Microstructural model of twinning and detwinning processes of the martensitic phase in shape memory alloys

A. A. Rogovoy

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 28 (2024) no. 3, pp. 516-542.

Résumé

Using the Cu–Al–Ni shape memory alloy as an example, the article substantiates an approach to describing at the microstructural level the processes of twinning and detwinning of the martensitic phase. The coordinated twinned martensitic structure is described by the Hadamard compatibility equation for deformations, the solution of which made it possible to determine the surfaces along which the shift occurs, the directions and the magnitude of sliding in an orthorhombic crystal cell corresponding to the material under consideration in the martensitic state, leading to the appearance and disappearance of the twin structure. It is shown that two types of twins simultaneously and inseparably exist in an alloy with shape memory: deformation and structural. The first is related to the deformation of a simple shear, that occurs in accordance with the Hadamard compatibility condition in a martensitic plate, which leads to bending this straight plate and the appearance of two elements rotated at a certain angle relative to each other, which form this twin. The structural twin is formed from two parts, in each of which the orthorhombic crystal cells of martensite are identically oriented, but one of the axes of these cells changes its direction by $90^\circ$ when moving to another part of the twin. The formation of a deformation twin initiates the occurrence of a simple shear strain in the medium, and a structural twin initiates a structural strain. It is shown that a certain position of the structural twin in the deformation one leads to the equality of these strains.

Détail

Keywords: microstructural modeling, anisotropic material, Hadamard compatibility condition, sliding surfaces and shear directions

Bibliographie

[1] Bhattacharya K., “Wedge-like microstructure in martensites”, Acta Metal. Mater., 39:10 (1991), 2431–2444 | DOI

[2] Hane K. F., Shield T. W., “Symmetry and microstructure in martensites”, Philos. Mag. A, 78:6 (1998), 1215–1252 | DOI

[3] Hane K. F., Shield T. W., “Microstructure in a copper–aluminium–nickel shape memory alloy”, Proc. R. Soc. Lond. A, 455:1991 (1999), 3901–3915 | DOI

[4] Hane K. F., Shield T. W., “Microstructure in a cubic to orthorhombic transition”, J. Elast., 59 (2000), 267–318 | DOI | Zbl

[5] Vedantam S., Constitutive modeling of Cu–Al–Ni shape memory alloys, Doctoral Dissertation, Massachusetts Institute of Technology, Massachusetts, 2000 https://dspace.mit.edu/handle/1721.1/34342

[6] Vedantama S., Abeyaratneb R., “A Helmholtz free-energy function for a Cu–Al–Ni shape memory alloy”, Int. J. Non-Linear Mechan., 40 (2005), 177–193 | DOI

[7] Truesdell C., A First Course in Rational Continuum Mechanics, v. 1: General Concepts, Pure and Applied Mathematics, 71, Academic Press, New York, 1977, xxiii+280 pp. | Zbl

[8] Likhachev V. A., Malinin V. G., Strukturno-analiticheskaia teoriia prochnosti [Structural and Analytical Theory of Strength], Nauka, St. Petersburg, 1993, 471 pp. (In Russian)

[9] Panin V. E., “Fundamentals of physical mesomechanics”, Fiz. Mezomekh., 1:1 (1998), 5–22 (In Russian)

[10] Panin V. E., Egorushkin V. E., “Basic physical mesomechanics of plastic deformation and fracture of solids as hierarchically organized nonlinear systems”, Fiz. Mezomekh., 18:5 (2015), 100–113 (In Russian) | DOI

[11] Trusov P. V., Shveikin A. I., Mnogourovnevye modeli mono- i polikristallicheskikh materialov: teoriia, algoritmy, primery primeneniia [Multilevel Models of Mono- and Polycrystalline Materials: Theory, Algorithms, Application Examples], Sibirsk. Otd. RAN, Novosibirsk, 2019, 605 pp. (In Russian)

[12] Trusov P. V., Ashikhmin V. N., Volegov P. S., Shveykin A. I., “Constitutive relations and their application to the description of microstructure evolution”, Fiz. Mezomekh., 12:3 (2009), 61–71 (In Russian)

[13] Trusov P. V., Shveykin A. I., Kondratiev N. S., Yants A. Yu., “Multilevel models in physical mesomechanics of metals and alloys: Results and prospects”, Fiz. Mezomekh., 23:6 (2020), 33–62 (In Russian) | DOI

[14] Belyaev F. S., Evard M. E., Volkov A. E., “Simulation of the plastic deformation of shape memory alloys considering shear anisotropy on the slip plane”, Mater. Phys. Mech., 51:1 (2023), 61-67 | DOI

[15] Belyaev F. S., Volkov A. E., Evard M. E., “Microstructural modeling of reversible and irreversible deformation under cyclic thermomechanical loading of titanium nickelide”, Tambov Univ. Reports. Ser. Natural Techn. Sci., 18:4 (2013), 2025–2026 (In Russian)

[16] Rogovoy A. A., Stolbova O. S., Stolbov O. V., “Numerical simulation of evolution of magnetic microstructure in Heusler alloys”, J. Appl. Mech. Techn. Phys., 62:5 (2021), 870–881 | DOI | DOI | Zbl

[17] Rogovoy A. A., Stolbova O. S., “Microstructural modeling of the magnetization process in Ni$_2$MnGa alloy polytwin crystals”, Magnetochem., 8:8 (2022), 78 | DOI

[18] Rogovoy A. A., Stolbova O. S., “Microstructural model of the behavior of a ferroalloy with shape memory in a magnetic field”, Mech. Adv. Mater. Struct., 31:2 (2022), 387–406 | DOI

[19] Rogovoy A. A., Stolbova O. S., “Microstructural model of magnetic and deformation behavior of single crystals and polycrystals of ferromagnetic shape memory alloy”, Magnetochem., 9:2 (2023), 40 | DOI

[20] Rogovoy A. A., Stolbova O. S., “Microstructural model of magnetic and deformation behavior of single crystals and polycrystals of ferromagnetic shape-memory alloy”, H. Altenbach, V. Eremeyev (eds). Advances in Linear and Nonlinear Continuum and Structural Mechanics, Advanced Structured Materials, 198, Springer, Cham, 397–442 | DOI

[21] Rogovoy A. A., Stolbova O. S., “An approach to describe the twinning and detwinning processes of the martensitic structure in ferromagnetic alloy with shape memory in magnetic and force fields”, Mech. Adv. Mater. Struct., 2024 (to appear) | DOI

[22] Rogovoi A. A., Formalizovannyi podkhod k postroeniiu modelei mekhaniki deformiruemogo tverdogo tela. Chast' 1. Osnovnye sootnosheniia mekhaniki sploshnykh sred [A Formalized Approach to the Construction of Models of Deformable Solid Mechanics. Part 1. Basic Relations of Continuum Mechanics], Uralsk. Otd. RAN, Perm', 2020, 288 pp. (In Russian)

[23] Kosilov A. T., Yuriev V. A., “Profiled Cu–Al–Ni single crystals with pseudoelasticity and shape memory effects”, Mezhdun. Nauchn. Zhurn. Alternativn. Energetika Ekologiia, 2015, no. 3, 49–61 (In Russian)

[24] Otsuka K., Shimizu K., “Morphology and crystallography of thermoelastic Cu–Al–Ni martensite analyzed by the phenomenological theory”, Trans. JIM, 15:2 (1974) | DOI

[25] Lur'e A. I., Nelineinaia teoriia uprugosti [Nonlinear Theory of Elasticity], Nauka, Moscow, 1980, 512 pp. (In Russian) | Zbl

[26] James R. D., “Finite deformation by mechanical twinning”, Arch. Ration. Mech. Anal., 77 (1981), 143–176 | DOI | Zbl

[27] Gurtin M. E., “Two-phase deformations of elastic solids”, Arch. Ration. Mech. Anal., 84 (1983), 1–29 | DOI | Zbl

[28] Yasunaga M., Funatsu Y., Kojima S., et al., “Measurement of elastuc constant”, Scripta Metallurg., 17:9 (1983), 1091–1094 | DOI