Modeling of phase transformations and superelastic hardening of unstable materials

E. A. Ilyina ; L. A. Saraev

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 22 (2018) no. 3, pp. 407-429.

Résumé

The article presents models of superelastic hardening of materials with unstable phase structure at a constant temperature. The kinetic equation of the process of formation and growth of spherical nuclei of a new phase is formulated depending on the level of development of inelastic structural deformations, according to which the new phase first represents separate inclusions from embryos, developing it forms the structures of the matrix mixture in the form of interpenetrating skeletons, and finally the new phase is transformed in a matrix with separate inclusions from the material of the remains of the old phase. The influence of structural deformations on the features of phase transformations and nonlinear hardening of inhomogeneous unstable materials with different degree of connectivity of the constituent phases is studied. Various variants of the microstructure material formed in the conditions of the phase transition in the form of separate inclusions and in the form of interpenetrating components are considered. New macroscopic determining relationships for unstable microinhomogeneous materials are established and their effective elastic moduli are calculated. Macroscopic conditions of direct and inverse phase transitions are obtained, their effective limits and hardening coefficients are calculated. It is shown that the values of the macroscopic elasticity moduli of the obtained models lie inside the fork of the lower and upper Hashin-Shtrikman boundaries. Numerical analysis of the developed models has shown good agreement with known experimental data.

Détail

Keywords: phases, macroscopic properties, elastic moduli, statistical homogeneity, structural deformations, ergodicity
Mots-clés : structure, phase transition, effective relations.

Bibliographie

[1] Isupova I. L., Trusov P. V., “Mathematical modeling of phase transformations in steel under thermomechanical loading”, PNRPU Mechanics Bulletin, 2013, no. 3, 126–156 (In Russian)

[2] Mishustin I. V., Movchan A. A., “Modeling of phase and structure transformations occurring in shape memory alloys under nonmonotonically varying stresses”, Mech. Solids, 49:1 (2014), 27–39 | DOI

[3] Mishustin I. V., Movchan A. A., “Analog of the plastic flow theory for describing martensitic inelastic strains in shape memory alloys”, Mech. Solids, 50:2 (2015), 176–190 | DOI

[4] Kazarina S. A., Movchan A. A., Sil'chenko A. L., “Experimental investigation the interaction between phase and structure deformations in shape memory alloys”, Mekhanika kompozitsionnykh materialov i konstruktsii [Composite Mechanics and Design], 22:1 (2016), 85–98 (In Russian)

[5] Movchan A. A., Sil'chenko A. L., Kazarina S. A., “Experimental study and theoretical simulation of the cross hardening effect in shape memory alloys”, Russ. Metall., 2017:10 (2017), 779–784 | DOI

[6] Trusov P. V., Volegov P. S., Isupova I. L., Kondrat'ev N. S., Makarevich E. S., Niashina N. D., Ostanina T. V., Sharifullina E. R., “Multilevel model for the description of solid-state phase transitions in multicomponent alloys”, Vestnik Permskogo nauchnogo tsentra URO RAN, 2016, no. 4, 83–90 (In Russian)

[7] Tikhomirova K. A., “Isothermal deformation of shape memory alloy in different temperature ranges. Uniaxial case”, Mekhanika kompozitsionnykh materialov i konstruktsii [Composite Mechanics and Design], 23:2 (2017), 263–282 (In Russian)

[8] Tikhomirova K. A., “Phenomenological modeling of phase and structural deformations in shape memory alloys. One-dimensional case”, Computational Mechanics of Continuous Media, 11:1 (2018), 36–50 (In Russian) | DOI

[9] Tikhomirova K. A., “Experimental and theoretical study of the relation between phase and structural deformations in shape memory alloys”, PNRPU Mechanics Bulletin, 2018, no. 1, 40–57 (In Russian) | DOI

[10] Mutter D., Nielaba P., “Simulation of the shape memory effect in a NiTi nano model system”, J. All. Compounds, 577 (2013), S83–S87, arXiv: [cond-mat.mtrl-sci] 1202.1078 | DOI

[11] Auricchio F., Bonetti E., Scalet G., Ubertini F., “Theoretical and numerical modeling of shape memory alloys accounting for multiple phase transformations and martensite reorientation”, Int. J. Plasticity, 59 (2014), 30–54 | DOI

[12] Yu C., Kang G., Kan Q., “Crystal plasticity based constitutive model of NiTi shape memory alloy considering different mechanisms of inelastic deformation”, Int. J. Plasticity, 54 (2014), 132–162 | DOI

[13] Elibol C., Wagner M. F.-X., “Investigation of the stress-induced martensitic transformation in pseudoelastic NiTi under uniaxial tension, compression and compression–shear”, Mat. Sci. Eng. A, 621 (2015), 76–81 | DOI

[14] Lobo P. S., Almeida J., Guerreiro L., “Shape memory alloys behaviour: A review”, Procedia Engineering, 114 (2015), 776–783 | DOI

[15] Yoo Y.-I., Kim Y.-J., Shin D.-K., Lee J.-J., “Development of martensite transformation kinetics of NiTi shape memory alloys under compression”, Int. J. Sol. Struct., 64–65 (2015), 51–61 | DOI

[16] Cisse C., Zaki W., Zineb T. B., “A review of constitutive models and modeling techniques for shape memory alloys”, Int. J. Plasticity, 76 (2016), 244–284 | DOI

[17] Fabrizio M., Pecoraro M., Tibullo V., “A shape memory alloy model by a second order phase transition”, Mech. Res. Com., 74 (2016), 20–26 | DOI

[18] Saraev L. A., Matematicheskoe modelirovanie uprugoplasticheskikh svoistv mnogokomponentnykh kompozitsionnykh materialov [Mathematical modeling of elastoplastic properties of multicomponent composite materials], Samara Science Center of RAS, Samara, 2017, 222 pp. (In Russian)

[19] Ilyina E. A., Saraev L. A., “The impact of the kinetics of phase transformations on the superelastic hardening of an unstable material”, Sovremennye materialy, tekhnika i tekhnologii, 2017, no. 7(15), 28–38 (In Russian)

[20] Christensen R. M., Mechanics of composite materials, Wiley Sons Inc., New York, 1979, xiv+348 pp.

[21] Shermergor T. D., Teoriia uprugosti mikroneodnorodnykh sred [The theory of elasticity of microinhomogeneous media], Nauka, Moscow, 1979, 399 pp. (In Russian)

[22] Saraev A. L., Saraev L. A., “Macroscopic elastic moduli of multicomponent composites with variable microstructure”, Mathematics, Economics and Management, 1:3 (2015), 35–40 (In Russian)

[23] Steurer W., “Crystal Structures of Metallic Elements and Compounds”, Physical Metallurgy, v. 1, eds. David E. Laughlin, Kazuhiro Hono, Elsevier Inc., 2014, 1–101 | DOI

[24] Murakami Y., “Lattice softening, phase stability and elastic anomaly of the $\beta$-Au-Cu-Zn alloys”, J. Phys. Soc. Jpn., 33:5 (1972), 1350–1361 | DOI

[25] Nakanishi N., Mori T., Miura S., Murakami Y., Kachi S., “Pseudoelasticity in Au-Cd thermoelastic martensite”, Philosophical Magazine, 28:2 (1973), 277–282 | DOI