Structural Thermomechanical Models for Shape Memory Alloy Components
Abstract
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.
Subject
shape memory alloyshysteresis
Preisach
thermomechanical
tension
torsion
bending
wire
springs
fatigue
functional degradation
thermomechanical fatigue
design
structural
Citation
Rao, Ashwin (2014). Structural Thermomechanical Models for Shape Memory Alloy Components. Doctoral dissertation, Texas A & M University. Available electronically from https : / /hdl .handle .net /1969 .1 /152721.