Plane-Strain Crack-Tip Fields for Pressure-Sensitive Dilatant Materials

[+] Author and Article Information
F. Z. Li, J. Pan

Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, MI 48109

J. Appl. Mech 57(1), 40-49 (Mar 01, 1990) (10 pages) doi:10.1115/1.2888321 History: Received December 21, 1988; Revised April 20, 1989; Online March 31, 2008


Plane-strain crack-tip stress and strain fields are presented for materials exhibiting pressure-sensitive yielding and plastic volumetric deformation. The yield criterion is described by a linear combination of the effective stress and the hydrostatic stress, and the plastic dilatancy is introduced by the normality flow rule. The material hardening is assumed to follow a power-law relation. For small pressure sensitivity, the plane-strain mode I singular fields are found in a separable form similar to the HRR fields (Hutchinson, 1968a, b; Rice and Rosengren, 1968). The angular distributions of the fields depend on the material-hardening exponent and the pressure-sensitivity parameter. The low-hardening solutions for different degrees of pressure sensitivity are found to agree remarkably with the corresponding perfectly-plastic solutions. An important aspect of the effects of pressure-sensitive yielding and plastic dilatancy on the crack-tip fields is the lowering of the hydrostatic stress and the effective stress directly ahead of the crack tip, which may contribute to the experimentally-observed enhancement of fracture toughness in some ceramic and polymeric composite materials.

Copyright © 1990 by The American Society of Mechanical Engineers
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