Radial Dependence of Near-Tip Continuum Fields for Plane Strain Tensile Crack Growth in Elastic-Ideally Plastic Solids

[+] Author and Article Information
W. J. Drugan

Department of Engineering Mechanics, University of Wisconsin, Madison, WI 53706

J. Appl. Mech 53(1), 83-88 (Mar 01, 1986) (6 pages) doi:10.1115/1.3171743 History: Received October 30, 1984; Revised July 02, 1985; Online July 21, 2009


This paper is an extension of work by Drugan et al. (1982) who derive the stress and deformation fields at the tip of a plane strain tensile crack that grows quasi-statically, under general nonsteady conditions, in an elastic-ideally plastic solid. Here I perform a higher-order analysis of the near-tip fields for this growing crack problem. My principal objectives are to determine the radial variation of the near-tip stress field and elucidate the structure of the deformation fields in the 90-deg sector ahead of the growing crack; this information was not provided by the lowest-order solution of Drugan et al. (1982). I also derive a crucial asymptotic expression for the normal radial component of the deformation rate tensor in a moving “centered fan” plastic sector, which was given without complete proof by Rice (1982). The analysis presented herein differs from typical perturbation analyses in that I am able to derive the higher-order structure of the continuum fields rather than having to assume expansions for them. Among the results, normal polar components of deviatoric stress are shown to vary as ( ln r) −1 , while the in-plane polar shear component varies as ( ln r) −2 , for small r > 0 in moving “centered fan” plastic sectors, r denoting distance from the (moving) crack tip. Further, in-plane strains proportional to ln| ln r| as r → 0 appear not to be precluded in the 90-deg sector ahead of the growing crack.

Copyright © 1986 by ASME
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