Gradient-based constitutive model to predict size effect in the response of SMA thin films

For sufficiently small dimensions, the response of shape memory alloy (SMA) actuators is not independent of the sample size. The response of SMA single crystal micro/nanopillars is shown to depend on the size of the specimen. An increase in the critical stresses for the start and finish of austenite to martensite transformation is seen when reducing the diameter into the submicron region. In addition, the damping observed in a pseudoelastic cycle of a nanopillar is much higher than that of a counterpart SMA bulk specimen. This phenomenon is furthermore observed in SMA wires where the critical stresses for the start of martensite and austenite transformations are -reported to increase for diameters \u3c100 µm. Finally, the hardness of SMA thin films obtained from micro- or -nanoindentation experiments was shown to depend on the indentation depth demonstrating an increased hardness for smaller indentation depths. SMAs have recently been used as a promising and high performance -material for application in micro–electro–mechanical systems in the form of thin films/beams. Nano/microindentation experiments, on the other hand, are one the major experimental routines to establish properties of SMA thin film actuators. Assessing the functionality of such microactuators requires numerical modeling tools that can take into account the observed size effect. Size effect in the SMA response cannot be simulated using conventional constitutive theories, which lack an intrinsic length scale in their constitutive modeling. To enable such a property, a new nonlocal thermodynamically consistent constitutive model is developed, which in addition to conventional internal variables of martensitic volume fraction and transformation strain, contains the spatial gradient of martensitic volume fraction as an internal variable. This allows the introduction of energetic and dissipative length scales in the model. The transformation surface in such a theory will be obtained from the solution of a partial differential equation. In conventional formulations, transformation surface is an algebraic equation. A boundary value problem, in this case, contains the equilibrium equation with its standard boundary conditions as well as the PDE for the transformation and associated martensitic volume fraction. The developed gradient theory is used to analytically simulate the uniaxial stretching of SMA wires, pure bending of SMA beams, and compression response of SMA micro/nanopillars. SMA beams with larger thickness show a response closer to the classical (local) model prediction, which in the nondimentional sense, is independent of the thickness of the beam. In addition, the nano/microindentation process was studied using the developed constitutive model. The response of the SMA structures using the developed gradient theory depends on the size, being stiffer for smaller dimensions and harder for smaller indentation depths

Finite element analysis of stable crack growth in shape memory alloy actuators

Shape memory alloys (SMAs) are a special class of intermetallic alloys that, because of their capability to recover large strains when subjected to thermal or mechanical loads, have been extensively used for actuation purposes. Because of their high work output per unit volume, SMA-based actuators are a better alternative compared to conventional electromagnetic actuators when a large force is required and thermodynamic efficiency is not important. As such, for better design and functioning of SMA-based actuators, it is imperative to understand the phenomenon of crack-initiation and growth during thermal actuation in SMAs. In this study, finite element analysis is carried out to study stationary and advancing cracks in an infinite, center-cracked shape memory alloy specimen subjected to thermal variations under constant plane strain mode-I tensile loading. Abaqus finite element suite is employed to compute mechanical fields close to the static crack and assuming linear elastic fracture mechanics and virtual crack closure technique is used to calculate the crack-tip energy release rate. An increase in the energy release rate during cooling by approximately an order of magnitude when compared with that due to constant mechanical loading is observed, which is attributed to the stress redistribution at the crack-tip induced by global phase transformation during cooling. Crack growth during actuation may thus occur when the crack-tip energy release rate reaches a material specific critical value. Fracture toughening behavior is observed during crack growth and is mainly associated with the energy dissipated by the progressively occurring phase transformation close to the moving crack tip. A sensitivity analysis of this toughening behavior with respect to key thermomechanical parameters is presented. Lastly, the effect of crack configuration on fracture toughness enhancement is studied by investigating static and advancing cracks in compact tensile and three-point bending SMA geometries as well

Thermo-mechanically coupled phase field model for simulating shape memory alloys response

Polycrystalline NiTi Shape Memory Alloys (SMAs) have been experimentally shown to exhibit some important features and effects under pure tension and more complex loading. These features are either rate dependent or connected to moving interface between austenite and marten site phases. They include observed peak and valley in stress during loading and unloading respectively, propagation stress plateaus, inhomogeneous deformation (transformation localization and front propagation) during transformation, stress relaxation, etc. It has also been experimentally observed that polycrystalline NiTi wires, strips, and tubes develop transformation strain via nucleation and growth of macroscopic martensitic domains under mechanical loading. Associated with these responses during transformation evolution are complex interactions between mechanical work, heat production, and loading rates. These interactions will affect the performance of SMAs when deployed as active components. Modeling effort is, therefore, needed to better understand this behavior. This study is a worthwhile contribution towards modeling these experimentally observed features and their effect so as to aid SMA design and applications. A 3D thermodynamically consistent, thermomechanical, macroscopic phase field model capable of modeling kinetics of phase transition and hysteretic response of SMAs is presented. Based on the notion of configurational (accretive) forces and their balance, a kinetic law similar to that of Ginzburg-Landau is developed. A scalar order parameter (a field variable) is used in this study to describe the local phase of the SMA (austenite or martensite). To demonstrate the capability of this model, SMA response was studied. Presented herein is the effect of latent heat, loading rates as well as that due to constant stress and strain during transformation for the SMA. Remarkable agreement between simulation for the SMA and experimental results reported in literature was observed