Title: Modeling of phase transformations in shape memory materials Author: Miroslav Frost Department: Mathematical Institute of Charles University Supervisor: Prof. Ing. František Maršík, DrSc., Mathematical Institute of Charles University Abstract: This thesis presents a new thermomechanical three-dimensional con- stitutive model of NiTi-based shape memory alloys. The model was formulated within the framework of generalised standard models and it features a novel form of the dissipation function, which combines contributions stemming from the phase transformation between austenite and martensite and from the reorienta- tion of martensite. The change in the material response associated with the phase transformation between austenite and R-phase as well as material anisotropy and tension-compression asymmetry are also covered. The time-evolutionary problem of a quasistatic mechanical loading of a NiTi body with prescribed temperature evolution was formulated and analyzed within the framework of energetic so- lutions. The corresponding time-incremental minimization problem provided a conceptual algorithm utilized in the numerical treatment. The constitutive mod- el was implemented into the finite element package Abaqus. Several numerical simulations were performed and compared with experiments. Keywords:...

For some alloys martensitic transformation is responsible for the so-called shape memory effect and pseudoelasticity. These properties are used in a wide range of industry applications. Each of these materials is transformed to the shape it was manufactured in when heated to its critical temperature (austenite phase) no matter how seriously it was deformed at lower temperatures (martensite phase). Looking at the microstructure, one can observe significant change of crystalographic lattice depending on temperature and deformation. This the- sis focuses on modelling the evolution of microstructure during deformation for materials in the martensite phase. In this case, the creation of multiple variants of martensite is observed, divided by interfaces where a part of energy is stored. This behaviour can be described by the phase-field model. The numerical im- plementation of this model using the standard finite element method requires large computational costs. The aim of this thesis is to implement this model in MATLAB using a spectral method based on the fast Fourier transform, which is suitable for solving problems on a periodic domain. It is interesting to com- pare the computation using spectral method on a conventional PC with the computation written in FEniCS computed on a cluster. However, the...

Mit Fe-Pd-Legierungen nahe der Zusammensetzung Fe70Pd30 kann man aufgrund des thermischen oder magnetischen Formgedächtniseffekts große Dehnungen erzeugen. Daher sind sie für Mikro- und Nanoaktoren sowie Sensoren von großem wissenschaftlichen und technologischen Interesse. Im Vergleich zu Massivmaterial und dünnen Schichten erwartet man für eindimensionale Geometrien wie Nanodrähte deutlich höhere Arbeitsfrequenzen und Dehnungen. Zur Herstellung von Nanodrähten eignet sich die elektrochemische Abscheidung in selbstordnende nanoporöse Membranen als effizienteste Methode gegenüber lithographischen oder physikalischen Methoden. Um den Formgedächtniseffekt auch in Fe-Pd-Nanodrähten mit ca. 30 at.% Pd zu nutzen, werden in dieser Arbeit entsprechende Herstellungsbedingungen wie Elektrolytsystem, Abscheideparameter und Nachbehandlung herausgearbeitet. Die Zusammenhänge zwischen Abscheidebedingungen und Morphologie, lokaler Mikrostruktur, Struktur sowie magnetischen Eigenschaften werden untersucht und bewertet. Es wird gezeigt, dass Fe-Pd-Nanodrähte trotz der Kombination aus edlem und unedlem Metall elektrochemisch hergestellt werden können. Ein komplexierter Fe-Pd-Elektrolyt in Kombination mit optimierten alternierenden Abscheidepotentialen führt reproduzierbar zu durchgehenden, nahezu defektfreien Nanodrähten nahe der Zusammensetzung Fe70Pd30. Mit einer nachträglichen Wärmebehandlung erreicht man eine vollständige Umwandlung der Fe-Pd-Legierung von der kubisch raumzentrierten zur kubisch flächenzentrierten Struktur. Die erfolgreiche Herstellung dieser Nanodrähte stellt eine Schlüsselposition auf dem Weg zu formgedächtnisbasierten Nanoaktoren dar. In dieser Arbeit konnten wichtige Ansatzpunkte zur Strukturkontrolle während der elektrochemischen Abscheidung und somit zur Aktivierung des Formgedächtniseffekts identifiziert werden. / Fe-Pd alloys at about 30 at.% Pd allow obtaining high length changes or strains in the percent range due to thermal or magnetic shape memory effect. They are especially promising candidates for smart and intelligent materials in micro- and nanoactuators as well as sensors. In comparison to bulk materials and thin films the utilization of nanowires promises higher actuation frequencies and strains, which further heighten the scientific and technological interest. Electrodeposition within self-organized nanoporous templates is a very time efficient method to prepare even large arrays of Fe-Pd nanowires of different length and diameter compared to lithographic or physical methods. The aim of this work is to exhibit the preparation conditions such as electrolyte system, deposition parameter and post treatment for shape memory active Fe-Pd nanowires at about 30 at.% Pd. Correlations between morphology, local microstructure, structure and magnetic properties are investigated and evaluated. Fe-Pd nanowires are successfully prepared by electrodeposition despite the combination of noble Pd and less noble Fe metals. The usage of an electrolyte with complexed Fe and Pd ions and an optimized alternating potential deposition regime leads to continuous and almost defect free nanowires close to the composition Fe70Pd30. The complete transition from the bcc to fcc structure of the Fe-Pd alloy is achieved by an additional heat treatment. However, the successful preparation of these nanowires represents a key element towards nanoactuators based on shape memory alloys. Fundamental knowledge about electrochemical preparation of Fe-Pd nanowires is gained. Important starting points towards structure control during deposition and activation of the shape memory effect are identified.

Magnetische Formgedächtnislegierungen sind Festkörper, die eine Phasenumwandlung erster Ordnung von einer hochsymmetrischen Phase (Austenit) zu einer niedersymmetrischen Phase (Martensit) durchlaufen. Dies kann in der Nähe von Raumtemperatur stattfinden und sowohl durch Temperaturänderung, als auch durch äußere Magnetfelder, mechanische Spannungen oder hydrostatischen Druck induziert werden. Daraus ergeben sich funktionale Eigenschaften, wie der magnetokalorische und der elastokalorische Effekt, eine magnetfeldinduzierte Dehnung und ein großer Magnetowiderstand. Zwillingsgrenzen im Martensit können durch äußere Magnetfelder bewegt werden, was zu großen reversiblen Längenänderungen führt. Der Ablauf der Phasenumwandlung und das Gefüge des Martensits werden dabei durch die elastischen Randbedingungen an der Phasengrenze bestimmt. In dieser Arbeit werden deshalb die Nukleation und das Wachstum des Martensits untersucht. Als Modellsystem werden epitaktische Schichten der Heuslerlegierung Ni-Mn-Ga verwendet. In der martensitischen Phase weist diese Legierung eine modulierte Kristallstruktur auf, die im Konzept des adaptiven Martensits durch eine Verzwillingung auf der atomaren Skala interpretiert werden kann. Im ersten Teil wird mit Röntgenbeugung die modulierte Struktur untersucht. Die Intensität der Überstrukturreflexe wird mit einer kinematischen Beugungssimulation verglichen. Dabei wird nachgewiesen, dass es sich um ein nanoverzwillingtes Gefüge mit einer hohen Dichte an Stapelfehlern handelt. Im zweiten Teil wird das martensitische Gefüge mit Elektronenbeugung im Rasterelektronenmikroskop und Texturmessungen durch Röntgenbeugung untersucht. Das martensitische Gefüge kann im Rahmen der phänomenologischen Martensittheorie quantitativ erklärt werden. Daraus ergibt sich ein geometrisches Modell des martensitischen Nukleus und seiner Wachstumsstadien. Die Phasenumwandlung wird temperaturabhängig im Elektronen- und im Atomkraftmikroskop untersucht und mit dem geometrischen Modell verglichen. Die begrenzte Gültigkeit des geometrischen Modells an makroskopischen Zwillingsgrenzen und an der Grenzfläche zum Schichtsubstrat werden diskutiert. Schließlich kann die Bildung des gesamten hierarchischen Zwillingsgefüges erklärt werden. Im dritten Teil wird die Energiebarriere der Nukleation untersucht. Da die Umwandlung bei konstanter Temperatur abläuft, wird geschlussfolgert, dass Autonukleationsprozesse zu einer starken Verringerung der Nukleationsbarrieren führen. Schließlich wird gezeigt, dass durch Nanoindentation die Nukleation gezielt beeinflusst werden kann. / Magnetic shape memory alloys are solids that undergo a first order phase transition from a high symmetry phase (austenite) into a low symmetry phase (martensite). This can happen close to room temperature and can be induced by changes of temperature, external magnetic fields, mechanical stresses or hydrostatic pressure. This leads to functional properties like the magnetocaloric and elastocaloric effect, a magnetic-field-induced strain and giant magnetoresistance. Twin boundaries in the martensite can be moved by external magnetic fields, which leads to giant reversible length changes. The process of the phase transition and the microstructure of martensite are determined by the elastic boundary conditions at the phase interface. In this work, nucleation and growth of the martensite are studied. Epitaxial films of the Heusler alloy Ni-Mn-Ga are used as a model system. This alloy exhibits a modulated crystal structure which is interpreted as twinning on the atomic scale in the framework of adaptive martensite. In the first part, the modulated structure is studied by X-ray diffraction. The intensity of the superstructure is compared to a kinematic diffraction simulation and it is shown that it is a nanotwinned microstructure with a high density of stacking faults. In the seond part, the martensitic microstructure is studied by electron diffraction in the scanning electron microscope and by texture measurements using X-ray diffraction. The martensitic microstructure can be explained quantitatively in the framework of the phenomenological theory of martensite. This leads to a geometrical model of the martensitic nucleus and its growth stages. The phase transformation is studied as a function of temperature in the scanning electron microscope and atomic force microscope and is compared to the geometric model. The limits of the geometrical model at macroscopic twin boundaries and at interfaces to the substrate are discussed. Finally, the formation of the entire twin microstructure can be explained. In the third part, the energy barrier of nucleation is studied. The transformation is isothermal which leads to the conclusion that autonucleation processes decrease the nucleation barrier significantly. Finally, the influence of nanoindentation on the nucleation is shown.

<div>Accelerating the development of novel materials is one of the central goals of the Materials Genome Initiative and improving the predictive power of computational</div><div>material science methods is critical to attain this goal. Molecular dynamics (MD) is one such computational technique that has been used to study a wide range of materials since its invention in the 1950s. In this work we explore some examples of using and increasing the predictive power of MD simulations to understand materials phenomena and provide guidelines to design tailored materials. We first demonstrate the use of MD simulations as a tool to explore the design space of shape memory alloys, using simple interatomic models to identify characteristics of an integrated coherent second phase that will modify the transformation characteristics of the base shape memory alloy to our desire. Our approach provides guidelines to identify potential coherent phases that will achieve tailored transformation temperatures and hysteresis. </div><div><br></div><div>We subsequently explore ideas to enhance the length and time scales accessible via MD simulations. We first discuss the use of kinetic Monte Carlo methods in MD simulations to predict the microstructure evolution of carbon fibers. We ?find our approach to accurately predict the transverse microstructures of carbon fibers, additionally predicting the transverse modulus of these fibers, a quantity difficult to measure via experiments. Another avenue to increase length and time scales accessible via MD simulations is to explore novel implementations of algorithms involved in machine-learned interatomic models to extract performance portability. Our approach here results in significant speedups and an efficient utilization of increasingly common CPU-GPU hybrid architectures.</div><div><br></div><div>We finally explore the use of machine learning methods in molecular dynamics, specifically developing machine learning methods to discover interpretable laws directly from data. As examples, we demonstrate the discovery of integration schemes for MD simulations, and the discovery of melting laws for perovskites and single elements. Overall, this work attempts to illustrate how improving the predictive capabilities of molecular dynamics simulations and incorporating machine learning ideas can help us design novel materials, in line with the goals of the Materials Genome Initiative.</div>

Many industries including the medical, aerospace, and automobile industries have increasingly adopted the use of shape memory alloys (SMAs) for a plethora of applications due to their unique thermomechanical properties. From the commercially available SMAs in the market, binary NiTi SMAs have shown the most desirable properties. However, SMA properties can be significantly affected by the fabrication process. One of the most familiar applications of NiTi SMAs is in the design of actuating devices where the shape memory effect properties are highly advantageous. Spring NiTi SMA actuators are among the most commonly used and are generally made by torsion loading a straight wire. Consequently, stress concentrations are formed causing a reduction in recovery force. Other methods for producing springs and other NiTi SMA components is the fast emerging manufacturing method of additive manufacturing (AM). AM often uses metal powders to produce the near-net shape components. A major challenge for SMAs, in particular, is their well-known composition sensitivity. Therefore, it is critical to control composition in NiTi SMAs. In this thesis, a novel method for processing NiTi SMAs for pre-alloyed NiTi SMA powders and springs is presented. A low pressure and low temperature hydriding-pulverization-dehydriding method is used for preparing the pre-alloyed NiTi SMA powders with well-controlled compositions, size, and size distributions from wires. By hydrogen charging as-drawn martensitic NiTi SMA wires in a heated H3PO4 solution, pulverizing, and dehydriding, pre-alloyed NiTi powders of various well-controlled sizes are produced. In addition, a low pressure and low temperature hydriding-dehydriding method is used for producing NiTi SMA helixes from wires. The helix pattern in the pre-alloyed NiTi SMA wires was obtained by hydrogen charging NiTi SMA 500 μm diameter wires at different time intervals, followed by dehydriding to remove the hydrogen. The wires, powders, and resulting helixes were characterized using scanning electron microscopy (SEM), differential scanning calorimetry (DSC), and x-ray diffraction (XRD). The relationship between the wire diameter, powder particle size, and helix geometry as a function of hydrogen charging time is investigated. Lastly, the recovery behavior due to the shape memory effect is also investigated after dehydriding.

Shape memory alloys (SMAs) are a new generation material which exhibits unique nonlinear deformations due to a phase transformation which allows it to return to its original shape after removal of stress or a change in temperature. It shows a shape memory effect (martensitic condition) and pseudoelasticity (austenitic condition) properties depends on various heat treatment conditions. The reason for these properties depends on phase transformation through temperature changes or applied stress. Many technological applications of austenite SMAs involve cyclical mechanical loading and unloading in order to take advantage of pseudoelasticity, but are limited due to poor fatigue life. In this thesis, I investigated two important mechanical feature to fatigue behavior in pseudoelastic NiTi SMA wires using high energy synchrotron radiation X-ray diffraction (SR-XRD). The first of these involved simple bending and the second of these involved relaxation during compression loading. Differential scanning calorimetry (DSC) was performed to identify the phase transformation temperatures. Scanning electron microscopy (SEM) images were collected for the initial condition of the NiTi SMA wires and during simple bending, SEM revealed that micro-cracks in compression regions of the wire propagate with increasing bend angle, while tensile regions tend to not exhibit crack propagation. SR-XRD patterns were analyzed to study the phase transformation and investigate micromechanical properties. By observing the various diffraction peaks such as the austenite (200) and the martensite (100), (110), and (101) planes, intensities and residual strain values exhibit strong anisotropy depending upon whether the sample is in compression or tension during simple bending. This research provides insight into two specific mechanical features in pseudoelastic NiTi SMA wires.

Cette thèse présente une approche globale de la modélisation du comportement thermomécanique et cyclique des alliages à mémoire de forme (AMF) en grandes déformations. Cette approche s’articule en trois étapes : i) La généralisation du modèle ZM de comportement des AMF en grandes déformations dans le cadre de la thermodynamique des processus irréversibles. Pour ce faire, le gradient de la transformation totale est décomposé sous la forme du produit de trois gradients : le gradient de transformation lié à la déformation élastique, le gradient lié au changement de phase et le gradient de transformation lié à la réorientation de la martensite. Cette décomposition permet ainsi la modélisation de la réponse des structures en AMF dans le cas de chargements multiaxiaux non-proportionnels en transformations fi nies. ii) La prise en compte du couplage thermomécanique en transformations fi nies. Pour ce faire, la déformation de Henckya été introduite. Le modèle obtenu intègre trois caractéristiques thermomécaniques importantes des AMF, à savoir l’effet de la coexistence de l’austénite et de deux variantes de martensites distinctes, la variation de la taille de la boucle d’hystérésis avec la température et la transition du processus de changement de phase, d’abrupt à doux. iii) Enfin, en vue de prédire la réponse des structures en AMF sous chargement thermomécanique cyclique, le modèle développé dans la deuxième étape est généralisé pour décrire la pseudoélasticité cyclique des AMF polycristallins. Le modèle obtenu permet la prise en compte de quatre caractéristiques fondamentales liées au comportement cyclique des AMF : la déformation résiduelle accumulée, la dégénérescence de la boucle d’hystérésis, l’évolution de la transformation de phase, d’abrupte à douce. La mise en œuvre numérique de ces modèles s’appuie sur des algorithmes d’intégration appropriés. Des exemples numériques on été traités pour valider chaque étape. / Shape Memory Alloys (SMAs) are a class of smart materials that possess two salient features known as pseudoelasticity (PE) and shape memory effect(SME). In industrial applications, SMA structures are typically subjected to complex service conditions, such as large deformations, thermomechanically coupled boundaries and loadings, and cyclic loadings. The reliability and durability analysis of these SMA structures requires a good understanding of constitutive behavior in SMAs. To this end, this work develops a comprehensive constitutive modeling approach to investigate thermomechanical and cyclic behavior of SMAs in fi nite deformations. The work is generally divided into three steps. First, to improve accuracy of SMA model infinite deformation regime, the ZM model proposed by Zaki and Moumni (2007b) is extended within a fi nite-strain thermodynamic framework. Moreover, the transformation strain is decomposed into phase transformation and martensite reorientation components to capture multi-axial non-proportional response. Secondly, in addition to the fi nite deformation, thermomechanical coupling effect is taken into account by developing a new fi nite-strain thermomechanical constitutive model. A more straightforward approach is obtained by using the fi nite Hencky strain. This model incorporates three important thermomechanical characteristics, namely the coexistence effect between austenite and two distinct martensite variants, the variation with temperature of hysteresis size, and the smooth transition at initiation and completion of phase transformation. Finally, with a view to studying SMA behavior under cyclic loading, the model developed in the second step is generalized to describe cyclic pseudoelasticity of polycrystalline SMAs. The generalized model captures four fundamental characteristics related to the cyclic behavior of SMAs: large accumulated residual strain, degeneration of pseudoelasticity and hysteresis loop, rate dependence, and evolution of phase transformation from abrupt to smooth transition. Numerical implementation of these models are realized by introducing proper integration algorithms. Finite element simulations, including orthodontic archwire, helical and torsion spring actuators, are carried out using the proposed models. The future directions of this work mainly involve plasticity and fatigue analysis of SMA structures.

We report the fabrication of Ni2.7Mn0.9Ga0.4/InGaAs bilayers on GaAs (001)/InGaAs substrates by molecular beam epitaxy. To form freestanding microtubes the bilayers have been released from the substrate by strain engineering. Microtubes with up to three windings have been successfully realized by tailoring the size and strain of the bilayer. The structure and magnetic properties of both, the initial films and the rolled-up microtubes, are investigated by electron microscopy, X-ray techniques and magnetization measurements. A tetragonal lattice with c/a = 2.03 (film) and c/a = 2.01 (tube) is identified for the Ni2.7Mn0.9Ga0.4 alloy. Furthermore, a significant influence of the cylindrical geometry and strain relaxation induced by roll-up on the magnetic properties of the tube is found. / Dieser Beitrag ist aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.

Shape memory alloys (SMAs) can recover large strains (e.g., up to 8%) by undergoing a temperature-induced phase transformation. This strain recovery can occur against large forces, resulting in their use as actuators. The SMA elements in such actuators integrate both sensory and actuation functions. This is possible because SMAs can inherently sense a change in temperature and actuate by undergoing a shape change, associated with the temperature-induced phase transformation. The objective of this work is to develop an SMA based cryogenic thermal conduction switch for operation between dewars of liquid methane and liquid oxygen in a common bulk head arrangement for NASA. The design of the thermal conduction switch is based on a biased, two-way SMA actuator and utilizes a commercially available NiTi alloy as the SMA element to demonstrate the feasibility of this concept. This work describes the design from concept to implementation, addressing methodologies and issues encountered, including: a finite element based thermal analysis, various thermo-mechanical processes carried out on the NiTi SMA elements, and fabrication and testing of a prototype switch. Furthermore, recommendations for improvements and extension to NASA's requirements are presented. Such a switch has potential application in variable thermal sinks to other cryogenic tanks for liquefaction, densification, and zero boil-off systems for advanced spaceport applications. The SMA thermal conduction switch offers the following advantages over the currently used gas gap and liquid gap thermal switches in the cryogenic range: (i) integrates both sensor and actuator elements thereby reducing the overall complexity, (ii) exhibits superior thermal isolation in the open state, and (iii) possesses high heat transfer ratios between the open and closed states. This work was supported by a grant from NASA Kennedy Space Center (NAG10-323) with William U. Notardonato as Technical Officer.