Bain’s deformation matrix for martensitic transition β1↔β1′ in CuAlNi alloy and the crystallographic resource of transformation

Keywords: shape memory effect, CuAlNi, single crystal, deformation matrix, crystallographic resource


Recently, the interest in copper-based alloys (in particular, CuAlNi alloys containing 10–14 % Al and 4–5 % Ni) having the narrow temperature hysteresis and showing a full return of deformation increased. However, at the moment, there are practically no works dealing with the modeling of the behavior of Cu-based alloys with shape memory, which determines the relevance of this study. The paper considers a microstructural model of the mechanical behavior of the CuAlNi-type alloy, taking into account the reversible martensitic transformation β1(D03)↔β1'(18R) occurring in this material. An important parameter – deformation matrix – is the basis of this model. The authors carried out necessary calculations in the deformation smallness assumption. The strain tensor matrix for this transformation is calculated based on the available crystallographic data in the literature. The authors used the obtained matrix for further modeling of functional properties of the CuAlNi-based alloys and performed calculations to determine the crystallographic transformation resource, i.e. the maximum deformation of the crystal lattice for given transformation. The simulation of the quasi-elastic behavior of a single CuAlNi crystal was carried out, which identified a certain orientation of a single crystal causing deformation approximately equal to the calculated value of the crystallographic resource. Thereby, the deformation matrix makes it possible to adequately simulate the behavior of the shape memory alloy under the study. The results obtained are in good agreement with the experimental data available in the literature, which suggests that the constructed deformation matrix can be used for further calculations.

Author Biographies

Tatiana Yu. Chernysheva, Saint-Petersburg State University

graduate student

Margarita E. Evard, Saint-Petersburg State University

PhD (Physics and Mathematics), Associate Professor


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Technical Sciences