Modelling, characterisation and uncertainties of stabilised pseudoelastic shape memory alloy helical springs

Abstract

The thermo-mechanical behaviour of pseudoelastic shape memory alloy helical springs is of concern discussing stabilised and cyclic responses. Constitutive description of the shape memory alloy is based on the framework developed by Lagoudas and co-workers incorporating two modifications related to hardening and sub-loop functions designated by Bézier curves. The spring model takes into account both bending and torsion of the spring wire, thus representing geometrical non-linearities. Simplified models are explored showing that a single point in the wire cross section is enough to represent the global spring behaviour in spite of complex stress–strain distributions. The experiments are carried out considering different deflection amplitudes, frequencies and ambient temperatures, which influence the spring behaviour to different extents. The model is fitted against a calibration data set resulting in 1.3% residual standard deviation relative to the full range force. Compared to the validation data set, the errors are below 10% relative to the full range of the complex modulus. Uncertainty analysis of the model parameters using a Markov chain Monte Carlo technique shows low to high parameter correlation, and the relative uncertainties are less than ±12%. Both the heat capacity and the convection coefficient are clearly identifiable from the performed experiments.

Rotor–bearing system integrated with shape memory alloy springs for ensuring adaptable dynamics and damping enhancement—Theory and experiment

“…The first type is made from an SMA, namely a pseudoelastic Nickel-Titanium alloy (Ni-Ti ratio of 56:44). In the following two sections the SMA parameters can be found in [23].…”

“…al [26] is used to describe the thermo-mechanical behaviour of the SMA. The modified version is presented in [23]. The spring behaviour is primarily governed by a plane stress field having one normal component and a shear component, and therefore a model reduction to two dimensions is used.…”

“…The sub-loop functions have a curvature controlling parameter that controls the size of the hysteresis and the tangential stiffness during 135 sub-looping. The hardening and sub-loop functions are modifications to the original model, and they are described in detail in [23]. The constitutive equations are coupled to the energy equation to take into account the latent heat of the phase transformations so that the SMA temperature may be different from the environmental conditions.…”

“…The model has a number of parameters related to the specific material. The values of the parameters are provided in [23] and they are based on model calibration to experimental force-deflection tests. The convection coefficientĥ may have changed from the calibration value, because the environmental conditions related to the forced convection are slightly different in this work.…”

“…The stress distribution is used for calculating the contributing bending and shear moments. However, the martensitic volume fraction can be considered constant throughout the wire cross section from a modelling point of view [23]. The result is a simple relation between a representative stress measure and the bending and shear moments:…”