Stochastic Dislocation Dynamics under Creep Conditions in Metals
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Stochastic Dislocation Dynamics under Creep Conditions in Metals Masato Hiratani1 and Hussein M. Zbib School of Mechanical and Materials Engineering, Washington State University Pullman, WA 99164-2920 ABSTRACT A stochastic model is proposed to study dislocation dynamics in metallic single crystals. A Langevin type thermal fluctuation is taken into account for the model to maintain thermal equilibrium. This approach works as Brownian motion of segmental dislocations. Additionally, a new model for implementing the cross slip mechanism in FCC metals is developed based on results obtained by atomistic simulations. This new model is capable of simulating realistic thermal processes such as thermally activated dislocation motion during easy glide or cross slip during cold working of metals. INTRODUCTION The development of computational models for dislocation dynamics (DD) over nano-meso scales is essential when investigating deformation phenomena in crystalline materials in today’s multi-scale modeling schemes. By utilizing a set of local rules extracted from finer models such as molecular dynamics, various DD models have been proposed to bridge atomistic models with continuum models. Indeed, DD models have been used as powerful tools to determine mechanical response of the materials for all deformation stages [1-5]. In DD models, the system is discretized in both space and time and at each time interval, external or internal interactive forces on each element, here, dislocation segments, are calculated to evaluate corresponding velocity and displacement. Then, the configuration of these segments is updated for the next time interval. Since all the schemes are based on deterministic Newtonian mechanics, once the loading conditions and initial conditions are known, the time evolution of dislocation configurations according to these models is also deterministic. However, the dislocation motion is intrinsically stochastic due to thermal fluctuations, and the Newtonian equation of dislocation motion describes only a representative trajectory of the dislocations. Due to lack of thermal fluctuations, thermal activation processes are not properly accounted for in the deterministic DD models. For instance, once a dislocation is pinned in front of localized obstacles under some constant applied load, it maintains a stationary state at mechanically balanced positions. In reality, however, weak obstacles can be overcome by thermal activation. To remedy the aforementioned problems, thermal forces are implemented into the equation of the dislocation motions, which drives the system to fluctuate around the thermal equilibrium state. The stochastic nature originates from the random rapid collision of dislocations with surrounding quasi-particles such as electrons, phonons, or magnons. Given that the interactions between dislocations and these particles are known (by other quantum mechanical calculations/ atomistic simulations) and the thermal fluctuations follow Gaussian process i.e. regarded as white noise, the stochastic component of
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