Two-State Conservation Integrals and Stress Singularities in Generic Wedges

The eigenvalues of Williams’ series expansion for generalized wedge problems, which include cracks, re-entrant corners, free edges, and cracks meeting with material interface, etc. are examined from the viewpoint of conservation laws like J-integral and M-integral. By use of the so-called two-state conservation laws or interaction energy, originally proposed by Eshelby and later treated by Chen and Shield, discussed is that the complementary pairs of eigenvalues exist in the J-integral sense and/or in the M-integral sense when these integrals are conserved. Similar results are shown to hold for the eigenvalues of three dimensional wedges.