Equation of motion for grain boundaries in polycrystals
Source abstract
Abstract
Abstract Grain boundary (GB) dynamics are largely controlled by the formation and motion of disconnections (with step and dislocation characters) along with the GB. The dislocation character gives rise to shear coupling; i.e. the relative tangential motion of two grains meeting at the GB during GB migration. In a polycrystal, the shear coupling is constrained by the presence of other grains and GB junctions, which prevents large-scale sliding of one grain relative to the other. We present continuum equations of motion for GBs that is based upon the underlying disconnection dynamics and accounts for this mechanical constraint in polycrystals. This leads to a reduced-order (zero-shear constrained) model for GB motion that is easily implemented in a computationally efficient framework, appropriate for the large-scale simulation of the evolution of polycrystalline microstructures. We validated the proposed reduced-order model with direct comparisons to full multi-disconnection mode simulations.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Microstructure and mechanical properties · Microstructure and Mechanical Properties of Steels · Magnetic Properties and Applications
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (44)
Show source-provided references
1. Sutton, A. P. and Balluffi, R. W. Interfaces in Crystalline Materials (1995).
2. Hillert, M. On the theory of normal and abnormal grain growth. Acta Metall. 13, 227–238 (1965).10.1016/0001-6160(65)90200-2 ↗
3. Mullins, W. Two-dimensional motion of idealized grain boundaries. J. Appl. Phys. 27, 900–904 (1956).10.1063/1.1722511 ↗
4. Ashby, M. F. Boundary defects, and atomistic aspects of boundary sliding and diffusional creep. Surface Sci. 31, 498–542 (1972).10.1016/0039-6028(72)90273-7 ↗
5. Bollmann, W. Crystal Defects and Crystalline Interfaces (1970).10.1007/978-3-642-49173-3 ↗
6. King, A. H. & Smith, D. A. The effects on grain-boundary processes of the steps in the boundary plane associated with the cores of grain-boundary dislocations. Acta Cryst. A36, 335–343 (1980).10.1107/S0567739480000782 ↗
7. Hirth, J. P. & Pond, R. C. Steps, dislocations and disconnections as interface defects relating to structure and phase transformations. Acta Mater. 44, 4749–4763 (1996).10.1016/S1359-6454(96)00132-2 ↗
8. Khater, H. A., Serra, A., Pond, R. C. & Hirth, J. P. The disconnection mechanism of coupled migration and shear at grain boundaries. Acta Mater. 60, 2007–2020 (2011).10.1016/j.actamat.2012.01.001 ↗
9. Rajabzadeh, A., Mompiou, F., Legros, M. & Combe, N. Elementary mechanisms of shear-coupled grain boundary migration. Phys. Rev. Lett. 110, 265507 (2013).10.1103/PhysRevLett.110.265507 ↗
10. Rajabzadeh, A., Legros, M., Combe, N., Mompiou, F. & Molodov, D. A. Evidence of grain boundary dislocation step motion associated to shear-coupled grain boundary migration. Philos. Mag. 93, 1299–1316 (2013).10.1080/14786435.2012.760760 ↗
11. Mompiou, F., Legros, M., Ensslen, C. & Kraft, O. In situ TEM study of twin boundary migration in sub-micron be fibers. Acta Mater. 96, 57–65 (2015).10.1016/j.actamat.2015.06.016 ↗
12. Thomas, S. L., Chen, K. T., Han, J., Purohit, P. K. & Srolovitz, D. J. Reconciling grain growth and shear-coupled grain boundary migration. Nature Commun. 8, 1764 (2017).10.1038/s41467-017-01889-3 ↗
13. Han, J., Thomas, S. L. & Srolovitz, D. J. Grain boundary kinetics: a unified approach. Prog. Mater. Sci. 98, 386–476 (2018).10.1016/j.pmatsci.2018.05.004 ↗
14. Zhang, L. C., Han, J., Xiang, Y. & Srolovitz, D. J. Equation of motion for a grain boundary. Phys. Rev. Lett. 119, 246101 (2017).10.1103/PhysRevLett.119.246101 ↗
15. Wei, C. Z., Thomas, S. L., Han, J., Xiang, Y. & Srolovitz, D. J. A continuum multi-disconnection-mode model for grain boundary motion. J. Mech. Phys. Solids 133, 103731 (2019).10.1016/j.jmps.2019.103731 ↗
16. Thomas, S. L., Wei, C. Z., Han, J., Xiang, Y. & Srolovitz, D. J. Disconnection description of triple junction motion. Proc. Natl. Acad. Sci. USA 116, 8756–8765 (2019).10.1073/pnas.1820789116 ↗
17. Wei, C. Z., Zhang, L. C., Han, J., Srolovitz, D. J. & Xiang, Y. Grain boundary triple junction dynamics: a continuum disconnection model. SIAM J. Appl. Math. 80, 1101–1122 (2020).10.1137/19M1277722 ↗
18. Cahn, J. W. & Taylor, J. E. A unified approach to motion of grain boundaries, relative tangential translation along grain boundaries, and grain rotation. Acta Mater. 52, 4887–4898 (2004).10.1016/j.actamat.2004.02.048 ↗
19. Cahn, J. W., Mishin, Y. & Suzuki, A. Coupling grain boundary motion to shear deformation. Acta Mater. 54, 4953–4975 (2006).10.1016/j.actamat.2006.08.004 ↗
20. Taylor, J. E. & Cahn, J. W. Shape accommodation of a rotating embedded crystal via a new variational formulation. Interfaces Free Boundaries 9, 493–512 (2007).10.4171/IFB/174 ↗
21. Winning, M., Gottstein, G. & Shvindlerman, L. S. Stress induced grain boundary motion. Acta Mater. 49, 211–219 (2001).10.1016/S1359-6454(00)00321-9 ↗
22. Winning, M., Gottstein, G. & Shvindlerman, L. S. On the mechanisms of grain boundary migration. Acta Mater. 50, 353–363 (2002).10.1016/S1359-6454(01)00343-3 ↗
23. Gottstein, G., Molodov, D. A., Shvindlerman, L. S., Srolovitz, D. J. & Winning, M. Grain boundary migration: misorientation dependence. Curr. Opin. Solid State Mater. Sci. 5, 9–14 (2001).10.1016/S1359-0286(00)00030-9 ↗
24. Molodov, D. A., Ivanov, V. A. & Gottstein, G. Low angle tilt boundary migration coupled to shear deformation. Acta Mater. 55, 1843–1848 (2007).10.1016/j.actamat.2006.10.045 ↗
25. Rupert, T. J., Gianola, D. S., Gan, Y. & Hemker, K. J. Experimental observations of stress-driven grain boundary migration. Science 326, 1686–1690 (2009).10.1126/science.1178226 ↗
26. Molteni, C., Francis, G. P., Payne, M. C. & Heine, V. First principles simulation of grain boundary sliding. Phys. Rev. Lett. 76, 1284–1287 (1996).10.1103/PhysRevLett.76.1284 ↗
27. Molteni, C., Marzari, N., Payne, M. C. & Heine, V. Sliding mechanisms in aluminum grain boundaries. Phys. Rev. Lett. 79, 869–872 (1997).10.1103/PhysRevLett.79.869 ↗
28. Hamilton, J. C. & Foiles, S. M. First-principles calculations of grain boundary theoretical shear strength using transition state finding to determine generalized gamma surface cross sections. Phys. Rev. B 65, 064104 (2002).10.1103/PhysRevB.65.064104 ↗
29. Chen, L. Q. & Kalonji, G. Finite temperature structure and properties of Σ = 5 (310) tilt grain boundaries in NaCl a molecular dynamics study. Philos. Mag. A 66, 11–26 (1992).10.1080/01418619208201510 ↗
30. Shiga, M. & Shinoda, W. Stress-assisted grain boundary sliding and migration at finite temperature: a molecular dynamics study. Phys. Rev. B 70, 054102 (2004).10.1103/PhysRevB.70.054102 ↗
31. Sansoz, F. & Molinari, J. F. Mechanical behavior of Σ tilt grain boundaries in nanoscale Cu and Al: a quasicontinuum study. Acta Mater. 53, 1931–1944 (2005).10.1016/j.actamat.2005.01.007 ↗
32. Trautt, Z., Adland, A., Karma, A. & Mishin, Y. Coupled motion of asymmetrical tilt grain boundaries: molecular dynamics and phase field crystal simulation. Acta Mater. 60, 6528–6546 (2012).10.1016/j.actamat.2012.08.018 ↗
33. Homer, E. R., Foiles, S. M., Holm, E. A. & Olmsted, D. L. Phenomenology of shear-coupled grain boundary motion in symmetric tilt and general grain boundarie. Acta Mater. 61, 1048–1060 (2013).10.1016/j.actamat.2012.10.005 ↗
34. Han, J., Vitek, V. & Srolovitz, D. J. Grain-boundary metastability and its statistical properties. Acta Mater. 104, 259–273 (2016).10.1016/j.actamat.2015.11.035 ↗
35. Mishin, Y., Mehl, M. J., Papaconstantopoulos, D. A., Voter, A. F. & Kress, J. D. Structural stability and lattice defects in copper: ab initio, tight-binding, and embedded-atom calculations. Phys. Rev. B Condens. Matter 63, 224106 (2001).10.1103/PhysRevB.63.224106 ↗
36. Chen, K. T., Han, J., Thomas, S. L. & Srolovitz, D. J. Grain boundary shear coupling is not a grain boundary property. Acta Mater. 167, 241–247 (2019).10.1016/j.actamat.2019.01.040 ↗
37. Hirth, J. P. and Lothe, J. Theory of Dislocations. 2nd ed (1982).10.1115/1.3167075 ↗
38. Qin, X. X., Zhang, L. C. & Xiang, Y. A three-dimensional continuum simulation method for grain boundary motion incorporating dislocation structure. Preprint at https://arxiv.org/abs/2102.00386 (2021).10.1007/s10915-021-01694-7 ↗
39. Zhu, X. H. & Xiang, Y. Continuum framework for dislocation structure, energy and dynamics of dislocation arrays and low angle grain boundaries. J. Mech. Phys. Solids 69, 175–194 (2014).10.1016/j.jmps.2014.05.005 ↗
40. Wang, Y. U., Jin, Y. M., Cuitino, A. M. & Khachaturyan, A. G. Nanoscale phase field microelasticity theory of dislocations: model and 3D simulations. Acta Mater. 49, 1847–1857 (2001).10.1016/S1359-6454(01)00075-1 ↗
41. Koslowski, M., Cuitino, A. M. & Ortiz, M. A phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals. J. Mech. Phys. Solids 50, 2597–2635 (2002).10.1016/S0022-5096(02)00037-6 ↗
42. Rodney, D., Le Bouar, Y. & Finel, A. Phase field methods and dislocations. Acta Mater. 51, 17–30 (2003).10.1016/S1359-6454(01)00379-2 ↗
43. Shen, C. & Wang, Y. Phase field model of dislocation networks. Acta Mater. 51, 2595–2610 (2003).10.1016/S1359-6454(03)00058-2 ↗
44. Xiang, Y., Cheng, L. T., Srolovitz, D. J. & Weinan, E. A level set method for dislocation dynamics. Acta Mater. 51, 5499–5518 (2003).10.1016/S1359-6454(03)00415-4 ↗