A Micromechanical Constitutive Model for Porous Shape Memory Alloys

Abstract:

A micromechanical constitutive model for responding the macroscopic behavior of porous shape memory alloys (SMA) has been proposed in this work. According to the micromechanical method, the stiffness tensor of the porous SMA is obtained. The critical stresses are calculated by elastic mechanics. Based on the general concept of secant moduli method, the effective secant moduli of the porous SMA is given in terms of the secant moduli of dense SMA and the volume fraction of pores. The model takes account of the tensile-compressive asymmetry of SMA materials and the effect of the hydrostatic stress. Only the material parameters of dense SMA are needed for numerical calculation, and can degenerate to dense material. Examples for the uniaxial response of porous SMA materials at constant temperature are then used to illustrate one possible application of the constitutive model. The numerical results have been compared with the experiment data for porous SMA, which show that the modeling results are in good agreement with the experiments.

• Periodical: Applied Mechanics and Materials (Volumes 29-32)
• Pages: 1855-1861
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.29-32.1855
• Online since: August 2010
• Authors: Bing Fei Liu, Guan Suo Dui, Yu Ping Zhu
• Keywords: Effective Secant Moduli, Porous Shape-Memory Alloy, Tensile-Compressive Asymmetry

References

[1] W. Teppei, W. Yoshimi and O. Hiroshi: Mater. Sci. Forum Vol. 475 (2005), p. (2063).

[2] Y.H. Li, L.J. Rong and Y.Y. Li: J. Alloys. Compd. Vol. 325 (2001), p.259.

[3] P.B. Entchev, D.C. Lagoudas: Mech. Mater. Vol. 34 (2002), p.1.

[4] S. Nemat-Nasser, Y. Su, W.G. Guo and J. Isaacs: J. Mech. Phys. Solids. Vol. 53 (2005), p.2320.

[5] Y.J. Xiong, Y.C. Li, X.J. Wang, P.D. Hodgson and C.E. Wen: J. Mech. Behav. Biomed. Vol. 1 (2007), p.269.

[6] J.D. Eshelby: Proc. R. Soc. London, Ser. A. Vol. 241 (1957), p.376.

[7] T. Mori, K. Tanaka: Acta Metal. Vol. 21 (1973), p.571.

[8] D.C. Lagoudas, Z. Bo and M.A. Qidwai: Mech. Compos. Mater. Struct. Vol. 3 (1996), p.153.

[9] K. Tanaka: Res. Mechanica Vol. 18 (1986), p.251.

[10] C. Liang, C.A. Roger: J. Intell. Mater. Syst. Struct. Vol. 1 (1990), p.207.

[11] J.M. Qu, M. Cherkaoui: Fundamentals of micromechanics of solids (John Wiley & Sons Inc, New Jersey 2006).

[12] S.P. Timoshenko, J.N. Gooder: Theory of Elasticity (Tsinghua University Press, Beijing 2004).

[13] M.A. Qidwai, D.C. Lagoudas: Int. J. Plast. Vol. 16 (2000), p.1309.

[14] L. Qrgeas, D. Favier: Acta. Mater. Vol. 46 (1998), p.5579.

[15] G.P. Tandon, J.P. Weng: J. Appl. Mech. Vol. 55 (1988), p.126.

[16] R. Hill: J. Mech. Phys. Solids. Vol. 15 (1967), p.79.