Analytical Modeling for Stress-Strain Curve of a Porous NiTi

[+] Author and Article Information
Ying Zhao

Department of Mechanical Engineering, University of Washington, Box 352600, Seattle, WA 98195-2600

Minoru Taya

Department of Mechanical Engineering, University of Washington, Box 352600, Seattle, WA 98195-2600tayam@u.washington.edu

J. Appl. Mech 74(2), 291-297 (Jan 17, 2006) (7 pages) doi:10.1115/1.2198250 History: Received April 07, 2005; Revised January 17, 2006

Two models for predicting the stress-strain curve of porous NiTi under compressive loading are presented in this paper. Porous NiTi shape memory alloy is considered as a composite composed of solid NiTi as matrix and pores as inclusions. Eshelby’s equivalent inclusion method and Mori-Tanaka’s mean-field theory are employed in both models. Two types of pore connectivity are investigated. One is closed cells (model 1); the other is where the pores are interconnected to each other forming an open-cell microstructure (model 2). We also consider two different shapes of pores, spherical and ellipsoidal. The stress-strain curves of porous shape memory alloy with spherical pores and ellipsoidal pores are compared. It is found that the ellipsoidal shape assumption is more reasonable than the assumption of spherical pores. Comparison of the stress-strain curves of the two models shows that use of open-cell microstructure (model-2) makes the predictions more agreeable to the experimental results of porous NiTi whose microstructure exhibits open-cell microstructure.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Linearized four-stage stress-strain curve of porous NiTi

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Figure 2

The Eshelby’s model for a porous SMA: (a) the problem of pores embedded in the NiTi matrix with stiffness Cijklm and transformation strain εijT, which can be converted to equivalent inclusion problem (b), where εij* is the fictitious eigenstrain, which is unknown.

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Figure 3

(a) Stress-strain curve of porous or solid sample (i=P or S), (b) stress-strain curve of solid NiTi

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Figure 4

(a) Eshelby’s model for interconnected pores in NiTi matrix, which is converted to equivalent inclusion problem (b)

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Figure 5

Comparison of the experimental data to predictions by the present two models

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Figure 6

Microstructure of 13% porosity specimen

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Figure 7

Stress-strain curves predicted by ellipsoidal and spherical open-cell model




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