Asymptotic Self-Similar Solution of the Creep Crack Problems in Damaged Materials under Mixed Mode Loading

Abstract

The creep crack problem in damaged materials under mixed mode loading is considered. The class of the 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 power-law damage evolution equation the near crack-tip stresses, creep strain rates and continuity distributions for plane stress conditions are obtained. The self-similar solutions are based on the hypothesis 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 gives rise to the nonlinear eigenvalue problems. The technique permitting to find 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 the eigenvalues different from the eigenvalues corresponding to the Hutchinson-Rice-Rosengren (HRR) problem are found. Having obtained the eigenspectra and eigensolutions the geometry of the completely damaged zone in the vicinity of the crack tip can be found for all values of the mixity parameter.