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Instabilities induced by phase transformation fronts coalescence during the phase transitions in a thin SMA layer: mechanism and analytical descriptions. (English) Zbl 1231.74344

Summary: Systematic experiments on stress-induced phase transitions in slender polycrystalline SMA specimens have revealed two interesting instability phenomena: the coalescence of two phase transformation fronts (a narrow zone between the pure austenite and pure martensite regions, which is also called the domain wall or macroscopic interface) during the loading process leads to a sudden stress drop and that during the unloading process leads to a sudden stress jump. In order to get an insight into these two phenomena, we carry out an analytical study on stress-induced phase transitions in a thin SMA layer. We derive a quasi-2D model with a non-convex effective strain energy function while taking into account the rate-independent dissipation effect. By using a coupled series-asymptotic expansion method, we derive a one-dimensional effective expression for the total energy dissipation, which only involves the leading order term of the axial strain. The equilibrium equations are obtained by maximizing the total energy dissipation, which can be solved analytically under suitable boundary conditions. The instability is then modeled as the switch of the layer’s configuration from a nontrivial solution mode to the trivial solution mode. The limit-point instability criterion is adopted to determine the bifurcation point. Descriptions for the whole coalescence processes are provided, which capture the morphology varies of the specimen and the accompanying stress drop or jump. It is revealed that the zero limit of the thickness-length ratio can lead to the smooth switch of nontrivial modes to trivial modes with no stress drop or jump.

MSC:

74N20 Dynamics of phase boundaries in solids
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
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