Calculation of the transformation plasticity strain in the shape memory cylinder

^{1, 2} Emperor Alexander I St.Petersburg State Transport University, Moskovsky ave., 9, Saint Petersburg, 190031, Russia
³ Saint-Petersburg State University, Universitetskiy ave., 28, Saint-Petersburg, 198504, Russia

^* Corresponding author: kukhareva@pgups.ru

Abstract

A connected thermomechanical boundary problem for an infinite shape memory alloy cylinder loaded by an axial force and subjected to heating or cooling from the surface is solved. The evolution of stress-strain state is calculated for a process of the transformation plasticity. The mechanical properties of a material point are given by a micromechanical model accounting for the deformations due to elasticity, thermal expansion and phase transformation. The obtained problem was solved numerically using the iterative procedure with a variable iterative parameter. The influence of the surface temperature rate and radius of cylinder on the transformation plasticity is investigated. It is shown, that the elongation due to the transformation plasticity effect decreases with the increasing temperature rate. The elongation also decreases with the increasing cylinder diameter. This phenomenon can be explained by an inhomogeneity of the temperature and stress fields causing different conditions for the phase transformation in different points of the body. Stress in the local region can overtop more than twice the mean value.