Microstructural Evolution in Inhomogeneous Elastic Media

Journal of Computational Physics

Volumn 131, Issue 1, 1997, Pages 109-148

  Jou, H J ^a   Leo, P H ^b   Lowengrub, J S ^c  

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

^b University of Minnesota   (United States)

^c UNIVERSITY OF MINNESOTA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BINARY ALLOYS; COARSENING; MORPHOLOGY; NUMERICAL METHODS; STRAIN;

APPLIED STRAIN; DIFFUSION FIELDS; DIFFUSIONAL TRANSFORMATIONS; ELASTIC FIELDS; FAR-FIELD; INHOMOGENEOUS ELASTIC MEDIAS; ISOTROPICS; MATRIX; MISMATCH STRAIN; TWO-DIMENSIONS;

MICROSTRUCTURAL EVOLUTION;

EID: 0000167670     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1996.5581     Document Type: Article

References (57)

1. Abinandanan T. A., Johnson W. C. Coarsening of elastically interacting coherent particles. II. Simulations of preferential coarsening and particle migrations. Acta Metall. 41:1993;27.
2. Abinandanan T. A., Johnson W. C. Coarsening of elastically interacting coherent particles. I. Theoretical formulation. Acta Metall. 41:1993;17.
3. Almgren R., Dai W., Hakim V. Scaling behavior in an anisotropic Hele-Shaw flow. Phys. Rev. Lett. 71:1993;3461.
4. Ardell A. J., Nicholson R. B. On the modulated structure of aged Ni-Al alloys. Acta Metall. 14:1966;1295.
5. G. Baker, A. Nachbin, Stable methods for vortex sheet motion with surface tension.
6. Beale J. T., Hou T. Y., Lowengrub J. S. Convergence of boundary integral methods for water waves. SIAM J. Num. Anal. 33:1996;1797.
7. Brebbia C. A., Telles J. C. F., Wrobel L. C. Boundary Element Techniques. 1984;Springer-Verlag, Berlin.
8. Christensen R. M. Mechanics of Composite Materials. 1979;Wiley, New York.
9. Conley J., Fine M. E., Weertman J. R. Effect of lattice disregistry variation on the late stage phase transformation behavior of precipitate in Ni-Al-Mo alloys. Acta Metall. 37:1989;1251.
10. Eshelby J. D. The elastic energy-momentum tensor. J. Elasticity. 5:1975;321.
11. Greenbaum A., Greengard L., McFadden G. B. Laplace's equation and the Dirichlet-Neumann map in multiply connected domains. J. Comput. Phys. 105:1993;267.
12. L. Greengard.
13. Greengard L., Rokhlin V. A fast algorithm for particle summations. J. Comput. Phys. 73:1987;325.
14. J. Helsing, An integral equation method for elastostatics of periodic composites.
15. Hort W., Johnson W. C. Coarsening of tetragonally misfitting second phase particles domain building and applied stress. Solid-Solid Phase Transformations. 1994;Minerals, Metals, and Materials Society. p. 629-.
16. T. Y. Hou, J. S. Lowengrub, M. J. Shelley, The long-time motion of vortex sheets with surface tension, Phys. Fluids A.
17. Hou T. Y., Lowengrub J. S., Shelley M. J. Removing the stiffness from interfacial flows with surface tension. J. Comput. Phys. 114:1994;312.
18. Jeon Y. An indirect boundary integral equation method for the biharmonic equation. SIAM J. Num. Anal. 34:1994;461.
19. Johnson W. C. Precipitate shape evolution under applied stress - Thermodynamics and kinetics. Metall. Trans. A. 18:1987;233.
20. Johnson W. C., Abinandanan T. A., Voorhees P. W. The coarsening kinetics of two misfitting particles in an anisotropic crystal. Acta Metall. 38:1990;1349.
21. Johnson W. C., Alexander J. I. D. Interfacial conditions for thermomechanical equilibrium in two-phase crystal. J. Appl. Phys. 59:1986;2735.
22. Johnson W. C., Berkenpas M. B., Laughlin D. E. Precipitate shape transitions during coarsening under uniaxial stress. Acta Metall. 36:1988;3149.
23. Johnson W. C., Voorhees P. W. Elastically-induced precipitate shape transitions in coherent solids. Solid State Phenom. 23:1992;87.
24. Johnson W. C., Voorhees P. W., Zupon D. E. The effects of elastic stress on the kinetics of ostwald ripening: the two-particle problem. Metall. Trans. A. 20:1989;1175.
25. H.-J. Jou, P. H. Leo, J. S. Lowengrub, Numerical simulations of diffusional evolution in inhomogeneous elastic media.
26. Jou H.-J., Leo P. H., Lowengrub J. S. Numerical calculation of precipitate shape evolution in elastic media. Johnson W. C., Howe J. M., Laughlin D. E., Soffa W. A. Solid-Solid Phase Transformations. 1994;635 Minerals, Metals and Materials Society.
27. Khachaturyan A. G., Semenovskaya S. V., Morris J. W. Jr. Theoretical analysis of strain-induced shape changes in cubic precipitates during coarsening. Acta Metall. 36:1988;1563.
28. Krasny R. A study of singularity formation in a vortex sheet by the point vortex approximation. J. Fluid Mech. 167:1986;65.
29. Larchè F. C., Cahn J. W. Thermochemical equilibrium of multiphase solids under stress. Acta Metall. 26:1978;1579.
30. Larchè F. C., Cahn J. W. The interactions of composition and stress in crystalline solids. Acta Metall. 33:1985;331.
31. Lee J. K. A study on coherency strain and precipitate morphology via a discrete atom method. Metall. Trans. A. 27:1996;1449.
32. Lee J. K. Coherency strain analysis via a dicrete atom method. Scripta Met. 32:1995;559.
33. Leo P. H., Jou H.-J. Shape evolution of an initially circular precipitate growing by diffusion in an applied stress field. Acta Metall. 41:1993;2271.
34. Leo P. H., Sekerka R. F. The effect of elastic fields on the morphological stability of a precipitate grown from solid solution. Acta Metall. 37:1989;3139.
35. Leo P. H., Sekerka R. F. The effect of surface stress on crystal-melt and crystal-crystal equilibrium. Acta Metall. 37:1989;3119.
36. Maheshwari A., Ardell A. J. Morphological evolution of coherent misfitting precipitates in anisotropic elastic media. Phys. Rev. Lett. 70:1993;2305.
37. McCormack M., Khatchaturyan A. G., Morris J. W. A two-dimensional analysis of the evolution of coherent precipitates in elastic media. Acta Metall. 40:1992;325.
38. Mikhlin S. G. Integral Equations and Their Applications to Certain Problems in Mechanics, Mathematical Physics, and Technology. 1957;Pergamon, New York.
39. Miyazaki T., Hakamura K., Mori H. Experimental and theoretical investigations on morphological changes ofgamma. J. Mater. Sci. 14:1979;1827.
40. Mullins W., Sekerka R. Morphological stability of a particle growing by diffusion or heat flow. J. Appl. Phys. 34:1963;323.
41. Mura T. Micromechanics of Defects in Solids. 1987;Nijhoff, Boston.
42. Reed M., Simon B. Functional Analysis. Methods of Modern Mathematical Physics. 1:1980;Academic Press, New York.
43. Rubinstein J., Sternberg P. Nonlocal reaction-diffusion equations and nucleation. I.M.A. J. Appl. Math. 48:1992;249.
44. Saad Y., Schultz M. R. GMRES: A generalized minimum residual method for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7:1986;856.
45. Sidi A., Israeli M. Quadrature methods for periodic singular and weakly singular Fredholm integral equations. J. Sci. Comput. 3:1988;201.
46. Socrate S., Parks D. M. Numerical determination of the elastic driving force for directional coarsening in Ni-superalloys. Acta Metall. 41:1993;2185.
47. Su C. H., Voorhees P. W. Dynamics of precipitate evolution in elastically stressed solids. I. Inverse coarsening. Acta Mater. 44:1996;1987.
48. Su C. H., Voorhees P. W. Dynamics of precipitate evolution in elastically stressed solids. II. Particle alignment. Acta Mater. 44:1996;2001.
49. Thompson M. E., Su C. S., Voorhees P. W. The equilibrium shape of a misfitting precipitate. Acta Metall. 42:1994;2107.
50. Tien J. K., Copley S. M. The effect of uniaxial stress on the periodic morphology of coherent gamma prime precipitates in nickel-base superalloy crystals. Met. Trans. 2:1971;215.
51. Voorhees P. W. The theory of Ostwald ripening. J. Stat. Phys. 38:1985;231.
52. Voorhees P. W., Boisvert R. F., McFadden G. B., Meiron D. I. Numerical simulation of morphological development during Ostwald ripening. Acta Metall. 36:1988;207.
53. Voorhees P. W., McFadden G. B., Johnson W. C. On the morphological development of second-phase particles in elastically-stressed solids. Acta Metall. 40:1992;2979.
54. Wang Y., Chen L. Q., Khachaturyan A. G. Kinetics of strain-induced morphological transformation in cubic alloys with a miscibility gap. Acta Metall. 41:1993;279.
55. 2. J. Am. Ceram. Soc. 76:1993;3029.
56. Wang Y., Khachaturyan A. G. Shape instability during precipitate growth in coherent solids. Acta Metall. 43:1995;1837.
57. Yoo Y. S., Yoon D. Y., Henry M. F. The effect of elastic misfit strain on the morphological evolution of γ′-precipitates in a model Ni-base superalloy. Metals and Mat. 1:1995;47.