A comprehensive investigation of the formulations of the interaction integral method for the evaluation of stress intensity factors of three-dimensional cracks in functionally graded materials

The interaction integral for functionally graded materials can be expressed in a number of formulations. In this paper, some of the formulations that were found in the literature in addition to some new formulations are discussed. The discussion will focus on the postulates of elastic constants in deriving the interaction integral formulations in the form of domain integrals. Mode I and mixed-mode crack problems of functionally graded materials are presented. Then, the accuracies of the stress intensity factors computed by the presented interaction integrals are critically compared. It was found that all the SIFs computed by the presented formulations are equally accurate.

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This paper discusses several formulations for the interaction integral of functionally graded materials, including both existing formulations in the literature and newly proposed formulations. The focus is on deriving the interaction integral expressions in the form of domain integrals based on the assumptions of elastic constants. Mode I and mixed-mode crack problems of functionally graded materials are presented, and the accuracies of the stress intensity factors computed by the presented interaction integrals are critically compared. It was found that all the SIFs computed by the presented formulations are equally accurate.