ASME Journal of Applied Mechanics, Vol. 72, No. 3, pp. 351-364, 2005
J.H. Kim and G.H. Paulino
Department of Civil and Environmental Engineering, University of Illinois
at Urbana-Champaign, Newmark
Laboratory, 205 North Mathews Avenue, IL
61801, U.S.A.
Abstract
The interaction integral method provides a unified framework for evaluating fracture parameters, such as stress intensity factors and T-stress, in functionally graded materials (FGMs). The method is based on a conservation integral involving auxiliary fields. In fracture of nonhomogeneous materials, the use of auxiliary fields developed for homogeneous materials results naturally in a violation of one of the basic relations of mechanics, i.e. equilibrium, compatibility or constitutive, which naturally leads to three independent formulations: "non-equilibrium", "incompatibility" and "constant-constitutive-tensor". Each formulation leads to a consistent form of the interaction integral in which extra terms are added to compensate for the difference in response between homogeneous and nonhomogeneous materials. The extra terms play a key role in ensuring path-independence of the interaction integral. This paper presents a critical comparison of the three consistent formulations and indicates both their advantages and drawbacks. Such comparison is made form a theoretical point of view and also by means of the numerical examples. The numerical implementation is based on finite elements that account for the spatial gradation of material properties at the element level (graded elements).
Key words: functionally graded material (FGM), interaction integral, finite element methods (FEM), generalized isoparametric formulation (GIF0, fracture mechanics, stress intensity factor (SIF), T-stress.