Applications of tensor functions in damage mechanics of anisotropic materials

This article will provide a short survey of some recent advances in the mathematical modelling of materials behaviour under creep conditions. The tertiary creep phase is accompanied by the formation of microscopic cracks on the grain boundaries, so that damage accumulation occurs. The damage state in a uni-axial tension specimen is discussed and the time to rupture has been calculated. Then, the paper is concerned with the creep behaviour of materials in a state of multiaxial stress. Because of its microscopic nature, damage generally has an anisotropic character even if the material was originally isotropic. The fissure orientation and length cause anisotropic macroscopic behaviour. Therefore, damage in an isotropic or anisotropic material which is in a state of multi-axial stress can only be described in a tensorial form. Thus, tensorial constitutive and damage evolutional equations have been developed. Some examples for practical use and simplified representations are proposed. Furthermore, important damage effective stress concepts are discussed in detail. Finally, some own experiments should be mentioned, which have been carried out in order to examine the validity of the mathematical modelling.