The dynamics of precipitate evolution in elastically stressed solids-II. Particle alignment

Abstract The effects of elastic stress on the spatial distribution and morphology of misfitting particles during coarsening in an elastically anisotropic system are examined. No assumptions are made on the morphology of the particles; they evolve in a manner consistent with the diffusion and elastic fields in the system. Through these calculations we have identified the microstructural signature of elastic-stress induced particle migration. In addition, we find that elastic stress leads not only to particle alignment along the elastically soft directions of the crystal, but also prevents particle coalescence. When the particles are aligned along the elastically soft directions of the crystal the morphology of the particles differs from the equilibrium shape of isolated particles in a manner which depends on the size of the particles. In addition, the elastic-stress induced equilibrium separation between aligned particles decreases with increasing particle size. We show that the effects of elastic stress, due to either applied tractions or other particles, on the morphology and spatial distribution of the particles can be understood in terms of the configurational forces generated by this stress. Configurational force fields generated by misfitting particles are used to explain the results of our dynamical calculations.

[1]  W. C. Johnson,et al.  Coarsening of elastically interacting coherent particles—II. Simulations of preferential coarsening and particle migrations , 1993 .

[2]  J. K. Knowles,et al.  Kinetic relations and the propagation of phase boundaries in solids , 1991 .

[3]  Nishimori,et al.  Pattern formation in phase-separating alloys with cubic symmetry. , 1990, Physical review. B, Condensed matter.

[4]  Hiroshi Imamura,et al.  The formation of “γ′ precipitate doublets” in NiAl alloys and their energetic stability , 1982 .

[5]  A. Khachaturyan Elastic Strains during Decomposition of Homogeneous Solid Solutions — Periodic Distribution of Decomposition Products , 1969 .

[6]  D. Fontaine,et al.  Elastic interaction energy calculations for guinier-preston zones in Al-Cu and Cu-Be , 1978 .

[7]  V. Bišs,et al.  The effect of molybdenum on γ′ coarsening and on elevated-temperature hardness in some experimental nickel-base superalloys , 1973 .

[8]  W. C. Johnson,et al.  Elastic interaction and stability of misfitting cuboidal inhomogeneities , 1987 .

[9]  Jong K. Lee Coherency strain analyses via a discrete atom method , 1995 .

[10]  K. Kawasaki,et al.  Statistical theory of Ostwald ripening with elastic field interaction , 1988 .

[11]  J. E. Dunn,et al.  Institute for Mathematics and Its Applicatiotrs , 2022 .

[12]  Peter W Voorhees,et al.  An elastically induced morphological instability of a misfitting precipitate , 1989 .

[13]  Peter W Voorhees,et al.  THE EQUILIBRIUM SHAPE OF A MISFITTING PRECIPITATE , 1994 .

[14]  Morton E. Gurtin,et al.  The nature of configurational forces , 1995 .

[15]  Ronald F. Boisvert,et al.  Numerical simulation of morphological development during Ostwald ripening , 1988 .

[16]  James K. Knowles,et al.  On the driving traction acting on a surface of strain discontinuity in a continuum , 1990 .

[17]  R. F. Boisvert,et al.  A boundary integral method for the simulation of two-dimensional particle coarsening , 1986 .

[18]  A. Ardell,et al.  Elastic interactions and their effect on γ' precipitate shapes in aged dilute Ni-Al alloys , 1992 .

[19]  D. Srolovitz,et al.  A Monte Carlo-finite element model for strain energy controlled microstructural evolution - 'Rafting' in superalloys , 1989 .

[20]  W. C. Johnson,et al.  Elastic interaction energy of two spherical precipitates in an anisotropic matrix , 1979 .

[21]  Peter W Voorhees,et al.  The coarsening kinetics of two misfitting particles in an anisotropic crystal , 1990 .

[22]  Yunzhi Wang,et al.  Kinetics of strain-induced morphological transformation in cubic alloys with a miscibility gap , 1993 .

[23]  W. C. Johnson,et al.  Elastically Induced Shape Bifurcations of Inclusions , 1984 .

[24]  M. Fine,et al.  Effect of lattice disregistry variation on the late stage phase transformation behavior of precipitates in NiAlMo alloys , 1989 .

[25]  Toru Miyazaki,et al.  The effects of elastic interaction energy on the γ′ precipitate morphology of continuously cooled nickel-base alloys , 1985 .

[26]  W. C. Johnson,et al.  Coarsening of elastically interacting coherent particles—I. Theoretical formulation , 1993 .

[27]  Nishimori,et al.  Anomalously slow domain growth due to a modulus inhomogeneity in phase-separating alloys. , 1991, Physical review. B, Condensed matter.

[28]  W. C. Johnson,et al.  The role of elastic energy in the morphological development of a NiTiAl alloy , 1988 .

[29]  Kozo Nakamura,et al.  Experimental and theoretical investigations on morphological changes of γ′ precipitates in Ni -Al single crystals during uniaxial stress-annealing , 1979 .

[30]  Ardell,et al.  Morphological evolution of coherent misfitting precipitates in anisotropic elastic media. , 1993, Physical review letters.

[31]  L. Truskinovskii,et al.  Dynamics of non-equilibrium phase boundaries in a heat conducting non-linearly elastic medium☆ , 1987 .

[32]  A. Ardell,et al.  On the modulated structure of aged Ni-Al alloys: with an Appendix On the elastic interaction between inclusions by J. D. Eshelby , 1966 .

[33]  M. Gurtin,et al.  The thermodynamics of evolving interfaces far from equilibrium , 1996 .

[34]  Yunzhi Wang,et al.  Strain-induced modulated structures in two-phase cubic alloys , 1991 .

[35]  W. C. Johnson,et al.  The effects of elastic stress on the kinetics of ostwald ripening: The two-particle problem , 1989 .

[36]  A. G. Khachaturi︠a︡n Theory of structural transformations in solids , 1983 .

[37]  A. Onuki,et al.  Freezing of Domain Growth in Cubic Solids with Elastic Misfit , 1991 .

[38]  Johnson,et al.  Development of spatial correlations during diffusional late-stage phase transformations in stressed solids. , 1988, Physical review letters.

[39]  A. Khachaturyan,et al.  Theoretical analysis of strain-induced shape changes in cubic precipitates during coarsening , 1988 .

[40]  Yunzhi Wang,et al.  Shape evolution of a precipitate during strain-induced coarsening , 1991 .

[41]  W. C. Johnson,et al.  On the morphological development of second-phase particles in elastically-stressed solids , 1992 .