Internal variable constitutive relations and their application to description of hardening in single crystals

The paper briefly considers the structure of internal variable constitutive relations. The mesoscale model required for determination of macroscale internal variables is taken to be one of the crystal plasticity (Lin's model), in which critical shear stress along slip systems assumes great importance. In this work, evolution equations for critical shear stress that take into account dislocation annihilation and reactions with the formation of Lomer-Cottrell barriers are proposed thus making possible description of the Bauschinger effect and additional hardening under complex loading. The potentialities of the model are demonstrated by numerical simulation of monotonic and cyclic uniaxial loading of polycrystals.