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.

Configurational Forces on Elastic Line Singularities

Configurational forces acting on two-dimensional (2D) elastic line singularities are evaluated by path-independent J-, M-, and L-integrals in the framework of plane strain linear elasticity. The elastic line singularities considered in this study are the edge dislocation, the line force, the nuclei of strain, and the concentrated couple moment that are subjected to far-field loads. The interaction forces between two similar parallel elastic singularities are also calculated. Self-similar expansion force, M, evaluated for the line force shows that it is exactly the negative of the strain energy prelogarithmic factor as in the case for the well-known edge dislocation result. It is also shown that the M-integral result for the nuclei of strain and the L-integral result for the line force yield interesting nonzero expressions under certain circumstances.