Elastic-Plastic Analysis of Combined Mode II and III Crack-Tip Fields Under Small-Scale Yielding Conditions

Abstract

Within the context of the small-strain approach, combined mode II and III small-scale yielding solutions of a stationary crack are obtained by finite element analysis. To investigate the behavior of the near-tip fields, the normalized stresses ahead of the crack tip are plotted as functions of the normalized radial distance to the tip for several combinations of prescribed mode II and III elastic K fields. The angular variations of the normalized stresses at a fixed radial distance deep within the plastic zone are also plotted for several combinations of remote mode II and III elastic K fields. These plots show an interesting pattern: Well within the plastic zone, the in-plane stresses can be said to be slightly less singular than r -1/(n+1) while the out-of-plane shear stresses are slightly more singular than r -1/(n+1) , where n is the strain-hardening exponent of the material. However, over physically relevant distances ahead of the tip and for the full range of combined mode II and III loadings, the ratio of the in-plane shear stress to the out-of-plane shear stress agrees well with the ratio estimated by linear elastic crack-tip fields.