Computational and theoretical aspects of a grain-boundary model that accounts for grain misorientation and grain-boundary orientation

A detailed theoretical and numerical investigation of the infinitesimal single-crystal gradient plasticity and grain-boundary theory of Gurtin (2008) "A theory of grain boundaries that accounts automatically for grain misorientation and grain-boundary orientation". Journal of the Mechanics and Physics of Solids 56 (2), 640-662, is performed. The governing equations and flow laws are recast in variational form. The associated incremental problem is formulated in minimization form and provides the basis for the subsequent finite element formulation. Various choices of the kinematic measure used to characterize the ability of the grain boundary to impede the flow of dislocations are compared. An alternative measure is also suggested. A series of three-dimensional numerical examples serve to elucidate the theory

Review on Slip Transmission Criteria in Experiments and Crystal Plasticity Models

A comprehensive overview is given of the literature on slip transmission criteria for grain boundaries in metals, with a focus on slip system and grain boundary orientation. Much of this extensive literature has been informed by experimental investigations. The use of geometric criteria in continuum crystal plasticity models is discussed. The theoretical framework of Gurtin (2008, J. Mech. Phys. Solids 56, p. 640) is reviewed for the single slip case. This highlights the connections to slip transmission criteria from the literature that are not discussed in the work itself. Different geometric criteria are compared for the single slip case with regard to their prediction of slip transmission. Perspectives on additional criteria, investigated in experiments and used in computational simulations, are given.Comment: in Journal of Materials Science, 201

Computational modelling of a multifield single-crystal gradient plasticity formulation

A model of higher-order single crystal plasticity is presented and reviewed in order to develop a corresponding finite-element framework. Contrary to the underlying model of Gurtin [Int. J. Plast. 24:702-725, 2008], here rather than the slip rate, the slip and its gradient constitute primary micro state variables. The resulting rate-dependent formulation accounts for size effects through the free energy depending on density of geometrically necessary dislocations. The relationship to multifield theories of continua with microstructure is pointed out. With the presented finite-element approach, the corresponding fully coupled initial-boundary value problem is solved monolithically, and features of the model are illustrated in two preliminary numerical example