ASCE Journal of Engineering Mechanics, Vol. 132, No. 1, pp. 1-15, 2006
M.C. Walters, G.H. Paulino and R. H. Dodds, Jr
Department of Civil and Environmental Engineering, University of Illinois
at Urbana-Champaign, Newmark
Laboraory, 205 North Mathews Avenue, IL
61801, U.S.A.
Abstract
This work applies a two-state interaction integral to obtain stress intensity factors along cracks in three-dimensional functionally-graded materials. The procedures are applicable to planar cracks with curved fronts under mechanical loading, including crack-face tractions. Interaction-integral terms necessary to capture the effects of material nonhomogeneity are identical in form to terms that arise due to crack-front curvature. A discussion reviews the origin and effects of these terms, and a simplified, approximate interaction-integral expression is used in this work to compute stress intensity factors. The selection of terms is driven by requirements imposed by material nonhomogeneity (and not crack-front curvature) in conjunction with appropriate mesh discretization along the crack front. Aspects of the numerical implementation with (isoparametric) graded finite elements are addressed, and examples demonstrate the accuracy of the proposed method.
Key words:
Interaction Integral; Functionally Graded Material; Mixed Mode Stress Intensity Factors; Three Dimensional; Graded Elements