A thermodynamic driving force approach for analyzing functional degradation of shape memory alloy components

ABSTRACT

With growing use of shape memory alloy (SMA) components in different engineering applications, the issue of material performance over its designed life is of great concern to researchers lately. In order to analyze SMA components performance under coupled thermomechanical effects, theories considering both mechanical and thermal effects in a single framework must be employed rather than modifying classical empirical fatigue theories (like S–N or ϵ–N) developed for capturing pure mechanical loading effects. The core idea is to use driving force versus number of cycles rather than classical S–N or ϵ–N curves to quantify thermomechanically coupled functional degradation and life under cyclic thermomechanical loads. To this end, a two-species Gibbs potential is employed to develop “thermodynamic driving force for the phase transformation” and “extent of phase transformation” relationships by separating the thermoelastic and dissipative part of the SMA component responses under tension and torsion loading cases. Such an approach can be used to analyze shakedown effects for cyclic superelastic responses and capture coupled thermomechanical responses and functional degradation for SMA. To demonstrate the application of this approach, experiments on SMA extension springs are performed using a custom designed thermomechanical test rig capable of simulating shape memory effect during thermal cycling of SMA springs held under constant deformation. For every thermomechanical cycle, load and thermocouple (temperature) are continually recorded as a function of time using LabVIEW^® software. The sensor data over the specimen lifetime is used to construct “driving force amplitude v/s no. of cycles” variation that can be used as a potential substitute to classical fatigue theories for analyzing functional degradation of SMA components. It is shown that different combinations of mechanical and thermal loads with approximately the same calculated driving force lead to approximately similar lives. In addition, cyclic stress–strain results on SMA wire capturing the superelastic responses are used to analyze shakedown effects in SMA components.

KEYWORDS:

• Shape memory alloy (SMA)
• springs
• shape memory effect
• fatigue
• torsion
• thermomechanical
• functional degradation
• design

Acknowledgments

Useful discussions with Dr. Vidyashankar Buravalla from GE Global Research is appreciated. Authors would like to thank Universal furnaces ( Bangalore, India), Sree Lakshmi Spring Industries (Bangalore, India), and Jace Curtis from T&M Instruments for their help during construction of the test rig discussed in this work.

Notes

1 For example: Torque and angle of twist for torsional loading or Bending Moment and Curvature for pure bending response.

2 The two species assumed here are Austenite (A) and a single variant of martensite (M). It must be highlighted that stress-free thermal cycles is between the twinned martensite and austenite as observed with DSC tests. However, in real applications, SMA components are subjected to some load at all times and they do not undergo stress-free thermal cycling in actual applications. In real world applications, SMA components could transform from austenite to a combination of many martensite variants (i.e., variants of detwinned martensite species). For simplicity, it is assumed that all transformation cases are between these two phases A and M for both shape memory and superelastic responses [49], [56].

3 It must be highlighted that in case of tension loading, the phase transformation front moves along the direction of loading and normal stress distribution across the sample cross-section can be assumed to be uniform for analysis. Hence, integrating stress resultants to obtain force–deformation relationship (experimentally measurable) is valid for a tensile loading case. However, this is not true in case of torsion as the stress distribution across the specimen cross section is not uniform. As pointed out by Rao and Srinivasa [51], [55], [56], it hard to comment on the nature of shear stress distribution across the specimen cross section as the phase transformation front moves from the outer surface inwards toward the neutral axis as the wire twists under torsion. With negligible shear strains at the core and no prior knowledge on the deformation history and the location of the phase transformation front, it is hard to justify the averaging or integration of stress resultants to obtain torque–angle of twist relationships for SMA components under torsion. Hence, the torsion model was directly formulated using torque–twist relationship and not shear stress–shear strain relationship.

4 This is due to the fact that the shear strains tends to zero at the core of the specimen cross section as the wire twists under torsion [51], [59]. The possibility of a fully transformed case is possible only the angle of twist asymptomatically reaches infinity at the core prior to the component failure [51], [57]–[59]. Doaré et al. [59] have reported experimental results on SMA wire subjected to different degrees of twist (100, 350, and 450 degrees twist) to illustrate this point of partial transformation (see Figure 4 in [59] for more details).

5 In private communications with Dr. Vidyashankar Buravalla, GE Global Research.

Additional information

Funding

We acknowledge the support of the National Science Foundation CMMI grant 1000790 in carrying out this work.