H. Ismar, F Streicher Computational Materials Science 16(1999)17-24 tension in that direction the fiber-matrix inter- face is loaded by compressive stress normal to the fiber surface m=8 After the cooling down process the substructure loaded by tension in the fiber direction. The resultant nonlinear behavior for a fiber volume fraction uf= 45% is shown in Fig. 3. The main damage mechanisms described above can be identified in the resulting stress-strain curve. Up to a the structure shows an elastic behavior Between 0002040.6081.012141.61.8 A and B multiple matrix cracking appears. At B matrix crack saturation is reached and it follows the fiber dominant part up to C. At C the first of Fig. 4. Calculated stress-strain diagrams of the substructure the two fibers present in the substructure breaks for 20 simulations and causes a reduction of stress from d to e there is a superposition of pull-out of the broken rameter leads to an enlarged scattering of fiber fiber and the further loading of the other fiber. The strength. Comparing the calculations for the sub second fiber also breaks at E, resulting in the pull- structure with mf=4, 8 and 16 an increased in ut of both fibers until each fiber is completely terval of strain between the fracture of the first and pulled out of the matrix. the last fiber can be observed for smaller values of Fig 4 shows the dependence of the substructure behavior on the statistical distribution of the Fig. 6 shows the variation of the fiber volume strength values. There the results of 20 simulations fraction. The Youngs moduli of the undamaged with different strength distribution can be seen. material were found to be 236 000, 228 000 and Within these 20 simulations phenomena such as 220 000 MPa for a fiber volume fraction of 30%, fiber and matrix cracking are clearly smeared over 45% and 60%, respectively. After crack saturation a wide range. The appearance of different pull-out in the matrix the stresses are mainly transferred by length can be identified by different friction stresses the fibers. Therefore, in this fiber dominant part of during the fiber pull-out the stress-strain curve after matrix crack satura- To indicate the influence of important param- tion a greater Youngs modulus for an increased eters on the behavior of the elementary cell pa- fiber volume fraction can be observed. It can also rameter studies were performed. In Fig. 5 the be seen that the stress of matrix crack initiation variation of the fiber Weibull-shape parameter mf and the subsequent stress reduction depend on Uf resented. a decreased fiber Weibull-shape pa- For a smaller fiber volume fraction matrix crack. ing is moved to higher stresses mainly because of lower residual stresses in the matrix after the a100v=45% cooling down process E 4. Macrostructure The unidirectionally reinforced Sic/SiC com- posite consists of many fibers. However, beyond a definite number of fibers. the statistical effects change only insignificantly. This is the reason why 002040.6081.0121.4 the main macroscopi enomena can be ined with a macrostructure composed of a suffi- Fig. 3. Calculated stress-strain diagram of the substructure cient number of substructures n. It was found intension in that direction. The ®ber±matrix inter￾face is loaded by compressive stress normal to the ®ber surface. After the cooling down process the substructure is loaded by tension in the ®ber direction. The resultant nonlinear behavior for a ®ber volume fraction vf ˆ 45% is shown in Fig. 3. The main damage mechanisms described above can be identi®ed in the resulting stress±strain curve. Up to A the structure shows an elastic behavior. Between A and B multiple matrix cracking appears. At B matrix crack saturation is reached and it follows the ®ber dominant part up to C. At C the ®rst of the two ®bers present in the substructure breaks and causes a reduction of stress. From D to E there is a superposition of pull-out of the broken ®ber and the further loading of the other ®ber. The second ®ber also breaks at E, resulting in the pull￾out of both ®bers until each ®ber is completely pulled out of the matrix. Fig. 4 shows the dependence of the substructure behavior on the statistical distribution of the strength values. There the results of 20 simulations with di€erent strength distribution can be seen. Within these 20 simulations phenomena such as ®ber and matrix cracking are clearly smeared over a wide range. The appearance of di€erent pull-out length can be identi®ed by di€erent friction stresses during the ®ber pull-out. To indicate the in¯uence of important param￾eters on the behavior of the elementary cell pa￾rameter studies were performed. In Fig. 5 the variation of the ®ber Weibull-shape parameter mf is presented. A decreased ®ber Weibull-shape pa￾rameter leads to an enlarged scattering of ®ber strength. Comparing the calculations for the sub￾structure with mf ˆ 4; 8 and 16 an increased in￾terval of strain between the fracture of the ®rst and the last ®ber can be observed for smaller values of mf. Fig. 6 shows the variation of the ®ber volume fraction. The Young's moduli of the undamaged material were found to be 236 000, 228 000 and 220 000 MPa for a ®ber volume fraction of 30%, 45% and 60%, respectively. After crack saturation in the matrix the stresses are mainly transferred by the ®bers. Therefore, in this ®ber dominant part of the stress±strain curve after matrix crack satura￾tion a greater Young's modulus for an increased ®ber volume fraction can be observed. It can also be seen that the stress of matrix crack initiation and the subsequent stress reduction depend on vf. For a smaller ®ber volume fraction matrix crack￾ing is moved to higher stresses mainly because of lower residual stresses in the matrix after the cooling down process. 4. Macrostructure The unidirectionally reinforced SiC/SiC com￾posite consists of many ®bers. However, beyond a de®nite number of ®bers, the statistical e€ects change only insigni®cantly. This is the reason why the main macroscopic phenomena can be exam￾ined with a macrostructure composed of a su- cient number of substructures n Fig. 3. Calculated stress±strain diagram of the substructure. . It was found in Fig. 4. Calculated stress±strain diagrams of the substructure for 20 simulations. H. Ismar, F. Streicher / Computational Materials Science 16 (1999) 17±24 21