Three-dimensional deformation response of a NiTi shape memory helical-coil actuator during thermomechanical cycling: experimentally validated numerical model

Shape memory alloy (SMA) actuators often operate under a complex state of stress for an extended number of thermomechanical cycles in many aerospace and engineering applications. Hence, it becomes important to account for multi-axial stress states and deformation characteristics (which evolve with thermomechanical cycling) when calibrating any SMA model for implementation in large-scale simulation of actuators. To this end, the present work is focused on the experimental validation of an SMA model calibrated for the transient and cyclic evolutionary behavior of shape memory Ni49.9Ti50.1, for the actuation of axially loaded helical-coil springs. The approach requires both experimental and computational aspects to appropriately assess the thermomechanical response of these multi-dimensional structures. As such, an instrumented and controlled experimental setup was assembled to obtain temperature, torque, degree of twist and extension, while controlling end constraints during heating and cooling of an SMA spring under a constant externally applied axial load. The computational component assesses the capabilities of a general, multi-axial, SMA material-modeling framework, calibrated for Ni49.9Ti50.1 with regard to its usefulness in the simulation of SMA helical-coil spring actuators. Axial extension, being the primary response, was examined on an axially-loaded spring with multiple active coils. Two different conditions of end boundary constraint were investigated in both the numerical simulations as well as the validation experiments: Case (1) where the loading end is restrained against twist (and the resulting torque measured as the secondary response) and Case (2) where the loading end is free to twist (and the degree of twist measured as the secondary response). The present study focuses on the transient and evolutionary response associated with the initial isothermal loading and the subsequent thermal cycles under applied constant axial load. The experimental results for the helical-coil actuator under two different boundary conditions are found to be within error to their counterparts in the numerical simulations. The numerical simulation and the experimental validation demonstrate similar transient and evolutionary behavior in the deformation response under the complex, inhomogeneous, multi-axial stress-state and large deformations of the helical-coil actuator. This response, although substantially different in magnitude, exhibited similar evolutionary characteristics to the simple, uniaxial, homogeneous, stress-state of the isobaric tensile tests results used for the model calibration. There was no significant difference in the axial displacement (primary response) magnitudes observed between Cases (1) and (2) for the number of cycles investigated here. The simulated secondary responses of the two cases evolved in a similar manner when compared to the experimental validation of the respective cases.