H Ismar, F Streicher/ Computational Materials Science 16(1999)17-24 b800y=45% 30% 00020.40.60.81 41.61.8 strain E, [% Substructures Macrostructure Fig. 9. Effect of the fiber volume fraction t'r on the behavior of the macrostructure Fig. 7. Fundamental modelling of the macrostructure. ber to the matrix after matrix crack initiation and fiber Weibull parameter. This can be accounted for pull-out length should be improved. Thereby a by the smaller scattering of the fiber fracture stress stronger interface leads to a reduced stress de- with increasing Weibull parameter. The maximum crease after crack initiation in the matrix and to a stress also grows with increasing me shorter pull-out length As a second parameter the fiber volume frac tion ur is varied by a constant fiber Weibull pa rameter mt =8. The different stresses of matrix 5. Conclusion crack initiation can be observed in Fig. 9. The maximum stress, which can be borne by the In the present study on ceramic composites it is composite decreases with decreasing fiber volume shown that the main failure properties leading to fraction. The strength values of the fiber-matrix nonlinear material behavior can be simulated with interface which were used had been optimized the selected substructure. The modelling of the parameter studies for a fiber volume fraction of substructure was carried out by taking the exper- 45%. Because of this there is an optimized load imental verified scattering of the strength values of transfer for uf=45%. For uf= 30% and 60% the the separate phases into account, using Weibull proportion between the load transfer from the fi- distribution. The guch as the fiber Weibull pa- eneral influence of important model parameter su rameter or the fiber volume fraction on the dam age behavior of the selected substructure was studied The composite was modelled by using a mac- 16 rostructure. Thereby the results obtained for 2 finite elements from which the macrostructure was built-up. The composite behavior was found to be 200 chanical behavior of the composite through the 0020.40.6081 variation of characteristic material quantities eter. fiber volume frac tion, etc.)could be shown. Fig. 8. Effect of the Weibull parameter mr on the behavior of Because of the micromechanical approach the macrostructure model will be able to profit from the fast incr the®ber Weibull parameter. This can be accounted for by the smaller scattering of the ®ber fracture stress with increasing Weibull parameter. The maximum stress also grows with increasing mf. As a second parameter the ®ber volume frac￾tion vf is varied by a constant ®ber Weibull pa￾rameter mf ˆ 8. The di€erent stresses of matrix crack initiation can be observed in Fig. 9. The maximum stress, which can be borne by the composite decreases with decreasing ®ber volume fraction. The strength values of the ®ber±matrix interface which were used had been optimized in parameter studies for a ®ber volume fraction of 45%. Because of this there is an optimized load transfer for vf ˆ 45%. For vf ˆ 30% and 60% the proportion between the load transfer from the ®- ber to the matrix after matrix crack initiation and pull-out length should be improved. Thereby a stronger interface leads to a reduced stress de￾crease after crack initiation in the matrix and to a shorter pull-out length. 5. Conclusion In the present study on ceramic composites it is shown that the main failure properties leading to nonlinear material behavior can be simulated with the selected substructure. The modelling of the substructure was carried out by taking the exper￾imental veri®ed scattering of the strength values of the separate phases into account, using Weibull distribution. The general in¯uence of important model parameter such as the ®ber Weibull pa￾rameter or the ®ber volume fraction on the dam￾age behavior of the selected substructure was studied. The composite was modelled by using a mac￾rostructure. Thereby the results obtained for 20 substructures were statistically distributed to the ®nite elements from which the macrostructure was built-up. The composite behavior was found to be nonbrittle. The possibility of in¯uencing the me￾chanical behavior of the composite through the variation of characteristic material quantities (strengths, Weibull parameter, ®ber volume frac￾tion, etc.) could be shown. Because of the micromechanical approach the model will be able to pro®t from the fast increase Fig. 9. E€ect of the ®ber volume fraction vf on the behavior of the macrostructure. Fig. 7. Fundamental modelling of the macrostructure. Fig. 8. E€ect of the Weibull parameter mf on the behavior of the macrostructure. H. Ismar, F. Streicher / Computational Materials Science 16 (1999) 17±24 23