A duality-based coupling of Cosserat crystal plasticity and phase field theories for modeling grain refinement

Baek, Jonghyuk; Chen, Jiun‐Shyan; Tupek, Michael; Beckwith, Frank; Fang, H. Eliot

doi:10.1002/nme.6884

Title: A duality-based coupling of Cosserat crystal plasticity and phase field theories for modeling grain refinement

Journal Article · 19 November 2021 · International Journal for Numerical Methods in Engineering

DOI: https://doi.org/10.1002/nme.6884 · OSTI ID:1834120

Baek, Jonghyuk ^[1];

^[1];

^[2]; Beckwith, Frank ^[2]; Fang, H. Eliot ^[2]

Univ. of California, San Diego, CA (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

High-rate deformation processes of metals entail intense grain refinement and special attention needs to be paid to capture the evolution of microstructure. In this article, a new formulation for coupling Cosserat crystal plasticity and phase field is developed. A common approach is to penalize kinematic incompatibility between lattice orientation and displacement-based elastic rotation. However, this can lead to significant solution sensitivity to the penalty parameter, resulting in low accuracy and convergence rates. To address these issues, a duality-based formulation is developed which directly imposes the rotational kinematic compatibility. A weak inf-sup-based skew-symmetric stress projection is introduced to suppress instabilities present in the dual formulation. An additional least squares stabilization is introduced to suppress the spurious lattice rotation with a suitable parameter range derived analytically and validated numerically. The required high-order continuity is attained by the reproducing kernel approximation. It is observed that equal order displacement-rotation-phase field approximations are stable, which allows efficient employment of the same set of shape functions for all independent variables. The proposed formulation is shown to yield superior accuracy and convergence with marginal parameter sensitivity compared to the penalty-based approach and successfully captures the dominant rotational recrystallization mechanism including block dislocation structures and grain boundary migration.

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Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); University of California, San Diego

Grant/Contract Number:: NA0003525

OSTI ID:: 1834120

Alternate ID(s):: OSTI ID: 1834438

Report Number(s):: SAND2021-15166J; {"Journal ID: ISSN 0029-5981",702119}

Journal Information:: International Journal for Numerical Methods in Engineering, Journal Name: International Journal for Numerical Methods in Engineering Journal Issue: 4 Vol. 123; ISSN 0029-5981

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

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