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Estimation of the limit strain tensor of a polycrystalline shape memory alloy

Mishustin Ilya V.

#### Abstract:

For a more complete study of the resistance asymmetry of polycrystalline shape memory alloys (SMAs) without texture, an algorithm for calculating the tensor of limit inelastic strain accumulated in the process of a complete direct phase transition under the action of a constant stress, was used. Known data on the geometry of the crystal cells of the phases and the ways of their transformation are used in the calculation. The algorithm is based on the assumption of a uniform distribution of orientations of the austenite phase cells in a representative volume of the material and consists in choosing for each of these orientations the most energy efficient variant of martensite orientation with subsequent averaging of the corresponding shape changes. Using equiatomic titanium nickelide as an example, the dependence of the limit inelastic strain deviator on the directing deviator of external stress and the relationship between strain and stress states were studied. It is shown that the crystallographic features of the SMA lead to its resistance asymmetry. When describing the phase transition, small strain tensor, Cauchy-Green finite strain tensor, and Hencky logarithmic strain tensor were used. In addition to averaging the specified strain tensors of the selected variants of martensite orientation, the deformation gradient tensors were averaged, followed by the calculation of the limit strain tensors of the specified types. Alternative methods of averaging led to close results. The deviator of the limit strain of the phase transition calculated by the described method is uniquely associated with the directing deviator of the external stress, regardless of its orientation. Their principal axes coincide, but the principal values are proportional only in uniaxial tension or compression. The limit phase transition strain deviator is represented as the sum of two terms, one of which is proportional to the directing deviator of the external stress, and the other term is proportional to the directing deviator, orthogonal to the first one. The dependence curves of the intensities of the limit strain deviator terms on the loading type parameter are plotted.

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