COMPUTATIONAL MATERIALS SCIENCE ELSEVIER Computational Materials Science 16(1999)17-24 Modelling and simulation of the mechanical behavior of ceramic matrix composites as shown by the example of Sic/sic H. Ismar. F. Streicher Lehrstuhl fur Technische Mechanik, Universitat des Saarlandes, Postfach 15 11 50, D-66 041 Saarbrucken, Germany Abstract modelling of the mechanical behavior of unidirectionally fiber-reinforced ceramic matrix composites(CMC) is presented by the example of SiC/Sic. The starting point of the modelling is a substructure (elementary cell) which includes on a micromechanical scale the statistical properties of the fiber, matrix and fiber-matrix interface and their interactions. The substructure is chosen in such a way that a macrostructure representative of the whole structure can be modelled from a suitable number of substructures. The typical damage behavior of ceramic composites is modelled by king fiber and matrix cracks into account. Cracks are inserted into the substructure by reducing the elastic coefficients of the material. The fracture criterion used is a surface represented by a spheroid in the principal stress space. The crack direction is determined by the criterion of the energy release rate. Interfacial behavior is simulated by consideration of fiber-matrix debonding and frictional sliding. The numerical evaluation of the model is accomplished by means of the finite element method (FEM). The effect of important parameters such as the fiber volume fraction or the fiber Weibull- shape parameter on the nonlinear behavior of the substructure is examined. Finally, a macrostructure is modelled to show the effects of these important parameters on the mechanical behavior of the whole structure. 1999 Elsevier Science B.v. all rights reserved. Keywords: Reinforced ceramics: Micromechanical-statistical modelling: Fiber/matrix cracking: Debonding: Friction; Fiber pull-out 1. Introduction structure. One means of making ceramics more reliable is to introduce amplifications such as ce- In the past years ceramic materials have become ramic fibers. Unlike the bulk materials, ceramic increasingly important. Especially for applications fiber composites show toughness because of energy which require high-strength at elevated tempera- dissipating mechanisms. These mechanisms are tures ceramics show a superior behavior. The shown schematically in Fig. 1. A matrix crack, problem of using ceramic materials in construction either newly formed or caused by the productio is their brittle damage behavior. A single defect process, grows because of external loading. When can lead to the total brittle damage of the whole the crack reaches the fiber surface debonding be- tween the fiber and the matrix takes place. The fiber is increasingly loaded until it reaches its ul nding author. Tel: +49-681-302-2157: fax: +49 timate strength and fiber failure occurs. During 68l-302-3992. subsequent fiber pull-out energy is dissipated by E-mail address friction in the fiber-matrix interface 0927-0256/99/. see front matter e 1999 Elsevier Science B v. All rights reserved PI:S0927-0256(99)00041-5Modelling and simulation of the mechanical behavior of ceramic matrix composites as shown by the example of SiC/SiC H. Ismar, F. Streicher * Lehrstuhl fur Technische Mechanik, Universitat des Saarlandes, Postfach 15 11 50, D-66 041 Saarbrucken, Germany Abstract Modelling of the mechanical behavior of unidirectionally ®ber-reinforced ceramic matrix composites (CMC) is presented by the example of SiC/SiC. The starting point of the modelling is a substructure (elementary cell) which includes on a micromechanical scale the statistical properties of the ®ber, matrix and ®ber±matrix interface and their interactions. The substructure is chosen in such a way that a macrostructure representative of the whole structure can be modelled from a suitable number of substructures. The typical damage behavior of ceramic composites is modelled by taking ®ber and matrix cracks into account. Cracks are inserted into the substructure by reducing the elastic coecients of the material. The fracture criterion used is a surface represented by a spheroid in the principal stress space. The crack direction is determined by the criterion of the energy release rate. Interfacial behavior is simulated by consideration of ®ber±matrix debonding and frictional sliding. The numerical evaluation of the model is accomplished by means of the ®nite element method (FEM). The e€ect of important parameters such as the ®ber volume fraction or the ®ber Weibull￾shape parameter on the nonlinear behavior of the substructure is examined. Finally, a macrostructure is modelled to show the e€ects of these important parameters on the mechanical behavior of the whole structure. Ó 1999 Elsevier Science B.V. All rights reserved. Keywords: Reinforced ceramics; Micromechanical±statistical modelling; Fiber/matrix cracking; Debonding; Friction; Fiber pull-out 1. Introduction In the past years ceramic materials have become increasingly important. Especially for applications which require high-strength at elevated tempera￾tures ceramics show a superior behavior. The problem of using ceramic materials in construction is their brittle damage behavior. A single defect can lead to the total brittle damage of the whole structure. One means of making ceramics more reliable is to introduce ampli®cations such as ce￾ramic ®bers. Unlike the bulk materials, ceramic ®ber composites show toughness because of energy dissipating mechanisms. These mechanisms are shown schematically in Fig. 1. A matrix crack, either newly formed or caused by the production process, grows because of external loading. When the crack reaches the ®ber surface debonding be￾tween the ®ber and the matrix takes place. The ®ber is increasingly loaded until it reaches its ul￾timate strength and ®ber failure occurs. During subsequent ®ber pull-out energy is dissipated by friction in the ®ber±matrix interface. Computational Materials Science 16 (1999) 17±24 * Corresponding author. Tel.: +49-681-302-2157; fax: +49- 681-302-3992. E-mail address: f.streicher@rz.uni-sb.de (F. Streicher). 0927-0256/99/$ - see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 0 2 5 6 ( 9 9 ) 0 0 041-5