Dislocation Patterns and Work-Hardening in Crystalline Plasticity

Abstract

We propose a continuum model for the evolution of the total dislocation densities in fcc crystals, in the framework of rate-independent plasticity. The basic physical features which are taken into account are: (i) the role of dislocations in hardening; (ii) the relations between the slip velocity and dislocation mobility; (iii) the energetics of self and mutual interactions between dislocations; (iv) nonlocal effects in the interaction between dislocations. A set of reaction-diffusion equations is obtained, with mobilities depending on the slip velocities, which is able to describe the formation of dislocation walls and cells. To this effect, the results of numerical simulations in two special cases are presented. (2000): 74C15, 74C20. Mathematics Subject Classifications

Non-local elasto-viscoplastic models with dislocations in finite elasto-plasticity. Part I: Constitutive framework

“…As a particular case we get those which appeared for instance in the paper by Bortoloni and Cermelli [22].…”

“…(11) together with (22) leads to the elastic power, described by the first two terms from (27), expressed through…”

“…We consider a purely mechanic theory based on the requirement that the temporal variation of the free energy of any part P be less than or equal to the internal power expended by a certain part of the body P. The theory presented here follows Gurtin's opinion 'that the power expended by each independent "rate-like" kinematic descriptor be expressible in terms of the associated force system consistent with its own balance', see, for instance, Gurtin [20,21] and Bortoloni and Cermelli [22]. The constitutive framework developed in this paper is compatible with the free energy imbalance which is postulated in Section 3 with respect to the configuration with torsion.…”

Disclinations and GND tensor effects on the multislip flow rule in crystal plasticity

“…Various extensions of classical models of crystalline plasticity concern: extensions of Schmid law in order to describe the evolution of plastic distortion [25, 26], the presence of tensorial variables, such as the GND tensor [23, 27] and non-local effects [28, 29].…”

“…Gurtin [40] states, ‘When more than one slip system is active the resulting system of equations is extremely difficult, as the usual problem of identifying the active slip systems is exacerbated by non-local yield conditions involving second-order plastic strain gradients.’ Thus, analytical solutions are proposed for problems involving one slip system and a shear band by Gurtin [40], an antiplane shear problem by Gurtin [31], single slip and dislocation wall formation by Cermelli and Gurtin [23] and two slip systems in a simplified model of grain boundary by Bortoloni and Cermelli [28]. Conversely, Teodosiu et al [41] and Cleja-Ţigoiu et al [36] account for all possible activated slip systems.…”