Load–Displacement Behavior of Helical Shape Memory Alloy Spring Actuators with Small Spring Diameter to Wire Diameter Ratios

A design methodology for fabricating and predicting the load–displacement behavior of shape memory alloy (SMA) spring actuators has been previously created and validated (Nicholson et al., Smart Mater Struct 23(12):13–23, 2014). However, it was found in this work that for springs with a spring index (ratio of spring diameter to wire diameter) below five, the load–displacement response of shape memory spring actuators no longer fits the previously established model. This paper explores the use of a correction factor in the governing equations to account for the plastic deformation that occurs when fabricating springs with very small spring indices. The plastic deformation induces an effective reduction in the volume of the transforming material, thus reducing the load-bearing and actuation capabilities of the spring. A semi-analytical solution to this problem is found which can be used to predict the load–displacement behavior. This is accomplished through a reduction in the effective wire diameter based on the approximate shear strain during loading. This approach is consistent with observations during thermomechanical cycling in SMAs, where the phase transformation remained mostly unhindered despite large residual inelastic and/or plastic strains, and has direct application in the design of actuators with small spring indices by quantifying the drop in actuation force and stroke.