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Analytical elastoplastic stress and deformation fields around a plane-strain crack tip for pressure-sensitive, dilatant materials such as rock, concrete, and ceramics are derived. Classical Prandtl field with an assembly of constant-stress and centered-fan sectors is valid for a stationary crack in a material following the Mohr-Coulomb yield condition. The dependence of the size of plastic zone and the crack-tip opening displacement on far-field loading through J-integral is evaluated and the role of internal friction angle (ϕ) for the pressure-dependent material is identified. An unloading elastic sector was found to be needed in the trailing zone of the crack-tip for growing conditions. The extent of this sector increases with the friction angle and is more than 90 degrees for ϕ = 30°. If near-tip crack opening displacement field can be assumed to be invariant during the crack propagation history, then the complete fracture resistance curve can be estimated. The J-resistance increases and approaches a steady state value similar to the experimental observations for concrete and different rocks. The validity of the analysis is performed by fitting the analytical resistance curve with the experimental data. The elastoplastic fields assume the crack faces to be traction-free and would be different for pressurized cracks such as fluid-driven fractures. The dependence of the fields and resistance curve on the crack pressure is also evaluated.
plastic crack growth, pressure-sensitivity, asymptotic crack fields, fracture resistance, size effect
Research associate, Cornell Theory Center, Cornell University, Ithaca, New York