Extension of a fourth-order damage theory to anisotropic history: Application to ceramic matrix compostites under a multi-axial non-proportional loading

Ceramic matrix composites have good thermo-mechanical properties at high or very high temperatures. The alliance of two brittle materials (e.g. SiC fibers and SiC matrix) via an interface allows a pseudo-ductile macroscopic behavior due to crack deviation. The modeling of the crack networks using damage mechanics is not straight forward. The main reason is the presence of a crack network oriented by the loading direction, which is not known a priori. The aim of this paper is to extend an anisotropic damage model able to describe such behaviors to multi-axial loadings. For that, compliance-like tensorial damage variables are used in a thermodynamic potential able to account for crack closure effects. The damage kinematic is initially completely free and imposed by the evolution laws. The key point of the present paper is to account for an anisotropic history of damage. The results obtained are put in relation to alternate torsion tests performed on SiC/SiC tubes and richly instrumented.