Abstract
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.
Highlights
Plastic deformation in single crystals can generally be construed as a process in which slip on a set of well-definedthe standard implementation in crystal plasticity (CP) models of crystallographic slip as a linear combination of plastic shear on a finite set of slip systems assumes that these slip systems are independent of each other [14,15,16]
When suitably adapted for CP models, such solvers could lead to fluctuations in plastic shear that can numerically break the symmetry in slip systems with identical Schmid factors
We verify that the stochastic solver in Algorithm 1 is capable of reproducing the results of deterministic CP calculations under generic loading and temperature conditions
Summary
Plastic deformation in single crystals can generally be construed as a process in which slip on a set of well-definedthe standard implementation in CP models of crystallographic slip as a linear combination of plastic shear on a finite set of slip systems assumes that these slip systems are independent of each other [14,15,16]. Computational Mechanics (2021) 68:1369–1384 of dislocation-mediated shear, which is often questionable and leads to an homogeneous plastic response even in cases where valid localized deformation pathways exist [12,17] Such homogenization is mathematically not problematic, as the underlying constitutive models intrinsically ensure stability in the solutions. When suitably adapted for CP models, such solvers could lead to fluctuations in plastic shear that can numerically break the symmetry in slip systems with identical Schmid factors. These fluctuations can be regarded as reflecting the natural intrinsic variability of certain internal variables, i.e., they can be justified as ‘physical’ in many cases
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