Engineering Fracture Mechanics, Vol. 71, Nos. 13-14, pp.1907-1950, 2004
G.H. Paulino and J.H. Kim
Department of Civil and Environmental Engineering, University of Illinois
at Urbana-Champaign, Newmark
Laboratory, 205 North Mathews Avenue, IL
61801, U.S.A.
Abstract
A ‘‘non-equilibrium’’ formulation is developed for evaluating T -stress in functionally graded materials with mixedmode
cracks. The T -stress is evaluated by means of the interaction integral (conservation integral) method in conjunction
with the finite element method. The gradation of material properties is integrated into the element stiffness
matrix using the so-called ‘‘generalized isoparametric formulation’’. The types of material gradation considered include
exponential, linear, and radially graded exponential functions; however, the present formulation is not limited to
specific functions and can be readily extended to micromechanics models. This paper investigates several fracture
problems (including both homogeneous and functionally graded materials) to verify the proposed formulation, and also
provides numerical solutions to various benchmark problems. The accuracy of numerical results is discussed by
comparison with available analytical, semi-analytical, or numerical solutions. The revisited interaction integral method
is shown to be an accurate and robust scheme for evaluating T -stress in functionally graded materials.
Keywords: Functionally graded material (FGM); T -stress; Stress intensity factor (SIF); Finite element method (FEM); Generalized isoparametric formulation (GIF); Interaction integral; Conservation integral