Henryk Petryk

Local High-Pressure Torsion (L-HPT) is a recently developed technological process that induces severe plastic deformation (SPD) within a boundary layer (BL) beneath a slowly rotating punch pressed against a metallic plate. In contrast to conventional high-pressure torsion (HPT), where the severe plastic deformation zone extends through the entire thickness of the processed metallic disk, the depth of such a zone and its microstructure after L-HPT are not known in advance and have not been previously investigated. Such novel results, obtained using scanning electron microscopy and nanoindentation, are presented in this work for an AA5083 aluminum alloy as a model system. Unlike conventional dry friction conditions, where BL thickness typically does not exceed ~ 10 μm, electron backscatter diffraction (EBSD) measurements have revealed that the BL with an ultrafine-grained (UFG) structure that develops near the contact interface between an AA5083 aluminum alloy sample and a rotating punch can reach the thickness of up to 500 μm, starting from about 2 mm distance from the rotation center. A gradient microstructure is observed in this region, with an average grain size of about 100–200 nm in the layer immediately adjacent to the punch surface with a thickness of about 50 μm. Within this layer, a Mackenzie-type random misorientation distribution is identified, associated with extreme shear strain and saturation flow stress. This is accompanied by a slightly noticeable trend toward an increase in nanohardness in the vicinity of the contact surface. The discussion of the experimental results encompasses analytical description and finite element simulation.

In metal single crystals, the observed formation of deformation banding pattern has been explained by greater latent hardening of slip systems than their self-hardening, which promotes spatial segregation of plastic slips and lamination towards single-slip domains. Numerical studies focusing on the formation of deformation bands usually involved initial imperfections, boundary-induced heterogeneity, or the postulate of minimal global energy expenditure which additionally promoted non-uniformity of deformation. This article analyses the case when no such mechanism enforcing locally non-uniform deformation is implemented in the finite element (FE) method, while the global system of equations of incremental equilibrium is solved in a standard way. The new finding in this paper is that the deformation banding pattern can appear spontaneously in FE simulations of homogeneous single crystals even in the absence of any mechanism favouring deformation banding in the numerical code. This has been demonstrated in several examples in the small strain formalism using a plane-strain model in which the twelve fcc slip systems are reduced to three effective plastic slip mechanisms. Incremental slips are determined at the Gauss-point level either by incremental work minimization in the rate-independent case or by rate-dependent regularization. In the rate-independent approach, the trust-region algorithm is developed for the selection of active slip systems with the help of the augmented Lagrangian method. Conditions under which a banding pattern appears spontaneously or is suppressed are discussed. In particular, a critical rate sensitivity exponent is identified.

Incremental energy minimization is revisited as a method of determining an incremental solution for rate-independent dissipative solids undergoing isothermal quasi-static deformation. The incremental minimization is applied to the total internal energy of the compound thermodynamic system that consists of a deforming body with internal variables, a conservative loading device, and an ambient heat reservoir. It is shown that the difference between the virtual and actual dissipation rates plays a fundamental role in this minimization, which is related to thermodynamic extremal principles of local and global type. The analysis is carried out within the gradient plasticity framework with the energetic forces derived as the variational derivative of the Helmholtz free energy depending on the spatial gradient of arbitrary internal variables. Specifications are given for existing models of gradient plasticity.

Summary: A new constitutive algorithm for the rate‐independent crystal plasticity is presented. It is based on asymptotically exact formulation of the set of constitutive equations and inequalities as a minimum problem for the incremental work expressed by a quadratic function of non‐negative crystallographic slips. This approach requires selective symmetrization of the slip‐system interaction matrix restricted to active slip‐systems, while the latent hardening rule for inactive slip‐systems is arbitrary. The active slip‐system set and incremental slips are determined by finding a constrained minimum point of the incremental work. The solutions not associated with a local minimum of the incremental work are automatically eliminated in accord with the energy criterion of path stability. The augmented Lagrangian method is applied to convert the constrained minimization problem to a smooth unconstrained one. Effectiveness of the algorithm is demonstrated by the large deformation examples of simple shear of a face‐centered cubic (fcc) crystal and rolling texture in a polycrystal. The algorithm is extended to partial kinematic constraints and applied to a uniaxial tension test in a high‐symmetry direction, showing the ability of the algorithm to cope with the non‐uniqueness problem and to generate experimentally observable solutions with a reduced number of active slip‐systems. Copyright © 2015 John Wiley & Sons, Ltd.