Intermediate self-similar asymptotic presentation of the stress and damage fields in the vicinity of the mixed mode crack tip under creep regime

Abstract

In the paper the class of the creep crack problems in damaged materials under mixed mode loading under creep-damage coupled formulation for plane strain conditions is considered. The class of the asymptotic self-similar solutions to the plane creep crack problems in a damaged medium under mixed-mode loading is given. With the similarity variable and the self-similar representation of the solution for a power-law creeping material and the classical Kachanov – Rabotnov power-law damage evolution equation the near crack-tip stresses, creep strain rates and damage distributions for plane strain and plane stress conditions are obtained. The similarity solutions are based on the idea of the existence of the completely damaged zone near the crack tip. It is shown that the asymptotical analysis of the near crack-tip fields results in nonlinear eigenvalue problems. The technique permitting to find all the eigenvalues numerically is proposed and numerical solutions of the nonlinear eigenvalue problems arising from the mixed-mode crack problems in a power-law medium under plane stress conditions are obtained. Using the approach developed the eigenvalues different from the eigenvalues corresponding to the Hutchinson-Rice-Rosengren (HRR) problem are found. For new eigenspectra and eigensolutions obtained the geometry of the completely damaged zone in the vicinity of the crack tip is found for all values of the mixity parameter.