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

Abstract

SUMMARYThe 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 ÿelds and their implications on the solution procedure are discussed in detail. The computational implementation is done using the ÿnite element method and thus the interaction energy contour integral is converted to an equivalent domain integral over a ÿnite region surrounding the crack tip. Several examples are given which show that the proposed method is convenient, accurate, and computationally e cient.

Optimization of material distribution in functionally graded structures with stress constraints

“…Those conventional models, such as Mori-Tanaka and self-consistent, have been applied to estimate the effective properties of FGM in the works of Zuiker and Dvorak [20], Reiter et al [21], Reiter and Dvorak [22], Tanaka et al [23] and Kim and Paulino [24]. However, they were originally developed for statistically homogeneous materials and are not able to capture the material gradient nature of the FGMs [25].…”

Fatigue Analysis of the Piston Rod in a Kaplan Turbine Based on Crack Propagation under Unsteady Hydraulic Loads

“…In the context of finite elements, the evaluation of area and volume integrals lead to more accurate and stable results than direct integration along a contour [13]. More details were discussed by Kim and Paulino [14] and by Wawrzynek and Carter [13].…”

Probabilistic Fracture Analysis of Functionally Graded Materials—Part I: Uncertainty and Probabilistic Analysis Method

“…As a numerical example, we consider an FGM composite strip with an edge crack [4]. Figure 1 in the companion paper [I] shows the configuration and the mesh details.…”