Open Access

ABSTRACT

Asymptotic Mode-I Crack-tip Stress Fields for Orthotropic Graded Materials

Vijaya Bhaskar Chalivendra¹

1 Department of Mechanical Engineering, University of Massachusetts Dartmouth, MA 02720, USA

The International Conference on Computational & Experimental Engineering and Sciences 2008, 5(1), 27-34. https://doi.org/10.3970/icces.2008.005.027

Abstract

Asymptotic analysis coupled with Westergaard stress function approach is used to develop quasi-static stress fields for a crack oriented along one of the principal axes of inhomogeneous orthotropic medium. In the formulation, four independent engineering constants, E₁₁, E₂₂, G₁₂, v₁₂ are replaced by an effective stiffness E = √E₁₁E₂₂, a stiffness ratio δ = (E₁₁/E₂₂), an effective Poisson's ratio v = √v₁₂v₂₁, and a shear parameter k = (E/2G₁₂)-v. It is assumed that the effective stiffness varies exponentially along one of the principal axes of orthotropy. The first two terms in the expansion of stress field are derived to explicitly bring out the influence of nonhomogeneity on the structure of the stress field. Using the derived stress field equations, the isochromatic fringe contours are developed to understand the variation of stress field around the crack tip as a function of both orthotropic stiffness ratio and non-homogeneous coefficient.

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