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

Yu, Qianran; Martínez, Enrique; Segurado, Javier; Marian, Jaime

doi:10.1007/s00466-021-02073-7

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

Journal Article · 20 August 2021 · Computational Mechanics

DOI: https://doi.org/10.1007/s00466-021-02073-7 · OSTI ID:1814553

; Martínez, Enrique; Segurado, Javier; Marian, Jaime

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.

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Research Organization:: Univ. of California, Los Angeles, CA (United States)

Sponsoring Organization:: National Science Foundation (NSF); Spanish Ministry of Education; USDOE; USDOE Office of Science (SC)

Grant/Contract Number:: SC0019157

OSTI ID:: 1814553

Journal Information:: Computational Mechanics, Journal Name: Computational Mechanics Journal Issue: 6 Vol. 68; ISSN 0178-7675

Publisher:: Springer Science + Business MediaCopyright Statement

Country of Publication:: Germany

Language:: English

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

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