1 May 1994 Micromechanical model for shape memory alloys and their hysteresis behavior during phase changes
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Recently the authors published a new micromechanical model to describe the kinetic behavior of shape memory alloys. Here the stress-strain-temperature-transformation behavior is investigated. The model describes a differential equation for the volume fraction of the new (martensitic) phase (which grows during a thermomechanical process) in dependence on the temperature and/or stress history of the process. In the newly extended version it contains, as a second basic equation, the differential relationship between strain, volume fraction of the new phase, temperature, and loadstress. The strain is an effective property of the considered system. Integrating the differential stress-strain-temperature-volume fraction relation under consideration of the initial conditions leads to a useful integral relation of the mentioned quantities. Of special interest is the hysteresis behavior during phase transformation. A friction-like term in the model changes sign when the process changes the direction. Thus the model also allows us to explain subloop behavior. Exact bounds for the dissipation energies for loops can be given. The agreement of the results of the model with experimental results is fairly good.
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Eduard Roman Oberaigner, Eduard Roman Oberaigner, Kikuaki Tanaka, Kikuaki Tanaka, Franz Dieter Fischer, Franz Dieter Fischer, } "Micromechanical model for shape memory alloys and their hysteresis behavior during phase changes", Proc. SPIE 2192, Smart Structures and Materials 1994: Mathematics and Control in Smart Structures, (1 May 1994); doi: 10.1117/12.174230; https://doi.org/10.1117/12.174230

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