Mixed-mode stress intensity factor evaluation by interaction integral method for quadratic tetrahedral finite element with correction terms

• A way to compute the mixed mode SIFs using the tetrahedral FE only is proposed.
• An interaction integral method which includes “correction terms” is proposed.
• Correction terms guarantee that the auxiliary solutions satisfy the equilibrium.
• Correction terms drastically improve the accuracies of evaluated SIFs.

In this paper, a simple and accurate formulation of the interaction integral method for the quadratic tetrahedral finite element is presented. It was found in the course of present investigation that the auxiliary solutions set by the asymptotic solutions of the crack did not satisfy the equilibrium in terms of the finite element model consisting of the quadratic tetrahedral element. Thus, the results of the interaction integral computations contained a large magnitude of numerical error. To overcome this problem, the authors propose to add correction terms to the asymptotic solutions and to form new auxiliary solutions. The correction terms are determined so that the auxiliary solutions satisfy the equilibrium of the finite element model by performing finite element computations. Some numerical demonstrations are presented and they show that proposed methodology can give more accurate stress intensity factor solutions than the case without the correction terms.