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TECHNICAL PAPERS

Deformation, Stress State, and Thermodynamic Force for a Transforming Spherical Inclusion in an Elastic-Plastic Material

[+] Author and Article Information
F. D. Fischer, E. R. Oberaigner

  Institute for Mechanics Montanuniversitat Leoben, A-8700 Leoben, Austria

J. Appl. Mech 67(4), 793-796 (Feb 14, 2000) (4 pages) doi:10.1115/1.1320453 History: Received June 23, 1999; Revised February 14, 2000
Copyright © 2000 by ASME
Topics: Force , Deformation , Stress
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References

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Kaganova,  I. M., and Roitburd,  A. L., 1989, “Effect of Plastic Deformation on the Equilibrium Shape of a New-Phase Inclusion and Thermodynamic Hysteresis,” Sov. Phys. Solid State, 31, pp. 545–550.
Nazyrov,  I. R., and Freidin,  A. B., 1998, “Phase Transformations in Deformation of Solids in a Model Problem of an Elastic Ball,” Mech. Solids, 33, pp. 39–56Izevestiya AN.MTT, 5, pp. 52–71.
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Lee,  J. K., Earmme,  Y. Y., Aronson,  H. J., and Russel,  K. C., 1980, “Plastic Relaxation of the Transformation Strain Energy of a Misfitting Spherical Precipitate: Ideal Plastic Behavior,” Metall. Trans. A, 11A, pp. 1837–1847.
Fischer,  F. D., Berveiller,  M., Tanaka,  K., and Oberaigner,  E. R., 1994, “Continuum Mechanical Aspects of Phase Transformations in Solids,” Arch. Appl. Mech., 64, pp. 54–85.
Lubliner, J., 1990, Plasticity Theory, Macmillan, New York.
Budiansky,  B., 1959, “A Reassessment of Deformation Theories in Plasticity,” ASME J. Appl. Mech., 81, pp. 259–264.
Franciosi,  P., Lormand,  G., and Fougeres,  R., 1998, “On Elastic Modeling of Inclusion Induced Microplasticity in Metallic Matrices From the Dilatating Sphere Problem,” Int. J. Plast., 14, pp. 1013–1032.
Böhm,  H. J., Fischer,  F. D., and Reisner,  G., 1997, “Evaluation of Elastic Strain Energy of Spheroidal Inclusions With Uniform Volumetric and Shear Eigenstrains,” Scr. Mater., 36, pp. 1053–1059.
Earmme,  Y. Y., Johnson,  W. C., and Lee,  J. K., 1981, “Plastic Relaxation of the Transformation Strain Energy of a Misfitting Spheroidal Precipitate: Linear and Power-Law Strain Hardening,” Metall. Trans. A, 12A, pp. 1521–1530.
Carrol,  M. M., 1985, “Radial Expansion of Hollow Spheres of Elastic-Plastic Hardening Material,” Int. J. Solids Struct., 21, pp. 645–670.
Fischer,  F. D., and Reisner,  G., 1998, “A Criterion for the Martensitic Transformation of a Microregion in an Elastic-Plastic Material,” Acta Mater., 46, pp. 2095–2102.
Rosakis,  Ph., and Knowles,  J. K., 1997, “Unstable Kinetic Relations and the Dynamics of Solid-Solid Phase Transitions,” J. Mech. Phys. Solids, 45, pp. 2055–2081.
Durban,  D., and Fleck,  N. A., 1997, “Spherical Cavity Expansion in a Drucker-Prager Solid,” ASME J. Appl. Mech., 64, pp. 743–750.

Figures

Grahic Jump Location
Profile of the relative radial stress |σrf| and the relative plastic strain |εp,ro| in relation to r/R for two values of κ
Grahic Jump Location
Plastic work WP in relation to total work WT, total work WT in relation to total work WTc in a purely elastic comparison material, dimensionless transformation barrier FB,int.(E/σf2) as function of the plasticity constant κ.

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