METHOD FOR CALCULATION OF DISPLACEMENT FIELDS AND STRESSES IN SYSTEM OF PARALLEL LENTICULAR MECHANICAL TWINS OCCURRING IN MARTENSITIC PHASE OF Ni2MnGa-MAGNETIC ALLOY HAVING PROPERTY OF SHAPE MEMORY

Nowadays mathematical modeling of peculiar features of a stress-strain state is considered as a perspective direction of research. In this regard the aim of this paper has been to make calculations of the stress-strain state initiated by a system of parallel lenticular residual mechanical twins that occur due to local surface deformation of  Ni₂MnGa single crystal martensitic phase.

The method is applied while using a superposition principle of fields and approximation of a continuous distribution of twinning dislocations on twin boundaries in a continuous elastic medium.

The calculations have made it possible to obtain distribution graphs of displacement fields and stresses and point out the fact that a configuration of displacement component distribution u_y is significantly different from the displacement of components u_x and u_z having a displacement distribution similar to each other. The highest value of displacement occurs in the component u_y in twins peaks.

The paper also presents results of calculations for six components of a stress field the tensor. The obtained results have revealed similarity in stress distribution character of the components  s_xz and s_zz, but they differ numerically from each other about in two times. The largest value of the stresses occurring in the lenticular twins has been observed in components s_xx, s_xz, s_yy, s_yz and it has been focused mainly at the borders and peaks  of twins.

A common feature of the obtained components of displacement and stresses in a lenticular twins system is symmetry with regard to OY. In addition, the stress distribution of all obtained tensor components has been mainly localized at the borders and at the tops of twins where the highest values of stresses capable of exerting a significant impact on dislocation and diffusion processes are generally concentrated.

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