On Relation between Contour Integral and Virtual Crack Extension Method of J- and J^^^-Integral

Abstract

In this paper, the methods for evaluating the nonlinear fracture mechanics parameters J-and J^^--integral are discussed in the framework of the virtual crack extension method. The equation for the virtual crack extension method was derived to evaluate the J-integral from the viewpoint different from the original method proposed by Parks or Hellen. Moreover, the equation for evaluating the J^^--integral was derived using the same procedure as in the J-integral. The relation between the contour integral and virtual crack extension method is also discussed. Several numerical examples are presented to verify the validity of the equations derived in this paper.