×

Self-accommodation in martensite. (English) Zbl 0771.73007

A shape-memory material is said to have self-accommodation property if it is able to transform from the high-temperature austenite to the low- temperature martensite phase without any apparent change in shape. The author undertakes a mathematical penetrating analysis of the self- accommodation in martensite. Necessary and sufficient conditions on the lattice parameters of material are given guaranteeing that the material forms a self-accommodation microstructure. In the particular case of the cubic austenite it is shown that the material is self-accommodating if and only if the volume is preserving, and a comparison of the results obtained with the available experimental data is given. Of real interest are conclusions and discussion in the final section of the paper.

MSC:

74A15 Thermodynamics in solid mechanics
74A60 Micromechanical theories
74M25 Micromechanics of solids
35Q72 Other PDE from mechanics (MSC2000)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Adachi, K. & Wayman, C. M., Transformation behaviour of nearly stoichiometric Ni-Mn alloys, and electron microscopic study of ?-phase martensite in Ni -Mn alloys, Met. Trans. A 16A (1985), 1567-1579, 1581-1597.
[2] Andersen, N. H., Lebech, B. & Poulsen, H. F., The structural phase diagram and oxygen equilibrium partial pressure of YBa2Cu3O6+x studied by powder diffraction and gas volumetry, Physica C 172 (1990), 31-42.
[3] Arlt, G., Twinning in ferroelectric and ferroelastic ceramics: stress relief, J. Mat. Sci. 22 (1990), 2655-2666.
[4] Avellaneda, M., Cherkaev, A. V., Lurie, K. A. & Milton, G. W., On the effective conductivity of polycrystals and a three dimensional phase-interchange inequality, J. Appl. Phys. 63 (1988), 4989-5003.
[5] Ball, J. M., Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63 (1977), 337-403. · Zbl 0368.73040
[6] Ball, J. M., Remarks on the paper ?Basic calculus of variations?, Pacific J. Math. 116 (1985), 7-10. · Zbl 0553.49012
[7] Ball, J. M., Currie, J. C. & Olver, P. J., Null Lagrangians, weak continuity and variational problems of arbitrary order, J. Func. Anal. 41 (1981), 135-174. · Zbl 0459.35020
[8] Ball, J. M. & James, R. D., Fine phase mixtures as minimizers of energy, Arch. Rational Mech. Anal. 100 (1987), 13-52. · Zbl 0629.49020
[9] Ball, J. M. & James, R. D., Proposed experimental tests of a theory of fine microstructure and the two well problem, Phil. Trans. Royal Soc. London A 338 (1992), 389-450. · Zbl 0758.73009
[10] Bhattacharya, K., Wedge-like microstructure in martensite, Acta Metall. 39 (1991), 2431-2444.
[11] Billington, E. W. & Tate, A., The Physics of Deformation and Flow, Mc-Graw Hill (1960). · Zbl 0499.73001
[12] Birnbaum, H. K. & Read, T. A., Stress induced twin boundary motion in AuCd ?? and ??’ alloys, Trans. Met. Soc. AIME 218 (1960), 662-669.
[13] Bowles, J. S. & MacKenzie, J. K., The crystallography of martensitic transformations I and II, Acta Metall. 2 (1954), 129-137, 138-147.
[14] Bywater, K. A. & Christian, J. W., Martensitic transformations in titanium-tantalum alloys, Phil. Mag. 25 (1972), 1249-1272.
[15] Chakravorty, S. & Wayman, C. M., The thermoelastic martensitic transformation in ?? Ni-Al alloys: I. Crystallography and morphology and II. Electron microscopy, Metall. Trans. A 7A (1976), 555-568, 569-582.
[16] Chang, L. C. & Read, T. A., Plastic deformation and diffusionless phase changes in metals ? the gold-cadmium beta phase, J. Metals Trans. AIME 191 (1951), 47-52.
[17] Chipot, M. & Kinderlehrer, D., Equilibrium configurations of crystals, Arch. Rational Mech. Anal. 103 (1988), 237-277. · Zbl 0673.73012
[18] Enami, K. & Nenno, S., Memory effect in Ni-36.8 at. pct. Al martensite, Metall. Trans. 2 (1971), 1487-1490.
[19] Ericksen, J. L., Nilpotent energies in liquid crystal theory, Arch. Rational Mech. Anal. 10 (1962), 189-196. · Zbl 0109.23002
[20] Ericksen, J. L., Nonlinear elasticity of diatomic crystals, Int. J. Solids Struc. 6 (1970), 951-957.
[21] Ericksen, J. L., On the symmetry and stability of thermoelastic solids, J. Appl. Mech. 45 (1978), 740-744.
[22] Ericksen, J. L., On the symmetry of deformable crystals, Arch. Rational Mech. Anal. 72 (1979), 1-13. · Zbl 0439.20031
[23] Ericksen, J. L., Some phase transitions in crystals, Arch. Rational Mech. Anal. 73 (1980), 99-124. · Zbl 0429.73007
[24] Ericksen, J. L., Continuous martensitic transitions in thermoelastic solids, J. Thermal Stresses 4 (1981), 107-119.
[25] Ericksen, J. L., The Cauchy and Born hypotheses for crystals, in Phase Transformations and Material Instabilities in Solids (ed. Gurtin, M. E.), Academic Press (1984), 61-78. · Zbl 0567.73112
[26] Ericksen, J. L., Some surface defects in unstressed thermoelastic solids, Arch. Rational Mech. Anal. 88 (1985), 337-345. · Zbl 0588.73188
[27] Ericksen, J. L., Constitutive theory for some constrained elastic crystals, Int. J. Solids Struc. 22 (1986), 951-964. · Zbl 0595.73001
[28] Evans, L. C., Weak Convergence Methods for Nonlinear Partial Differential Equations, Amer. Math. Soc., C.B.M.S. 74 (1990). · Zbl 0698.35004
[29] Firoozye, N. B., Bhattacharya, K., James, R. D. & Kohn, R. V., Restrictions on microstructure, in preparation (1992).
[30] Foos, M., Frantz, C. & Gantios, M., Shape memory effect and anelasticity associated with the martensitic transformation in the stoichiometric Fe3Pt alloy, in Shape Memory Effects in Alloys (ed. Perkins, J.), Plenum Press (1975), 407-417.
[31] Forsbergh, P. W., Domain structures and phase transitions in barium titanate, Phys. Rev. 76 (1949), 1187-1201.
[32] Fosdick, R. L. & Hertog, B., Material symmetry and crystals, Arch. Rational Mech. Anal. 110 (1990), 43-72. · Zbl 0696.73002
[33] Fonseca, I., Variational methods for elastic crystals, Arch. Rational Mech. Anal. 97 (1985), 189-220. · Zbl 0611.73023
[34] Gurtin, M. E., Two phase deformations of elastic solids, Arch. Rational. Mech. Anal. 84 (1983), 1-29. · Zbl 0525.73054
[35] Guttman, L., Crystal structures and transformations in Indium-Thallium solid solutions, J. Metals Trans. AIME 188 (1950), 1472-1477.
[36] Hanson, C. G., Rivlin, V. G. & Hatt, B. A., The ?-phase transformation of some zirconium-thorium alloys, J. Nuclear Mat. 12 (1964), 83-93.
[37] James, R. D., Displacive phase transformations in solids, J. Mech. Phys. Solids 34 (1986), 359-394. · Zbl 0585.73198
[38] James, R. D., The stability and metastability of quartz, in Metastability and Incompletely Posed Problems (eds. Antman, S., Ericksen, T. L., Kinderlehrer, D. & Müller, I.) IMA Vol. 3, Springer-Verlag (1987), 147-176.
[39] James, R. D. & Kinderlehrer, D., Theory of diffusionless phase transitions, in Partial Differential Equations and Continuum Models of Phase Transitions (eds. Rascle, M., Serre, D. & Slemrod, M.), Lectures Notes in Physics 344, Springer-Verlag (1989), 51-84. · Zbl 0991.74504
[40] Kinderlehrer, D. & Pedregal, P., Characterizations of Young measures generated by gradients, Arch. Rational Mech. Anal. 115 (1991), 329-365. · Zbl 0754.49020
[41] Krasevec, V., The complex martensite in quenched Ni-Mn alloy, Phys. Stat. Sol. A30 (1975), 241-250.
[42] Kudoh, Y., Tokonami, M., Miyazaki, S. & Otsuka, K., Crystal structure of the martensite in Ti-49.2 at. % Ni alloy analyzed by the single crystal X-ray diffraction method, Acta Metall. 33 (1985), 2049-2056.
[43] Maki, T. & Tamura, I., Shape memory effect in ferrous alloys, Proc. Int. Conf. Mart. Trans. (1986), 963-970.
[44] Masson, D. B. & Barrett, C. S., Effect of deformation and low temperatures on the structure of AgCd and AuZn, Trans. Met. Soc. AIME 212 (1958), 260-265.
[45] Miyazaki, S. & Otsuka, K., Development of Shape Memory Alloys, Iron Steel Inst. Jap. 29 (1989), 353-377.
[46] Miyazaki, S., Otsuka, K. & Wayman, C. M., The shape memory mechanism associated with the martensitic transformation in TiNi alloys ? I. Self-accommodation and II. Variant Coalescence and shape recovery, Acta Metall. 37 (1989), 1873-1884, 1885-1890.
[47] Morrey, C. B., Multiple Integrals in the Calculus of Variations, Springer-Verlag (1966). · Zbl 0142.38701
[48] Morton, A. J. & Wayman, C. M., Theoretical and experimental aspects of the ?(225)? austenite-martensite transformation in iron alloys, Acta Metall 14 (1966), 1567-1581.
[49] Murakami, Y. & Kanchi, S., Microscopic observation of thermoelastic ?2 Ni-Zn-Cu martenstite, Trans. Jap. Inst. Metals 18 (1977), 423-426.
[50] Murakami, Y., Kanchi, S. & Shimizu, S., Martensitic transformation and elastic properties of the ternary Ni-Zn base ? 2 phase alloy, Trans. Jap. Inst. Metals 17 Suppl. (1976), 147-157.
[51] Murat, F., Compacité par compensation, Ann. Sci. Norm. Sup. Pisa 5 (1978), 489-507. · Zbl 0399.46022
[52] Murat, F., Compacité par compensation II, in Recent Methods in Nonlinear Analysis (eds. De Giorgi, E., Magenes, E. & Mosco, U.), Pitagora (1979), 245-256.
[53] Murat, F. & Tartar, L., Calcul des variations et homogenéisation, Les Méthodes de l’homogenéisation: Théorie et Applications en Physique, Dir. des Etudes et Recherches de l’EDF, Eyrolles, Paris (1985), 319-370.
[54] Nittono, O. & Koyoma, Y., Crystal structures and phase transformations in indium rich solid solution, Sci. Rep. Research Inst. Tohoku U. A29 Suppl. 1 (1981), 53-60.
[55] Okamoto, H., Oka, M. & Tamura, I., Coupling of thin-plate martensites in an Fe-Ni-C alloy, Trans. Jap. Inst. Metals 19 (1978), 674-684.
[56] Okamoto, K., Ichinose, S., Morii, K., Otsuka, K. & Shimizu, K., Crystallography of ? 1 ? 1 stress induced martensitic transformation in a Cu-Al-Ni alloy, Acta Metall. 34 (1986), 2065-2073.
[57] Pitteri, M., Reconciliation of local and global symmetries of crystals, J. Elasticity 14 (1984), 175-190. · Zbl 0543.73001
[58] Pitteri, M., On ? + 1-lattices, J. Elasticity 15 (1985), 3-25. · Zbl 0568.73112
[59] Saburi, T. & Wayman, C. M., Crystallographic similarities in shape memory martensites, Acta Metall. 27 (1979), 979-995.
[60] Serre, D., Formes quadratiques et calcul des variations, J. Math. Pures. Appl. 62 (1983), 117-196. · Zbl 0529.49005
[61] Sohmura, T., Oshima, R. & Fujita, F. E., Thermoelastic FCC-FCT martensitic transformation in Fe-Pd alloys, Scripta Met. 14 (1980), 855-856.
[62] Subbarao, E. C., Zirconia ? an overview, in Science and Technology of Zirconia (eds. Heuer, A. H. & Hobbs, L. W.), Adv. in Ceramics 3, Amer. Ceramics Soc. (1980), 1-24.
[63] Tadaki, T. & Shimizu, K., High tetragonality of the thermoelastic Fe3Pt martensite and small volume change during the transformation, Scripta Metall. 9 (1975), 771-776.
[64] Tan, S. & Xu, H., Observations on a CuAlni single crystal, Cont. Mech. Thermodynamics 2 (1990), 241-244.
[65] Tartar, L., Compensated compactness and applications to partial differential equations, Nonlinear Analysis and Mechanics (ed. Knops, R. J.), Pitman Research Notes 39 (1978), 136-212.
[66] Tas, H., Delaey, L. & Deruyttere, A., The self-accommodating character of the ??1 copper aluminum martensite, Metall. Trans. 4 (1973), 2833-2840.
[67] Van Tendeloo, G. & Amelinckx, S., Group theoretical considerations concerning domain formation in ordered alloys, Acta Cryst. A30 (1974), 431-440.
[68] Van Tendeloo, G., private communication (1991).
[69] Watanabe, M. & Wayman, C. M., Crystallography of the martensite transformation in Fe-Al-C alloys, Metall. Trans. 2 (1971), 2229-2236.
[70] Wechsler, M. S., Lieberman, D. S. & Read, T. A., On the theory of the formation of martensite, J. Metals Trans. AIME 197 (1953), 1503-1515.
[71] Young, L. C., Lectures on the Calculus of Variations and Optimal Control Theory, Saunders (1969). · Zbl 0177.37801
[72] Zanzotto, G., On the material symmetry group of elastic crystals and the Born rule, Arch. Rational Mech. Anal. 121 (1992), 1-36. · Zbl 0781.73005
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.