Matched asymptotic expansions in nonlinear fracture mechanics—II. Longitudinal shear of an elastic work-hardening plastic specimen |
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Authors: | T.M. Edmunds J.R. Willis |
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Affiliation: | School of Mathematics, University of Bath, Claverton Down, Bath BA2 7AY, England |
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Abstract: | Earlier analysis given by T.M. Edmunds and J.R. Willis (1976) is extended to deal with cracks in elastic work-hardening plastic specimens subjected to longitudinal shear loads. Solutions are expressed in terms of a set of parameters that are determined from linear elastic solutions alone. It is proved, for any specimen geometry and any loading symmetric about the plane of the crack, that a ‘plastic-zone correction’, obtained by solving a linear elastic problem for a crack which is a length ry longer than the actual crack, provides a two-term asymptotic expansion for the J-integral, if ry is defined suitably in terms of the linear elastic stress concentration factor and the initial slope of the work-hardening curve. The general method is applied in detail to a strip of finite width containing an edge crack, for which the effect of the work-hardening on the maximum extent of the plastic zone and on the J-integral is summarized graphically. |
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