We study the equilibrium stress field in an annulus composed of a material that admits stress-induced displacive phase transformation that preserves volume. A standard example is the austenite to martensite transformation in shape memory alloys. Attention is restricted to isothermal and axisymmetric load increase. The constitutive model follows a standard formulation appropriate for small strains and incorporates a single internal variable (the martensite phase fraction). A plane-stress boundary value problem is analyzed so as to determine the partitioning of the annulus into regions of (pure) austenite, (pure) martensite, and austenite/martensite mixture. Structure maps are presented, giving concise descriptions of the phase partitioning as the loads increase.
Issue Section:
Technical Papers
1.
Birman
, V.
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.2.
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.3.
Bernardini, D., and Pence, T. J., 2002, “Shape-Memory Materials, Modeling,” Encyclopedia of Smart Materials, M. Schwartz, ed., J. Wiley & Sons, New York, pp. 964–979.
4.
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Lim
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,” ASME J. Eng. Mater. Technol.
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.7.
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10.
Chi
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, “Plane Stress Analysis of a Shape Memory Annular Plate Subject to Edge Pressure
,” J. Phys. IV
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), pp. 9
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, “On Thermomechanics and Transformation Surfaces of Polycrystalline NiTi Shape Memory Alloy Material
,” Int. J. Plast.
, 16
, pp. 1309
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Briggs
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, and Ponte Castaneda
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, “Variational Estimates for the Effective Response of Shape Memory Alloy Actuated Fiber Composites
,” ASME J. Appl. Mech.
, 69
(4
), pp. 470
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.14.
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, Krishnan
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, and Warlimont
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, “Review: Thermoelasticity, Pseudoelasticity and the Memory Effects Associated With Martensitic Transformations. Part 1: Structural and Microstructural Changes Associated With the Transformations
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, “One-Dimensional Thermomechanical Constitutive Relations for Shape Memory Materials
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, “A Constitutive Model for Hysteretic Phase Transition Behavior
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