Representation of crack-tip plasticity in pressure sensitive geomaterials

This paper presents a model based on dislocation theory for representation of crack tip plasticity in a pressure sensitive material. The basic equations are derived from a simple model of the crack tip plasticity which represents the plasticity by superdislocations placed at the effective centres of the complete slip process distributed around the crack tip. The positions and strengths of the superdislocations are determined by imposing the following conditions: (i) the total stress-intensity factor at the crack tip is zero (ii) the total stress minus the self stress of the superdislocation acting at the superdislocation position is just equal to the friction stress due to the Mohr-Coulomb yield criterion and (iii) the total crack opening displacement produced by the model is maximized. Condition (iii) enables the angle of the slip band on which the superdislocation lies to be determined. The results are presented in a dimensionless form allowing the discussion of particular cases and the recognition of the dominant parameters. A series of parametric studies are carried out to demonstrate that the model can capture the essentials of the crack tip plasticity.