An accurate scheme for mixed-mode fracture analysis of functionally graded materials using the interaction integral and micromechanics models

The interaction integral is a conservation integral that relies on two admissible mechanical states for evaluating mixed-mode stress intensity factors (SIFs). The present paper extends this integral to functionally graded materials in which the material properties are determined by means of either continuum functions (e.g. exponentially graded materials) or micromechanics models (e.g. self-consistent, Mori–Tanaka, or three-phase model). In the latter case, there is no closed-form expression for the material-property variation, and thus several quantities, such as the explicit derivative of the strain energy density, need to be evaluated numerically (this leads to several implications in the numerical implementation). The SIFs are determined using conservation integrals involving known auxiliary solutions. The choice of such auxiliary elds and their implications on the solution procedure are discussed in detail. The computational implementation is done using the nite element method and thus the interaction energy contour integral is converted to an equivalent domain integral over a nite region surrounding the crack tip. Several examples are given which show that the proposed method is convenient, accurate, and computationally e cient.