Validity of J-Q-T_z Parameter for Three Dimensional Asymptotic Crack Tip Fields in Non-Hardening Materials

摘要

This paper outlines a framework for evaluating the asymptotic crack tip field solution incorporating T_z parameter in three-dimensional crack problems. Assessment was done based on the comparisons with analytical solutions and results from three-dimensional crack-tip finite element analysis. Fully plastic asymptotic crack tip stress field solutions were provided by carrying out detailed full field finite element analysis on single edge deeply cracked bar subjected to bending load based on a non-hardening material response. Two out-of-plane specimen thicknesses were considered for the bar to evaluate the effect of out-of-plane constraint on the distribution of crack tip stress field. The asymptotic solutions of thick bend bars were found to be contained within a Prandtl crack tip field at the center of the specimen. At the free surface of the specimen, a corner field develops, causing deviation of the J-O-T_z solution from the three-dimensional surface crack-tip field. The results also showed that the three dimensional asymptotic crack tip solution, J-Q-Tz has limited capabilities in characterizing the crack tip fields for thin specimen.