Theory and methods of constructing equations for the evolutionary damageability of materials

The theory and methods for constructing equations (functions) of evolutionary damage and rupture of materials in the Kachanov model (creep rupture and fatigue rupture) are presented. In general, it is proved that the factorized Kachanov model is identical to the Palmgren-Miner rule, which is often not confirmed experimentally. To construct damageability functions adequate to the experimental data, new mathematical objects (potential and normalized potential) are introduced. If the entire history of changes in the damage variable is known in experiments, then the use of the potential makes it possible to construct a damageability function of any complexity without integrating the evolutionary equation (explicit method). For cases where only rupture moments are recorded in experiments, a criterion for the adequacy of the normalized potential is formulated and an implicit method for its construction is developed. It is supplemented with a recursive algorithm that generates an unlimited number of such potentials. The implicit method is illustrated by examples, following which the reader can construct a damageability equation for his material without a thorough study of the theory.