The unique thermo-mechanical behavior of Shape Memory Alloys (SMAs), such as their ability to recover the original shape upon heating or being able to tolerate large deformations without undergoing plastic transformations, makes them a good choice for actuators. This work studies their application in the aerospace and defense industries where SMA components can serve as release mechanisms for gates of enclosures that have to be deployed remotely. This work provides a novel approach in evaluating the stress and heat induced change of phase in a SMA, in terms of the transformation strain tensor. In particular, the FEA tool ANSYS has been used to perform a 2-D analysis of a Cu-Al-Zn-Mn SMA specimen undergoing a nontraditional loading path in two steps with stress and heating loads. In the first load step, tensile displacement is applied, followed by the second load step in which the specimen is heated while the end displacements are held constant. A number of geometric configurations are examined under the two step loading path. Strain results are used to calculate transformation strain which provides a quantitative measure of phase at a material point; when transformation strain is zero, the material point is either twinned martensite, or austenite depending on the temperature. Transformation strain value of unity corresponds to detwinned martensite. A value between zero and one indicates mixed phase. In this study, through two step loading in conjunction with transformation strain calculations, a method for mapping transient non-uniform distribution of phases in an SMA is introduced. Ability to obtain drastically different phase distributions under same loading path by modifying the geometry is demonstrated. The failure behavior of SMAs can be designed such that the load level the crack initiates and the path it propagates can be customized.

Polycrystalline NiTi shape memory alloys have the ability to recover their original, pre-deformed shape in the presence of external loads when heated through a solid-solid phase transformation from a lower-symmetry B19' martensite phase to a higher-symmetry B2 austenite phase. The strain associated with a shape memory alloy in an actuator application typically has thermal, elastic and inelastic contributions. The objective of this work was to investigate the aforementioned strains by recourse to in situ neutron diffraction experiments during selected combinations of heating, cooling and/or mechanical loading. The primary studies were conducted on polycrystalline Ni49.9Ti50.1 specimens on the Spectrometer for MAterials Research at Temperature and Stress (SMARTS) at Los Alamos National Laboratory. Quantitative information on the phase-specific strain, texture and phase fraction evolution was obtained from the neutron data using Rietveld refinement and single-peak analyses, and compared with macroscopic data from extensometry. First, the lattice strain evolution during heating and cooling in an unloaded sample (i.e., free-recovery experiment) was studied. The lattice strain evolution remained linear with temperature and was not influenced by intergranular stresses, enabling the determination of a thermal expansion tensor that quantified the associated anisotropy due to the symmetry of B19' NiTi. The tensor thus determined was subsequently used to obtain an average coefficient of thermal expansion that was consistent with macroscopic dilatometric measurements and a 30,000 grain polycrystalline self-consistent model. The accommodative nature of B19' NiTi was found to account for macroscopic shape changes lagging (with temperature) the start and finish of the transformation. Second, the elastic response of B19' martensitic NiTi variants during monotonic loading was studied. Emphasis was placed on capturing and quantifying the strain anisotropy which arises from the symmetry of monoclinic martensite and internal stresses resulting from intergranular constraints between individual variants and load re-distribution among variants as the texture evolved during variant reorientation and detwinning. The methodology adopted took into account both tensile and compressive loading given the asymmetric response in the texture evolution. Plane specific elastic moduli were determined from neutron measurements and compared with those determined using a self-consistent polycrystalline deformation model and from recently reported elastic stiffness constants determined via ab initio calculations. The comparison among the three approaches further helped understand the influence of elastic anisotropy, intergranular constraint, and texture evolution on the deformation behavior of polycrystalline B19' NiTi. Connections were additionally made between the assessed elastic properties of martensitic NiTi single crystals (i.e., the single crystal stiffness tensor) and the overall macroscopic response in bulk polycrystalline form. Lastly, the role of upper-cycle temperature, i.e., the maximum temperature reached during thermal cycling, was investigated during load-biased thermal cycling of NiTi shape memory alloys at selected combinations of stress and temperature. Results showed that the upper-cycle temperature, under isobaric conditions, significantly affected the amount of transformation strain and thus the work output available for actuation. With the objective of investigating the underlying microstructural and micromechanical changes due to the influence of the upper-cycle temperature, the texture evolution was systematically analyzed. While the changes in transformation strain were closely related to the evolution in texture of the room temperature martensite, retained martensite in the austenite state could additionally affect the transformation strain. Additionally, multiple thermal cycles were performed under load-biased conditions in both NiTi and NiTiPd alloys, to further assess and understand the role of retained martensite. Dimensional and thermal stabilities of these alloys were correlated with the volume fraction and texture of retained martensite, and the internal strain evolution in these alloys. The role of symmetry, i.e., B19' monoclinic martensite vs. B19 orthorhombic martensite in these alloys was also assessed. This work not only established a methodology to study the thermal and elastic properties of the low symmetry B19' monoclinic martensite, but also provided valuable insight into quantitative micromechanical and microstructural changes responsible for the thermomechanical response of NiTi shape memory alloys. It has immediate implications for optimizing shape memory behavior in the alloys investigated, with extension to high temperature shape memory alloys with ternary and quaternary elemental additions, such as Pd, Pt and Hf. This work was supported by funding from NASAÂ s Fundamental Aeronautics Program, Supersonics Project (NNX08AB51A) and NSF (CAREER DMR-0239512). It benefited additionally from the use of the Lujan Neutron Scattering Center at Los Alamos National Laboratory, which is funded by the Office of Basic Energy Sciences (Department of Energy) and is operated by Los Alamos National Security LLC under DOE Contract DE-AC52-06NA25396.

This thesis concerns the mathematical modelling of phase transformations with a special emphasis on martensitic phase transformations and their application to the modelling of steels. In Chapter 1, we develop a framework that determines the optimal transformation strain between any two Bravais lattices and use it to give a rigorous proof of a conjecture by E.C. Bain in 1924 on the optimality of the so-called Bain strain. In Chapter 2, we review the Ball-James model and related concepts. We present some simplification of existing results. In Chapter 3, we pose a conjecture for the explicit form of the quasiconvex hull of the three tetragonal wells, known as the three-well problem. We present a new approach to finding inner and outer bounds. In Chapter 4, we focus on highly compatible, so called self-accommodating, martensitic structures and present new results on their fine properties such as estimates on their minimum complexity and bounds on the relative proportion of each martensitic variant in them. In Chapter 5, we investigate the contrary situation when self-accommodating microstructures do not exist. We determine, whether in this situation, it is still energetically favourable to nucleate martensite within austenite. By constructing different types of inclusions, we find that the optimal shape of an inclusion is flat and thin which is in agreement with experimental observation. In Chapter 6, we introduce a mechanism that identifies transformation strains with orientation relationships. This mechanism allows us to develop a simpler, strain-based approach to phase transformation models in steels. One novelty of this approach is the derivation of an explicit dependence of the orientation relationships on the ratio of tetragonality of the product phase. In Chapter 7, we establish a correspondence between common phenomenological models for steels and the Ball-James model. This correspondence is then used to develop a new theory for the (5 5 7) lath transformation in low-carbon steels. Compared to existing theories, this new approach requires a significantly smaller number of input parameters. Furthermore, it predicts a microstructure morphology which differs from what is conventionally believed.

Les alliages à base de Ni-Mn-In ont attiré une attention considérable en raison de leurs propriétés multifonctionnelles depuis leur découverte en 2004, telles que l’effet de mémoire de forme métamagnétique (Metamagnetic shape memory effect MMSME), l'effet magnétocalorique (MCE) et l'effet de magnétorésistance (MR). Cependant, certaines connaissances fondamentales sur ces alliages manquent toujours jusqu'à présent, telles que la structure cristalline de la martensite, les caractéristiques cristallographiques de microstructure et de transition magnétostructurale. Dans cette thèse, les caractéristiques cristallographiques, les comportements mécaniques et les propriétés magnétiques des alliages Ni-Mn-In base ont été étudiés théoriquement et expérimentalement. Tout d'abord, les structures cristallines des alliages Ni-Mn-In ont été déterminées avec précision par la méthode de Rietveld dans le cadre de la théorie du superespace. Ensuite, la microstructure de la martensite, notamment l'organisation et l'interface des variantes, ainsi que les caractéristiques cristallographiques de la transformation martensitique, telles que les relations d'orientation (OR), le chemin de déformation de la transformation et la compatibilité géométrique entre l'austénite et la martensite, ont été systématiquement étudiés. Enfin, avec cette connaissance fondamentale sur les alliages Ni-Mn-In, les comportements et les mécanismes de sélection /réarrangement des variantes de martensite sous deux types de stratégies de chargement mécanique, à savoir le chargement à l'état martensitique et le chargement durant la transition structurelle, et les effets du recuit sur l'effet MCE et les pertes d'hystérésis associées ont été explorées. Les principaux résultats sont les suivants. La martensite modulé a une structure cristalline incommensurable avec la structure cristalline 6M et le groupe de superespace I2/m(α0γ)00 qui peut être approximée par un modèle de superstructure de multiplicité 3 dans l'espace à tridimensionnel. La microstructure de martensite est en forme de plaques et auto-organisée en colonies. Chaque colonie a quatre variantes d'orientations distinctes. Le maximum de 6 colonies distinctes et 24 variantes peut être généré à l'intérieur d'un grain austénitique. Bien que jusqu'à 14 types de relations de maclage sont proposées dans le cadre des théories cristallographiques de transformation martensitique, seuls trois types de relations de maclage sont généralement observés, à savoir des macles de type I, type II et composées. Les interfaces des variantes sont définies à l'échelle mésoscopique par leur plan de maclage K1 correspondant. Cependant, à l'échelle atomique, la macle de type I a une interface cohérente, alors que celles de type-II et les macles composées ont des interfaces étagées. Les deux relations d'orientations K-S et Pitsch sont appropriés pour décrire la correspondance de réseau entre austénite et martensite dans les alliages Ni-Mn-In. Cependant, le chemin de déformation lié à la relation de Pitsch est mis en évidence pour être efficace pour la déformation de la structure. Avec le chemin de transformation déterminé, le mécanisme sous-jacent de l'organisation des variantes est révélé. À travers la transformation martensitique, en dépit de l'existence d'une relativement large couche contrainte (de l'ordre de 20 nm), le plan d'habitat est bordé par une variante de martensite simple avec l'austénite plutôt que la structure généralement observée "en sandwich", ce qui suggère une relativement bonne compatibilité géométrique entre les phases correspondantes. Pour le chargement en compression à l'état martensitique, l'arrangement des variantes est réalisé par des processus de démaclage. Il est démontré que l'état de variante unique dans certaines colonies pourrait être obtenu lorsque l'orientation de chargement est située dans la zone de Facteur de Schmid (SF) positif commune pour les trois systèmes de démaclage. [...] / Ni-Mn-In based alloys have attracted considerable attention due to their multifunctional properties since its discovery in 2004, such as metamagnetic shape memory effect (MMSME), magnetocaloric effect (MCE) and magnetoresistance (MR) effect. However, some fundenmental knowledge on these alloys is still missing until now, such as crystal structure of martensite, crystallographic features of microstructure and magnetostructural transition. In this dissertation, the crystallographic features, mechanical behaviors and magnetic properties of Ni-Mn-In based alloys were studied theoretically and experimentally. First, the crystal structures of Ni-Mn-In alloys were accurately determined by Rietveld method in the frame of superspace theory (Chapter 3). Then, the microstructure of martensite (Chapter 4), such as variant organization and interface structure, and the crystallographic features of martensitic transformation, such as orientation relationship (OR), transformation strain path and geometrical compatibility between austenite and martensite, were systematically studied (Chapter 5). Finally, with this fundamental knowledge on Ni-Mn-In alloys, the behaviors and mechanisms of martensite variant rearrangement/ selection under two kinds of mechanical loading strategies, i.e. loading at martensite state and loading across the structural transition, and the effects of annealing on MCE and its related hysteresis loss were explored (Chapter 6). The main results are as follows. The modulated martensite has an incommensurate 6M crystal structure with superspace group I2/m(α0γ)00 that can be approximated by a three-fold superstructure model in the three-dimensional space. The microstructure of martensite is in plate shape and self-organized in colonies. Each colony has four distinct orientation variants. The maximum of 6 distinct colonies and 24 variants can be generated within one austenite grain. Although as many as 14 kinds of twin relations are suggested in the frame of crystallographic theories of martensitic transformation, only three types of twin relations are generally detected, i.e. type-I, type-II and compound twin. Variant interfaces are defined by their corresponding twinning plane K1 at mesoscopic scale. However, at atomic scale, the type-I twin has a coherent interface, whereas type-II and compound twins have “stepped” interfaces. Both the K-S and Pitsch ORs are appropriate to describe the lattice correspondence between austenite and martensite in Ni-Mn-In alloys. However, the strain path related to the Pitsch relation is evidenced to be the effective for the structural distortion. With the determined transformation path, the underlying mechanism of variant organization is revealed. Across the martensitic transformation, despite the existence of a relative wide stressed layer (around 20 nm), the habit plane is bordered by single martensite variant with austenite rather than the generally observed “sandwich-like” structure, implying a relative good geometrical compatibility between the corresponding phases. For compressive loading at martensite, variant arrangement is realized by the detwinning process. It is evidenced that a single variant state in some colonies can be obtained when the loading orientation is located in the common positive Schmid factor (SF) zone of the three detwinning systems. For loading across the structural transition, the prestrain is obtained by variant selection in which the number of colonies is significantly reduced and the variant organization within colony is greatly changed. The SF for transformation strain path is introduced to evaluate the possible selection of variants. Heat treatment can significantly enhance the magnetic entropy change ΔSM but simultaneously increase the magnetic hysteresis loss. For ΔSM, the chemical ordered degree should play a prominent role [...]