On deformation and structural twins in the shape memory alloys

Abstract

Using the Ni${}_2$MnGa shape memory alloy as an example, the article substantiates an approach to describing at the microstructural level the processes of twinning and detwinning of the martensitic phase. The coordinated twinned martensitic structure is described by the Hadamard compatibility equation for deformations, the solution of which made it possible to determine the surfaces along which the shift occurs, the directions and the magnitude of sliding in a tetragonal crystal cell corresponding to the material under consideration in the martensitic state, leading to the appearance and disappearance of the twinned structure. It is shown that two types of twins simultaneously and inseparably exist in an alloy with shape memory: deformation and structural. The first is related to the deformation of a simple shear, that occurs in accordance with the Hadamard compatibility condition in a martensitic plate, which leads to the kink of this straight plate and the appearance of two elements rotated at a certain angle relative to each other, which form this twin. The structural twin is formed from two parts, in each of which the tetragonal crystal cells of martensite are identically oriented, but the short axes of all these tetragonal cells make up an angle of $90^0$ when these cells are located in different parts of the twin. The positions of the structural twin elements relative to the shear plane, determined as a result of solving the twinning equation, are in good agreement with the experimental data. The formation of a deformation twin as a result of a shift in the material leads to the occurrence of a corresponding strain. The formation of a structural twin initiates a structural strain. It is shown that a certain position of the structural twin in the deformation one leads to the equality of these strains.