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An intermediate asymptotic solution of the coupled creep-damage crack problem in similarity variables

Using the similarity variable the asymptotic solutions to mode I and mode III crack problems are obtained. The asymptotic stress, creep strain rate and damage fields near the crack tip are analyzed by solving nonlinear eigenvalue problems resulting in a new far stress distribution. The configurations of the totally damaged zone governed by the new far stress field are found and analyzed. | Vietnam Journal of Mechanics, VAST, Vol. 31, No. 3 &4 (2009), pp. 133 – 146 AN INTERMEDIATE ASYMPTOTIC SOLUTION OF THE COUPLED CREEP-DAMAGE CRACK PROBLEM IN SIMILARITY VARIABLES Larisa V. Stepanova Samara State University, 443011, Akad. Pavlov str., 1, Samara, Russia Abstract. The class of self-similar solutions to coupled (creep-damage) crack problems is considered. The constitutive model is based on continuum damage mechanics. The conventional Kachanov-Rabotnov creep-damage theory is utilized to study the asymptotic behavior of damage in the region very near the crack tip. The totally damaged zone where the damage (integrity) parameter reaches its critical value is assumed to exist in the vicinity of the crack tip. Using the similarity variable the asymptotic solutions to mode I and mode III crack problems are obtained. The asymptotic stress, creep strain rate and damage fields near the crack tip are analyzed by solving nonlinear eigenvalue problems resulting in a new far stress distribution. The configurations of the totally damaged zone governed by the new far stress field are found and analyzed. 1. INTRODUCTION Analysis of effects of material damage on the stress and strain fields near crack tip in non-linear materials is the very important problem for evaluation of crack behavior in elements of structures. The influence of damage on crack-tip fields has been the subject of many papers, especially for cracks in brittle materials [1], elastic-plastic-brittle cracks [2, 3], creep cracks [4-6] and fatigue cracks [7]. Thus, the phenomenon of crack growth in materials undergoing deformations coupled with damage has been investigated extensively over the past twenty years. Some of the essential aspects of the considered set of twodimensional crack problems and the results obtained can be highlighted. 1. The damage gives significant influence on the stress and strain (strain rate) fields near the crack tip. 2. The mathematical structure of governing equations is .