The boussinesq wedge and the J_k, L and M integrals

This paper examines the application of the J_k, L and M integrals, in complex-variable form, to the Boussinesq wedge. The wedge is symmetrical and subjected to a point couple and point forces at the apex of the wedge. In the case of a point couple acting at the wedge apex the J_y, L and M integrals are found to vanish for all wedge angles whereas J_x displays a 1/r³ path-dependence; where r is a radial dimension measured from the wedge apex. When the wedge is subjected to point forces at the wedge apex then J_x and J_y are 1/r path-dependent whereas L and M are path-independent. The property that the L and M integrals are path-independent for the Boussinesq wedge is applied to the problem of determining the modes I and II stress intensity factors for a corner-loaded edge crack in a half-plane subjected to both normal and parallel point forces to the free surface of the half-plane.