Application of the Jk integral to mixed mode crack problems for anisotropic composite laminates

Abstract

The $\text{J}{}_{\mathrm{k}}$ integral method for determining mixed mode stress intensity factors separately in the cracked anisotropic plate is developed. Stress intensity factors are indirectly determined from the value of $\text{J}{}_1$ and $\text{J}{}_2$. The $\text{J}{}_2$ integral can be evaluated efficiently from a finite element solution, neglecting the contribution from the portion of the integration contour along the crack faces, by selecting the integration contour in the vicinity of the crack tip. Using functions of a complex variable, the complete relations between $\text{J}{}_1$, $\text{J}{}_2$ and $\text{K}{}_{\mathrm{I}}$, $\text{K}{}_{\mathrm{II}}$ for anisotropic materials are derived conveniently by selecting narrow rectangular contours shrinking to the crack tip. Compared to the existing path independent integral methods, the present method does not involve calculating the auxiliary solution and hence numerical procedures become quite simple. Numerical results to various propblems are given and demonstrate the accuracy, stability and versatility of the method.