Parsing the effect of slip-twin interactions on the strain rate and thermal sensitivities of Magnesium (Mg) alloys has been a challenging endeavor for scientists preoccupied with the mechanical behavior of hexagonal close-packed alloys, especially those with great latent economic potential such as Mg. One of the main barriers is the travail entailed in fitting the various stress-strain behaviors at different temperatures, strain rates, loading directions applied to different starting textures. Taking on this task for two different Mg alloys presenting different textures and as such various levels of slip-twin interactions were modeled using VPSC code. A recently developed routine that captures dislocation transmutation by twinning interfaces on strain hardening within the twin lamellae was employed. While the strong texture was exemplified by traditional rolled AZ31 Mg alloys, the weak texture was represented by ZEK100 Mg alloy sheets. The transmutation model casted within a dislocation density based hardening model showed tremendous flexibility in predicting the complex strain rate and thermal sensitive behavior of Mg textures’ response to various mechanical loadings schemes.

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<p><strong>Abstract</strong></p> <p>The objective of this research is to develop an understanding of the mechanical behavior, failure and microstructure evolution of aluminum tubes under internal pressure loading, and to delineate the physical and mechanical origins of spatially-localized plastic deformation. Traditional approaches to the study of plastic instabilities, necking and failure have either been based on kinematic considerations, such as finite strain effects and geometric softening, or physics-based concepts. In this study, we develop a framework that combines both approaches to investigate the tube deformation and failure behavior at various loading conditions.</p> <p>A rate-dependent dislocation-based MTS model has been developed to study the tube hydro-forming process at high temperatures and at various strain rates. The development and application of the MTS model led to an advanced industrial application of PRF bottle forming, which has been fully investigated. This simulation shows a good agreement between experimental results and prediction. The model has been used extensively throughout the PRF bottle development, with several patent applications.</p> <p>The crystal plasticity based finite element model is selected to simulate surface roughening and localized necking in aluminum alloy tubes under internal pressure. The measured electron backscatter diffraction (EBSD) data are directly incorporated into the finite element model and the constitutive response at an integration point is described by the single crystal plasticity theory. The effects of the spatial grain orientation distribution, strain rate sensitivity, work hardening, and initial surface topography on surface roughening and necking are discussed. It is demonstrated that while localized necking is very sensitive to both the initial texture and its spatial orientation distribution, the initial surface topography has only a small influence on necking, but a large influence on surface roughness of the formed product.</p> <p>An elastic-viscoplastic based finite element model has been developed to study the necking behavior of tube expansion for rate dependent monolithic materials and laminated materials during dynamic loading. Numerical study shows that a high strain rate sensitivity can significantly delay the onset of necking for both monolithic and laminated sheets, and affect the multiple-neck formation in high speed dynamic loading. The model also shows that higher volume fractions of a clad layer with positive rate sensitivity material in laminated sheet could improve the sheet ductility as well.</p> <p>A commercial FE package, ABAQUS, is employed as a finite element method solver in this research work, and several user subroutines were developed to model various hydro-forming processes. Interfaces between the ABAQUS user subroutine UMAT and the ABAQUS main code are developed to allow further extension of the current method.</p> / Doctor of Philosophy (PhD)

Titanium-7%wt-Aluminum (Ti-7Al) has been of interest to the aerospace industry owing to its good structural and thermal properties. However, extensive research is still needed to study the structural behavior and determine the material properties of Ti-7Al. The homogenized macro-scale material properties are directly related to the crystallographic structure at the micro-scale. Furthermore, microstructural uncertainties arising from experiments and computational methods propagate on the material properties used for designing aircraft components. Therefore, multi-scale modeling is employed to characterize the microstructural features of Ti-7Al and computationally predict the macro-scale material properties such as Young's modulus and yield strength using machine learning techniques. Investigation of microstructural features across large domains through experiments requires rigorous and tedious sample preparation procedures that often lead to material waste. Therefore, computational microstructure reconstruction methods that predict the large-scale evolution of microstructural topology given the small-scale experimental information are developed to minimize experimental cost and time. However, it is important to verify the synthetic microstructures with respect to the experimental data by characterizing microstructural features such as grain size and grain shape. While the relationship between homogenized material properties and grain sizes of microstructures is well-studied through the Hall-Petch effect, the influences of grain shapes, especially in complex additively manufactured microstructure topologies, are yet to be explored. Therefore, this work addresses the gap in the mathematical quantification of microstructural topology by developing measures for the computational characterization of microstructures. Moreover, the synthesized microstructures are modeled through crystal plasticity simulations to determine the material properties. However, such crystal plasticity simulations require significant computing times. In addition, the inherent uncertainty of experimental data is propagated on the material properties through the synthetic microstructure representations. Therefore, the aforementioned problems are addressed in this work by explicitly quantifying the microstructural topology and predicting the material properties and their variations through the development of surrogate models. Next, this work extends the proposed multi-scale models of microstructure-property relationships to magnetic materials to investigate the ferromagnetic-paramagnetic phase transition. Here, the same Ising model-based multi-scale approach used for microstructure reconstruction is implemented for investigating the ferromagnetic-paramagnetic phase transition of magnetic materials. The previous research on the magnetic phase transition problem neglects the effects of the long-range interactions between magnetic spins and external magnetic fields. Therefore, this study aims to build a multi-scale modeling environment that can quantify the large-scale interactions between magnetic spins and external fields. / Doctor of Philosophy / Titanium-Aluminum (Ti-Al) alloys are lightweight and temperature-resistant materials with a wide range of applications in aerospace systems. However, there is still a lack of thorough understanding of the microstructural behavior and mechanical performance of Titanium-7wt%-Aluminum (Ti-7Al), a candidate material for jet engine components. This work investigates the multi-scale mechanical behavior of Ti-7Al by computationally characterizing the micro-scale material features, such as crystallographic texture and grain topology. The small-scale experimental data of Ti-7Al is used to predict the large-scale spatial evolution of the microstructures, while the texture and grain topology is modeled using shape moment invariants. Moreover, the effects of the uncertainties, which may arise from measurement errors and algorithmic randomness, on the microstructural features are quantified through statistical parameters developed based on the shape moment invariants. A data-driven surrogate model is built to predict the homogenized mechanical properties and the associated uncertainty as a function of the microstructural texture and topology. Furthermore, the presented multi-scale modeling technique is applied to explore the ferromagnetic-paramagnetic phase transition of magnetic materials, which causes permanent failure of magneto-mechanical components used in aerospace systems. Accordingly, a computational solution is developed based on an Ising model that considers the long-range spin interactions in the presence of external magnetic fields.

<p dir="ltr">Energetic materials contain microstructural defects like cracks, voids, grain boundaries, and interfaces which act as nucleation sites for ignition and detonation when shocked. Finite element (FE) models are currently unable to capture explicit microstructure with voids, cracks, and randomly oriented grains with representative mechanics, thermal conduction, and reactivity that exhibit the full shock to detonation transition (SDT). Modern computational efforts seek to accurately model material response while also balancing efficiency and speed. Work presented in this thesis will highlight all of these microstructural features, investigate mechanical and thermal response of each microstructure, connect these results to what is observed in other experimental and computational work, and bring computational modeling even closer to an efficient model that contains all processes necessary to replicate SDT.</p><p dir="ltr">In energetic materials (EM), voids are irregular in shape, but most computational work has focused on circular void collapse behavior. However, geometries that contain irregularities or corners are more likely to act as initiation sites due to stress concentrations. Validation and calibration of void simulations with experimental lengthscales and loading conditions is still limited. Plus, pore collapse modeling efforts at low impact velocities do not model fracture, and it is known that cracks cause more extreme temperatures than pores.</p><p dir="ltr">Other microstructure characteristics like cracks and grains have sub-micrometer length scale, and influence the mechanical and thermal response of materials under extreme conditions. However, approximations and coarse-graining must be applied to continuum FE simulations to fit length and timescales required to capture phenomena such as detonations that occur at a millimeter scale. With the use of machine learning (ML), numerical models can be trained on results of small-scale microstructure simulations and applied to larger length and time-scale simulations. The ML model follows Microstructure-Informed Shock-induced Temperature net (MISTnet) model and is trained upon stress, strain, temperature, pressure, and slip data and includes crystal plasticity, fracture, friction, an equation of state, and heat conduction. The ML model is able to predict temperature fields behind the shock, concentrations at grain boundaries, and the influence of grain orientation.</p><p dir="ltr">Accurate temperature values are extremely important to modeling EM because thermal hot spots (HS) are the main cause of ignition. Critical HS cause the chemical reactions which transition the shock front into a detonation, but many continuum models do not include chemistry in their framework. A 1-step Arrhenius reaction model is added to FE mechanics model to investigate the relationship HS have on the run to detonation (RTD).</p>

Crystallographic texture and its evolution are known to be major sources of anisotropy in polycrystalline metals. Highly simplified phenomenological models cannot usually provide reliable predictions of the materials anisotropy under complex deformation paths, and lack the fidelity needed to optimize the microstructure and mechanical properties during the production process. On the other hand, physics-based models such as crystal plasticity theories have demonstrated remarkable success in predicting the anisotropic mechanical response in polycrystalline metals and the evolution of underlying texture in finite plastic deformation. However, the integration of crystal plasticity models with finite element (FE) simulations tools (called CPFEM) is extremely computationally expensive, and has not been adopted broadly by the advanced materials development community. The current dissertation has mainly focused on addressing the challenges associated with integrating the recently developed spectral database approach with a commercial FE tool to permit computationally efficient simulations of heterogeneous deformations using crystal plasticity theories. More specifically, the spectral database approach to crystal plasticity solutions was successfully integrated with the implicit version of the FE package ABAQUS through a user materials subroutine, UMAT, to conduct more efficient CPFEM simulations on both fcc and bcc polycrystalline materials. It is observed that implementing the crystal plasticity spectral database in a FE code produced excellent predictions similar to the classical CPFEM, but at a significantly faster computational speed. Furthermore, an important application of the CPFEM for the extraction of crystal level plasticity parameters in multiphase materials has been demonstrated in this dissertation. More specifically, CPFEM along with a recently developed data analysis approach for spherical nanoindentation and Orientation Imaging Microscopy (OIM) have been used to extract the critical resolved shear stress of the ferrite phase in dual phase steels. This new methodology offers a novel efficient tool for the extraction of crystal level hardening parameters in any single or multiphase materials.

A constitutive model has been developed to model the shock response of single crystal aluminum from peak pressures ranging from 2-110 GPa. This model couples a description of higher-order thermoelasticity with a dislocation-based viscoplastic formulation, both of which are formulated for single crystals. The constitutive model has been implemented using two numerical methods: a plane wave method that tracks the propagating wave front; and an extended one-dimensional, finite-difference method that can be used to model spatio-temporal evolution of wave propagation in anisotropic materials. The constitutive model, as well as these numerical methods, are used to simulate shock wave propagation in single crystals, polycrystals, and pre-textured polycrystals. Model predictions are compared with extensive existing experimental data and are then used to quantify the influence of the initial material state on the subsequent shock response. A coarse-grained model is then proposed to capture orientation-dependent deformation heterogeneity, and is shown to replicate salient features predicted by direct finite-difference simulation of polycrystals in the weak shock regime. The work in this thesis establishes a general framework that can be used to quantify the influence of initial material state on subsequent shock behavior not only for aluminum single crystals, but for other face-centered cubic and lower symmetry crystalline metals as well.

Superalloys have performed well as blade and disc materials in turbine engines due to their exceptional elevated temperature strength, high resistance to creep, oxidation and corrosion as well as good fracture toughness. This study explores the use of a relatively new technique of strain measurement, high resolution electron backscatter diffraction (HR-EBSD) to measure local deformation fields. The heart of the HR-EBSD technique lies in comparing regions in EBSD patterns from a strained region of a sample to those in a pattern from an unstrained region. This method was applied to study the elastic strain fields and geometrically necessary dislocation density (GND density) distribution near hard carbide particles in a nickel-based superalloy MAR-M-002. Significant thermal strains were initially induced by thermal treatment, which included a final cooling from the ageing temperature of 870°C. Elastic strains were consistent with a compressive radial strain and tensile hoop strain that was expected as the matrix contracts around the carbide. The mismatch in thermal expansion coefficient of the carbide particles compared to that of the matrix was sufficient to have induced localized plastic deformation in the matrix leading to a GND density of 3 x 10¹³ m^–2 in regions around the carbide. These measured elastic strain and GND densities have been used to help develop a crystal plasticity finite element model in another research group and some comparisons under thermal loading have also been examined. Three-point bending was then used to impose strain levels within the range ±12% across the height of a bend bar sample. GND measurements were then made at both carbide-containing and carbide-free regions at different heights across the bar. The average GND density increases with the magnitude of the imposed strain (both in tension and compression), and is markedly higher near the carbide particles. The higher GND densities near the carbides (order of 10¹⁴ per m²) are generated by the large strain gradients produced around the plastically rigid inclusion during monotonic mechanical deformation with some minor contribution from the pre-existing residual deformation from thermal loading. A method was developed of combining the local EBSD measurements with FE modelling to set the average residual strains within the mapped region even when a good strain free reference point was unavailable. Cyclic loading was then performed under four point loading to impose strain levels of about ±8% across the height of bend bar samples. Similar measurements as in the case of monotonic deformation were made at several interruptions to fatigue loading. Observations from the cyclic loading such as slip features, carbide cracking, GND density accumulation have been explored around carbide particles, at regions away from them and near a grain boundary.

Les propriétés des matériaux métalliques sont très liées à leurs caractéristiques microstructurales. Par exemple il est bien connu que la taille de grains joue sur la limite élastique du matériau ainsi que sur ses capacités d'écrouissage. Ainsi, la compréhension et la modélisation de l'évolution de la microstructure d'un métal pendant un traitement thermomécanique est d'une importance primordiale afin de prédire finement son comportement ainsi que ses propriétés finales. Dans le cadre de cette thèse, nous nous sommes concentrés sur la modélisation, à l'échelle d'un agrégat polycristallin, de la plasticité cristalline, de la recristallisation statique et de la croissance des grains dans un contexte de mobilité et d'énergie d'interface isotrope. Un modèle à champ complet dans un cadre éléments finis (EF) est proposé. Les grains sont représentés grâce à un formalisme level-set. L'étude EF développée peut être divisée en trois grandes parties: la génération statistique de microstructures digitales, la modélisation de la plasticité cristalline et la modélisation de la migration des joins de grains en régime de recristallisation statique. Concernant la génération statistique des microstructures digitales, une étude comparative entre deux méthodes de génération (Voronoï et Laguerre-Voronoï) a été réalisée. La capacité de la deuxième approche à respecter une microstructure basée sur des données expérimentales est mise en valeur en 2D et en 3D. Dans une deuxième étape, la plasticité cristalline des matériaux métalliques est étudiée. Deux modèles d'écrouissage ont été implémentés et validés : un premier modèle considérant uniquement les densités de dislocations totales, et un deuxième modèle différenciant les dislocations statistiquement stockées (SSDs) des dislocations géométriquement nécessaires (GNDs). Afin de valider l'implémentation de ces deux modèles issus de la littérature deux cas ont été étudiés : le premier correspond à l'étude à chaud d'un essai de compression plane d'un acier 304L, et le deuxième correspond à l'étude d'un essai à froid de compression simple d'un oligocristal de tantale composé de 6 grains. Les résultats numériques obtenus sont comparés avec les données expérimentales des deux essais. La migration des joints de grains est étudiée dans le contexte des régimes de recristallisation statique et de croissance de grains. Par rapport aux travaux pre-existants dans un cadre level-set, l'accent est mis sur la prise en compte des forces capillaires. La croissance des grains pure est en effet développée dans le formalisme éléments finis/level set considéré, et des validations à partir de résultats analytiques connus sont présentées. De plus, un travail d'analyse de modèles de croissance des grains à champ moyen existant dans la littérature est réalisé. Deux modèles en particuliers sont étudiés : celui de Burke et Turnbull et celui de Hillert/Abbruzzese. En comparant ces modèles avec les résultats obtenus par l'approche en champ complet développée, il est mis en évidence que le modèle simple de Burke et Turnbull n'est pas approprié pour décrire la croissance de grains pour tout type de distribution initiale de taille de grains. La recristallisation statique est ensuite abordée, avec une prise en compte des deux forces motrices liées (i) aux gradients d'énergies stockées sous la forme de dislocations, et (ii) aux effets capillaires. L'influence des effets de capillarité apparaît comme fortement liée à la distribution spatiale des nouveaux germes. Finalement, les résultats des simulations réalisées en plasticité cristalline sont utilisés comme données d'entrée du modèle de recristallisation statique développé. La comparaison des prédictions obtenues comparativement aux résultats expérimentaux sur 304L permet d'illustrer la pertinence d'une approche de type SSD/GND afin de prédire les sites de germination potentiels. / Mechanical and functional properties of metals are strongly related to their microstructures, which are themselves inherited from thermal and mechanical processing. For example, the material grain size distribution plays an important role on the material yield limit and work hardening. The understanding of these microstructure evolutions during thermo-mechanical processes is of prime importance for a better prediction and control of the material mechanical properties. During this Ph.D., we have worked on the modelling of crystal plasticity, static recrystallization and grain growth at the mesoscopic scale in the context of isotropic mobility and interface energy. The full field model developed is based on a finite element formulation combined with a level set framework used to describe the granular structure. This Ph.D. thesis is divided in three main parts: statistical generation of digital microstructures, crystal plasticity modelling and grain boundary migration modelling. In what concerns the digital microstructures statistical generation, a comparative study between two methods (Voronoï and Laguerre-Voronoï) is presented. The ability of the second approach to respect a given grain size distribution is highlighted in 2D and 3D. Secondly, the metallic materials crystal plasticity is studied. Two hardening laws have been implemented and validated: the first one considering the total dislocation density and a second one that differentiates the statistically stored dislocations (SSD) from geometrically necessary dislocations (GNDs). Two different tests cases are used in order to validate the implementation of both hardening laws in the considered crystal plasticity model. The first one corresponds to a planar hot compression test (channel die test) on a 304L stainless steel whereas the second one corresponds to a simple cold compression test on a tantalum olygocrystal composed by six different grains. The obtained results are compared to experimental data for both cases. Grain boundary migration is studied for static recrystallization and grain growth phenomena. Compared to previous work in the considered level-set framework, the focus is on the consideration of capillary forces. Indeed pure grain growth is developed in the considered finite elements/level set formalism and this algorithm is validated using well-known analytical results. Moreover, the results of the developed full field grain growth model are compared in 2D with several well-known mean field grain growth models (Burke and Turbull model and Hillert/Abbruzzese model). The results obtained illustrate that only the Hillert/Abbruzzese model accurately describes grain growth kinetics for all initial grain size distributions. The validity of the Burke and Turnbull model is, on the contrary, restricted to specific distributions. Static recrystallization is then discussed considering both driving forces: (i) internal energy gradient and (ii) grain boundaries capillarity effects. The influence of capillary effects appears to be strongly related to the spatial distribution of the new grains. Finally, the crystal plasticity numerical results are used as input data of the developed static recrystallization full field model. The comparison of the numerical predictions obtained with 304L experimental results allows illustrating the relevance of the SSDs/GNDs formalism used concerning the prediction of the nuclei potential position.