Thermomechanical boundary problems for a cylinder and sphere made of shape memory alloy

The paper presents the solutions of the coupled boundary value problems for a thick-walled cylinder and a sphere made of shape memory alloy (SMA). Their material undergoes a direct thermoelastic martensitic phase transformation upon cooling under a constant internal pressure. We have considered slow cooling processes in which the temperature distribution over the material at each instant of time can be considered as uniform. The results are compared with the analytical solutions of the same problems previously obtained within the assumption of a uniform distribution over the material of the martensitic volume part parameter. A quasistatic motion is simulated in the material of the fronts of the onset and completion of the phase transition, as well as the redistribution of stresses and strains along the cross section associated with these motions. It is established that a direct phase transformation begins on the inner surface of the shells. The phase transition zone is quite fast (compared to the growth of the phase composition parameter at the points of the inner surface) propagating along the radial coordinate to the outer surface. After this, the phase transition develops over the entire thickness, the magnitude of the martensitic volume part parameter q being a weakly decreasing function of the radial coordinate (the difference in the values q on the inner and outer surfaces is a small fraction of the maximum q value equal to 1). The completion of the phase transition is observed for the first time on the inner surface, after which the boundary of the phase transition end rapidly moves through the thickness from the inner surface to the outer surface. The intensity of stresses and the annular stress in the process of the phase transition vary non-monotonically and in different ways for the inner and outer surfaces. On the inner surface, these stresses have the maximum values at the points of the beginning and the end of the phase transition; and the minimum values take place at an intermediate point. On the contrary, in case of the external surface, the minimum values of stresses are observed at the beginning and the end of the phase transition, while the maximum value take place at the intermediate point of the process.