Large-scale simulation of normal grain growth via diffusion-generated motion

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 467, Issue 2126, 2011, Pages 381-401

  Elsey, Matt ^a   Esedoglu, Selim ^a   Smereka, Peter ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Grain growth; Level set; Microstructure; Simulation

Indexed keywords

DIFFUSION; GRAIN SIZE AND SHAPE; MICROSTRUCTURE; NUMERICAL METHODS;

FULLY RESOLVED SIMULATIONS; GRAIN RADIUS; GRAIN-SIZE DISTRIBUTION; LARGE SCALE SIMULATIONS; LEVEL SET; LEVEL SET METHOD; NORMAL GRAIN GROWTH; SELF-SIMILAR; SIGNED DISTANCE FUNCTION; SIMULATION; SIMULATION RESULT; SQUARE ROOTS; THEORETICAL PREDICTION; THREE DIMENSIONS; TOPOLOGICAL TRANSITIONS;

GRAIN GROWTH;

EID: 79551628300     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2010.0194     Document Type: Conference Paper

References (52)

1. Aboav, D. A. 1970 The arrangement of grains in a polycrystal. Metallurgy 3, 383-390. (doi:10.1016/0026-0800(70)90038-8)
2. Anderson, M. P., Grest, G. S. & Srolovitz, D. J. 1989 Computer simulation of normal grain growth in three dimensions. Phil. Mag. B 59, 293-329. (doi:10.1080/13642818908220181)
3. Beck, P. 1952 Interface migration in recrystallization. In Metal interfaces (ed. R. Brick), pp. 208-247. Cleveland, OH: American Society for Metals.
4. Cahn, J. W. 1967 The significance of average mean curvature and its determination by quantitative metallography. Trans. Am. Inst. Metall. Eng. 239, 610-616.
5. Desch, C. H. 1919 The solidification of metals from the liquid state. J. Inst. Metals 22, 241-276.
6. Edwards, S. F. & Pithia, K. D. 1994 A note on the Aboav-Weaire law. Phys. A 205, 577-584. (doi:10.1016/0378-4371(94)90222-4)
7. Elsey, M., Esedoglu, S. & Smereka, P. 2009 Diffusion generated motion for grain growth in two and three dimensions. J. Comput. Phys. 228, 8015-8033. (doi:10.1016/j.jcp.2009.07.020)
8. Esedoglu, S. & Smereka, P. 2008 A variational formulation for a level set representation of multiphase flow and area preserving curvature flow. Commun. Math. Sci. 6, 125-148.
9. Esedoglu, S., Ruuth, S. & Tsai, R. 2010 Diffusion generated motion using signed distance functions. J. Comput. Phys. 229, 1017-1042. (doi:10.1016/j.jcp.2009.10.002)
10. Fan, D. & Chen, L.-Q. 1997 Computer simulation of grain growth using a continuum field model. Acta Mater. 45, 611-622. (doi:10.1016/S1359-6454(96) 00200-5) (Pubitemid 127415430)
11. Fayad, W., Thompson, C. V. & Frost, H. J. 1999 Steady-state grain-size distributions resulting from grain growth in two dimensions. Scr. Mater. 40, 1199-1204. (doi:10.1016/S1359-6462(99)00034-2)
12. Feltham, P. 1957 Grain growth in metals. Acta Metall. 5, 97-105. (doi:10.1016/0001-6160(57)90136-0)
13. Garcke, H., Nestler, B. & Stoth, B. 1999 A multiphase field concept: numerical simulations of moving phase boundaries and multiple junctions. SIAM J. Appl. Math. 60, 295-315. (doi:10.1137/S0036139998334895)
14. Glicksman, M. E., Rios, P. R. & Lewis, D. J. 2009 Mean width and caliper characteristics of network polyhedra. Philos. Mag. 89, 389-403. (doi:10.1080/14786430802651513)
15. Harker, D. & Parker, E. 1945 Grain shape and grain growth. Trans. Am. Soc. Met. 34, 156-201.
16. Herring, C. 1951 Surface tension as a motivation for sintering. In The physics of powder metallurgy (ed. W. Kingston), pp. 143-179. New York, NY: McGraw-Hill.
17. Hilgenfeldt, S., Kraynik, A. M., Koehler, S. A. & Stone, H. A. 2001 An accurate von Neumann's law for three-dimensional foams. Phys. Rev. Lett. 86, 2685-2688. (doi:10.1103/PhysRevLett.86.2685) (Pubitemid 32286732)
18. Hillert, M. 1965 On the theory of normal and abnormal grain growth. Acta Metall. 13, 227-238. (doi:10.1016/0001-6160(65)90200-2)
19. Hull, F. C. 1988 Plane section and spatial characteristics of equiaxed β-brass grains. Mater. Sci. Technol. 4, 778-785.
20. Kawasaki, K., Nagai, T. & Nakashime, K. 1989 Vertex models for two-dimensional grain growth. Phil. Mag. B 60, 399-421. (doi:10.1080/ 13642818908205916)
21. Kelvin, W. T. 1887 On the division of space with minimum partitional area. Philos. Mag. 24, 503-514.
22. Kim, S. G., Kim, D. I., Kim, W. T. & Park, Y. B. 2006 Computer simulations of two-dimensional and three-dimensional ideal grain growth. Phys. Rev. E 74, 061605. (doi:10.1103/PhysRevE.74.061605) (Pubitemid 46130654)
23. Kinderlehrer, D., Lee, J., Livshits, I., Rollett, A. & Ta'asan, S. 2004 Mesoscale simulation of grain growth. Mater. Sci. Forum 67-70, 1057-1062. (doi:10.4028/www.scientific.net/MSF.467-470.1057)
24. Krill III, C. E. & Chen, L.-Q. 2002 Computer simulation of 3-D grain growth using a phase-field model. Acta Mater. 50, 3059-3075. (doi:10.1016/S1359-6454(02)00084-8)
25. Liu, G., Yu, H., Song, X. & Qin, X. 2001 A new model of three-dimensional grain growth: theory and computer simulation of topology-dependency of individual grain growth rate. Mater. Des. 22, 33-38. (doi:10.1016/S0261-3069(00)00040-6)
26. Louat, N. P. 1974 On the theory of normal grain growth. Acta Metall. 22, 721-724. (doi:10.1016/ 0001-6160(74)90081-9)
27. MacPherson, R. & Srolovitz, D. 2007 The von Neumann relation generalized to coarsening of three-dimensional microstructures. Nature 446, 1053-1055. (doi:10.1038/nature05745) (Pubitemid 46676059)
28. Mantegazza, C., Novaga, M. & Tortorelli, V. M. 2004 Motion by curvature of planar networks. Ann. Scuola Norm. Super. Pisa-Cl. Sci. 3, 235-324.
29. Meijering, J. L. 1953 Interface area, edge length, and number of vertices in crystal aggregates with random nucleation. Phillips Res. Rep. 8, 270-290.
30. Merriman, B., Bence, J. K. & Osher, S. 1994 Motion of multiple junctions: a level set approach. J. Comput. Phys. 112, 334-363. (doi:10.1006/jcph.1994.1105) (Pubitemid 124013436)
31. Mullins, W. W. 1956 Two-dimensional motion of idealized grain boundaries. J. Appl. Phys. 27, 900-904. (doi:10.1063/1.1722511)
32. Mullins, W. W. 1989 Estimation of the geometrical rate constant in idealized three dimensional grain growth. Acta Metall. 37, 2979-2984. (doi:10.1016/0001-6160(89)90333-7) (Pubitemid 20622872)
33. Reitich, F. & Soner, H. M. 1996 Three-phase boundary motion under constant velocities. I: The vanishing surface tension limit. Proc. R. Soc. Edin. 126A, 837-865. (Pubitemid 126766842)
34. Rhines, F. R. & Patterson, B. R. 1982 Effect of the degree of prior cold work on the grain volume distribution and the rate of grain growth of recrystallized aluminum. Metall. Trans. A 13, 985-993. (doi:10.1007/BF02643395)
35. Rios, P. R., Dalpian, T. G., Brandão, V. S., Castro, J. A. & Oliveira, A. C. L. 2006 Comparison of analytical grain size distributions with three-dimensional computer simulations and experimental data. Scr. Mater. 54, 1633-1637. (doi:10.1016/j.scriptamat.2006.01.007) (Pubitemid 43289285)
36. Russo, G. & Smereka, P. 2000 A remark on computing distance functions. J. Comput. Phys. 163, 51-67. (doi:10.1006/jcph.2000.6553)
37. Ruuth, S. J. 1998a A diffusion-generated approach to multiphase motion. J. Comput. Phys. 145, 166-192. (doi:10.1006/jcph.1998.6028) (Pubitemid 128341070)
38. Ruuth, S. J. 1998b Efficient algorithms for diffusion-generated motion by mean curvature. J. Comput. Phys. 144, 603-625. (doi:10.1006/jcph.1998.6025) (Pubitemid 128341059)
39. Smereka, P. 2006 The numerical approximation of a delta function with application to level set methods. J. Comput. Phys. 211, 77-90. (doi:10.1016/j.jcp.2005.05.005) (Pubitemid 41363975)
40. Smith, C. S. 1952 Grain shapes and other metallurgical applications of topology. In Metal interfaces (ed. R. Brick), pp. 65-114. Cleveland, OH: American Society for Metals.
41. Smith, C. S. 1964 Some elementary principles of polycrystalline microstructure. Met. Rev. 9, 1-48.
42. Suwa, Y., Saito, Y. & Onodera, H. 2008 Parallel computer simulation of three-dimensional grain growth using the multi-phase-field model. Mater. Trans. 49, 704-709. (doi:10.2320/matertrans.MRA2007225) (Pubitemid 351742882)
43. Wakai, F., Enomoto, N. & Ogawa, H. 2000 Three-dimensional microstructural evolution in ideal grain growth-general statistics. Acta Mater. 48, 1297-1311. (doi:10.1016/S1359-6454(99)00405-X)
44. Wakai, F., Shinoda, Y., Ishihara, S. & Dominguez-Rodriguez, A. 2001 Topological transformation of grains in three-dimensional normal grain growth. J. Mater. Res. 16, 2136-2142. (doi:10.1557/JMR.2001.0291) (Pubitemid 34574487)
45. Weaire, D. 1974 Some remarks on the arrangement of grains in a polycrystal. Metall. 7, 157-160. (doi:10.1016/0026-0800(74)90004-4)
46. Weaire, D. & Glazier, J. A. 1993 Relation between volume, number of faces and threedimensional growth laws in coarsening cellular patterns. Phil. Mag. Lett. 68, 363-365. (doi:10.1080/09500839308242429)
47. Weygand, D. & Bréchet, Y. 1999 Three-dimensional grain growth: a vertex dynamics simulation. Philos. Mag. B 79, 703-716. (doi:10.1080/ 13642819908205744)
48. Williams, R. E. 1968 Space-filling polyhedron: its relation to aggregates of soap bubbles, plant cells, and metal crystallites. Science 161, 276-277. (doi:10.1126/science.161.3838.276)
49. Williams, W. M. & Smith, C. S. 1952 A study of grain shape in an aluminum alloy and other applications of stereoscopic microradiography. Trans. Am. Inst. Min. Met. Eng. 194, 755-765.
50. Zhang, C., Suzuki, A., Ishimaru, T. & Enomoto, M. 2004 Characterization of three-dimensional grain structure in polycrystalline iron by serial sectioning. Metall. Mater. Trans. A 35A, 1927-1933. (doi:10.1007/s11661- 004-0141-5)
51. Zhao, H.-K. 2004 A fast sweeping method for Eikonal equations. Math. Comput. 74, 603-627. (doi:10.1090/S0025-5718-04-01678-3)
52. Zhao, H.-K., Chan, T., Merriman, B. & Osher, S. 1996 A variational level set approach to multiphase motion. J. Comput. Phys. 127, 179-195. (doi:10.1006/jcph.1996.0167v)