Computations of J-integral and T*-integral in elastic–plastic fracture by the quadrature element method

Abstract

In this paper, J-integral and T*-integral in elastic–plastic fracture are computed by the quadrature element method (QEM). Since high stress gradients exist in the immediate vicinity of the crack front, computing these integrals accurately is not a trivial task. The QEM facilitates the construction of arbitrarily high-order elements, which effectively capture the stress gradients, making it particularly suitable for this computation. After performing an elastoplastic stress–strain analysis of the fracture problem, the stress and deformation states are further formulated to compute the integrals. The integrals are formulated in several forms, including the contour and domain forms, as well as the incremental and total forms. Classical numerical examples are solved to demonstrate the effectiveness and high accuracy of the method. Overall, the equivalent domain integral (EDI) form outperforms the contour integral form because errors at the local contour have less effect on the integral. Moreover, the QEM yields more accurate solutions than the popular finite element method (FEM) that employs low-order finite elements and shares the same number of degrees of freedom. Additionally, it is found that the EDI form solution is not very sensitive to the specific type of the S function. Therefore, a linear function is suggested for convenience.