Structural Thermomechanical Models for Shape Memory Alloy Components
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Thermally responsive shape memory alloys (SMA) demonstrate interesting properties like shape memory effect (SME) and superelasticity (SE). SMA components in the form of wires, springs and beams typically exhibit complex, nonlinear hysteretic responses and are subjected to tension, torsion or bending loading conditions. Traditionally, simple strength of materials based models/tools have driven engineering designs for centuries, even as more sophisticated models existed for design with conventional materials. In light of this, an effort to develop strength of materials type modeling approach that can capture complex hysteretic SMA responses under different loading conditions is undertaken. The key idea here is of separating the thermoelastic and the dissipative part of the hysteretic response by using a Gibbs potential and thermodynamic principles. The dissipative part of the response is later accounted for by a discrete Preisach model. The models are constructed using experimentally measurable quantities (like torque?twist, bending moment?curvature etc.), since the SMA components subjected to torsion and bending experience an in-homogeneous non-linear stress distribution across the specimen cross-section. Such an approach enables simulation of complex temperature dependent superelastic responses including those with multiple internal loops. The second aspect of this work deals with the durability of the material which is of critical importance with increasing use of SMA components in different engineering applications. Conventional S-N curves, Goodman diagrams etc. that capture only the mechanical loading aspects are not adequate to capture complex thermomechanical coupling seen in SMAs. Hence, a novel concept of driving force amplitude v/s number of cycles equivalent to thermodynamical driving force for onset of phase transformations is proposed which simultaneously captures both mechanical and thermal loading in a single framework. Recognizing the paucity of experimental data on functional degradation of SMAs (especially SMA springs), a custom designed thermomechanical fatigue test rig is used to perform user defined repeated thermomechanical tests on SMA springs. The data from these tests serve both to calibrate the model and establish thermodynamic driving force and extent of phase transformation relationships for SMA springs. A drop in driving force amplitude would suggest material losing its ability to undergo phase transformations which directly corresponds to a loss in the functionality/smartness of SMA component. This would allow designers to set appropriate driving force thresholds as a guideline for analyzing functional life of SMA components.