Description: A residual stress field often occurs in a structure due to a number of reasons such as service loads that produce plasticity, a metal forming process in the absence of an anneal treatment, thermal effects, or swelling effects. When the residual stresses are significant, the standard definition of the contour integral may lead to a path-dependent value. An additional term due to the residual stress field is now included when evaluating the contour integral value to ensure its path independence.