Unified theoretical solutions for describing the crack-tip stress fields of mode-II cracked specimens under the fully plastic condition

•Theoretical solutions for the mode-II crack-tip stress fields are proposed.•Special functions to describe the coefficients of normalized stresses are proposed.•Parameterized studies on two common mode-II cracked specimens are conducted. Potential novel singular solutions to the crack-tip stress fields beyond the asymptotic solution frame are discussed in this study. It is believed that one of them is not only suitable for the crack-tip stress fields of mode-I cracked specimens but also for those of mode-II cracked specimens. The crack-tip stress fields of mode-II cracked specimens are investigated based on the singular solution and the stress factor of mode-II cracked specimen derived from energy density equivalence principle. Further, special functions for describing the coefficients of normalized stress distributions of mode-II cracked specimens are proposed. The method to determine the parameters in the theoretical solutions are introduced. To give an example, one set of parameters for compact shear specimen under plane-strain conditions are determined by the finite element analysis of a few typical materials and geometries conditions. Finally, comparisons of radial and circumferential stress distributions and contour lines of equivalent stress are completed for the compact shear specimens and Arcan-shaped shear specimens of power-law plastic materials under plane-strain and plane-stress conditions. And the results show that the applicability and reliability of the proposed unified theoretical solutions are verified.