Effect of axial preloads on torsional behavior of superelastic shape memory alloy tubes – experimental investigation and simulation/predictions of intricate inner loops

Abstract

Shape memory alloy (SMA) devices (utilizing wires/rods, springs or tubes) engage unique superelastic/pseudoelastic (SE) phenomenon for large stroke recovery, energy dissipation and damping applications. In particular, SMA components in torsion are also generally subjected to some pre-tension loads and hence understanding their combined effects on the torsional response is vital. In this work, some intricate internal loop and outer loop responses (large twists > 1500°) of SMA tubes under different twisting-untwisting scenarios are investigated to understand the effects of static pre-load on torsional responses. Key SMA hysteretic features like sink point memory (SPM) and return point memory (RPM) have not been well understood under torsion (with and without axial loads) have been investigated here. Further, a modified two variant thermodynamic Preisach modeling approach is proposed to simulate responses of twisted tubes with varying extents of twist and different axial loads. The central principle here is the use of a Gibbs Potential framework to separate the dissipative and thermoelastic parts of the SE responses using well established thermodynamic principles and then utilizing a non-ideal switching type disjunctive Preisach model to fit the nonlinear hysteretic dissipative section of the SE response. By using the outer loop response for model calibration, other complex loading unloading scenarios leading to intricate internal loops and effects of axial loads on these can be predicted. It is also shown that addition of a single interior loop detail for model calibration significantly enhances prediction of other more intricate internal loops. This approach dramatically simplifies the experimental data needed for the simulation of SMA components even under complex loading.

Keywords:

• Shape memory alloy (SMA)
• torsion
• combined loading
• intricate internal loops
• superelastic/pseudoelastic effect
• tube
• return point memory(RPM)
• sink point memory (SPM)

Acknowledgments

We wish to highlight the support of CMMI grant 1000790 from the National Science Foundation in carrying out this work. We thank Texas A&M University at Qatar staff for their co-ordination and support during visits of Arun R. Srinivasa and Ashwin Rao to Doha, Qatar campus.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Shape memory effect (SME) is the capacity of SMA to return to a pre-determined shape by recognizing a non-mechancial external impetus like magnetic/temperature change [1, 2]. On the other hand, superelastic or pseudoelastic effect (SE) is the capability of SMA to reclaim large strain ∼6/8% accompanied along with highly non-linear hyseterisis due to mechanical loading and unloading at temperature greater than Austentic finish (A_f) [3].

2 An internal loop is a consequence of intermediate loading and unloading preceding complete transformation that results in smaller hysteretic responses which closely mimics the characteristics of outer loops that is fully transformed. The area of these smaller hysteretic loops depends on the extent of the loading and unloading level which the component is subjected to during service within the transformation regime (plateau region) [3, 27].

3 The force/stress levels depend on the wire diameter, spring index, extent of transformation and other factors but most of the practical applications of SMA springs are used for low force, high stroke applications.

4 For example, in many real-world applications, torque tubes/torsional actuators have some form of bearing support to prevent axial motion and hence this would produce some axial loads/stresses typically not large enough to induce phase transformation on their own but might change the overall torsional response [65, 72, 73]. In light of this, understanding the effect of these axial pre-loads on the overall outer loop torsional response and internal loops is important from an application point of view.

5 The generic approach is by dividing them into three annular regions of untransformed Austenite core followed by transition Austenite-Martensite region and an outer transformed SIM layer.

6 ASTM F2516 [99] test standard for tension testing of superelastic NiTi defines “Upper Plateau strength (UPS) and lower plateau strength (LPS) as the stress level at 3% strain during loading and the stress at 2.5% strain during unloading respectively”. Though not directly applicable for torsional loading this could be used as a good yardstick for comparison purposes.

7 The proposed model can also be used to evaluate many other practical situations like predicting responses at different working temperatures under superelastic conditions (see Figures 10 and 11 in [28]; Figures 13 and 14 in [29], Figure 10 in [96] for illustrations), predicting torsional responses for different diameter (see Figure 12 in [28] for illustration) etc. The idea here is to calibrate the model with one reference dataset and use to hysterons to recalculate responses either at a different operating temperature (changing θ during reverse calculations) or a different wire diameter (changing Polar Moment of Interia during reverse calculations) with the underlying assumption that the dissipative part of the response is unchanged and they just linear scale with the change in operating temperature or Polar Moment of Interia values.