The theory of stress concentrations with round vertices

  • L. T. Berezhnitskii
  • P. S. Kachur
  • L. P. Mazurak


Asymptotic formulas have been derived for the local elastic displacement patterns together with the corresponding strains and stresses around a curvilinear hole or crack or an absolutely rigid or elastic inclusion with allowance for the radius of curvature at the vertex of the stress concentrator. The pattern is described by means of generalized stress intensity coefficients, which are coefficients to the principal term (1/√gr+2r) in the expansion of the stresses σy and Txy along the longitudinal axis of the concentrator. In the limiting cases of an elastic inclusion, curvilinear holes, or rigid inclusion, the stress intensity coefficients in the classical sense (with 1/√2r dependence) are obtained by passing to the limit ρ→0 from the generalized coefficients. The general asymptotic representations are used to derive near and far asymptotes, which characterize the variations in those quantities correspondingly in the stress concentration and intensity zones around curved defects. The limits to the application of the asymptotes have been established, together with relationships of Irwin type for holes between the generalized intensity coefficients and the stress concentration coefficients (deformation coefficients) for the defect vertices. The limiting sharpness of a vertex has been identified starting with which a stress concentrator can be considered of crack type, i.e., having points of return on the edge.


Stress Concentration Stress Concentrator Rigid Inclusion Elastic Displacement Principal Term 
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Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • L. T. Berezhnitskii
    • 1
  • P. S. Kachur
    • 1
  • L. P. Mazurak
    • 1
  1. 1.Karpenko Physicomechanics InstituteUkrainian Academy of SciencesLvov

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