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.
Cite This Article
Chalivendra, V. B. (2008). Asymptotic Mode-I Crack-tip Stress Fields for Orthotropic Graded Materials. The International Conference on Computational & Experimental Engineering and Sciences, 5(1), 27–34.
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