Application of the Orthotropic Damage Growth Rule to Variable Principal Directions

The classical orthotropic brittle damage law [Kachanov (1958)] is applicable for principal directions of the stress tensor. When shear stresses are accounted, the principal directions of the stress tensor rotate with time and, hence, a tensorial formulation of the damage is required [Chow and Lu (1992)]. In general, current principal directions of the stress tensora, and of the damage tensorp3B do not coincide, however, when the principal axes of stress rotate due to the shear effect, the principal axes of damage follow them. The symmetric second rank damage tensor 2 [Murakami and Ohno (1981)] is applied, and the objective derivative Q of the damage tensor is adopted, to account for the effect of rotation of principal directions on the damage accumulation process. Then, a current transformation to the global coordinate system (sampling coordinate space) is performed. The similarity of deviators based on the flow theory and on the time hardening hypothesis, associated with the orthotropic damage growth rule, both written for current principal directions of stress, are taken as constitutive relationships for creep [Boyle and Spence (1983), Kachanov (1986)]. Three examples are considered: rotationally-symmetric disk subjected to stationary radial and tangential forces, disk subjected to sustained radial tension and multiple reverse torsion. and disk subjected to alternating body forces due to acceleration/breaking cycles.