International Journal for Numerical Methods in Engineering, Vol. 58, No.10, pp.1457-1497, 2003
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 is a conservation integral that relies on two admissible
mechanical states for evaluating mixed-mode stress intensity factors (SIFs).
The present paper extends this integral to functionally graded materials in
which the material properties are determined by means of either continuum functions
(e.g. exponentially graded materials) or micromechanics models (e.g. self-consistent,
Mori–Tanaka, or three-phase model). In the latter case, there is no closed-form
expression for the material-property variation, and thus several quantities,
such as the explicit derivative of the strain energy density, need to be evaluated
numerically (this leads to several implications in the numerical implementation).
The SIFs are determined using conservation integrals involving known auxiliary
solutions. The choice of such auxiliary fields and their implications on the
solution procedure are discussed in detail. The computational implementation
is done using the nite element method and thus the interaction energy contour
integral is converted to an equivalent domain integral over a nite region surrounding
the crack tip. Several examples are given which show that the proposed method
is convenient, accurate, and computationally efficient.
Key words: functionally graded material (FGM), fracture mechanics, stress intensity factor (SIF), finite element method (FEM), interaction integral, conservation integral, micromechanics models.