PLANE STRAIN DEFORMATION NEAR A CRACK TIP IN A POWER LAW HARDENING MATERIAL
BROWN UNIV PROVIDENCE RI DIV OF ENGINEERING
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Crack tip strain singularities are investigated with the aid of an energy line integral exhibiting path independence for all contours surrounding a crack tip in a two dimensional deformation field of an elastic material or elastic-plastic material treated by a deformation theory. It is argued that the product of stress and strain exhibits a singularity varying inversely with distance from the tip in all materials. Corresponding near crack tip stress and strain fields are obtained for the plane straining of an incompressible elastic- plastic material hardening according to a power law. A noteworthy feature of the solution is the rapid rise of triaxial stress concentration above the flow stress with increasing values of the hardening exponent. Results are presented graphically for a range of hardening exponents, and the interpretation of the solution is aided by a discussion of analogous results in the better understood anti-plane strain case.