Dependence of instability strain upon damage in thermoviscoplastic materials

Based on the field equation for the number density of voids and the expression for the expansion of a spherical void in a perfectly plastic infinite body subjected to a uniform hydrostatic tensile stress, an expression for the rate of dilatation of voids is derived. Damage is defined as the volume density of voids. The flow stress of the material is assumed to decrease affinely with an increase in the damage. It is used to find the instability strain in a thermoviscoplastic body deformed in simple shear and simultaneously subjected to a uniform hydrostatic tensile stress. The instability strain is determined by two methods: (i) the Considere condition, i.e., when the shearing traction becomes maximum, and (ii) by studying the stability of a slightly perturbed homogeneous solution of equations governing thermomechanical deformations of a thermoviscoplastic body. Both techniques give essentially the same value of the instability strain. Assuming that failure occurs when the accumulated damage equals 0.3, the failure strain is computed. For a 4340 steel, values of the instability and the failure strains as a function of the nominal strain rate and the hydrostatic pressure are computed.