Abstract
A systematic study of a specific martensitic microstructure, called the X-microstructure, is carried out with the focus on the CuAlNi shape memory alloy undergoing the cubic-to-orthorhombic transformation. The set of all crystallographically distinct candidate X-microstructures is determined, and it is shown that, according to the crystallographic theory of martensite, none of them is compatible. Almost compatible X-microstructures, which involve elastic strains, are thus examined. These microstructures are searched in the neighborhood of all candidate X-microstructures by minimizing the total elastic strain energy with respect to the microstructure parameters. Several low-energy X-microstructures are found, and it is shown that the total elastic strain energy correlates reasonably well with one of the indicators which characterize incompatibility of the corresponding candidate X-microstructure.
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Balandraud X., Delpueyo D., Grediac M., Zanzotto G.: Almost compatible microstructures in shape memory alloys. Acta Mater. 58, 4559–4577 (2010)
Balandraud X., Zanzotto G.: Stressed microstructures in thermally induced M9R–M18R martensites. J. Mech. Phys. Solids 55, 194–224 (2007)
Ball J.M., James R.D.: Fine phase mixtures as minimizers of energy. Arch. Ration. Mech. Anal. 100, 13–50 (1987)
Basinski Z.S., Christian J.W.: Experiments on the martensitic transformation in single crystals of indium-thalium alloys. Acta Metall. 2, 148–166 (1954)
Bhattacharya K.: Microstructure of Martensite: Why it Forms and How it Gives Rise to the Shape-Memory Effect. Oxford University Press, Oxford (2003)
Bowles, J.S., MacKenzie, J.K.: The crystallography of martensitic transformations I and II. Acta Metall. 2, 129–137, 138–147 (1954)
Chu, C.: Hysteresis and microstructures: a study of biaxial loading on compound twins of copper-aluminum-nickel single crystals. Ph.D. thesis, University of Minnesota (1993)
Delville R., Kasinathan S., Zhang Z., Van Humbeck J., James R.D., Schryvers D.: Transmission electron microscopy study of phase compatibility in low hysteresis shape memory alloys. Philos. Mag. 90, 177–195 (2010)
Glatz, O., Seiner, H., Landa, M.: FEM modelling of elastically strained interfacial microstructures in Cu-Al-Ni single crystals. In: Sittner, P., Heller, L., Paidar, V. (eds.) ESOMAT 2009—The 8th European Symposium on Martensitic Transformations, p. 03006. EDP Sciences (2009). doi:10.1051/esomat/200903006
Hane K.F.: Bulk and thin film microstructures in untwinned martensites. J. Mech. Phys. Solids 47, 1917–1939 (1999)
Hane K.F., Shield T.W.: Microstructure in a cubic to orthorhombic transition. J. Elast. 59, 267–318 (2000)
Khachaturyan A.G.: Theory of Structural Transformations in Solids. Wiley, New York (1983)
Kohn R.V., Müller S.: Branching of twins near an austenite–twinned-martensite interface. Philos. Mag. A 66(5), 697–715 (1992)
Maciejewski G., Stupkiewicz S., Petryk H.: Elastic micro-strain energy at the austenite–twinned martensite interface. Arch. Mech. 57, 277–297 (2005)
Novák V., Šittner P., Ignacová S., Černoch T.: Transformation behaviour of prism shaped shape memory alloy single crystals. Mater. Sci. Eng. A 438–440, 755–762 (2006)
Petryk H., Stupkiewicz S.: Interfacial energy and dissipation in martensitic phase transformations. Part I: Theory. J. Mech. Phys. Solids 58, 390–408 (2010)
Roytburd A.L.: Martensitic transformation as a typical phase transformation in solids. In: Seitz, D., Turnbull, D. (eds) Solid State Physics, vol. 33, pp. 317–380. Academic Press, New York (1978)
Roytburd A.L.: Thermodynamics of polydomain heterostructures II. Effect of microstresses. J. Appl. Phys. 83(1), 239–245 (1998)
Ruddock G.J.: A microstructure of martensite which is not a minimizer of energy: the X-interface. Arch. Ration. Mech. Anal. 127, 1–39 (1994)
Sedlak P., Seiner H., Landa M., Novak V., Sittner P., Manosa L.: Elastic constants of bcc austenite and 2H orthorhombic martensite in CuAlNi shape memory alloy. Acta Mater. 53, 3643–3661 (2005)
Seiner H., Glatz O., Landa M.: Interfacial microstructures in martensitic transitions: from optical observations to mathematical modelling. Int. J. Multiscale Comp. Eng. 7, 445–456 (2009)
Seiner H., Sedlak P., Landa M.: Shape recovery mechanism observed in single crystals of Cu–Al–Ni shape memory alloy. Phase Trans. 81, 537–551 (2008)
Stupkiewicz S.: The effect of stacking fault energy on the formation of stress-induced internally faulted martensite plates. Eur. J. Mech. A/Solids 23, 107–126 (2004)
Stupkiewicz S., Maciejewski G., Petryk H.: Low-energy morphology of the interface layer between austenite and twinned martensite. Acta Mater. 55, 6292–6306 (2007)
Suezawa M., Sumino K.: Behaviour of elastic constants in Cu-Al-Ni alloy in the close vicinity of M s -point. Scr. Metall. 10, 789–792 (1976)
Wechsler M.S., Lieberman D.S., Read T.A.: On the theory of the formation of martensite. Trans. AIME J. Metals 197, 1503–1515 (1953)
Yasunaga M., Funatsu Y., Kojima S., Otsuka K., Suzuki T.: Measurement of elastic constants. Scr. Metall. 17, 1091–1094 (1983)
Zhang Z., James R.D., Muller S.: Energy barriers and hysteresis in martensitic phase transformations. Acta Mater. 57, 4332–4352 (2009)
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This work has been partially supported by the Ministry of Science and Higher Education in Poland under Grant no. N N501 071935.
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Communicated by Andreas Öchsner.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Stupkiewicz, S., Górzyńska-Lengiewicz, A. Almost compatible X-microstructures in CuAlNi shape memory alloy. Continuum Mech. Thermodyn. 24, 149–164 (2012). https://doi.org/10.1007/s00161-011-0222-9
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DOI: https://doi.org/10.1007/s00161-011-0222-9