TY - JOUR
T1 - A three-dimensional misorientation axis- and inclination-dependent Kobayashi–Warren–Carter grain boundary model
AU - Admal, Nikhil Chandra
AU - Segurado, Javier
AU - Marian, Jaime
N1 - This work has been supported by the US Department of Energys Office of Fusion Energy Sciences , Grant No. DE-SC0012774:0001 . Computer time allocations at UCLAs IDRE Hoffman2 supercomputer are acknowledged. Javier Segurado acknowledges the joint sponsorship by the Fulbright Program and the Spanish Ministry of Education through the Salvador de Madariaga Program, grant PRX17/00103. We would like to thank Matt Jacobs and Stanley Osher for useful discussions and suggesting to us the grim-reaper problem studied in this paper.
This work has been supported by the US Department of Energys Office of Fusion Energy Sciences, Grant No. DE-SC0012774:0001. Computer time allocations at UCLAs IDRE Hoffman2 supercomputer are acknowledged. Javier Segurado acknowledges the joint sponsorship by the Fulbright Program and the Spanish Ministry of Education through the Salvador de Madariaga Program, grant PRX17/00103. We would like to thank Matt Jacobs and Stanley Osher for useful discussions and suggesting to us the grim-reaper problem studied in this paper.
PY - 2019/7
Y1 - 2019/7
N2 - The Kobayashi–Warren–Carter (KWC) phase-field model was originally conceived for two-dimensional systems to model grain boundary migration and grain rotation, which play a crucial role in nanocrystalline materials, and in phenomena such as superplasticity and recrystallization. Existing generalizations of the KWC model to three-dimensions construct the grain boundary energy as a function of misorientation angle between the grains, described as a scalar, and the inclination of the grain boundary. It is well-known that grain boundary energy is described on a five-dimensional space, where three dimensions describe misorientations and two describe inclinations. In this work, we generalize the KWC model by constructing a frame-invariant energy density that is sensitive to all the five-dimensions of misorientations and inclinations. In addition, we derive representations for energy density that result in different forms of anisotropies in inclination and misorientation. The developed framework enables us to introduce the effect of material symmetry on the inclination-dependence. We demonstrate the richness of the model using various three-dimensional numerical examples that simulate anisotropic grain coarsening and grain rotation.
AB - The Kobayashi–Warren–Carter (KWC) phase-field model was originally conceived for two-dimensional systems to model grain boundary migration and grain rotation, which play a crucial role in nanocrystalline materials, and in phenomena such as superplasticity and recrystallization. Existing generalizations of the KWC model to three-dimensions construct the grain boundary energy as a function of misorientation angle between the grains, described as a scalar, and the inclination of the grain boundary. It is well-known that grain boundary energy is described on a five-dimensional space, where three dimensions describe misorientations and two describe inclinations. In this work, we generalize the KWC model by constructing a frame-invariant energy density that is sensitive to all the five-dimensions of misorientations and inclinations. In addition, we derive representations for energy density that result in different forms of anisotropies in inclination and misorientation. The developed framework enables us to introduce the effect of material symmetry on the inclination-dependence. We demonstrate the richness of the model using various three-dimensional numerical examples that simulate anisotropic grain coarsening and grain rotation.
KW - Crystal plasticity
KW - Finite elements
KW - Grain boundaries
KW - Microstructures
KW - Polycrystalline material
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U2 - 10.1016/j.jmps.2019.03.020
DO - 10.1016/j.jmps.2019.03.020
M3 - Article
AN - SCOPUS:85063984427
SN - 0022-5096
VL - 128
SP - 32
EP - 53
JO - Journal of the Mechanics and Physics of Solids
JF - Journal of the Mechanics and Physics of Solids
ER -