Abstract
Abstract Crack-tip fields in an elastic power-law hardening material under plane stress mode I loading are presented. Using a generalized asymptotic expansion of the stress function, the higher-order terms are found, and a series solution is obtained for the elastic-plastic crack-tip fields. Comparing the results with that for the plane strain mode I loading shows that (1) the effect of higher-order solutions on the crack-tip fields is much smaller, (2) the path-independent integral J also controls the second-order or third-order term in the asymptotic solutions of the crack-tip fields for most of the engineering materials (1 < n < 11) in plane stress, while J does not control the second and the third-order terms for plane strain mode I case for n ≥ 3. This theoretical results imply that the crack-tip fields can be well characterized by J-integral, and can be used as a criterion for fracture initiation in the plane stress state. This is in agreement with existing full-field solutions and experiments that J at crack growth initiation is essentially independent of specimen geometry. The comparison confirms the theoretical asymptotic solutions developed in this study.
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