Sharp-interface and phase-field theories of recrystallization in the plane

Physica D: Nonlinear Phenomena

Volumn 130, Issue 1-2, 1999, Pages 133-154

  Gurtin, Morton E ^a   Lusk, Mark T ^b  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b Department of Geology and Geological Engineering   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0346965755     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(98)00323-6     Document Type: Article

References (25)

1. P.G. Shewmon, Transformations in Metals, McGraw-Hill, New York, 1969.
2. J.E. Bailey, P.B. Hirsch, Recrystallization processes in some polycrystalline metals, Proc. Roy. Soc. London 267 (1962) 11-30.
3. J.D. Eshelby, The force on an elastic singularity, Phil. Trans. A 244 (1951) 87-112.
4. M.E. Gurtin, Multiphase thermomechanics with interfacial structure. 1. Heat conduction and the capillary balance law, Arch. Rational Mech. Anal. 104 (1988) 185-221.
5. M.E. Gurtin, A. Struthers, Multiphase thermomechanics with interfacial structure. 3. Evolving phase boundaries in the presence of bulk deformation, Arch. Rational Mech. Anal. 112 (1990) 97-160.
6. M.E. Gurtin, The nature of configurational forces, Arch. Rational Mech. Anal. 131 (1995) 67-100.
7. E. Fried, M.E. Gurtin, Continuum theory of thermally induced phase transitions based on an order parameter, Physica D 68 (1993) 326-343.
8. M.E. Gurtin, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance, Physica D 92 (1996) 178-192.
9. M.P. Anderson, D.J. Srolovitz, G.S. Grest, P.S. Sahni, Computer simulation of grain growth-I. kinetics, Acta Met. 32 (1984) 783-791.
10. M.P. Anderson, D.J. Srolovitz, G.S. Grest, P.S. Sahni, Computer simulation of recrystallization-I. Homogeneous nucleation and growth, Acta Met. 34 (1986) 1833-1845.
11. M.E. Gurtin, Thermomechanics of Evolving Phase Boundaries in the Plane, Oxford Press, Oxford, 1993.
12. F.J. Humphreys, M. Hatherly, Recrystallization and Related Annealing Phenomena, Pergamon Press, New York, 1995.
13. L. Bragg, J.F. Nye, A dynamical model of a crystal structure, Proc. Roy. Soc. London 190 (1947) 474-481.
14. D.A. Porter, K.E. Easterling, Phase Transformations in Metals and Alloys, Chapman and Hall, London, 1993.
15. B.D. Coleman, W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal. 13 (1963) 245-261.
16. E. Fried, Correspondence between a phase-field theory and a sharp-interface theory for crystal growth, Cont. Mechs. Thermo., 1996, in press.
17. E. Fried, M.E. Gurtin, A phase-field theory for solidification based on a general anisotropic sharp-interface theory with interfacial energy and entropy, Physica D 72 (1996) 287-308.
18. J. Rubinstein, P. Sternberg, J. Keller, Fast reaction, slow diffusion, and curve shortening, SIAM J. Appl. Math. 49 (1989) 116-133.
19. N, Proc. Roy. Soc. Edinberg A 116 (1990) 207-220.
20. L.C. Evans, H.M. Soner, P. Souganidis, Phase transitions and generalized motion by mean curvature, Comm. Pure Appl. Math. 45 (1992) 1097-1123.
21. L. Bronsard, R. Kohn, Motion by mean curvature as the singular limit of Ginzburg-Landau dynamics, J. Diff. Eqts. 90 (1991) 211-237.
22. L. Bronsard, F. Reitich, On three-phase boundary motion and the singular limit of a vector-valued Ginzburg-Landau equation, Arch. Rational Mech. Anal. 124 (1993) 355-379.
23. I. Steinbach, F. Pezolla, B. Nestler, M. Seebelberg, R. Prieler, G.J. Schmitz, J.L.L. Rezende, A phase-field concept for multi phase systems, Physica D (1996) 35-147.
24. H. Garcke, B. Nestler, B. Stoth, A multi phase-field concept: numerical simulations of moving phase boundaries and multiple junctions, SIAM J. Appl. Math., 1998, submitted for publication.
25. A.A. Wheeler, G.B. McFadden, On the notion of a ζ-vector and a stress tensor for a general class of anisotropic diffuse interface models, Proc. Roy Soc. London A453 (1997) 1611-1630.