Continuum Mechanics and Thermodynamics

, Volume 30, Issue 1, pp 53–68 | Cite as

Numerical simulation and experimental investigation of the elastocaloric cooling effect in sputter-deposited TiNiCuCo thin films

  • F. Welsch
  • J. Ullrich
  • H. Ossmer
  • M. Schmidt
  • M. Kohl
  • C. Chluba
  • E. Quandt
  • A. Schütze
  • S. Seelecke
Original Article


The exploitation of the elastocaloric effect in superelastic shape memory alloys (SMA) for cooling applications shows a promising energy efficiency potential but requires a better understanding of the non-homogeneous martensitic phase transformation. Temperature profiles on sputter-deposited superelastic \({\mathrm {Ti_{55.2}Ni_{29.3}Cu_{12.7}Co_{2.8}}}\) shape memory alloy thin films show localized release and absorption of heat during phase transformation induced by tensile deformation with a strong rate dependence. In this paper, a model for the simulation of the thermo-mechanically coupled transformation behavior of superelastic SMA is proposed and its capability to reproduce the mechanical and thermal responses observed during experiments is shown. The procedure for experiment and simulation is designed such that a significant temperature change from the initial temperature is obtained to allow potential cooling applications. The simulation of non-local effects is enabled by the use of a model based on the one-dimensional Müller–Achenbach–Seelecke model, extended by 3D mechanisms such as lateral contraction and by non-local interaction, leading to localization effects. It is implemented into the finite element software COMSOL Multiphysics, and comparisons of numerical and experimental results show that the model is capable of reproducing the localized transformation behavior with the same strain rate dependency. Additionally to the thermal and the mechanical behavior, the quantitative prediction of cooling performance with the presented model is shown.


Elastocaloric cooling Shape memory alloy TiNiCuCo thin film Thermo-mechanical coupling Rate dependence Localization Propagating transformation fronts Finite element analysis Phase transformation Thermodynamics 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



The authors gratefully acknowledge the support of the DFG priority program 1599 “Caloric effects in ferroic materials: New concepts for cooling” (


  1. 1.
    Fähler, S., Rößler, U.K., Kastner, O., Eckert, J., Eggeler, G., Emmerich, H., Entel, P., Müller, S., Quandt, E., Albe, K.: Caloric effects in ferroic materials: new concepts for cooling. Adv. Eng. Mater. 14, 10–19 (2012)CrossRefGoogle Scholar
  2. 2.
    Cui, J., Wu, Y., Muehlbauer, J., Hwang, Y., Radermacher, R., Fackler, S., Wuttig, M., Takeuchi, I.: Demonstration of high efficiency elastocaloric cooling with large Delta T using NiTi wires. Appl. Phys. Lett. 101, 25–28 (2012)Google Scholar
  3. 3.
    Cui, J., Takeuchi, I., Wuttig, M., Wu, Y., Reinhard, R., Hwang, Y., Muehlbauer, J.: Thermoelastic cooling. (2012)
  4. 4.
    Schmidt, M., Schütze, A., Seelecke, S.: Cooling efficiencies of a NiTi-based cooling process. In: ASME 2013 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, p. V001T04A014 (2013)Google Scholar
  5. 5.
    Schmidt, M., Schütze, A., Seelecke, S.: Experimental investigation on the efficiency of a control dependent NiTi-based cooling process. In: ASME 2014 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, pp. V002T04A013 (2014). doi: 10.1115/SMASIS2014-7561
  6. 6.
    Schmidt, M., Schütze, A., Seelecke, S.: Scientific test setup for investigation of shape memory alloy based elastocaloric cooling processes. Int. J. Refrig. 54, 88–97 (2015)CrossRefGoogle Scholar
  7. 7.
    Ullrich, J., Schmidt, M., Schütze, A., Wieczorek, A., Frenzel, J., Eggeler, G., Seelecke, S.: Experimental investigation and numerical simulation of the mechanical and thermal behavior of a superelastic shape memory alloy beam during bending. In: ASME 2014 Conference on Smart Materials, Adaptive Structures and Intelligent Systems (2014) (to appear)Google Scholar
  8. 8.
    Ossmer, H., Chluba, C., Krevet, B., Quandt, E., Rohde, M., Kohl, M.: Elastocaloric cooling using shape memory alloy films. J. Phys. Conf. Ser. 476, 12138 (2013)CrossRefGoogle Scholar
  9. 9.
    Ossmer, H., Lambrecht, F., Gültig, M., Chluba, C., Quandt, E., Kohl, M.: Evolution of temperature profiles in TiNi films for elastocaloric cooling. Acta Mater. 81, 9–20 (2014)CrossRefGoogle Scholar
  10. 10.
    Ossmer, H., Chluba, C., Gueltig, M., Quandt, E., Kohl, M.: Local evolution of the elastocaloric effect in TiNi-based films. Shape Mem. Superelasticity 1, 142–152 (2015)CrossRefGoogle Scholar
  11. 11.
    Carmo, J.P., Silva, M.F., Ribeiro, J.F., Wolffenbuttel, R.F., Alpuim, P., Rocha, J.G., Gonçalves, L.M., Correia, J.H.: Digitally-controlled array of solid-state microcoolers for use in surgery. Microsyst. Technol. 17, 1283–1291 (2011)CrossRefGoogle Scholar
  12. 12.
    El-Ali, J., Perch-Nielsen, I.R., Poulsen, C.R., Bang, D.D., Telleman, P., Wolff, A.: Simulation and experimental validation of a SU-8 based PCR thermocycler chip with integrated heaters and temperature sensor. Sens. Actuators A Phys. 110, 3–10 (2004)CrossRefGoogle Scholar
  13. 13.
    Bechtold, C., Chluba, C., Lima De Miranda, R., Quandt, E.: High cyclic stability of the elastocaloric effect in sputtered TiNiCu shape memory films. Appl. Phys. Lett. 101, 091903 (2012)ADSCrossRefGoogle Scholar
  14. 14.
    Chluba, C., Ge, W., Lima de Miranda, R., Strobel, J., Kienle, L., Quandt, E., Wuttig, M.: Ultralow-fatigue shape memory alloy films. Science 348, 1004–1007 (2015)Google Scholar
  15. 15.
    Frenzel, J., Wieczorek, A., Opahle, I., Maaß, B., Drautz, R., Eggeler, G.: On the effect of alloy composition on martensite start temperatures and latent heats in Ni-Ti-based shape memory alloys. Acta Mater. 90, 213–231 (2015)CrossRefGoogle Scholar
  16. 16.
    Achenbach, M., Müller, I.: A model for shape memory. J. Phys. Colloq. 43, C4-163–C4-167 (1982)CrossRefGoogle Scholar
  17. 17.
    Achenbach, M.: A model for an alloy with shape memory. Int. J. Plast. 5, 371–395 (1989)CrossRefGoogle Scholar
  18. 18.
    Boyd, J.G., Lagoudas, D.C.: A thermodynamical constitutive model for shape memory materials. Part I. The monolithic shape memory alloy. Int. J. Plast. 12, 805–842 (1996)CrossRefzbMATHGoogle Scholar
  19. 19.
    Brinson, L.C.C.: One-dimensional constitutive behavior of shape memory alloys: thermomechanical derivation with non-constant material functions and redefined martensite internal variable. J. Intell. Mater. Syst. Struct. 4, 229–242 (1993)CrossRefGoogle Scholar
  20. 20.
    Chemisky, Y., Duval, A., Patoor, E., Ben Zineb, T.: Constitutive model for shape memory alloys including phase transformation, martensitic reorientation and twins accommodation. Mech. Mater. 43, 361–376 (2011)CrossRefGoogle Scholar
  21. 21.
    Heintze, O., Seelecke, S.: A coupled thermomechanical model for shape memory alloys-from single crystal to polycrystal. Mater. Sci. Eng. A. 481–482, 389–394 (2008)CrossRefGoogle Scholar
  22. 22.
    Lagoudas, D.C.: Shape Memory Alloys. Springer, Boston (2010)zbMATHGoogle Scholar
  23. 23.
    Seelecke, S., Müller, I.: Shape memory alloy actuators in smart structures: modeling and simulation. Appl. Mech. Rev. 57, 23 (2004)ADSCrossRefGoogle Scholar
  24. 24.
    Seelecke, S.: Modeling the dynamic behavior of shape memory alloys. Int. J. Nonlinear Mech. 37, 1363–1374 (2002)ADSCrossRefzbMATHGoogle Scholar
  25. 25.
    Smith, R.C., Seelecke, S., Dapino, M., Ounaies, Z.: A unified framework for modeling hysteresis in ferroic materials. J. Mech. Phys. Solids. 54, 46–85 (2006)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Shaw, J.A., Kyriakides, S.: Thermomechanical aspects of NiTi. J. Mech. Phys. Solids. 43, 1243–1281 (1995)ADSCrossRefGoogle Scholar
  27. 27.
    Chang, B.-C., Shaw, J., Iadicola, M.: Thermodynamics of shape memory alloy wire: modeling, experiments, and application. Contin. Mech. Thermodyn. 18, 83–118 (2006)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Duval, A., Haboussi, M., Ben Zineb, T.: Modelling of localization and propagation of phase transformation in superelastic SMA by a gradient nonlocal approach. Int. J. Solids Struct. 48, 1879–1893 (2011)CrossRefGoogle Scholar
  29. 29.
    Grandi, D., Maraldi, M., Molari, L.: A macroscale phase-field model for shape memory alloys with non-isothermal effects: influence of strain rate and environmental conditions on the mechanical response. Acta Mater. 60, 179–191 (2012)CrossRefGoogle Scholar
  30. 30.
    Depriester, D., Maynadier, A., Lavernhe-Taillard, K., Hubert, O.: Thermomechanical modelling of a NiTi SMA sample submitted to displacement-controlled tensile test. Int. J. Solids Struct 51, 1901–1922 (2014)CrossRefGoogle Scholar
  31. 31.
    Levitas, V.I., Lee, D.-W., Preston, D.L.: Interface propagation and microstructure evolution in phase field models of stress-induced martensitic phase transformations. Int. J. Plast. 26, 395–422 (2010)CrossRefzbMATHGoogle Scholar
  32. 32.
    Furst, S.J., Crews, J.H., Seelecke, S.: Numerical and experimental analysis of inhomogeneities in SMA wires induced by thermal boundary conditions. Contin. Mech. Thermodyn. 24, 485–504 (2012)ADSCrossRefGoogle Scholar
  33. 33.
    Richter, F., Kastner, O., Eggeler, G.: Implementation of the Müller–Achenbach–Seelecke model for shape memory alloys in ABAQUS. J. Mater. Eng. Perform. 18, 626–630 (2009)CrossRefGoogle Scholar
  34. 34.
    Yang, S., Seelecke, S.: FE analysis of SMA-based bio-inspired bone–joint system. Smart Mater. Struct. 18, 104020 (2009)Google Scholar
  35. 35.
    Müller, I., Seelecke, S.: Thermodynamic aspects of shape memory alloys. Math. Comput. Model. 34, 1307–1355 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Young, M.L., Wagner, M.F.X., Frenzel, J., Schmahl, W.W., Eggeler, G.: Phase volume fractions and strain measurements in an ultrafine-grained NiTi shape-memory alloy during tensile loading. Acta Mater. 58, 2344–2354 (2010)CrossRefGoogle Scholar
  37. 37.
    COMSOL AB: COMSOL Multiphysics, User’s Guide, Version 5.1 (2015)Google Scholar
  38. 38.
    Brinson, L.C., Schmidt, I., Lammering, R.: Stress-induced transformation behavior of a polycrystalline NiTi shape memory alloy: Micro and macromechanical investigations via in situ optical microscopy. J. Mech. Phys. Solids. 52, 1549–1571 (2004)ADSCrossRefzbMATHGoogle Scholar
  39. 39.
    Khalil-Allafi, J., Hasse, B., Klönne, M., Wagner, M., Pirling, T., Predki, W., Schmahl, W.W.: In-situ diffraction investigation of superelastic NiTi shape memory alloys under mechanical stress with neutrons and with synchrotron radiation. Materwiss. Werksttech. 35, 280–283 (2004)CrossRefGoogle Scholar
  40. 40.
    Schmahl, W.W., Khalil-Allafi, J., Hasse, B., Wagner, M., Heckmann, a, Somsen, C.: Investigation of the phase evolution in a super-elastic NiTi shape memory alloy (50.7 at.%Ni) under extensional load with synchrotron radiation. Mater. Sci. Eng. A. 378, 81–85 (2004)CrossRefGoogle Scholar
  41. 41.
    Schmidt, M., Schütze, A., Seelecke, S.: Elastocaloric cooling processes: the influence of material strain and strain rate on efficiency and temperature span. APL Mater. 4, 0-6 (2016)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Intelligent Material Systems LabSaarland UniversitySaarbrueckenGermany
  2. 2.Lab for Measurement TechnologySaarland UniversitySaarbrueckenGermany
  3. 3.Institute of Microstructure TechnologyKarlsruhe Institute of TechnologyKarlsruheGermany
  4. 4.Institute for Material ScienceUniversity of KielKielGermany

Personalised recommendations