CRACK-TIP FIELDS IN ELASTIC-PLASTIC MATERIAL UNDER PLANE-STRESS MODE-I LOADING

Results on the crack-tip fields in an elastic power-law hardening mate rial under plane stress mode I loading are presented. Using a generali zed asymptotic expansion of the stress function, higher-order terms ar e found which have newly-discovered characteristics. A series solution is obtained for the elastic-plastic crack-tip fields. The expansion o f stress fields contains both the r(ti)sigma(pq)((i))(theta; t(i)) and Re[r(tk)sigma(rs)((k))(theta; t(k))] terms where t(i) is real and t(k ) is complex; the terms sigma(pq)((i))(theta; t(k)) and sigma(rs)((k)) (theta; t(k)) are real and complex functions of theta respectively. Co mparing the results with that for the plane strain mode I loading show s that: (I) the effect of higher-order solutions on the crack-tip fiel ds is much smaller; and (2) the path independent integral J also contr ols the second-order or third-order term in the asymptotic solutions o f the crack-tip fields for most of the engineering materials (1 < n < 11) in plane stress, while the J-integral does not control the second and the third-order terms for the plane strain mode I case for n > 3. These theoretical results imply that the crack-tip fields can be well characterized by the J-integral, and can be used as a criterion for fr acture initiation under plane stress mode I loading. This is in agreem ent with existing full field solutions and experimental data that J at crack growth initiation is essentially independent of in-plane specim en geometry. The comparison confirms the theoretical asymptotic soluti ons developed in this study.