The role of higher order eigenfields in elastic–plastic cracks

Abstract The two-state conservation law is utilized, in conjunction with finite element analysis, to obtain the complete Williams eigenfunction series for elastic–plastic cracks, including the intensities not only for the inverse square 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 the contributions from the mutual interaction between all complementary pairs of the eigenfields. The same applies to the M-integral with a slightly different definition for the complementary pair. Particularly, it is found that the higher order singularities interact with the nonsingular higher order eigenfields to generate the extra configurational force, in addition to the energy release rate resulting from the inverse square root singularity. This additional J-value is associated with the translation of the plastic zone 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 plastic zone size is small, but that the higher order terms make a difference in the plastic zone configuration through the interaction between the singular and the nonsingular terms in the case of the large scale yielding.

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