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Stability cramped rods from a shape memory alloy in the reverse martensitic phase transformation

Savchenko L.G.

#### Abstract:

This article is a continuation of [1], which was considered cramped buckling rod of shape memory alloy (SMA) is the reverse thermoelastic martensitic phase transformation in a simplified statement. [1] was used assumption of the immutability (the length of the rod) additional areas of the phase transformation, emerging from the SPF in the rod under buckling, which allowed us to obtain a simple relation permitting. However, such a solution to be possible, when the buckling of the rod must be present small variations in the external load, including kinematic nature. As a result, in accordance with the concept of “ongoing loading” due to select the desired variation of the “external load” can be found the most dangerous critical characteristics of sustainability, within the concept of ‘fixed-phase composition “- the least dangerous. Due to the special choice of variations of “external load” can be found as critical characteristics, which occupy an intermediate position. It is understood that a certain interest is the decision based on the concept of “elastic unloading”, when buckling rod variations in external loads are not allowed at all. [1] it pointed out that under the simplifying provisions regarding additional areas of the phase transformation to achieve such a solution is not possible. To obtain a solution in the absence of any variations in load during buckling, it is necessary to abandon the above simplifying assumptions and to consider additional phase transition zone of variable length of the rod. In this paper, a solution is obtained. It is shown that the problem is reduced to solving a system of ordinary differential equations with unknown parameters, for which may, for example, is the value of the phase component of the strain accumulated during the previous direct martensitic transformation. In the numerical solution of this system can be found critical phase component of strain created in the preceding process of the martensitic transformation in dependence upon a parameter volume fraction of martensitic phase. It is interesting to note that, for any value of the parameter found critical phase of deformation is very close to the critical phase of deformation, resulting in [1] in a simplified formulation for the particular case when the step of buckling is not allowed variation of axial displacement of the poles, but there is variation sweatshop axial load.

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