The role of higher order eigenfields in elastic-plastic cracks

The two-state conservation law is utilized, in conjunction with finite elem ent analysis, to obtain the complete Williams eigenfunction series for elas tic-plastic cracks, including the intensities not only for the inverse squa re root singularity and the T-stress but for the higher order singular and nonsingular terms as well. It is shown that the J-integral comprises only t he contributions from the mutual interaction between all complementary pair s of the eigenfields. The same applies to the M-integral with a slightly di fferent definition for the complementary pair. Particularly, it is found th at the higher order singularities interact with the nonsingular higher orde r eigenfields to generate the extra configurational force, in addition to t he energy release rate resulting from the inverse square root singularity. This additional J-value is associated with the translation of the plastic z one alone, with the crack tip being fixed. Numerical examples show that the effect of the higher order terms is negligible in terms of J when the plas tic zone size is small, but that the higher order terms make a difference i n the plastic zone configuration through the interaction between the singul ar and the nonsingular terms in the case of the large scale yielding. (C) 2 001 Published by Elsevier Science Ltd.