In this paper, governing equations and solutions for asymptotic singular and nonsingular crack-tip sectors in perfectly plastic materials are first summarized under combined in-plane and out-of-plane shear loading conditions. The crack-tip fields under mixed mode II/III loading conditions are then investigated. An assembly of crack-tip sectors is adopted with stress discontinuities along the border of the two constant stress sectors. The solutions of the crack-tip fields under pure mode II, mixed mode II/III, and nearly pure mode III loading conditions are presented. The trends of the angular variations of the mixed mode II/III crack-tip stresses agree with those of the available computational analysis and the asymptotic analysis for low strain hardening materials. The pure mode II crack-tip stresses are similar to those of Hutchinson, and the nearly pure mode III stresses are similar to those of the pure mode III crack-tip field of Rice.
Asymptotic Crack-Tip Fields in Perfectly Plastic Solids Under Mixed Mode II/III Loading Conditions
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Pan, J., and Lin, P. (August 15, 2006). "Asymptotic Crack-Tip Fields in Perfectly Plastic Solids Under Mixed Mode II/III Loading Conditions." ASME. J. Pressure Vessel Technol. November 2007; 129(4): 664–669. https://doi.org/10.1115/1.2767355
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