Stress-strain behavior shape-memory alloys

This class of smart materials is the mechanical equivalent of electrostrictive and magnetostrictive materials. Elastorestrictive materials exhibit high hysteresis between strain and stress (14,15). This hysteresis can be caused by motion of ferroelastic domain walls. This behavior is more compHcated and complex near a martensitic phase transformation. At this transformation, both crystal stmctural changes iaduced by mechanical stress and by domain wall motion occur. Martensitic shape memory alloys have broad, diffuse phase transformations and coexisting high and low temperature phases. The domain wall movements disappear with fully transformation to the high temperature austentic (paraelastic) phase. 

Figure 9 is a stress-strain curve for a single-crystal specimen of a Cu-39.1Zn shape-memory alloy deformed in tension at about 50 °C above its temperature (Schroeder and Wayman, 1979). Yielding at an essentially constant stress (upper plateau) corresponds to the formation of 9R stress-induced martensite (SIM) from the B2 parent. At about 9 7o strain the specimen becomes fully martensitic. When the stress is released, the strain follows the lower plateau and fully recovers as the SIM reverts to the parent. This behavior corresponds to a mechanical (as opposed to a thermal) shape memory. A stress-strain relationship such as that shown in Figure 9 is frequently referred to as a superelastic stress-strain loop. The stress necessary to... 

Figure 10 is a stress-strain-temperature diagram for a Ni-Ti shape-memory alloy that summarizes its mechanical behavior. At the extreme rear the stress-strain curve shown in the a-t plane corresponds to the deformation of martensite below Mf. The induced strain, about 4%, recovers between A and Af after the applied stress has been removed and the specimen heated, as seen in the e-T plane. At a temperature above Mj (and Af) SIM is formed, leading to a superelastic loop with an upper and lower plateau, the middle o-e plane. At a still higher temperature and above M, the front a-e plane, no SIM is formed. Instead, the parent phase undergoes ordinary plastic deformation. 

Figure 10. Stress-strain-temperature diagram for a Ni-Ti (Nitinol) shape-memory alloy showing shape-memory and superelastic characteristics and the deformation behavior of the parent phase above the temperature (above which no martensite can form regardless of the magnitude of the stress). Temperature increases from upper right to lower left...

Figure 10.38 Typical stress-strain-temperature behavior of a shape-memory alloy, demonstrating its thermoelastic behavior. Specimen deformation, corresponding to the curve from A to B, is carried out at a temperature below that at which the martensitic transformation is complete (i.e., Mf of Figure 10.37). Release of the applied stress (also at Mf) is represented by the curve BC. Subsequent heating to above the completed austenite-transformation temperature Af, Figure 10.37) causes the deformed piece to resume its original shape (along the curve from point C to point D).

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