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A theoretical model for functionally graded shape memory alloy cylinders subjected to internal pressure

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Abstract

A theoretical model for the Functionally Graded Shape Memory Alloy (FG-SMA) cylinders subjected to internal pressure is investigated. The gradient properties in this work are embodied in the Young’s modulus and Poisson’s ratio gradient through the thickness of the cylinder. The critical transformation stresses and maximum formation strain are all assumed to be constant. Combining the elasticity and exponential function of the Young’s modulus and Poisson’s ratio with the different gradient parameters, the elastic stress distributions and displacement distributions for the FG-SMA cylinder under the internal pressure are obtained, respectively. To get the theoretical solution, the Tresca yield function and the ideal elastic–plastic constitutive model are selected for the shape memory alloy to illustrate the phase transformation. The relationships between the internal pressure and total strain at the internal radius with different gradient parameters are then given, and the results show that the total strains are greatly influenced by the different parameters.

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References

  1. M. Koizumi: The concept of FGM. Ceram. Trans. 39, 3–10 (1993).

    Google Scholar 

  2. B. Skoczen: Functionally graded structural members obtained via the low temperature strain induced phase transformation. Int. J. Solids Struct. 44, 5182–5207 (2007).

    Article  CAS  Google Scholar 

  3. P. Sittner, L. Heller, J. Pilch, C. Curfs, T. Alonso, and D. Favier: Young’s modulus of austenite and martensite phases in superelastic NiTi wires. J. Mater. Eng. Perform. 23(7), 2303–2314 (2014).

    Article  CAS  Google Scholar 

  4. S.U. Rehman, M. Khan, A.N. Khan, L. Ali, and S.H.I. Jaffery: Two-step martensitic transformation in an aged Ti50Ni15Pd25Cu10 high temperature shape memory alloys. Acta Phys. Pol., A 128(2B), B125–B127 (2015).

    Article  CAS  Google Scholar 

  5. X-B. Wang, J.V. Humbeeck, B. Verlinden, and S. Kustov: Thermal cycling induced room temperature aging effect in Ni-rich NiTi shape memory alloy. Scr. Mater. 113, 206–208 (2016).

    Article  CAS  Google Scholar 

  6. C. Haberland, M. Elahinia, J.M. Walker, H. Meier, and J. Frenzel: On the development of high quality NiTi shape memory and pseudoelastic parts by additive manufacturing. Smart Mater. Struct. 23(10), 64–75 (2014).

    Article  CAS  Google Scholar 

  7. H-B. Lu, C-R. Lu, W-M. Huang, and J-S. Leng: Chemo-responsive shape memory effect in shape memory polyurethane triggered by inductive release of mechanical energy storage undergoing copper(II) chloride migration. Smart Mater. Struct. 24(3), 035018 (2015).

    Article  CAS  Google Scholar 

  8. H-B. Lu, J-S. Leng, and S-Y. Du: A phenomenological approach for the chemo-responsive shape memory effect in amorphous polymers. Soft Matter 9(14), 3851–3858 (2013).

    Article  CAS  Google Scholar 

  9. M. Samadpour, M. Sadighi, M. Shakeri, and H.A. Zamani: Vibration analysis of thermally buckled SMA hybrid composite sandwich plate. Compos. Struct. 119, 251–263 (2015).

    Article  Google Scholar 

  10. H. Asadi, Y. Kiani, M. Shakeri, and M.R. Eslami: Exact solution for nonlinear thermal stability of hybrid laminated composite Timoshenko beams reinforced with SMA fibers. Compos. Struct. 108, 811–822 (2014).

    Article  Google Scholar 

  11. D.C. Lagoudas: Shape Memory Alloys: Modeling and Engineering Applications (Springer, New York, 2008).

    Google Scholar 

  12. Z.W. Zhong and C.K. Yeong: Development of a gripper using SMA wire. Sens. Actuators, A 126(2), 375–381 (2006).

    Article  CAS  Google Scholar 

  13. S. Guo, J. Oohira, and T. Fukuda: A novel type of micropump using SMA actuator for microflow application. Presented at the IEEE Int. Conference Robot. Autom. Vol. 987–992, 2003.

  14. J-H. Qiu, Y-X. Bian, H-L. Ji, and K-J. Zhu: The application of intelligent material structure in the aviation field. Aviat Manuf. Tech. 3, 26–29 (2009). (in Chinese).

    Google Scholar 

  15. B.T. Lester, Y. Chenisky, and D.C. Lagoudas: Transformation characteristics of shape memory alloy composites. Smart Mater. Struct. 20, 094002 (2011).

    Article  CAS  Google Scholar 

  16. Y-Q. Fu, H-J. Du, and S. Zhang: Functionally graded TiN/TiNi shape memory alloy films. Mater. Lett. 57, 2995–2999 (2003).

    Article  CAS  Google Scholar 

  17. S. Belyaev, V. Rubanik, N. Resnina, V. Rinamol, Jr, O. Rubanik, and V. Borisov: Martensitic transformation and physical properties of ‘steel-TiNi’ bimetal composite, produced by explosion welding. Phase Transitions 83(4), 276–283 (2010).

    Article  CAS  Google Scholar 

  18. H. Tian, D. Schryvers, K.P. Mohanchandra, G.P. Carman, and J.V. Humbeeck: Fabrication and characterization of functionally graded Ni–Ti multilayer thin films. Funct. Mater. Lett. 2(2), 61–66 (2009).

    Article  CAS  Google Scholar 

  19. B. Zheng, J. Xu, and M. Qi: Preparation of graded DLC film on TiNi SMA by plasma enhanced deposition and behavior of corrosion-resistance. J. Funct. Mater. 38(1), 115–118 (2007).

    CAS  Google Scholar 

  20. B.F. Liu, G.S. Dui, and S.Y. Yang: On the transformation behavior of functionally graded SMA composites subjected to thermal loading. Eur. J. Mech. A-Solid. 40, 139–147 (2013).

    Article  Google Scholar 

  21. A. Pequegnat, A. Michael, J. Wang, K. Lian, Y. Zhou, and M.I. Khan: Surface characterizations of laser modified biomedical grade NiTi shape memory alloys. Mater. Sci. Eng., C 50(3), 367–378 (2015).

    Article  CAS  Google Scholar 

  22. S. Belyaev, V. Rubanik, N. Resnina, V. Rinamol, Jr, and I. Lomakin: Functional properties of ‘Ti50Ni50–Ti49.3Ni50.7’ shape memory composite produced by explosion welding. Smart Mater. Struct. 23, 085029 (2014).

    Article  CAS  Google Scholar 

  23. J.H. Lim, M.S. Kim, J.P. Noh, Y.W. Kim, and T.H. Nam: Compositionally graded Ti–Ni alloys prepared by diffusion bonding. J. Nanosci. Nanotechnol. 14(12), 9042–9046 (2014).

    Article  CAS  Google Scholar 

  24. R.M.S. Martins, N. Schell, H. Reuther, L. Pereira, K.K. Mahesh, R.J.C. Silva, and F.M.B. Fernandes: Texture development, microstructure and phase transformation characteristics of sputtered Ni–Ti shape memory alloy films grown on TiNi〈111〉. Thin Solid Films 519(1), 122–128 (2010).

    Article  CAS  Google Scholar 

  25. Z. Yan, L-S. Cui, and Y-J. Zheng: Microstructure and martensitic transformation behaviors of explosively welded NiTi/NiTi laminates. Chin. J. Aeronaut. 20, 168–171 (2007).

    Article  Google Scholar 

  26. Y-P. Zhang, X-P. Zhang, and Z-Y. Zhong: Fabrication, transformation and superelasticity behavior of NiTi memory alloy with large pore-size and gradient porosity. Acta Metall. Sin. 43(11), 1221–1227 (2007).

    CAS  Google Scholar 

  27. B.S. Shariat, Y-N. Liu, and G. Rio: Modelling and experimental investigation of geometrically graded NiTi shape memory alloys. Smart Mater. Struct. 22, 025030 (2013).

    Article  CAS  Google Scholar 

  28. B.S. Shariat, Y-N. Liu, and G. Rio: Thermomechanical modelling of microstructurally graded shape memory alloys. J. Alloys Compd. 541, 407–414 (2012).

    Article  CAS  Google Scholar 

  29. Q-L. Meng, Y-N. Liu, H. Yang, B.S. Shariat, and T.H. Nam: Functionally graded NiTi strips prepared by laser surface anneal. Acta Mater. 60(4), 1658–1668 (2012).

    Article  CAS  Google Scholar 

  30. B.S. Shariat, Y-N. Liu, Q-L. Meng, and G. Rio: Analytical modelling of functionally graded NiTi shape memory alloy plates under tensile loading and recovery of deformation upon heating. Acta Mater. 61(9), 3411–3421 (2013).

    Article  CAS  Google Scholar 

  31. M.F. Razali and A.S. Mahmud: Gradient deformation behavior of NiTi alloy by ageing treatment. J. Alloys Compd. 618, 182–186 (2015).

    Article  CAS  Google Scholar 

  32. D. Hartl and D.C. Lagoudas: Aerospace applications of shape memory alloys. J. Aerospace Eng. 221(4), 535–552 (2007).

    CAS  Google Scholar 

  33. M.A. Qidwai, P.B. Entchrv, D.C. Lagoudas, and V.G. DeGiorgi: Modeling of the thermomechanical behavior of porous shape memory alloys. Int. J. Solids Struct. 38, 8653–8671 (2001).

    Article  Google Scholar 

  34. A.S. Mahmud, Y-N. Liu, and T.H. Nam: Gradient anneal of functionally graded NiTi. Smart Mater. Struct. 17, 015031 (2008).

    Article  CAS  Google Scholar 

  35. V. Birman: Stability of functionally graded shape memory alloy sandwich panels. Smart Mater. Struct. 6, 278–286 (1997).

    Article  Google Scholar 

  36. J-C. Han, L. Xu, B-L. Wang, and X-H. Zhang: The research progress and prospects of functionally gradient materials. J. Solid Rocket Technol. 27(3), 207–215 (2004). (in Chinese).

    CAS  Google Scholar 

  37. H. Asadi, A.H. Akbarzadeh, Z-T. Chen, and M.M. Aghdam: Enhanced thermal stability of functionally graded sandwich cylindrical shells by shape memory alloys. Smart Mater. Struct. 24(4), 045022 (2015).

    Article  CAS  Google Scholar 

  38. E. Bagherizadeh, Y. Kiani, and M.R. Eslami: Mechanical buckling of functionally graded material cylindrical shells surrounded by Pasternak elastic foundation. Compos. Struct. 93(11), 3063–3071 (2011).

    Article  Google Scholar 

  39. R. Mirzaeifar, M. Shakeri, R. Desroches, and A. Yavari: A semi-analytic analysis of shape memory alloy thick-walled cylinders under internal pressure. Arch. Appl. Mech. 81(8), 1093–1116 (2011).

    Article  Google Scholar 

  40. D.J. Miller, L.A. Fahnestock, and M.R. Eatherton: Development and experimental validation of a nickel–titanium shape memory alloy self-centering buckling-restrained brace. Eng. Struct. 40, 288–298 (2012).

    Article  Google Scholar 

  41. J. Leng, X. Yan, X. Zhang, D. Huang, and Z. Gao: Design of a novel flexible shape memory alloy actuator with multilayer tubular structure for easy integration into a confined space. Smart Mater. Struct. 25(2), 025007 (2016).

    Article  CAS  Google Scholar 

  42. F.B. Hildebrand: Introduction to Numerical Analysis (McGraw-Hill, New York, America, 1974).

    Google Scholar 

  43. B-F. Liu, G-S. Dui, and Y-P. Zhu: On phase transformation behavior of porous shape memory alloys. J. Mech. Behav. Biomed. Mater. 5(1), 9–15 (2012).

    Article  CAS  Google Scholar 

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ACKNOWLEDGMENTS

The authors acknowledge the financial support of National Natural Science Foundation of China (Nos. 11502284; U1533103; 51505483; and 11272136) and it is also supported by the Fundamental Research Funds for the Central Universities (3122016C006) of China.

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Authors and Affiliations

  1. Airport College, Civil Aviation University of China, Tianjin, 300300, China

    Bingfei Liu & Yanan Zhang

  2. Sino-European Institute of Aviation Engineering, Civil Aviation University of China, Tianjin, 300300, China

    Shilong Hu & Wei Zhang

  3. College of Aeronautical Engineering, Civil Aviation University of China, Tianjin, 300300, China

    Wei Zhang & Rui Zhou

  4. Key Laboratory of Seismic Observation and Geophysical Imaging, Institute of Geophysics, China Earthquake Administration, Beijing, 100081, China

    Yuping Zhu

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  1. Bingfei Liu
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  2. Shilong Hu
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  3. Wei Zhang
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  5. Yanan Zhang
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Correspondence to Wei Zhang.

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Liu, B., Hu, S., Zhang, W. et al. A theoretical model for functionally graded shape memory alloy cylinders subjected to internal pressure. Journal of Materials Research 32, 1397–1406 (2017). https://doi.org/10.1557/jmr.2016.468

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