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Analytical solution for shape evolution of a coherent precipitate in triaxially stressed solid

Published online by Cambridge University Press:  01 October 2004

Hua Wang  and
Zhonghua Li
Hua Wang
Affiliation:
School of Civil Engineering and Mechanics, Shanghai Jiaotong University, 200240 Shanghai Minhang, People’s Republic of China
Zhonghua Li*
Affiliation:
School of Civil Engineering and Mechanics, Shanghai Jiaotong University, 200240 Shanghai Minhang, People’s Republic of China
*
a) Address all correspondence to this author. e-mail: zhli@sjtu.edu.cn
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Abstract

An analytical solution for shape evolution of a coherent misfit precipitate in triaxially stressed solid has been proposed based on Eshelby inclusion theory. With complete energy consideration, the free energy that controls the shape evolution of the precipitate is a function of the precipitate shape, size, triaxially applied stresses, misfit strains, and Young’s moduli of the precipitate and the matrix. Based on the energy analysis, a comprehensive picture of shape evolution of the precipitate is presented.

Keywords

Second phasesMorphology

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Type
Articles
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Journal of Materials Research , Volume 19 , Issue 10 , October 2004 , pp. 3068 - 3075
Copyright
Copyright © Materials Research Society 2004

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References

REFERENCES

1Ardel, A.J.: Diffraction contrast at planar interface of large coherent precipitates. Philos. Mag. A 16, 147 (1967).CrossRefGoogle Scholar
2Doi, M., Miyazaki, T. and Wakatsuki, T.: Effects of elastic interaction energy on the gamma prime precipitate morphology of continuously cooled nickel-base alloys. Mater. Sci. Eng. 74, 139 (1985).CrossRefGoogle Scholar
3Li, D.Y. and Chen, L.Q.: Shape evolution and splitting of coherent particles under applied stresses. Acta Mater. 47, 247 (1998).CrossRefGoogle Scholar
4Taylor, J.E.: Crystalline variational problems. Bull. Am. Math. Soc. 84, 568 (1978).CrossRefGoogle Scholar
5Fonseca, I.: The Wul theorem revisited. Proc. R. Soc. Lond. Ser. A 432,125 (1991).Google Scholar
6Thompson, M.E., Su, C.S. and Voorhees, P.W.: The equilibrium shape of a misfitting precipitate. Acta Metall. Mater. 42 62107 (1994).CrossRefGoogle Scholar
7Lee, J.K.: A study on coherent strain and precipitate morphology via a discrete atom method. Metall. Mater. Trans. 27A, 1449 (1996).CrossRefGoogle Scholar
8Lee, J.K.: Coherence strain analysis via a discrete atom method. Scripta Metall. Mater. 32, 559 (1995).CrossRefGoogle Scholar
9Choy, J.H. and Lee, J.K.: On the shape evolution of a two-dimensional coherent precipitate with a general misfit strain. Mater. Sci. Eng. A 285,195 (2000).CrossRefGoogle Scholar
10Leo, P.H., Lowengrub, J.S. and Jou, H.J.: Diffuse interface model for microstructural evolution in elastically stressed solids. Acta Mater. 46, 2113 (1998).CrossRefGoogle Scholar
11Leo, P.H., Lowengrub, J.S. and Nie, Q.: Microstructural evolution in orthotropic elastic media. J. Comp. Phys. 157, 44 (2000).CrossRefGoogle Scholar
12Kolling, S., Mueller, R. and Gross, D.: The influence of elastic constants on the shape of an inclusion. Int. J. Solids Struct. 40, 4399 (2003).CrossRefGoogle Scholar
13Schmidt, I. and Gross, D.: A strategy for determining the equilibrium shape of an inclusion. Arch. Mech. 47, 379 (1995).Google Scholar
14Mueller, R. and Gross, D.: 3D simulation of equilibrium morphologies of precipitates. Comp. Mater. Sci. 11, 35 (1998).CrossRefGoogle Scholar
15Wang, Y. and Khachaturyan, A.G.: Three-dimensional field model and computer modeling of martensitic transformations. Acta Mater. 45, 759 (1997).CrossRefGoogle Scholar
16Lee, J.K.: Morphology of coherent precipitates via a discrete atom method. Mater. Sci. Eng. A 238, 1 (1997).CrossRefGoogle Scholar
17Thompson, M.E. and Voorhees, P.W.: Equilibrium particle morphologies in elastically stressed coherent solids. Acta Mater. 47, 983 (1999).CrossRefGoogle Scholar
18Khachaturyan, A.G.: Theory of Structural Transformations in Solids (John Wiley, New York, 1983)Google Scholar
19Johnson, W.C. and Cahn, J.W.: Elastically induced shape bifurcations of inclusions. Acta Metall. 32, 1925 (1984).CrossRefGoogle Scholar
20Johnson, W.C. and Voorhees, P.W.: Elastic interaction and stability of mistting cuboidal inhomogeneities. J. Appl. Phys. 61, 1610 (1987).CrossRefGoogle Scholar
21Khachaturyan, A.G., Semenovskaya, S.V., Morris, J.W. and Jr., : Theoretical analysis of strain-induced shape changes in cubic precipitates during coarsening. Acta Metall. 36, 1563 (1988).CrossRefGoogle Scholar
22Miyazaki, T. and Doi, M.: Shape bifurcations in the coarsening of precipitates in elastically constrained systems. Mater. Sci. Eng. A 110, 175 (1989).CrossRefGoogle Scholar
23Johnson, W.C., Abinandanan, T.A. and Voorhees, P.W.: Coarsening kinetics of two misfitting particles in an anisotropic crystal. Acta Metall. Mater. 38, 1349 (1990).CrossRefGoogle Scholar
24Johnson, W.C., Berkenpas, M.B. and Laughlin, D.E.: Precipitate shape transitions during coarsening under uniaxial stress. Acta Metall. 36, 3149 (1988).CrossRefGoogle Scholar
25Eshelby, J.D.: Elastic inclusions and inhomogeneities. In Progress in Solid Mechanics, edited by Sneddon, I.N. and Hill, R. (North-Holland, Amsterdam, The Netherlands, 1961), p. 89Google Scholar
26Lee, J.K., Barnett, D.M. and Aaronson, H.L.: Elastic strain energy of coherent ellipsoidal precipitates in anisotropic crystalline solids. Metall. Trans. 8A, 963 (1977).CrossRefGoogle Scholar
27Mura, T.: Micromechanics of Defects in Solids, 2nd ed. (Martinus Nijhoff, Dondrecht, The Netherlands, 1987), pp. 177CrossRefGoogle Scholar
28Eshelby, J.D.: The determination of the elastic field of a spheroidal inclusion, and related problems. Proc. R. Soc. Ser. A 241, 376 (1957).Google Scholar
29Wang, H. and Li, Z.: Diffusive shrinkage of a void within a grain of a stressed polycrystal. J. Mech. Phys. Solids 51, 961 (2003).CrossRefGoogle Scholar
30Sun, B., Suo, Z. and Evans, A.G.: Emergence of cracks by mass transport in elastic crystals stressed at high temperatures. J. Mech. Phys. Solids 42, 1653 (1994).CrossRefGoogle Scholar
31Suo, Z. and Wang, W.: Diffusive void bifurcation in stressed solid. J. Appl. Phys. 76,3410 (1994).CrossRefGoogle Scholar
32Tien, J.K. and Copley, S.M.: The effect of uniaxial stress on the periodic morphology of coherent gamma prime precipitates in nickel-base superalloy crystals. Metall. Trans. 2, 215 (1971).CrossRefGoogle Scholar
33Pineau, A.: Influence of uniaxial stress on the morphology of coherent precipitates during coarsening–elastic energy considerations. Acta Metall. 24, 559 (1976).CrossRefGoogle Scholar