dynamic loading can be calculated from the experimental data. Fig. 3. The typical curve of α–t in the 2D-C/SiC composite sample. Fig. 4. The typical true stress vs. time curve of the 2D-C/SiC composites under dynamic compression. As shown in Fig. 5, the elastic modulus varies linearly with the logarithm of strain rate. Therefore, it can be defined in the following equation: Ed = ES + A ln  ε˙ ε˙0  (3) where Ed and ES are the elastic modulus at different strain rate and referenced elastic modulus, respectively. ε˙ and ε˙0 are the strain rate and referenced strain rate, respectively. A is a param￾eter to be ascertained. 3.2. The Weibull distribution of the dynamic failure strength The dynamic failure strengths of the 2D-C/SiC compos￾ites are also scattered at the strain rate of 2800 s−1 (as shown in Fig. 6). The average strength and mean squared error are 427.5 and 56.7 MPa, respectively. As well be known, the strength of brittle materials tallies with Weibull distribution. For fiber-reinforced ceramic matrix composites, the three basic con￾Fig. 5. The elastic modular vs. logarithm strain rate curve of 2D-C/SiC com￾posites.