Damage evaluation for the dispersed microdefects with the aid of M- integral

A unified method of evaluating the dispersed microdefects’ equivalent damage area/volume is innovatively proposed by using the M-integral. The corresponding damage evolution rate and fatigue driving force is preliminarily studied for the dispersed microdefects. First, the analytical expression of M-integral is deduced by using the Lagrangian energy density function (Λ), and the corresponding physical meaning of the M-integral is elucidated as the change of the total potential energy due to the damage evolution. Second, the actual damage area/volume induced by underlying dispersed microdefects are assumed equivalent to the area/volume of an individual circular/spherical void while the corresponding values of the M-integral for both cases are equal. As examples, the equivalent damage area associated with the M-integral for a series of representative defect(s) configurations is calculated, including the singular defect (void, crack, and ellipse) and the interactive defects (two voids, two cracks, one void, and one crack). The influences of the defects interaction effect and distribution on the damage level are analyzed quantitatively. Finally, the present method of damage evaluation is proposed to predict fatigue problems of the dispersed defects. A unified fatigue damage evolution law for the dispersed microdefects is preliminarily defined, and a protocol to experimentally measure the damage evolution rate is proposed. The present research will be beneficial to the damage tolerance design and lifetime prediction of engineering structures with dispersed microdefects.