Computation of dynamic stress intensity factors for cracks in three-dimensional functionally graded solids

Dynamic stress intensity factors are important parameters in the dynamic fracture behavior of a cracked body. In this paper, an interaction integral method is utilized to compute the mixed-mode dynamic stress intensity factors of three-dimensional functionally graded material solids. Using a proper definition of actual and auxiliary fields, a new formulation and application of the interaction integral is proposed, which is independent of the derivatives of the material properties. ABAQUS finite element package is applied to analyze the functionally graded material cracked bodies. Accordingly, a user material subroutine is written for implementing the continuous variation of the material properties. Temperature was used as an additional variable to consider the variation of density. A research code is developed to compute the interaction integral. This code is then validated by solving some homogeneous and functionally graded material problems. Furthermore, the effect of the material properties on the dynamic stress intensity factors of FGM bodies with elliptical crack is investigated by taking the sigmoidal model into account. Several important fracture behavior of functionally graded material cracked bodies under dynamic loadings for different material property profiles are explored in detail.