Finite element evaluation of mixed mode stress intensity factors in functionally graded materials

TLDR

The study aims to compute fracture parameters for functionally graded material assemblies of arbitrary geometry with stationary cracks using finite element methods. Graded finite elements with spatially varying elastic moduli are incorporated into the stiffness matrix, and stress intensity factors for mode I and mixed‑mode two‑dimensional problems are evaluated via path‑independent J*k‑integral, modified crack‑closure integral, and displacement‑correlation techniques. The accuracy of these methods is assessed by comparison with available theoretical, experimental, or numerical solutions. © 2001 John Wiley & Sons, Ltd.

Abstract

Abstract This paper is directed towards finite element computation of fracture parameters in functionally graded material (FGM) assemblages of arbitrary geometry with stationary cracks. Graded finite elements are developed where the elastic moduli are smooth functions of spatial co‐ordinates which are integrated into the element stiffness matrix. In particular, stress intensity factors for mode I and mixed‐mode two‐dimensional problems are evaluated and compared through three different approaches tailored for FGMs: path‐independent J * k ‐integral, modified crack‐closure integral method, and displacement correlation technique. The accuracy of these methods is discussed based on comparison with available theoretical, experimental or numerical solutions. Copyright © 2001 John Wiley & Sons, Ltd.