A nanoscale model of crystal plasticity

In this paper a nanoscale model of crystal plasticity is introduced. The model is characterized by distinct, separate slip surfaces on which discontinuity for the deformation function takes place. Slip displacements considered on the slip surfaces are a measure of plastic deformation. In the case when the slip surface does not intersect the whole body, evolution of boundary of this surface is also considered. Criteria for initiation and stopping of slips are discussed. Evolution equations for slip displacements and for the boundary of the slip surface displacements are introduced. Nanoscale modelling is expressed in the model by distinguishing slip surfaces as well as by the form of the free energy which takes into account details appropriate for this scale. In particular, criteria for initiation of slip are expressed by means of the form of the free energy. As a result the slip systems are also defined by means of this function. More fine effects such as inhomogeneities in crystal structure, induced by defects and dislocations, are represented within the model by internal state variables. The possibility of creep modelling within the concepts presented is discussed.