Surface strain tensor plastic deformation

Surface stress — The surface area A of a solid electrode can be varied in two ways In a plastic deformation, such as cleavage, the number of surface atoms is changed, while in an elastic deformation, such as stretching, the number of surface atoms is constant. Therefore, the differential dUs of the internal surface energy, at constant entropy and composition, is given by dUs = ydAp + A m g m denm, where y is the interfacial tension, dAp is the change in area due to a plastic deformation, gnm is the surface stress, and enm the surface strain caused by an elastic deformation. Surface stress and strain are tensors, and the indices denote the directions of space. From this follows the generalized Lippmann equation for a solid electrode ... 

The proportionality constant A adjusts itself at any given strain rate e-P to ensure that the deviatoric stress tensor cannot leave the yield surface during plastic deformation. 

The essential features of this as5rmmetry are represented by a yield function that has the form (7.52) with (3 being constant, independent of deformation history. The location of the yield surface = 0 in stress space for any given straining history represented by is specified by the symmetric tensor If plastic deformation occurs with zero volume change, that... 

Based on the previous descriptions, it is conceivable, that the plasticity and deformability of an active contact region of the friction surface, depend on the actual stress and strain state of the given environment. The stress and strain state of a loaded contact can be described by a stress and a strain tensor. 

The stress deviator is responsible for the plastic deformation, but the deformability is governed by the hydrostatic sphere tensor. In other words, the plastic deformation of the near surface layer of the first body is caused by the deviator of the local stress state, but the particle detachment, which is a consequence of the ductile fracture of the near surface layer, is determined by the whole stress state. For the analysis of the behaviour of the near surface layer, we have to take the dependence of the deformability on the actual stress state into consideration too, beside the dependence of the plasticity on the temperature and the strain rate. 

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