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A deformation theory of gradient plasticity is employed to study elastoplastic axisymmetric boreholes subjected to far-field biaxial tension. The gradient dependence is introduced in the constitutive framework by assuming that the flow stress (i.e., an effective stress measure) depends not only on an effective strain measure but also on the Laplacian thereof. The classical theory of linear elasticity is adopted for the elastic deformations while strain softening is assumed for the plastic part, where an equivalent work hypothesis is used to associate the stress state to the final total strain. Representative stress distributions are illustrated and compared in the context of size effects, which originate from the presence of the gradient term in the governing equations. The influence of the borehole radius on the initiation of plastic deformation, the nominal stress-strain response and the evolution of the elastoplastic interface are examined. Moreover, a maximum principal strain failure criterion is employed to discuss size effects on the onset of macroscopic fracture. The obtained results show that narrower boreholes have higher plastic and failure strength.

An elastoplastic axisymmetric borehole problem using a deformation theory of gradient plasticity