Computational modeling of softening in a structural phase transformation

Multiscale Modeling and Simulation

Volumn 3, Issue 4, 2005, Pages 764-781

  Bělík, Pavel ^a   Luskin, Mitchell ^b  

^a UNIVERSITY OF ST THOMAS   (United States)

^b UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Austenite; Martensite; Phase transformation; Precursor; Softening; Tweed

Indexed keywords

AUSTENITE; COOLING; CRYSTAL MICROSTRUCTURE; ELASTIC MODULI; HEATING; MARTENSITE; MATHEMATICAL MODELS; SINGLE CRYSTALS; THERMAL EFFECTS; THIN FILMS;

FREE ENERGY DENSITY MODEL; HIGH-TEMPERATURE CUBIC PHASE; LOW-TEMPERATURE TETRAGONAL PHASE; PRECURSOR; SOFTENING; TWEED;

PHASE TRANSITIONS;

EID: 29244444775     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/040604339     Document Type: Article

References (34)

1. R. Aberyarante and S. Vedantam, A lattice-based model of the kinetics of twin boundary motion, J. Mech. Phys. Solids, 51 (2003), pp. 1675-1700.
2. R. Adams, Sobolev Spaces, Academic Press, New York, 1975.
3. J. M. Ball and R. D. James, Fine phase mixtures as minimizers of energy, Arch. Rational Mech. Anal., 100 (1987), pp. 13-52.
4. J. M. Ball and R. D. James, Proposed experimental tests of a theory of fine microstructure and the two-well problem, Philos. Trans. Roy. Soc. London Ser. A, 338 (1992), pp. 389-450.
5. P. Bělík and M. Luskin, A computational model for the indentation and phase transformation of a martensitic thin film, J. Mech. Phys. Solids, 50 (2002), pp. 1789-1815.
6. P. Bělík and M. Luskin, A total-variation surface energy model for thin films of martensitic crystals, Interfaces Free Bound., 4 (2002), pp. 71-88.
7. K. Bhattacharya and R. D. James, A theory of thin films of martensitic materials with applications to microactuators, J. Mech. Phys. Solids, 47 (1999), pp. 531-576.
8. K. Bhattacharya and R. V. Kohn, Elastic energy minimization and the recoverable strains of polycrystalline shape-memory materials, Arch. Rational Mech. Anal., 139 (1997), pp. 99-180.
9. M. A. Carpenter and E. K. H. Salje, Elastic anomalies in minerals due to-structural phase transitions, Eur. J. Mineral., 10 (1998), pp. 693-812.
10. P. Ciarlet, Mathematical Elasticity, Vol. 1: Three Dimensional Elasticity, North-Holland, Amsterdam, 1988.
11. 2MnGa thin films, J. Appl. Phys., 95 (2004), pp. 2593-2600.
12. W. E, W. Ren, and E. Vanden-Eijnden, Energy landscapes and rare events, in Proceedings of the International Congress of Mathematicians, Vol. III, Higher Education Press, Beijing, China, 2002, pp. 621-630.
13. J. L. Ericksen, Bifurcation and martensitic transformations in Bravais lattices, J. Elasticity, 28 (1992), pp. 55-78.
14. J. L. Ericksen, Local bifurcation theory for thermoelastic Bravais lattices, in Microstructure and Phase Transition, IMA Vol. Math. Appl. 54, Springer-Verlag, New York, 1993, pp. 57-84.
15. L. C. Evans and R. F. Graiepy, Measure Theory and Fine Properties of Functions, CRC Press, Boca Raton, FL, 1992.
16. D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, New York, 1998.
17. E. Giusti, Minimal Surfaces and Functions of Bounded Variation, Birkhäuser Verlag, Basel, Boston, MA, 1984.
18. M. E. Gurtin, Topics in Finite Elasticity, CBMS-NSF Regional Conf. Ser. in Appl. Math. 35, SIAM, Philadelphia, 1981.
19. R. C. Jun, Martensitic Phase Transformation and Ferromagnetic Shape Memory Effect in Fe-Pd Single Crystals, Ph.D. thesis, University of Minnesota, Minneapolis, MN, 2001.
20. S. Kartha, J. A. Krumhansl, J. P. Sethna, and L. K. Wickham, Disorder-driven pretransitional tweed in martensitic transformations, Phys. Rev. B, 52 (1995), pp. 803-822.
21. W. Kerr, M. Killough, A. Saxena, P. Swart, and A. Bishop, Role of elastic compatibility in martensitic texture evolution, Phase Transitions, 69 (1999), pp. 247-270.
22. D. Kinderlehrer, Twinning in crystals II, in Metastability and Incompletely Posed Problems, IMA Vol. Math. Appl. 3, S. Antman, J. Ericksen, D. Kinderlehrer, and I. Müller, eds., Springer-Verlag, New York, 1987, pp. 185-211.
23. R. Kohn and S. Muller, Surface energy and microstructure in coherent phase transitions, Comm. Pure Appl. Math., 47 (1994), pp. 405-435.
24. M. Kružík and F. Otto, A phenomenological model for hysteresis in polycrystalline shape memory alloys, ZAMM Z. Angew. Math. Mech., to appear.
25. A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity, Dover, New York, 1944.
26. M. Luskin, On the computation of crystalline microstructure, in Acta Numer. 5, Cambridge University Press, Cambridge, UK, 1996, pp. 191-258.
27. M. Luskin, Computational modeling of microstructure, in Proceedings of the International Congress of Mathematicians, Vol. III, Higher Education Press, Beijing, China, 2002, pp. 707-716.
28. S. Muto, R. Oshima, and F. Fujita, Elastic softning and elastic strain energy consideration in the FCC-FCT transformation of Fe-Pd alloys, Acta Metall. Mater., 38 (1990), pp. 685-694.
29. S.-C. Ngan and L. Truskinovsky, Thermo-elastic aspects of dynamic nucleation, J. Mech. Phys. Solids, 50 (2002), pp. 1193-1229.
30. J. Nocedal and S. Wright, Numerical Optimization, Springer-Verlag, New York, 1999.
31. K. Otsuka and C. M. Wayman, Shape Memory Materials, Cambridge University Press, Cambridge, UK, 1998.
32. M. Pitteri and G. Zanzotto, Continuum Models for Twinning and Phase Transitions in Crystals, Chapman and Hall, London, 1996.
33. P. Plechác and T. Roubíček, A visco-elasto-plastic model for phase transformations, Math. Methods Appl. Sci., 25 (2000), pp. 1281-1298.
34. A. Vainchtein, Dynamics of phase transitions and hysteresis in a viscoelastic Ericksen's bar on an elastic foundation, J. Elasticity, 57 (1999), pp. 243-280.