A stochastic solver based on the residence time algorithm for crystal plasticity models

The deformation of crystalline materials by dislocation motion takes place in discrete amounts determined by the Burgers vector. Dislocations may move individually or in bundles, potentially giving rise to intermittent slip. This confers plastic deformation with a certain degree of variability that can be interpreted as being caused by stochastic fluctuations in dislocation behavior. However, crystal plasticity (CP) models are almost always formulated in a continuum sense, assuming that fluctuations average out over large material volumes and/or cancel out due to multi-slip contributions. Nevertheless, plastic fluctuations are known to be important in confined volumes at or below the micron scale, at high temperatures, and under low strain rate/stress deformation conditions. Here, we develop a stochastic solver for CP models based on the residence-time algorithm that naturally captures plastic fluctuations by sampling among the set of active slip systems in the crystal. The method solves the evolution equations of explicit CP formulations, which are recast as stochastic ordinary differential equations and integrated discretely in time. The stochastic CP model is numerically stable by design and naturally breaks the symmetry of plastic slip by sampling among the active plastic shear rates with the correct probability. This can lead to phenomena such as intermittent slip or plastic localization without adding external symmetry-breaking operations to the model. The method is applied to body-centered cubic tungsten single crystals under a variety of temperatures, loading orientations, and imposed strain rates.

Effects of plastic anisotropy on localization in orthotropic materials: new explicit expressions for the orientation of localization bands in flat specimens subjected to uniaxial tension

This paper presents a theoretical investigation on the inception of plastic localization bands in specimens taken from orthotropic metallic sheets, and subjected to uniaxial tension. For the first time, it is shown that the orientations of the localization bands can be obtained directly from experimental measurements of the uniaxial tensile flow stresses and Lankford coefficients (r-values) of the metallic sheet.

Lower Bound Limit Load Estimation Using a Linear Elastic Analysis

We present a scheme that utilizes one elastic stress field (no iterations) to compute lower bound limit load multipliers of structures that collapse through gross (or localized) plasticity. A criterion to distinguish between these collapse modes is presented. For structures that collapse through gross plasticity, we demonstrate that the m′ multiplier proposed by Mura et al. (1965, Extended Theorems of Limit Analysis,” Q. Appl. Math., 23(2), pp. 171–179) is a lower bound in the context of deformation theory. For structures that undergo plastic localization at collapse, we present a criterion that identifies (approximately) the subvolumes of the structure that participate in the collapse. Multiplier m′ is computed over the selected subvolumes, denoted as m'S, and demonstrated to be a lower bound multiplier in the context of deformation theory. We consider numerical examples of structures that collapse by localized or gross plasticity and show that our proposed multiplier is lower than the corresponding multiplier obtained through elastic–plastic analysis and the proposed multiplier is not overly conservative.

Ductility of Thin Metallic Films

Depending on the loading conditions, geometry and material characteristics, the ductility of thin metallic films is controlled either by the resistance to plastic localization or by the resistance to internal damage. New on-chip tensile tests performed on submicron aluminium films show significant strain hardening capacity leading to relatively good resistance to necking, while damage occurs through void nucleation at grain boundaries followed by their growth and coalescence. These results are discussed in the light of several other studies presented in the recent literature in order to unravel the origins of the frequently reported poor ductility of thin metallic films, and the various means existing to improve it.