Three Dimensional Large Deformation Analysis of Phase Transformation in Shape Memory Alloys

XIA Kai-ming; PAN Tong-yan; LIU Shan-hong

doi:10.3879/j.issn.1000-0887.2010.10.007

Volume 31 Issue 10

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XIA Kai-ming, PAN Tong-yan, LIU Shan-hong. Three Dimensional Large Deformation Analysis of Phase Transformation in Shape Memory Alloys[J]. Applied Mathematics and Mechanics, 2010, 31(10): 1201-1210. doi: 10.3879/j.issn.1000-0887.2010.10.007

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Three Dimensional Large Deformation Analysis of Phase Transformation in Shape Memory Alloys

doi: 10.3879/j.issn.1000-0887.2010.10.007

1.
Division of Engineering, Colorado School of Mines, Golden, CO 80401, USA;

Received Date: 1900-01-01
Rev Recd Date: 2010-07-30
Publish Date: 2010-10-15

Abstract

Abstract

Shape memory alloys (SMAs) have been explored as smart materials and used as dampers, actuator elements and smart sensors.An important character of SMAs is its ability to recover all of its large deformations in mechanical loading-unloading cycles, without showing permanent deformation.A stress-induced phenomenological constitutive equation for SMAs, which can be used to describe the superelastic hysteresis loops and phase transformation between martensite and austenite was presented.The martensite fraction of SMAs was assumed to be dependent on deviatoric stress tensor.Therefore phase transformation of shape memory alloys was volume preserving during the phase transformation.The model was implemented in large deformation finite element code and cast in the updated Lagrangian scheme.In order to use Cauchy stress and the linear strain in constitutive laws, a frame indifferent stress objective rate has to be used and the Jaumann stress rate was used. The results of the numerical experiments conducted show that the superelastic hysteresis loops arising with the phase transformation can be effectively captured.
- shape memory alloys,
- phase transformation,
- superelasticity,
- large deformation,
- finite element

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References(16)

References

[1]	BirmanV. Review of mechanics of shape memory alloy structures[J].Applied Mechanics Reviews, 1997, 50(11)：629-645. doi: 10.1115/1.3101674
[2]	Duerig T W, Melton K N, Stockel D, Wayman C M.Engineering Aspects of Shape Memory Alloys[M].London: Butterworth-Heinemann, 1990, 137-148.
[3]	Lubliner J, Auricchio F. Gereralized plasticity and shape memory alloys[J]. International Journal of Solids and Structures, 1996, 33(7)：991-1003. doi: 10.1016/0020-7683(95)00082-8
[4]	Auricchio F, Taylor R L, Lubliner J. Shape-memory alloys: macromodelling and numerical simulations of the superelastic behavior[J]. Comp Meths Appl Mech Eng, 1997,146(3/4)：281-312. doi: 10.1016/S0045-7825(96)01232-7
[5]	Barret D J, Sullivan B J. A three-dimensional phase transformation model for shape memory alloys[J]. J Intelligent Mater Syst Struct, 1995, 6(6): 831-839.
[6]	Brinson L C, Lammering R. Finite-element analysis of the behavior of shape memory alloys and their applications[J]. International Journal of Solids and Structures,1993, 30(23): 3261-3280.
[7]	Qidwai M A, Lagoudas D C. Numerical implementation of a shape memory alloy thermomechanical constitutive model using return mapping algorithms[J]. Int J Numer Meths Eng, 2000, 47(6): 1123-1168.
[8]	Rengarajan G, Kumar R K, Reddy J N. Numerical modeling of stress induced martensitic phase transformations in shape memory alloys[J].International Journal of Solids and Structures,1998, 35(14): 1489-1513.
[9]	Tanaka K, Nishimura F, Hayashi T, Tobushi H, Lexcellent C. Phenomenological analysis on subloops and cyclic behavior in shape memory alloys under mechanical and/or thermal loads[J]. Mechnica of Materials,1995,19(4): 281-292.
[10]	Masud A, Xia K. A variational multiscale method for computational inelasticity: application to superelasticity in shape memory alloys[J]. Comp Meths Appl Mech Engrg,2006,195(33/36): 4512-4531.
[11]	Masud A, Panahandeh M, Aurrichio F. A finite-strain finite element model for the pseudoelastic behavior of shape memory alloys[J]. Comp Meths Appl Mech Engrg, 1997, 148(1/2): 23-37. doi: 10.1016/S0045-7825(97)00080-7
[12]	Auricchio F. A robust integration-algorithm for a finite-strain shape memory alloy superelastic model[J].Int J Plasticity, 2001,17(7): 971-990. doi: 10.1016/S0749-6419(00)00050-4
[13]	Stein E, Sagar G. Theory and finite element computation of cyclic martensitic phase transformation at finite strain[J]. Int J Numer Meth Engrg,2008,74(1): 1-31. doi: 10.1002/nme.2148
[14]	Hughes T J R, Winget J. Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis[J]. Int J Numer Methods Eng,1980, 15(12): 1862-1876.
[15]	Simo J C, Hughes T J R. Computational Inelasticity[M].New York:Springer-Verlag, 1998.
[16]	Belytschko T, Liu W K, Moran B. Nonlinear Finite Elements for Continua and Structures[M]. John Wiley & Sons Ltd,2000.