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A method for the evaluation of regular components of the stress field in the plastic zone near the tip of a mode-I crack

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Abstract

We propose a method aimed at the evaluation of the amplitude of singularity and dimensionless angular distributions of the second terms in the expansions of stresses, strains, and displacements in the plastic zone in the vicinity of the crack tip. The method is based on the combination the Hutchinson-Rice-Rosengren-type analytic solution and a numerical solution obtained by using a modified method of boundary layer. The presented results enable us to analyze the effects of constraints in broad ranges of conditions of biaxial loading.

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Translated from Problemy Prochnosti, No. 3, pp. 43–59, May–June, 2006.

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Shlyannikov, V.N. A method for the evaluation of regular components of the stress field in the plastic zone near the tip of a mode-I crack. Strength Mater 38, 248–260 (2006). https://doi.org/10.1007/s11223-006-0038-1

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Keywords

  • effect of constraints
  • biaxial loading
  • polar and radial distributions
  • second term of the expansion
  • amplitude of singularity
  • parameter of constraint