ASME Journal of Applied Mechanics, Vol. 70, No.4, pp.531-542, 2003
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.
A.C. Fannjiang and Y.-S. Chan
Department of Mathematics, University of California,Davis, CA 95616, U.S.A.
Abstract
Anisotropic strain gradient elasticity theory is applied to the solution of a mode III crack in a functionally graded material. The theory possesses two material characteristic lengths, l and l', which describe the size scale effect resulting from the underlining microstructure, and are associated to volumetric and surface strain energy, respectively. The governing differential equation of the problem is derived assuming that shear modulus is a function of the Cartesian coordinate y, i.e. G = G(y) = G0egy where G0 and g are material constants. The crack boundary value problem is solved by means of Fourier transforms and the hypersingular integrodifferential equation method. The integral equation is discretized using the collocation method and a Chebyshev polynomial expansion. Formulae for stress intensity factors, KIII, are derived, and numerical results of KIII for various combinations of l , l' and g are provided. Finally, conclusions are inferred and potential extensions of this work are discussed.
Key words: High-order
continuum, gradient elasticity, fracture mechanics, functionally graded
materials (FGM)