The Microstructure of Martensite and Its Implications for the Shape-Memory Effect

  • Kaushik Bhattacharya
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 54)


Crystalline solids undergoing martensitic phase transformation display fine scale microstructure. The microstructure plays an important role in determining the macroscopic properties of these solids. The aim of this investigation is to understand what role the lattice parameters of the material play in determining the microstructure and consequently the macroscopic properties. The lattice parameters measure the size and shape of the crystal lattices and may be determined experimentally. In particular, the aim here is to determine if the lattice parameters of the technologically significant shape-memory alloys are special in any respect.


Transformation Strain Young Measure Shape Strain Austenite Lattice Twinning Shear 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Adachi, K. and Wayman, C.M., 1985, Transformation behaviour of nearly stoichiometric Ni-Mn alloys, Metallurgical Transactions A, 16 A, 1567–1579.ADSCrossRefGoogle Scholar
  2. [2]
    Adachi, K. and Wayman, C.M., 1985, Electro microscopy study of q-phase martensites in Ni-Mn alloys, Metallurgical Transactions, A 16 A, 1581–1597.ADSCrossRefGoogle Scholar
  3. [3]
    Andersen, N. H., Lebech, B. and Poulsen, H. F., 1990, The structural phase diagram and oxygen equilibrium partial pressure of YBa2Cu3O6+a studied by neutron powder diffraction and gas volumetry, Physica C, 172, 31–42.ADSCrossRefGoogle Scholar
  4. [4]
    Arlt, G., 1990, Twinning in ferroelectric and ferroelastic ceramics: stress relief, Journal of Materials Science, 22, 2655–2666.ADSCrossRefGoogle Scholar
  5. [5]
    Ball, J.M., 1988, A version of the fundamental theorem for Young measures, PDEs and continuum models of phase transitions, (ed. Rascle, M., Serre, D. and Slemrod, M.), Lecture notes in physics, 344, Springer -Verlag, 207–215.Google Scholar
  6. [6]
    Ball, J.M. and James, R.D., 1987, Fine phase mixtures as minimizers of energy, Archive for Rational Mechanics and Analysis, 100, 15–52.MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    Ball, J.M. and James, R.D., 1991, Proposed experimental tests of a theory of fine microstructure and the two well problem, to appear in Philosophical Transactions of the Royal Society of London, Series A.Google Scholar
  8. [8]
    Bhattacharya, K. , 1991, Wedge-like microstructure in martensite, to appear in Acta Met-allurgica.Google Scholar
  9. [9]
    Bhattacharya, K. , 1991, Self-accommodation in martensites,IMA Preprint.Google Scholar
  10. [10]
    Bhattacharya, K., 1991, Ph. D Thesis, University of Minnesota, MinneapolisGoogle Scholar
  11. [11]
    Billington, E. W. AND Tate, A., 1960, The Physics of Deformation and Flow,Mc-Graw HillGoogle Scholar
  12. [12]
    Birnbaum, H.K. and Read, T.A., 1960, Stress induced twin boundary motion in AuCd β’ and /β““ alloys, Transactions of the Metallurgical Society of AIME, 218, 662–669.Google Scholar
  13. [13]
    Bowles, J.S. and Mackenzie, J.K., 1954, The crystallography of martensitic transformations I and II, Acta Metallurgica, 2, 129–137, 138–147.CrossRefGoogle Scholar
  14. [14]
    Bywater, K.A. and Christian, J.W., 1972, Martensitic transformations in titanium-tantalum alloys, Philosophical Magazine, 25, 1249–1272.ADSCrossRefGoogle Scholar
  15. [15]
    Chakravorty, S., 1975, Thesis, University of Illinois, Urbana-Champaign.Google Scholar
  16. [16]
    Chakravorty, S. and Wayman, C.M., 1976, The thermoelastic martensitic transformation in Ni-Al alloys: I. Crystallography and morphology and II. Electron microscopy,Metallurgical Transactions A, 7A, 555–568 and 569–582.ADSCrossRefGoogle Scholar
  17. [17]
    Chang, L.C. and Read, T. A., 1951, Plastic deformation and diffusionless phase changes in metals - the gold-cadbim beta phase, Journal of metals, Transactions AIME, 191, 47–52.Google Scholar
  18. [18]
    Dacarogna, B., 1989, Direct methods in the calculus of variations,Springer-Verlag.Google Scholar
  19. [19]
    Duggin, M.J. and Rachinger, W.A., 1964, The nature of the martensitic transformation in a copper-aluminum-nickel alloy, Acta Metallurgica, 12, 529–535.CrossRefGoogle Scholar
  20. [20]
    Enami, K. and Nenno, S., 1971, Memory effect in Ni-36.8 at. pct. Al martensite, Metallurgical Transactions, Vol 2, 1487–1490.Google Scholar
  21. [21]
    Ericksen, J.L., 1977, Special topics in elastostatics, Advances in Applied Mechanics, Academic Press 7, 189–243.MathSciNetGoogle Scholar
  22. [22]
    Ericksen, J.L., 1979, On the symmetry of deformable crystals, Archive for Rational Mechanics and Analysis, 72, 1–13.MathSciNetADSMATHCrossRefGoogle Scholar
  23. [23]
    Ericksen, J.L., 1980, Some phase transitions in crystals, Archive for Rational Mechanics and Analysis, 73, 99–124.MathSciNetADSMATHCrossRefGoogle Scholar
  24. [24]
    Ericksen, J.L., 1984, The Cauchy and Born hypotheses for crystals, Phase transformations and material instabilities in solids (ed. Gurtin, M. ), Academic Press, 61–78.Google Scholar
  25. [25]
    Ericksen, J.L., 1985, Some surface defects in unstressed thermoelastic solids, Archive for Rational Mechanics and Analysis, 88, 337–345.MathSciNetADSMATHCrossRefGoogle Scholar
  26. [26]
    Ericksen, J.L., 1986, Stable equilibrium configurations of elastic crystals, Archive for Rational Mechanics and Analysis, 94, 1–14.MathSciNetADSMATHCrossRefGoogle Scholar
  27. [27]
    Ericksen, J.L., 1989, Weak martensitic transformations in Bravais lattices, Archive for Rational Mechanics and Analysis, 107, 23–36.MathSciNetADSMATHCrossRefGoogle Scholar
  28. [28]
    Ericksen, J.L., 1990, Local bifurcation theory for thermoelastic Bravais latices,to appear.Google Scholar
  29. [29]
    Foos, M., Frantz, C. and Gantios, M., 1975, Shape memory effect and an elasticity associated with the martensitic transformation in the stoichiometric Fe3Pt alloy, Shape Memory Effects in Alloys (ed. Perkins, J. ), Plenum Press.Google Scholar
  30. [30]
    Forsbergh, P.W., 1949, Domain structures and phase transitions in Barium Titanate, Physical Review, 76 1187–1201.ADSCrossRefGoogle Scholar
  31. [31]
    Guttman, L., 1950, Crystal structures and transformations in Indium-Thallium solid solutions, Journal of metals, Transactions AIME, 188, 1472–1477.Google Scholar
  32. [32]
    Hanson, C.G., Rivlin, V.G. AND Hatt, B.A., 1964, The /3-phase transformation of some zirconium-thorium alloys, Journal of Nuclear Materials, 12, 83–93.ADSCrossRefGoogle Scholar
  33. [33]
    Ichinose, S., Fanatsu,Y. and Otsuka, K., 1985, Type II deformation twinning in yI martensite in a Cu-Al-Ni alloy, Acta Metallurgica, 33, 1613–1620.CrossRefGoogle Scholar
  34. [34]
    James, R.D., 1986, Displacive phase transformations in solids, Journal of Mechanics and Physics of Solids, 34, 359–394.ADSMATHCrossRefGoogle Scholar
  35. [35]
    James, R.D., 1987, The stability and metastability of quartz, Metastability and incompletely posed problems, IMA, Vol 3, Springer-Verlag, 147–176.Google Scholar
  36. [36]
    James, R.D. AND Kinderlehrer, D.,1989, PDEs and continuum models of phase transitions, (ed. Rascle, M., Serre, D. and Slemrod, M.), Lecture notes in physics, 344, Springer -Verlag, 51–84.Google Scholar
  37. [37]
    Koyoma, Y., Ukena, T. AND Nittono, O., 1980, Phase transformations and shape memory effect in Indium Lead alloys, Journal of the Japan Institute of Metals, 44, 431–1439.Google Scholar
  38. [38]
    Koyoma, Y. AND Nittono, O., 1979, Shape memory in In-Cd alloys, Journal of the Japan Institute of Metals, 43, 262–270.Google Scholar
  39. [39]
    Krasevec, V., 1975, The complex microstructure in quenched Ni-Mn alloy, Physica Status Solidi A, 30, 241–250.ADSCrossRefGoogle Scholar
  40. [40]
    Kudoh, Y., Tokonami, M., Miyazaki, S. and Otsuka, K., 1985, Crystal structure of the martensite in Ti 49.2 at % Ni alloy analyzed by the single crystal X-ray diffraction method, Acta Metallurgica, 33, 2049–2056.CrossRefGoogle Scholar
  41. [41]
    Masson, D.B. AND Barrett, C.S., 1958, Effect of deformation and low temperatures on the structure of AgCd and AuZn, Transactions of the Metallurgical Society of AIME, 212, 260–265.Google Scholar
  42. [42]
    Miyazaki, S. and Otsuka, K., 1989, Development of Shape Memory Alloys, ISIJ International, 29, 353–377.CrossRefGoogle Scholar
  43. [43]
    Miyazaki, S., Otsuka, K. AND Wayman, C.M., 1989, The shape memory mechanism associated with the martensitic transformation in TiNi alloys - I. Self-accommodation and II. Variant Coalescence and shape recovery, Acta Metallurgica, 37, 1873–1884 and 1885–1890.CrossRefGoogle Scholar
  44. [44]
    Morton, A.J. AND Wayman, C.M., 1967, Theoritical and experimental aspects of the “(225)” austenite-martensite transformation in iron alloys, Acta Metallurgica, 14, 1567–1581. (47).CrossRefGoogle Scholar
  45. [45]
    Murakami, Y. AND Kanchi, S., 1977, Microscopic observation of thermoelastic a2 Ni-Zn-Cu martensitic, Transactions of the Japan Institute of Metals, 18, 423–426.Google Scholar
  46. [46]
    Murakami, Y., Kanchi, S. AND Shimizu, S., 1976, Martensitic transformation and elastic properties of the ternary Ni-Zn /32 base phase alloy, New aspects of martensitic transformations, Supplement to the Transactions of the Japan Institute of Metals, 17, 147–157.Google Scholar
  47. [47]
    Nittono, O. AND Koyoma, Y., 1981, Crystal structure and phase transformations in Indium rich solid solution, Science reports of the Research Institutes of Tohoku University, A 29, Supplement 1, 53–60.Google Scholar
  48. [48]
    Okamoto, H., Oka, M. AND Tamura, I., 1978, Coupling of thin-plate martensites in an Fe-Ni-C alloy, Transactions of the Japan Institute of Metals, 19, 674–684.Google Scholar
  49. [49]
    Okamoto, K., Ichinose, S., Morii, K., Otsuka, K. AND Shimizu, K., 1986, Crystallography of 01–ryl stress induced martensitic transformation in a Cu-Al-Ni alloy, Acta Metallurgica, 34, 2065–2073.CrossRefGoogle Scholar
  50. [50]
    Otsuka, K., 1971, Origin of memory effect in Cu-Al-Ni alloy, Japanese Journal of Applied Physics, 10, 571–579.Google Scholar
  51. [51]
    Otsuka, K., 1986, Crystallography of martensitic transformation and type II twinning, Proceedings of the International Conference on Martensitic Transformations (ICOMAT-86), 35–42.Google Scholar
  52. [52]
    Otsuka, K. AND Shimizu, K., 1969, Morphology and crystallography of thermoelastic g Cu-Al-Ni martensite, Japanese Journal of Applied Physics, 8, 1196–1204.ADSCrossRefGoogle Scholar
  53. [53]
    Otsuka, K. AND Shimizu, K., 1974, Morphology and crystallography of thermoelastic Cu-Al-Ni martensite analyzed by the phenomenological theory, Transactions of the Japan Institute of Metals, 15, 103–108.Google Scholar
  54. [54]
    Otsuka, K. AND Shimizu, K., 1975, Optical and electron microscope observations of transformation and deformation characteristics in Cu-Al-Ni marmem alloys, Shape Memory Effects in Alloys (ed. Perkins, J. ), Plenum Press, 59–87.Google Scholar
  55. [55]
    Pitteri, M., 1984, Reconciliation of the local and global symmetries of crystals, Journal of Elasticity, 14, 175–190.MathSciNetMATHCrossRefGoogle Scholar
  56. [56]
    Pitteri, M., 1985, On v + 1-lattices, Journal of Elasticity, 15, 3–25.MathSciNetMATHCrossRefGoogle Scholar
  57. [57]
    Saburi, T. AND Wayman, C.M., 1977, Crystallographic similarities in shape memory marten-sites, Acta Metallurgica, 27, 976–995.Google Scholar
  58. [58]
    Shimizu, K., 1990, Private communication.Google Scholar
  59. [59]
    Sohmura, T., Oshima, R. AND Fujita, F.E., 1980, Thermoelastic FCC-FCT transformation in martensitic transformation in Fe-Pd alloys, Scripta Metallurgica, 14, 855–856.CrossRefGoogle Scholar
  60. [60]
    Subbarao, E.C., 1980, Zirconia - an overview, Science and Technology of Zirconia (ed. Heuer, A.H. and Hobbs, L.W. ), Advances in Ceramics, 3, 1–24.Google Scholar
  61. [61]
    Tadaki, T. AND Shimizu, K., 1975, High tetragonality of the thermoelastic martensitic transformation and small volume change during the transformation, Scripta Metallurgica, 9, 771–776.CrossRefGoogle Scholar
  62. [62]
    Tas, H., Delaey, L. AND Deruyttere, A., 1973, The self-accommodating character of the N copper aluminum martensite, Metallurgical Transactions, 4, 2833–2840.CrossRefGoogle Scholar
  63. [63]
    Tan, S. AND Xu, H., 1990, Observations on a CuAlNi single crystal, Continuum Mechanics and Thermodynamics 2, 241–244.ADSCrossRefGoogle Scholar
  64. [64]
    Umemoto, M. AND Wayman, C.M., 1978, Crystallography and morphology studies of Fe-Pt martensites: Lenticular to thin plate transition and thin plate morphologies, Acta Metallurgica, 26, 1529–1549.CrossRefGoogle Scholar
  65. [65]
    Van Tendeloo, G., 1991, Private communication.Google Scholar
  66. [66]
    Watanabe, M. AND Wayman, C.M., 1971, Crystallography of the martensite transformation in Fe-Al-C alloys, Metallurgical Transactions, 2, 2229–2236.CrossRefGoogle Scholar
  67. [67]
    Wechsler, M.S., Lieberman, D.S. AND Read, T.A., 1953, On the theory of the formation of martensite, Journal of metals, Transactions AIME, 197, 1503–1515.Google Scholar
  68. [68]
    Xu, H., 1991, Private communication.Google Scholar
  69. [69]
    Zanzotto, G., 1990, On the material symmetry group of elastic crystals and the Born rule, To appear.Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 1993

Authors and Affiliations

  • Kaushik Bhattacharya
    • 1
  1. 1.Department of Aerospace Engineering and MechanicsUniversity of MinnesotaMinneapolisUSA

Personalised recommendations