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

The creep crack problems in damaged materials under mixed mode loading (Mode I and Mode II loading) in the framework of creep-damage coupled formulation are 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 KachanovRabotnov power-law damage evolution equation the near crack-tip stresses, creep strain rates and continuity distributions for plane stress and plane strain conditions are obtained. The similarity solutions are based on the hypothesis of the existence of the completely damaged zone near the crack tip. It is shown that the asymptotic analysis of the near crack-tip fields gives rise to the 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. The angular distributions of the stress and the continuity fields are selected as the crack tip fields of interest. Having obtained the eigenspectra and eigensolutions the geometry of the completely damaged zone in the vicinity of the crack tip is found for all values of the mixity parameter.