Asymptotic deformation and stress fields at the tip of a sharp notch in an elastic-plastic material

The singular elastic-plastic stress, strain and the displacement fields at the tip of a sharp notch for both plane stress and plane strain conditions are investigated analytically. The material is assumed to be governed by the deformation theory of plasticity with linear strain hardening characteristic. Since the elastic strain is retained in the analysis, the final strain and displacement fields can be separated into the elastic and the plastic parts. In the case with zero notch angle, the results reduce to the classical crack problem. The relationship of the amplitude of the near crack tip elastic-plastic field to the elastic far field is obtained. Both mode I and mode II cases are investigated. The mixed mode case is also discussed.