Orientation of the Localized Damage Zone in Brittle Solid under True Triaxial Compression

Abstract

The problem of finding the optimal orientation of the localized damage zone in a brittle material under triaxial compression with intermediate stress varying from the minimum (Karman scheme) to the maximum (Becker scheme) principal stress values is considered in the thin weak layer approximation. The undamaged material is described by the relations of the linear-elastic isotropic body, the weak zone is described by the model of nonlinear elasticity of Academician of the Russian Academy of Sciences V.P. Myasnikov with elastic moduli linearly dependent on the scalar parameter of the damage. The orientation of the weakened zone is given by two angles relative to the direction of action of the two principal stresses, and the degree of weakening is given by the value of the damage parameter. The search for the optimal orientation of the zone for fixed values of the control parameters consists in maximizing the function that determines the rate of damage growth in this zone.

As a result of the solution of the problem, the optimal orientations of the localized damage zone have been established for different ratios of principal stresses and damage level. It is shown that with intermediate stress increase the angle of inclination of the zone relative to the direction of the maximum principal stress decreases, as well as a narrowing of the interval of possible orientations of the zone relative to the direction of the intermediate principal stress. Based on the analysis of the ratio of the values of the shear components of the stress tensor in the plane of the localized damage zone, the possible shear directions along this zone are determined.