Three-dimensional, non-isothermal phase-field modeling of thermally and stress-induced martensitic transformations in shape memory alloys

Abstract The transition between austenite and martensite provides shape memory alloys (SMAs) with many unique properties. A three-dimensional, non-isothermal phase-field model was employed to comprehensively investigate the latent heat and elastocaloric effects in SMAs, which are originated from the thermoelastic martensitic transformations (MTs). We analyzed thermally induced MTs upon cooling and heating and stress-induced MTs at different temperatures in Mn–Cu alloys. It was observed that the size of twinned martensitic domain varied with temperature and large internal stresses resulted in thermoelastic equilibrium between austenite and martensite. The evolution of temperature field, caused by the latent heat effect, was obtained and the maximum temperature was found nearby the phase interface during the transformation. Twinned and single-variant martensites formed upon uniaxial tension and compression, respectively. Above the thermodynamic equilibrium temperature between austenite and martensite, with the occurring of reverse MT during unloading, superelasticity was realized. The localized temperature change and global elastocaloric effect during uniaxial loading and unloading were obtained and discussed. This model helps understand and explain the uniformity of temperature, stress and microstructural fields in the phase-field method.

[1]  K. Ishida,et al.  Ferrous Polycrystalline Shape-Memory Alloy Showing Huge Superelasticity , 2010, Science.

[2]  L. Mañosa,et al.  Large temperature span and giant refrigerant capacity in elastocaloric Cu-Zn-Al shape memory alloys , 2013 .

[3]  Austenite–martensite interface in shape memory alloys , 2010 .

[4]  Mahmood Mamivand,et al.  Phase Field Modeling of the Tetragonal-to-Monoclinic Phase Transformation in Zirconia , 2013 .

[5]  Y. Rong,et al.  Grain size dependence of the martensite morphology – A phase-field study , 2016 .

[6]  Eckhard Quandt,et al.  Ultralow-fatigue shape memory alloy films , 2015, Science.

[7]  M. Tang,et al.  One-dimensional model of martensitic transformations , 2002 .

[8]  W. Huang,et al.  Transformation characteristics of shape memory alloys in a thermal cycle , 2006 .

[9]  H. Kawano,et al.  Self-accommodation of B19′ martensite in Ti–Ni shape memory alloys – Part I. Morphological and crystallographic studies of the variant selection rule , 2012 .

[10]  X. Moya,et al.  Caloric materials near ferroic phase transitions. , 2014, Nature materials.

[11]  Jian Liu,et al.  Elastocaloric effect in Ni50Fe19Ga27Co4 single crystals , 2015 .

[12]  P Stanley,et al.  Beginnings and Early Development of Thermoelastic Stress Analysis , 2008 .

[13]  T. Fukuda,et al.  An interpretation of the kinetics of martensitic transformation in a Ni45Co5Mn36.5In13.5 alloy , 2014 .

[14]  P. Nordblad.  Magnetocaloric materials: Strained relations. , 2013, Nature materials.

[15]  L. Mañosa,et al.  Elastocaloric effect associated with the martensitic transition in shape-memory alloys. , 2008, Physical review letters.

[16]  A. G. Khachaturi︠a︡n.  Theory of structural transformations in solids , 1983 .

[17]  J. Juan,et al.  Martensite nucleation on dislocations in Cu–Al–Ni shape memory alloys , 2007 .

[18]  C. M. Wayman,et al.  Shape-Memory Materials , 2018 .

[19]  M. Mamivand,et al.  Shape memory effect and pseudoelasticity behavior in tetragonal zirconia polycrystals: A phase field study , 2014 .

[20]  A. Ahadi,et al.  Effects of grain size on the rate-dependent thermomechanical responses of nanostructured superelastic NiTi , 2014 .

[21]  X. Y. Wang,et al.  Magnetic-field-induced strain in an antiferromagnetic γ‐MnNi alloy , 2006 .

[22]  Anisha Roy,et al.  Multiphase phase field theory for temperature- and stress-induced phase transformations , 2015 .

[23]  Q. Zhai,et al.  Athermal nature of the martensitic transformation in Heusler alloy Ni–Mn–Sn , 2013 .

[24]  Nucleation of austenite in mechanically stabilized martensite by localized heating , 2013 .

[25]  Mahmood Mamivand,et al.  A review on phase field modeling of martensitic phase transformation , 2013 .

[26]  Yunzhi Wang,et al.  Three-dimensional field model and computer modeling of martensitic transformations , 1997 .

[27]  G. B. Olson,et al.  Reply to "On the equilibrium temperature in thermoelastic martensitic transformations" , 1977 .

[28]  A. Khachaturyan,et al.  Phase field microelasticity modeling of heterogeneous nucleation and growth in martensitic alloys , 2007 .

[29]  A. Chrysanthou,et al.  Martensitic-Austenitic phase transformation of Ni-Ti SMAs : Thermal properties , 2012 .

[30]  Oliver Gutfleisch,et al.  Giant magnetocaloric effect driven by structural transitions. , 2012, Nature materials.

[31]  Xuejun Jin,et al.  Elastocaloric effect by a weak first-order transformation associated with lattice softening in an Fe-31.2Pd (at.%) alloy , 2015 .

[32]  B. Blanpain,et al.  An introduction to phase-field modeling of microstructure evolution , 2008 .

[33]  A. Borgenstam,et al.  Effect of external loading on the martensitic transformation – A phase field study , 2013 .

[34]  M. Mitsuhara,et al.  In situ scanning electron microscopy study of the thermoelastic martensitic transformation in Ti-Ni shape memory alloy , 2016 .

[35]  T. Furuhara,et al.  Substructures of lenticular martensites with different martensite start temperatures in ferrous alloys , 2009 .

[36]  Ji Ma,et al.  Superelastic response of a single crystalline FeMnAlNi shape memory alloy under tension and compression , 2015 .

[37]  Akinori Yamanaka,et al.  Elastoplastic phase-field simulation of martensitic transformation with plastic deformation in polycrystal , 2010 .

[38]  Tongxi Yu,et al.  Experimental study on rate dependence of macroscopic domain and stress hysteresis in NiTi shape memory alloy strips , 2010 .

[39]  A. A. Likhachev,et al.  Giant magnetic-field-induced strain in NiMnGa seven-layered martensitic phase , 2002 .

[40]  Hemantha Kumar Yeddu,et al.  Stress-assisted martensitic transformations in steels: A 3-D phase-field study , 2013 .

[41]  G. Ravichandran,et al.  Stress-induced martensitic phase transformation in thin sheets of Nitinol , 2007 .

[42]  Y. Rong,et al.  Microstructural evolution of Mn-rich antiferromagnetic Mn–Cu alloy under temperature field , 2010 .

[43]  Long-Qing Chen.  Phase-Field Models for Microstructure Evolution , 2002 .

[44]  G. Miyamoto,et al.  Precise measurement of strain accommodation in austenite matrix surrounding martensite in ferrous alloys by electron backscatter diffraction analysis , 2009 .

[45]  Temperature analysis of one-dimensional NiTi shape memory alloys under different loading rates and boundary conditions , 2013 .

[46]  Nailu Chen,et al.  Interface stress evolution of martensitic transformation in MnCu alloys: A phase-field study , 2016 .

[47]  J. Humbeeck,et al.  Isothermal and athermal martensitic transformations in Ni–Ti shape memory alloys , 2012 .

[48]  Hemantha Kumar Yeddu,et al.  Three-dimensional phase-field modeling of martensitic microstructure evolution in steels , 2012 .

[49]  Jie Shen,et al.  Applications of semi-implicit Fourier-spectral method to phase field equations , 1998 .

[50]  F. Yin,et al.  Effects of transformation twin on Hall–Petch relationship in MnCu alloy , 2008 .

[51]  M. Wuttig,et al.  Designing shape-memory Heusler alloys from first-principles , 2011 .

[52]  Dean L. Preston,et al.  Three-dimensional Landau theory for multivariant stress-induced martensitic phase transformations. I. Austenite↔martensite , 2002 .

[53]  Y. Rong,et al.  Kinetics, mechanism, and pathway of reorientation of multi-variants in Ni-Mn-Ga shape memory alloys under continuous compressive stress: Phase-field simulation , 2012 .

[54]  L. Molari,et al.  A macroscale, phase-field model for shape memory alloys with non-isothermal effects: influence of strain-rate and environmental conditions on the mechanical response , 2011, 1107.5998.

[55]  V. Levitas,et al.  Interface Propagation and Microstructure Evolution in Phase Field Models of Stress-Induced Martensitic Phase Transformations , 2010 .

[56]  F. Falk.  Model free energy, mechanics, and thermodynamics of shape memory alloys , 1980 .

[57]  T. Fukuda,et al.  On the physical nature of high reversible strain in Fe–Pd single crystals exhibiting lattice softening , 2013 .

[58]  K. Shimizu,et al.  Crystallographic and Morphological Studies on the FCC to FCT Transformation in Mn–Cu Alloys , 1982 .

[59]  X. Liang,et al.  Stable elastocaloric effect under tensile stress of iron-palladium alloy and its in situ X-ray observation , 2016 .

[60]  P. Wen,et al.  A phase field study focuses on the transverse propagation of deformation twinning for hexagonal-closed packed crystals , 2016 .

[61]  T. Nam,et al.  Effect of pseudoelastic cycling on the Clausius–Clapeyron relation for stress-induced martensitic transformation in NiTi , 2008 .

[62]  Jordi Ortín,et al.  Thermodynamic analysis of thermal measurements in thermoelastic martensitic transformations , 1988 .

[63]  G. B. Olson,et al.  Thermoelastic behavior in martensitic transformations , 1975 .

[64]  M. Kohl,et al.  Evolution of temperature profiles in TiNi films for elastocaloric cooling , 2014 .

[65]  Ping Wu,et al.  Phase-field simulations of stress-strain behavior in ferromagnetic shape memory alloy Ni2MnGa , 2008 .

[66]  V. Novák,et al.  In situ TEM observation of stress-induced martensitic transformations and twinning processes in CuAlNi single crystals , 2010 .

[67]  H. Sehitoglu,et al.  Elastocaloric cooling potential of NiTi, Ni2FeGa, and CoNiAl , 2015 .

[68]  N. Babacan,et al.  Finite element simulations of microstructure evolution in stress-induced martensitic transformations , 2016 .

[69]  E. Werner,et al.  Temperature distribution due to localised martensitic transformation in SMA tensile test specimens , 2003 .