A Statistical Evolution Equation of Microdamage and Its Application

A general equation governing the evolution of number density of microdamage in the phase space has been derived previously, based on the concept of ideal microdamage. The phase space consists of necessary mesoscopic variables describing the state of microdamage. In the cases of parallel penny-shaped microcracks and spherical microvoids, two independent variables, that is, their current and initial sizes, play a significant role in the evolution. This paper focuses on the two-dimensional (current and initial sizes) version of the equation and its solution. These results constitute a basis for the understanding of the underlying mechanisms governing damage evolution. Experimental techniques dealing with the statistical evolution of microcracks under impact and fatigue loadings are reported. These include specimen design, testing methods providing multifrozen stages of microdamage evolution, counting of microdamage, etc. Data processing, especially the conversion from sectional counting to volumetric distribution of microdamage, is provided. In this way, the microdamage evolution is measured. As applications to the damage evolution under impact loading, two inverse problems are discussed, that is, nucleation and growth rates are deduced from the measured data of statistical evolution of microcracks. Another application is the prediction of the evolution of continuum damage in terms of nucleation rate, nN, and microdamage front, cf D.j=α∫0∞cfj(t,c0;σ)nN(c0;σ)dc0 This expression concisely links continuum damage evolution to its underlying mesoscopic dynamics. This approach can be effective until a cascade of coalescence of microdamages leads to an evolution-induced catastrophe—a critical failure.