THE FRACTURE MECHANICS OF A SLIT CRACK WITH CRACK-TIP DUAL ZONES (ELASTIC CORE, DUGDALE, OPENING DISPLACEMENT)

An idealized analytic model for Mode I cracking with crack-tip dual zones of an elastic core zone and a plastic strip zone is proposed in this dissertation. It is assumed that the material in the elastic core zone obeys stress-strain relations of linear elasticity and that the normal displacement across the crack face possesses a jump of uniform value there. The plastic strip zone is a zone of Dugdale plastic yielding with negligible strain-hardening. The normal stress in this zone is assumed to be equal to the material yield strength everywhere. This work is motivated by the recent electron microsope observations of dislocation pile-ups at the crack-tip region in several materials that reveal the fact that an elastic zone is often present between the crack-tip and the plastic zone.; A Papkovick-Neuber formulation is used to reduce the problem to a set of quadruple intergral equations. An exact solution of these equations is obtained by employing a modified finite Hilbert transform technique. With the condition of boundedness of stresses in the plastic zone, the analytic results for the stress and displacement fields are derived.; Based on these results, an inverse square root of stress singularity occurs at the crack-tip and a relaxation of stresses in the crack-tip elastic zone is realized. Stress distributions, the crack-tip stress-intensity factor, the crack-opening displacements, the dual-zone lengths and the crack-face displacement profiles are obtained. They are shown to depend upon the dual-zone lengths and the crack size. These quantities are expressed in terms of elliptic integrals and Heuman's lambda functions.; The generalized analytic model is applied to obtain the solution of a three-crack problem with specified displacements between the cracks. In addition, the limiting cases of the generalized solution yields results for two well-known problems: the Dugdale model and the problem involving a system of triple cracks in an isotropic elastic medium.