Crack-tip fields in elastic-plastic material under plane stress mode I loading

New results on the 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, higher-order terms are found which have newly-discovered characteristics. A series solution is obtained for the elastic-plastic crack-tip fields. The expansion of stress fields contains both the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ r^{t_i } \sigma _{pq}^{(i)} (\theta ;t_i ) $$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \operatorname{Re} [r^{t_k } \sigma _{rs}^{(k)} (\theta ;t_k )] $$\end{document} terms where ti is real and tk is complex; the terms σ(i)pq(θti) and σ(k)rsθtk) are real and complex functions of θ respectively. 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; and (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 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 fracture initiation under plane stress mode I loading. This is in agreement with existing full-field solutions and experimental data that J at crack growth initiation is essentially independent of in-plane specimen geometry. The comparison confirms the theoretical asymptotic solutions developed in this study.