Finite Strain Shape Memory Alloys Modeling - Scuola di Dottorato in ...

such phenomena as the Bauschinger effect and preferred orientation, which occur asa result of different plastic deformation of grains with different orientations,demonstrate the effect of crystal structure on plastic behavior. In single crystals forwhich crystallographic slip is assumed to be the only mechanism of plasticdeformation, the material flows through the lattice via dislocation motion, while thelattice itself, with the material embedded to it, undergoes elastic deformation androtation. If the discrete dislocation substructure is ignored, the plastic deformationcan be considered to occur in the form of smooth shearing on the slip planes and inthe slip directions. This continuum slip model from the pioneering work of Taylor(1938) was employed and further developed by Hill (1950), Hill and Rice (1972) andAsaro (1983). For a crystal with a single slip system denoted by { sm , } withms ⋅ =0 and m = s = 1, this micromechanical description can be illustrated as inFig. 4.1. The unit vectors { sm , } are attached to the lattice, and the plastic flow ischaracterized by the tensor Fpdefined as:F = 1+ γs⊗m (4.1)pwhere γ is the plastic shearing on the crystallographic slip system defined by{ sm , }. Furthermore, the total deformation of the crystal is decomposed as:F= FF(4.2)epwhereFpis the part due to the slip only that moves the material through the latticevia dislocation motion, while Ferotates and distorts the crystal lattice.57