On the basis of the physical concept of pore formation, origin and growth of pores, generalized determining relations of the tensor model of plastic damage of metals based on three invariants are formulated. The multiplicative decomposition of the metric transform tensor andthe thermodynamic formulation of the defining relations lead to a symmetric damage tensor of the second rank with a clear physical meaning. Its first invariant determines the damage associated with the plastic dilatance of the material due to pore growth, the second invariant of the deviant tensor - damage associated with a change in the shape of defects, the third invariant of the deviant tensor describes the effect on the damage of the type of stress state (Lode angle),including the effect of the rotation of the main axes of the stress tensor (change of the Lode angle). The introduction of three component measures with the corresponding physical meaning allows the kinetic process of deformation damage to be represented by an equivalent parameter in a three-dimensional vector space, including the criterion conditions for plastic destruction. A measure of plastic damage based on three invariants can be useful in assessing the quality of the mesostructure of metal products obtained by pressure treatment methods.