Elastic-plastic Analysis of Combined Mode I and Iii Crack-tip Fields under Small-scale Yielding Conditions

WITHIN THE context of the small-strain approach, combined mode I and III near-tip fields of a stationary crack in an elastic-plastic solid are obtained by finite element analysis under small-scale yielding conditions. 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 1 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 I and III elastic K fields. These plots show an unmistakeable pattern : the in-plane stresses are more singular than the out-of-plane shear stresses. Over a certain distance, the near-tip in-plane stresses can be said to be more singular than r’ ‘“+ ‘) while the near-tip out-of-plane shear stresses are less singular than rI’(“+ I), where I is the radial distance to the tip and n is the strain hardening exponent of the material. lmpli~tions of these features as they relate to three-dimensional engineering fracture analyses are discussed.