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Research Papers

A Phenomenological Approach for Real-Time Simulation of the Two-Way Shape Memory Effect in NiTi Alloys

[+] Author and Article Information
C. Maletta1

Department of Mechanical Engineering, University of Calabria, Arcavacata di Rende Cosenza 87030, Italycarmine.maletta@unical.it

A. Falvo, F. Furgiuele

Department of Mechanical Engineering, University of Calabria, Arcavacata di Rende Cosenza 87030, Italy

1

Corresponding author.

J. Eng. Mater. Technol 130(1), 011003 (Dec 20, 2007) (9 pages) doi:10.1115/1.2806264 History: Received December 07, 2006; Revised August 01, 2007; Published December 20, 2007

A phenomenological model to simulate the two-way shape memory effect (TWSME) in nickel-titanium alloys (NiTi) is proposed. The model is based on the Prandtl–Ishlinksii operator and it is able to simulate the hysteretic behavior of the material in the strain-temperature response. Starting from some experimental measurements of well known thermomechanical characteristics of NiTi alloys, the parameters of the phenomenological model are identified by simple and efficient numerical procedures. The model was developed in the commercial software package SIMULINK ® and it is able to simulate the effects of applied stresses on the TWSME as well as partial thermal cycles, which generate incomplete martensitic transformations. A systematic comparison between experimental measurements, carried out under different values of applied stress, and numerical predictions are illustrated for both complete and incomplete phase transformations. The results are considered satisfactory both in accuracy and in computational time; therefore, the method is robust and suitable for use in real-time applications.

Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 2

Example of training cycle: (1) loading, (2) unloading, (3) heating up to Af, and (4) cooling down to Mf

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Figure 3

Measured deformations versus number of training cycles: εtot, εre, εtw, and εp

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Figure 4

Stress-free thermal hysteresis behavior of the trained material

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Figure 5

Thermal hysteresis behavior under fixed tensile stress

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Figure 6

PTTs versus applied stress

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Figure 7

Two-way shape memory strain versus the applied stress: effect of mismatch between Young’s modulus of martensite and austenite, Δεmech; effect of increased volume fraction of favorably oriented martensite variants Δεmem

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Figure 8

Numerical fitting of the experimental data: (a) comparison between exponential curves and experimental measurements; (b) numerical fitting in the T-loge(ε) plane to identify the parameters of the exponential curve in the heating branch of the hysteresis loop

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Figure 9

(a) Generalized backlash operator; (b) complex hysteretic loop obtained by a weighted superposition of three backlash operators

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Figure 10

SIMULINK model of the Prandtl–Ishlinskii hysteresis operator

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Figure 11

Numerically simulated loop for a thermal cycle between the temperatures T0<Mf and T1>Af obtained by the Prandtl–Ishlinskii model

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Figure 12

SIMULINK model of the modified Prandtl–Ishlinskii hysteresis operator

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Figure 13

Numerically simulated loop for a thermal cycle between the temperatures T0<Mf and T1>Af obtained by the modified Prandtl–Ishlinskii model

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Figure 14

Comparison between experimental measurements and numerical predictions for a stress-free thermal cycle between the temperatures T0<Mf and T1>Af

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Figure 15

Comparison between experimental measurements and numerical predictions for a thermal cycle between the temperatures T0<Mf and T1>Af under a fixed tensile stress: (a) 50MPa; (b) 100MPa

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Figure 16

Comparison between experimental measurements and numerical predictions for two different temperature-time paths: (a) incomplete A→M transformations; (b) incomplete M→A transformations.

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Figure 17

Numerical predictions for a temperature-time path that involves both incomplete A→M and M→A phase transformations: (a) stress-free condition; (b) under a fixed tensile stress of 100MPa

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Figure 18

Numerical predictions for subsequent complete transformations under different fixed values of applied stress

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Figure 1

Specimen for thermomechanical cycle

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