Effect of microstructure on the hardening and softening behavIors of polycrystalline shape memory alloys Part I: Micromechanics constitutive modeling

Delaey L, Krishnan RV, Tas H, et al. Review: Thermoelasticity, pseudoelasticity and memory effect associated with martensitic transformations.J Mat Sci, 1974, 9: 1521–1555 Otsuka K, Shimizu K. Morphology and crystallography of thermoelastic Cu−Al−Ni martensite analyzed by the phenomenological theory.Trans Japan Inst Metals, 1974, 15: 103–108 Otsuka K, Shimizu K. Stress-induced martensitic transformations and martensite-to martensite transformations. In: Aaronson HI, et al eds. Proceedings of an International Conference on Solid-Solid Phase Transformation, Warrendale, PA, 1981. AIME, 1982. 1267–1286 Wayman CM. Martensitic transformation: An overview. In: Aaronson HI et al eds. Proceedings of an International Conference on Solid-Solid Phase Transformation, Warrendale, PA, 1981. AIME, 1982. 1119–1144 Funakubo H. Shape Memory Alloys. New York: Gordon and Breach Science Publishers, 1987 Olson GB, Owen NS, Martensite, A Tribute to Morris Cohen. ASM International, 1992 Christian JW. Crystallographic theories, interface structures, and transformation mechanisms.Metall and Mater Trans, 1995, 25A:1821–1839 Fischer FD, Sun QP, Tanaka K. Transformation-induced plasticity (TRIP).Appl Mech Rev, 1996, 49: 317–364 Falk F. Model free energy, mechanics and thermodynamics of shape memory alloys.Acta Metall, 1980, 28: 1773–1780 Falk F. Ginzburg-Landau theory and solitary waves in shape memory alloys.Z Physik, 1984, 54B: 159–167 Falk F, Konopka P. Three-dimensional Landau theory describing the martensite phase transformation of shape memory alloys.J Phys: Condens Matter, 1990, 2: 61–77 Friedman A, Sprekels J. Steady states of austenitic-martensitic domains in the Ginzburg-Landau theory of shape memory alloys.Continuum Mech Thermodyn, 1990, 2: 199–213 Bales GS, Gooding RJ. Interfacial dynamics at a first-order phase transition involving strain: dynamic twin formation.Phys Rev Lett, 1991, 67: 3412–3415 Barsch GR, Krumhansl JA. Twin boundaries in ferroelastic media without interface dislocations.Phys Rev Lett, 1984, 53: 1069–1072 Barsch GR, Krumhansl JA. Nonlinear physics in martensitic transformation. In: Olson GB and Owen NS eds. Martensite, A Tribute to Morris Cohen. ASM International, 1992. 125–147 Burns JA, Spies RD. A nuermical study of parameter sensitiveties in Landau-Ginzburg models of phase transitions in shape memory alloys.J Intell Mat Syst Struct, 1994, 5: 321–332 James RD. Displacive phase transformations in solids.J Mech Phys Solids, 1986, 34: 359–394 Fried E. Construction of two-phase equilibria in non-elliptic hyperelastic material.J of Elasticity, 1993, 31: 71–123 Jiang Q. A continuum model for phase transformation in thermoelastic solids.J of Elasticity, 1993, 32: 61–91 Abeyaratne R, Knowles JK. A continuum model of a thermoelastic solid capable of undergoing phase transition.J Mech Phys Solids, 1993, 41: 541–574 Abeyaratne R, Kim SJ, Knowles JK. A one-dimensional continuum model for shape memory alloys.Int J Solids Struct, 1994, 31: 2229–2250 Tanaka K. A thermomechanical sketch of shape memory effect, one dimensional tensile behavior.Res Mech, 1986, 18: 251–263 Liang C, Rogers CA. One dimensional thermomechanical constitutive relations for shape memory materials.J Intell Mater Syst Struct, 1990, 1: 207–234 Zhang XD, Rogers CA, Liang C. Modelling of two-way memory effect.Philos Mag, 1992, 65A: 1199–1215 Brinson LC, Lammering R. Finite element analysis of the behavior of shape memory alloys and their application.Int J Solids Struct, 1993, 30: 3261–3280 Bekker A, Brinson LC. Temperature-induced phase transformation in a shape memory alloy: phase diagram based kinetics approach.J Mech Phys Solids, 1997 45: 949–988 Patoor E, Eberhardt A, Berveiller M. Thermomechanical behavior of shape memory alloys.Arch Mech, 1988, 40: 775–794 Patoor E, Eberhardt A, Berveiller M. Micromechanical modelling of the shape memory behavior. In: Brinson LC, Moran B eds. Mechanics of Phase Transformations and Shape Memory Alloys, AMD-Vol. 189/PVP-Vol. 292. ASME, 1994. 23–37 Sun QP, Hwang KC. Micromechanics modelling for the constitutive behavior of polycrystalline shape memory alloys, I: Derivation of general relations. II: Study of the individual phenomena.J Mech Phys Solids, 1993, 41: 1–17, 19–33 Sun QP, Hwang KC. Micromechanics constitutive description of thermoelastic martensitic transformation. In: Hutchison JW and Wu TY eds. Advances in Applied Mechanics, Vol. 31. New York: Academic Press, 1994, 249–298 Raniecki B, Lexcellent C.R L -models of pseudoelasticity and their specification for some shape memory solids.Eur J Mech, 1994, 13A: 21–33 Boyd JG, Logoudas DC. A thermodynamical constitutive model for shape memory materials, Part 1: The monolithic shape memory alloy.Int J Plasticity, 1996, 12: 805–842 Lu ZK, Weng G. Martensitic transformation and stress-strain relations of shape memory alloys.J Mech Phys Solids, 1997, 45: 1905–1928 Lu ZK, Weng G. A self-consistent model for the stress strain behavior of shape memory alloy polycrystals.Acta Mater, 1998, 46: 5423–5433 Yan WY, Sun QP, Hwang KC. A generalized micromechanics constitutive theory of single crystal with thermoelastic martensitic transformations.Science in China, 1998, 41A: 878–886 Huang MS, Brinson LC. A multivariants model for single crystal shape memory alloy behavior.J Mech Phys Solids, 1998, 46: 1379–1409 Siredey N, Patoor E, Berveiller M, et al. Constitutive equations for polycrystalline thermoelastic shape memory alloys. I. Intragranular interactions and behavior of grain.Int J of Solids Struct, 1999, 36: 4289–4315 Lin PH, Tobushi H, Tanaka K, et al. Pseudoelastic behaviour of TiNi shape memory alloy subjected to strain variations.J Intell Mater Syst Struct, 1994, 5: 694–701 Lin PH, Tobushi H, Tanaka K, et al. Deformation properties of TiNi shape memory alloy.JSME International Journal, 1996, 39A: 108–116 Shaw JA, Kyriakides S. Thermomechanical aspects of NiTi.J Mech Phys Solids, 1995, 43: 1243–1281 Shaw JA, Kyriakides S. On the nucleation and propagation of phase transformation fronts in a NiTi alloy.Acta Mater, 1997, 45: 683–700 Shaw JA, Kyriakides S. Initiation and propagation of localized deformation in elasto-plastic strips under uniaxial tension.Int J Plasticity, 1998, 13: 837–871 Song CQ, Sun QP, Hwang KC. Micromechanics constitutive modeling for polycrystalline SMA. In: Argoul P et al eds. IUTAM Symposium on Variations of Domain and Free Boundary Problems in Solid Mechanics. Paris, France, 22–25, April, 1997. Dordrecht: Kluwer Academic Publisher, 1999. 25–33 Leo PH, Shield TW, Bruno OP. Transient heat transfer effects on the pseudoelastic behavior of shape memory wires.Acta Metall Mater, 1993, 41: 2477–2485 Abeyaratne R, Kim SJ, Knowles JK. Continuum modeling of shape memory alloys. In: Mechanics of Phase Transformations and Shape Memory Alloys, AMD-Vol. 189/PVP-Vol. 292, ASM International, 1994. 59–69 Bruno OP, Leo PH, Reitich F. Free boundary conditions at austenite-martensite interface.Phys Rev Lett, 1995, 74: 746–749 Ball JM, James RD. Fine phase mixtures as minimizers of energy.Arch Rat Mech Anal, 1987, 100: 13–52 Bhattacharya K. Self-accommodation in matensite.Arch Rat Mech Anal, 1992, 120: 201–244 Chu CH. Hysteresis and microstructures: A study of biaxial loading on compound twins of copper-aluminum-nickel single crystals. Ph.D thesis. University of Minnesota, USA, 1993 Sun QP, Zhang XY, Xu TT. Some recent advances in experimental study of shape memory alloys. In: Proceedings of IUTAM Symposium on “Micro- and Macrostructural Aspects of Thermoplasticity”, Bochum, Germany, Aug 25–29, 1997. 407–416 Zhang XY, Sun QP, Yu SW. On the non-invariant plane model of the A-M interface in CuAlNi single crystal shape memory alloys.J Mech Phys Solids, 2000, 48: 2163–2182 Wechsler MS, Lieberman DS, Read T. On the theory of the formation of martensite.Trans Am Inst Min Eng (Trans AIME), 1953, 197: 1503–1515 Wayman CM. Introduction to the Crystallography of Martensite Transformations. New York: Macmillan, 1964 Muller I, Xu H. On the pseudoelastic hysteresis.Acta Metall Mater, 1991, 39: 263–271 Olson GB, Cohen M. Dislocation theory of martensitic transformations. In: Nabarro FRN ed. Dislocation in Solids. North-Holland: Elsevier Science Publishers, 1986. 295–407 Grujicic M, Ling HC. Haezebrouck DM, et al. The growth of martensite. In: Olson GB, Owen NS eds. Martensite, A Tribute to Morris Cohen. ASM International, 1992. 175–196 Mori T, Tanaka K. Average stress in matrix and average elastic energy of materials with misfitting inclusions.Acta Metall, 1973, 21: 571–574 Mura T. Micromechanics of Defects in Solids. 2nd ed. Dordrecht, Martinus Nijhoff, 1987 Benveniste Y. A new approach to the application of Mori-Tanaka theory in composite materials.Mech Mat 1987, 6: 147–157 Song GQ. Study on micromechanics constitutive models for martensitic transformation materials (in Chinese). Ph D Thesis. Beijing: Tsinghua University, 1996 Raniecki B, Tanaka K. On the thermodynamic driving force for coherent phase transformations.Int J Engng Sci, 1994, 32: 1845–1858 Sittner P, Hara Y, Takakura M, et al. On the general stress controlled thermoelastic martensitic transformation.Res Rep Fac Eng Mie Univ, 1994, 19: 19–24