Analysis of the stress-strain state of the torsion actuator made of shape memory alloy at the operating conditions in the course of the constrained deformation

Metallurgy and Material Science

Material science


Saganov E. B.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia



The work is devoted to the theoretical modeling of the behavior of the torsional actuator with a working body made of shape memory alloy (SMA). Devices of this type are very promising for the use in the elements of mechanization of the wing, empennage, aircraft or missile control systems.

In the frame of this work the problem of reverse martensitic transformation in the working body of the actuator with elastic counter-body, and fix condition for rods with solid circular cross-section made from SMA was solved. In both formulations of the problem with the heating rod made from SMA feels constrained deformation, the consequence of which is emergence of reactive stresses, which lead to an increase in torque.

The analysis is performed in the framework of the non-linear model of straining of SMA in phase and structure transition in coupled formulation with the possibility of occurrence of the structural transition. It is believed that stresses in this process are small enough, so that plastic deformation not occurs. The influence of the stiffness of the counter-body on the thermomechanical response of the actuator is studied.The dependences of the dimensionless twist and torque from the dimensionless parameter of temperature, as well as diagrams of dimensionless stress for different stages of the heating rod are obtained.

In this work it is established that in the process of heating the SMA actuator the bigger part of the cross-section rod is experiencing an increase in stresses. This requires to take into account the structural transition in solving problems of Reverse Phase Transformation (RPT) in the case of constrained deformation. The increase in the torque is a function of the stiffness of the counter-body and the torque, which active in case of Direct Phase transformation, and then the higher the torque then the greater the torsional stiffness has a counter-body. In the case of the RPT with fixed total deformations the phase deformations have transformed into an elastic deformation. This causes an increase in stress and torque. The maximum level of stress and torque at the end of the RPT is higher than the similar values for RPT with counter-body.


actuator, shape memory alloys, rods, reverse martensitic transformation, structure transition, counter-body


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