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
A new interaction integral formulation is developed for evaluating the elastic T-stress for mixed-mode crack problems with arbitrarily oriented straight or curved cracks in orthotropic nonhomogeneous materials. The development includes both the Lekhnitskii and Stroh formalisms. The former is physical and relatively simple, and the latter is mathematically elegant. These two formalisms are implemented using the finite element method and are shown to be equivalent. The gradation of orthotropic material properties is integrated into the element stiffness matrix using a "generalized isoparametric formulation" and (especial) graded elements. The specific types of material gradation considered include exponential and hyperbolic-tangent functions, but micromechanics models can also be considered within the scope for the present formulation. This paper investigates several fracture problems to validate the proposed method and also provides numerical solutions, which can be used as benchmark results (e.g. investigation of laboratory specimens). The accuracy of results is verified by comparison with analytical solutions.
Key words: Functionally graded material, Fracture mechanics, orthotropic materials, T-stress, interaction integral, Finite element method (FEM)