Analytical solution for the pseudoelastic response of a shape memory alloy thick-walled cylinder under internal pressure
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Analytical solutions are derived for the isothermal pseudoelastic response of a shape memory alloy (SMA) thick-walled cylinder subjected to internal pressure. The Tresca transformation criterion and linear hardening are used. Equations are given for the radial and circumferential stresses, transformation strains and radial displacement at various steps of loading and unloading. A structural pressure-temperature phase diagram is provided for the cylinder, analogous to the stress-temperature phase diagram of SMA materials. Pressurization of an initially 100% austenitic cylinder causes the martensite to initially form at the inner radius. For a relatively thin-walled cylinder the transformation front reaches the outer radius before the transformation has completed at the inner radius, whereas for a thick-walled cylinder the transformation completes at the inner radius while there is still an outer ring of 100% austenite. For a given OD/ID ratio, a critical temperature is derived that stipulates which of these two cases occurs. An analytical result is provided for the pressure that will cause the transformation to complete at the inner radius. During unloading, the reverse transformation can start at either the inner or the outer surface of the cylinder and can propagate outward and then reverse its direction and propagate back to the inner surface. The effect of martensitic transformation on the structural yield strength due to plasticity is also investigated and it is shown that the pressure required to initiate yielding can be substantially decreased or increased depending on the temperature and the state of transformation achieved, even though the yield stress of the material is independent of temperature. Finally, the effectiveness of the Tresca transformation criterion to derive closed-form solutions for this problem is demonstrated by comparing with finite element solutions using the von Mises theory. 2013 IOP Publishing Ltd.
