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 intermitten...
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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-timealgorithm 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.
Standard Monte Carlo algorithms with constant pair interactions within the first coordination shell are usually quite effective for the description of ordering, tracer diffusion, chemical diffusion (but without Kirken...
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Standard Monte Carlo algorithms with constant pair interactions within the first coordination shell are usually quite effective for the description of ordering, tracer diffusion, chemical diffusion (but without Kirkendall shift effect) within any already existing ordered intermediate phase. Yet, one encounters big problems if one tries to simulate the formation and growth of ordered intermediate phase or, especially, simultaneous formation and growth of several intermediate phases during interdiffusion. Two algorithms providing solution of this problem, are discussed. The first algorithm is known (but not widely used for reactive growth) - account of interactions in the two coordination shells with negative mixing energy in the first coordination shell and positive mixing energy in the second one. The second algorithm is new: interactions only within the first coordination shell of each atom but depending on the local composition within the cluster around interacting atoms. Both algorithms are shown to provide formation and growth of the ordered intermediate phases with rather narrow concentration ranges, growing with time (after some initial period) according to parabolic law.
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