Three-dimensional anisotropic damage accumulation

Abstract

Directional damage or, more precisely, damage anisotropy in creep conditions under nonproportional loading requires a modification of the simple scalar description of the damage growth rule (Chap. 2) and the creep-damage coupling in constitutive equations. The complexity of the description depends on the loading path or, more strictly, on the question whether the principal directions of the stress tensor are constant or rotate with respect to material particles, as examined, e.g., by Trgpczynski, Hayhurst, and Leckie, 1981 (Fig. 3.1). Chow and Lu (1992) developed and utilized a damage-coupled elasto-plastic model suitable for ductile fracture examination under both proportional and nonproportional loading conditions. It was based on a damage-perturbed updated Lagrangian formulation and an implicit concept of the objective derivative applied to the second-rank symmetric damage tensor. A similar problem was investigated by Lis (1992), who expressed damage rates in a rotating coordinate system coinciding with the principal directions of the stress tensor, and then accumulated them on a global sampling plane by an implicit concept of the objective derivative. In what follows, a concept of the damage induced creep anisotropy is developed using the second-rank damage tensor and the orthotropic damage growth rule applied to current principal stress directions. For simplicity, any effect of the damage anisotropy on the elastic stiffnesses is disregarded.