The plane elasticity problem for a nonhomogeneous medium containing a crack is considered. It is assumed that the Poisson's ratio of the medium is constant and the Young's modulus E varies exponentially with the coordinate parallel to the crack. First the half plane problem is formulated and the solution is given for arbitrary tractions along the boundary. Then the integral equation for the crack problem is derived. It is shown that the integral equation having the derivative of the crack surface displacement as the density function has a simple Cauchy type kernel. Hence, its solution and the stresses around the crack tips have the conventional square root singularity. The solution is given for various loading conditions. The results show that the effect of the Poisson's ratio and consequently that of the thickness constraint on the stress intensity factors are rather negligible.

/pdf/the-crack-problem-for-a-nonhomogeneous-plane-1ujwjgpna0.pdf

The crack problem for a nonhomogeneous plane

Three-dimensional Problems of the Theory of Elasticity. By A. I. Lur’e.1964. (Interscience Publishers)

The nonhomogeneous materials considered in this work are of a class whose elastic moduli are specified by continuous and generally differentiable functions of the spatial coordinates. The elastic stress and displacement fields near a crack tip in a two-dimensional nonhomogeneous cracked body are derived utilizing an extension of the Wiliams eigenfunction expansion technique. The nature of the stress and strain singularity is ascertained to be precisely of the same form as the well-known inverse square root stress singularity near a crack tip in a homogeneous material, independent of the functional form of the elastic moduli variation. A new quasipath-independent integral has been generated which proves useful for computing the energy release rate and mixed-mode stress intensity factors in nonhomogeneous cracked bodies. The integral is used in conjunction with finite element analysis for purposes of computing stress intensity factors. Numerical results are compared with certain exact solutions which are available for nonhomogeneous cracked bodies. Cracked composite bodies have traditionally been modeled and analyzed as possessing discontinuous elastic moduli, but are treated here as having rapid, but smooth variations of the material properties.

Fracture of nonhomogeneous materials

http://ssi.civil.ntua.gr/downloads/journals/2006-SDEE_Footings%20under%20seismic%20loading_Analysis%20and%20design%20issues%20with%20emphasis%20on%20bridge%20foundations.pdf

M. K. Kassir

Papers

Chloride-induced corrosion of reinforced concrete bridge decks

The Stress-Intensity Factor for a Penny-Shaped Crack Between Two Dissimilar Materials

Impact Response of a Cracked Orthotropic Medium

Interaction functions of a rigid strip bonded to saturated elastic half-space

Moving Griffith crack in an orthotropic material