An interaction integral and a modified crack closure integral for evaluating piezoelectric crack-tip fracture parameters in BEM

To evaluate the crack-tip field intensity factors of a piezoelectric crack with, any inclined angle, the current widely-used interaction integral method (I-integral) is here extended to the boundary element applications under some coordinate transformations. As well, a new modified crack closure integral method (MCCI) is proposed by considering the discontinuous quarter-point singular elements for the crack-face discretization arising from the dual boundary element method (BEM). This dual BEM involves the strongly singular displacement boundary integral equations (BIEs) for the external boundary and the hypersingular traction BIEs for the crack faces. The crack-tip fracture parameters evaluated by the I-integral and MCCI are verified by the existing analytical solutions and meanwhile, compared with those results achieved by the classical displacement extrapolation method and the J-integral. Three examples are presented to show the high accuracy of the interaction integral method and the improvement of MCCI for the piezoelectric crack problems.