Asymptotics of the near-crack-tip stress field of a growing fatigue crack in damaged materials: Numerical experiment and analytical solution

In this paper, an asymptotic analysis of growing fatigue near-crack-tip fields in a damaged material is performed. The integrity parameter describing the damage accumulation process in the vicinity of the crack tip is incorporated into the constitutive law of an isotropic linear elastic material. An asymptotic solution based on the eigenfunction expansion method is obtained. It is shown that the problem is reduced to a nonlinear eigenvalue problem. An analytical solution of the nonlinear eigenvalue problem is found by the artificial small parameter method. The perturbation theory approach allows us to derive the analytical presentation of the stress and integrity distributions near the crack tip. The technique proposed permits us to find higher-order terms of the asymptotic expansions of the stress components and the integrity parameter. © 2015, Pleiades Publishing, Ltd.