Magnesium alloys have garnered much interest in automotive and aerospace industries, where simultaneously light-weight and strong components are needed to improve energy efficiency without sacrificing structural stability. However, the widespread application of magnesium has been limited due to its poor room temperature formability, which renders it incompatible with modern industrial processing methods, such as rolling, forming, die punching and extrusion techniques. Unlike traditional structural metals that deform primarily by dislocation slip, the deformation of magnesium alloys is carried out by a combination of dislocations motion and the development of deformation twins. Twinning deformation occurs on the grain scale and can strongly influence the mechanical properties of the material, such as ductility, strength, and stability. Thus, a fundamental understanding of how dislocations and twins interact with each other and with other common microstructural features found in magnesium alloys is critical in the design of useful magnesium components for industrial applications.

In this work, an elasto-viscoplastic fast-Fourier-transform (EVP-FFT) computation model was used in order to investigate the interaction between twins and two commonly encountered microstructural features: precipitates and free surfaces. First, we consider a newly propagated twin that intersects a Mg17Al12 basal precipitates in AZ91. It is shown that these precipitates can impede the propagation and thickening of twins, however, the impingement of a twin against one side of a precipitate can cause local stress concentrations to develop along the precipitate-matrix boundary, where a new twin of the same or different twin variant can nucleate from. Both the relative thickness and length of the precipitate, in relation to the thickness of the twin, are important factors that determine how twins can continue to develop. The size of the precipitate is a key factor in controlling twinning deformation during the early stages of development and determining the twinning pathways that emerge.

Next, a dislocation-density based hardening law was incorporated into EVP-FFT framework in order to reveal the evolution of the spatial distribution of dislocation densities in the microstructure. Here, defect content in addition to adequate stresses are used as indicators for the determining how twins will continue developing. By considering twinning from the early stages of deformation, a two-step twin growth mechanism is proposed: starting with an initial twin propagation front that impinges upon a precipitate, resulting in a stress concentration that develops on the other side of the precipitate that prompts the formation of a second twin. Subsequently, the backstresses around the first twin are relaxed by the propagation of a second twin, allowing the first twin to grow at the twin-precipitate junction and eventually engulf the precipitate. This mechanism suggests that twin growth can be achieved locally with minimal additional external forces, explaining how relatively large twin domains can develop even in the presence of arrays of precipitates, despite contradictory reports that precipitates harden against twin growth. The precipitate spacing is shown to affect the stresses and dislocation generated near the twin-precipitate interaction site that support twin growth.

Twinning can be an essential deformation mechanism in hexagonal close packed (HCP) materials and when it occurs, can significantly change plastic behavior, causing, for instance, noticeable tension and compression asymmetry. In this thesis research, crystal plasticity models, such as elasto-plastic self-consistent (EPSC) model, viscoplastic self-consistent (VPSC) model, and elasto-viscoplastic fast Fourier transformation model, are applied to investigate twin-related hardening mechanisms in HCP alloys. A shared feature of these models is that all models are coupled with dislocation density-based hardening laws, which can predict the underlying dislocation slip activity. How twinning is represented is different among these models. In EPSC and VPSC, a composite grain model is employed to account for twinning, while in EVP-FFT, the intragranular twin domain is model explicitly within the single crystal. Based on their respective advantages, the VPSC and EPSC models are selected to first research dislocation-twin interactions in polycrystalline in commercially pure titanium (CP-Ti) and Mg-Y alloys, and later, the EVP-FFT model is applied for twin-twin interactions within Mg alloy crystals.As mentioned, in the first part of this research, the EPSC model was employed to study the interaction between slip and twinning in CP-Ti under cyclic loading. There are a variety of active mechanisms in CP-Ti at room temperature, including prismatic ⟨a⟩, basal ⟨a⟩, pyramidal slip ⟨c+a⟩, {101 ̅2} tensile twin, and {112 ̅2} compressive twin. A model for the development of a “slip-system-level” backstress due to dislocation density accumulation is included in the EPSC model to advance the model to treat cyclic loading and in particular predict the Bauschinger effect. Material parameters associated with the slip strengths for the three HCP slip modes are determined and newly reported. The model identifies the few systems within the pyramidal slip mode responsible for developing the most backstress among the three slip modes. The analysis also indicates that the backstress that developed in the forward loading path promotes pyramidal slip in the reversal loading path. In addition, reverse loading negligibly changes the relative slip mode contributions from monotonic loading, but it strongly affects the twinning-detwinning behavior. The novel conclusions are that pyramidal slip mode activity and detwinning and their interactions are largely responsible for the strong Bauschinger effect in CP-Ti. Second, dislocation-twin interactions in Mg-Y alloys are investigated using the VPSC model. The research is motivated by experimental tests on alloys performed elsewhere. The model is applied to understand tests in which the alloys were deformed in tension and compression in the rolling direction and in compression in the normal direction to invoke distinct proportions of slip and twin mechanisms with each test. Within the single-crystal hardening model used in VPSC polycrystal modeling, a slip-twin interaction law is introduced to account for dislocation density reductions due to dislocation absorption during twin boundary migration. To obtain a more comprehensive understanding, Mg alloys with four different Y concentrations, including Mg 0.2 wt%, Mg 0.6 wt%, Mg 1.0 wt%, and Mg 3.0 wt %, are researched. For each alloy, the model identifies a single set of material parameters that successfully reproduces all measured stress-strain curves and achieves agreement with measured deformation textures and twin area fractions. During deformation, the plastic anisotropy in yield stress, tension-compression asymmetry, and amount of {101 ̅2}⟨1 ̅011⟩ twinning is found to decrease with increasing Y. The model interpretation of the flow responses suggests that increased concentrations of Y increase the critical resolved shear stress for basal slip but have negligible effects on the other slip modes. The observed reductions in plastic anisotropy with increases in Y is explained by a concomitant decrease in the prismatic-to-pyramidal slip critical resolved shear stress ratio. The calculations suggest migrating twin boundaries in Mg–Y with different concentrations have the same dislocation absorption rate. Therefore, the chief finding identifies differences in slip strengths among the HCP slip modes as a critical link to macroscale plastic anisotropy. Finally, the EVP-FFT model was applied to research {1 ̅012} twin-twin interactions in Mg alloys. In the simulation, two non-parallel intersecting twins with the same zone axis are modeled explicitly within a grain (within a polycrystal). These two twins form a co-zone twin-twin junction structure (TTJ). The study reveals important effects the TTJ has on the growth of the impinging twin (IT) and the recipient (RT) twin, as well as the ability of the IT to apparently cross the RT. In addition, the effect of the relative twin thickness between the IT and RT on these twinning activities is investigated. These TTJ simulations are also performed on three different Mg alloys to reveal the effect of alloy additions on the local stress field produced by the TTJ. The results show that increasing the RT thickness does not affect IT growth, while increasing the IT thickness promotes the reformation of the IT on the other side of the RT, giving the appearance of twin-crossing. The latter apparent crossing is not automatic and requires additional loading to occur. Alloy additions are shown to not significantly alter twin growth mechanisms around the TTJ. However, the formation of non-co-zone twins is more likely to happen in an alloy with low plastic anisotropy.

Polycrystalline materials are characterized by complex microstructures, which present significant challenges in accurately predicting their overall properties. Among the critical factors complicating the prediction of mechanical properties is the heterogeneous nature of plastic deformation, manifested as localized slip bands in these materials. Microscopic slip within slip bands has been shown to govern macro-scale material properties, such as strength and toughness. Yet, our understanding of the spatial heterogeneity associated with slip remains surprisingly limited.

While ductility in polycrystalline materials stems from slip accumulation, localized slip is also implicated in crack initiation, propagation, and ultimate material failure. Recent experimental investigations have revealed that the observed trade-off between strength and toughness is attributed to the localized slip occurring within slip bands at the microscopic level. Over the past few decades, significant advancements in microscopy and characterization techniques have enabled researchers to capture slip bands and associated microstructural phenomena in polycrystals. However, these techniques are often expensive, challenging to interpret, and time-consuming to explore the multifaceted localization behavior under different conditions. Despite the breakthroughs in experimental capabilities, our computational capacity to model the development and implications of slip bands in polycrystalline solids have remained limited.

Motivated by recent advancements in slip band characterization and the growing demand for a numerical method to complement the experiments, this dissertation aims to develop a crystal plasticity-based computational framework to explicitly model slip bands and heterogeneous micromechanical fields associated with them. Slip bands are treated as discrete microstructural entities, enabling the computation of associated stress and strain fields. The proposed model is validated against a wide range of experimental results and subsequently applied to multiple microstructure settings to elucidate micro- and macro-scale phenomena observed in various polycrystalline materials. These phenomena include neighbor-affected slip band localization, the role of slip bands in triggering subsequent slip or twin bands or orientation deviation zones in the neighboring grain, and the link between macroscopic strength and microscopic slip in polycrystalline materials, to name a few. Explicit slip band modeling is, furthermore, combined with machine learning and data-driven approaches to design materials with superior, targeted properties, such as reduced anisotropy or strain delocalization in titanium alloys.

Integration of the framework developed here with novel experimental techniques holds immense potential to significantly advance our capabilities in predicting material properties. This transformative combination will bridge existing gaps in our understanding and enable more efficient and effective materials development, ultimately leading to improved material performance.

Advanced characterization techniques in materials science permit a greater understanding of how a material's processing history affects the microstructure of metallic alloys. With the goal of understanding how different processing and loading conditions impact the relationship between microstructure, damage, and defect evolution, an investigation on dislocation-void interactions, what defects exist in as-built materials, and how grain-level properties such as grain size and orientation affect the development of defect structures in a variety of material systems. This investigation was performed by using 3D spatially resolved orientation information obtained via TriBeam Tomography to calculate 3D spatial mappings of Geometrically Necessary Dislocations (GNDs), which are dislocations that satisfy elastic-plastic compatibility when grains within polycrystals develop lattice orientation gradients. A general approach to calculating GND densities is provided, emphasizing the ability to calculate GND densities for any crystal structure, provided proper motivation for the inclusion of specific slip systems or modes. Implementing this theory and extending it from FCC slip systems to BCC and HCP, GND density maps for IN718, AlNiCo, AM pure Ta, spalled wrought Ta, spalled Additively Manufactured (AM) Ta, and Ti7Al are investigated. AM IN718, pure Ta, and AlNiCo exhibit GND densities present in the as-built microstructures, with various subboundaries clearly present in the IN718 and pure Ta microstructures but not apparent in the AlNiCo material. GND density formation is also shown to be linked to void growth in response to shock loading for the spalled wrought Ta and spalled AM Ta samples, with grain boundary nucleation of voids preferred over nucleation of voids near high GND density subboundaries in the AM spalled Ta specimen. GND densities were also shown to accumulate in Ti7Al in response to plastic deformation, and the disparity in calculated GND densities between the differently strained samples supported the idea that microstructures experiencing greater mechanical strain have a greater amount of stored dislocations, and are important to include in forward modeling approaches. The 3D microstructures used for these GND calculations clearly provide the 3D information crucial for calculating a full Nye tensor and are necessary for full characterization of subboundaries and other subgranular features in a variety of pure metals and alloys.

A better understanding of failure mechanisms in metals allows engineers to build more reliable structural components.One such failure mechanism is ductile failure, defined by the nucleation, growth, and eventual coalescence of voids in a material.

This thesis focuses on how crystallographic orientation, as well as triaxiality, grain boundary misorientation, grain or phase boundary inclination, phase orientation relationship, and material differences between two phases affect the growth of voids in polycrystalline metals.

Void growth in face-centered cubic (FCC) and body-centered cubic (BCC) metals is studied using two crystal-plasticity (CP) fast-Fourier transform (FFT)-based models: a small-strain dilatational viscoplastic (DVP) FFT algorithm and a large-strain (LS) elasto-viscoplastic (EVP) FFT algorithm. The macroscopic response, including the growth of the void, is in good agreement between the DVP-FFT and LS-EVP-FFT algorithms.

The study begins with an investigation of the growth of intragranular voids in single-crystal and polycrystal FCC microstructures. This study indicates that the loading type plays a significant role in the relationship between the crystal orientation and void growth. In strain-rate controlled simulations, voids in the hardest [111] crystals grow the fastest in time, whereas in stress-controlled simulations, voids in the softest [100] crystal grow the fastest in time. Void growth rate increases with triaxiality, which has been widely observed in the literature. Then, intergranular voids in FCC bicrystalline and tricrystalline simulations are studied. This study indicates that the grain boundary misorientation and inclination have very little effect on the overall rate of void growth. Crystal orientation remains a strong indicator of the rate of void growth, although there are some voids at grain junctions that appear to grow faster than within any constituent single crystal. Grain boundary inclination affected how quickly the voids grew within one part of the bicrystal or tricrystal simulations because of the stress and strain rate states in which the inclination angle placed each constituent grain. Finally, the study concludes with a focus on voids at FCC/BCC phase interfaces. This study confirms that the behaviors seen in single-phase bicrystals apply in most cases to biphase interfaces, but the hardening rate difference between Cu and Ta caused the void growth to exceed the average growth rate of a void in each crystal alone. Finally, the void grew slightly faster in the BCC phase when more slip systems were available.

Hexagonal close packed HCP materials are already being widely used as structural materials in several key industries, and there is currently great interest in expanding their employment in many next-generation engineering applications. The use of HCP materials necessitates understanding and modeling their deformation response, whether in processing or in service. The plastic deformation response of materials with an HCP crystal structure is governed by the glide of dislocations on both low index and high index planes. For an HCP crystal, whether it deforms in a brittle or ductile manner depends on the relative amounts of moving dislocations contributed on these low index and high index planes. The ease of dislocation motion is largely a consequence of the characteristics of the dislocation core structure, such as number of planes on which it extends, whether it dissociates into smaller partial dislocations, its splitting distance, and the width of the individual partials. Therefore, understanding individual dislocations (at the nanoscale level) on the unique slip planes of HCP metals, sheds important insight onto the deformation of HCP materials. Isolating individual dislocations is difficult to do experimentally and is limited by length and time scales in many quantum/atomistic models. As such, we employ a phase field formulation that incorporates periodic potentials, from first principle calculations, to model individual dislocations on the distinct HCP slip planes. This work explores individual dislocations using the phase field dislocation dynamics PFDD model which had to go through several code developments to account for the lower symmetry of HCP crystallography and its unique slip plane energetics, elastic anisotropy, and thermal fluctuations. This work explores dislocation dissociation, morphology, and mobility on the basal, prismatic and pyramidal II slip planes in HCP materials, taking a special focus on the relatively unstudied pyramidal-II plane. 10 different HCP materials are modeled over the course of this work, but special attention is given to understanding dislocations in Mg for its promises in lightweighting applications, as well as Ti and Zr which are also commonly studied HCP materials. The temperature dependencies of dislocation glide are studied by the additional consideration of thermal fluctuations into the energy minimization framework of the model. Since dislocation motion is largely a consequence of the characteristics of the dislocation core structure (number of planes on which is extends, whether it dissociates into smaller partial dislocations, its splitting distance, and the width of the individual partial cores) modeling dislocation dynamics in HCP requires a model that is capable of capturing these characteristics of dislocation core structure. Previously, the PFDD model was written for the symmetry of cubic crystal structures and had only been applied to face-centered cubic FCC materials. So for our work, the PFDD model is first extended to determine the static and dynamic properties of discrete dislocations belonging to all types of slip modes in the HCP crystal, such as the basal ⟨a⟩, prismatic ⟨a⟩, and pyramidal II ⟨c + a⟩ slip modes [1]. This is the first time a phase-field based dislocation dynamics model has been used to model HCP materials, so we look at equilibrium dislocation cores and dislocation dissociation under no stress so we can compare our results with results from other atomistic models and experiments for validation. The dissociation simulations using the HCP capable PFDD method incorporate directly density functional theory DFT-calculated generalized stacking fault energy GSFE surfaces and curves for the different HCP slip planes and employ isotropic elasticity. The results demonstrated good agreement with available results from molecular statics MS, DFT, or experimental observations of dislocations structures in Mg. We move forward into a deeper exploration of the pyramidal II plane, on which dislocation behavior remains elusive and the resulting material effects are unknown. We employ an elastically anisotropic version of the PFDD approach, to compute the equilibrium core structures of pyramidal-II ⟨c + a⟩ dislocations under zero externally applied stress conditions in ten HCP metals: Be, Co, Mg, Re, Ti, Zn, Cd, Hf, Y, and Zr. In all these metals, under zero applied stress, the initialized perfect ⟨c + a⟩ pyramidal dislocations dissociate into two partials that separate in plane, creating extended structures, with nanometer-sized splitting distances referred to as equilibrium stacking fault widths eSFW (that is the fully relaxed or equilibrated distance between partials under zero external applied stress). The eSFWs for these 10 metals scales inversely with their normalized intrinsic stacking fault energy I from their GSFE curves. In most cases, the dislocation partial core widths and Burgers vectors are not ideally equal. These asymmetries in the dislocation structures are explained by deviations in the pyramidal II GSFE landscape from that expected of a metal with an ideal c/a ratio and symmetric landscape. Metals with higher levels of elastic anisotropy have wider separation distances (20–35%) for both screw and edge character dislocations than what would be expected with effective isotropic constants. The discovery of the asymmetric dislocation cores on the pyramidal II plane prompted the following question: will the same energetics that result in asymmetric dislocation cores, also gives rise to asymmetric dislocation slip? We then applied an external shear stress that initiates dislocation glide along the slip plane of interest and note any changes in the splitting distances of the partial dislocations as they glide in tandem. If the partial dislocations and associated stacking fault glide while maintaining a consistent splitting distance between the two partial dislocations, we refer to this as the dynamic stacking fault width dSFW. We find glissile dislocations on the pyramidal II plane have dSFW that are directionally dependent. That is to say, if we apply a shear stress to initiate glide along one direction the measured dSFW differs from the dSFW measured when we apply a shear stress to induce glide in the opposite direction.The directional dependency of the dSFW is due to the asymmetries in GSFE curves and the decomposition of the Burgers vector for each partial dislocation. We explore this further by using a Frank-Read FR source to generate expanding dislocation loops. We calculate the critical shear stress σc for loop expansion for each FR source. We consider both screw and edge type initial dislocations in a FR source of different lengths on the basal and the pyramidal II plane and find the loop shape is dominated by screw type sections to minimize the line tension energy of the expanding loop. We also note large variations in the stacking faults throughout the FR loop expansion until the loop had expanded beyond its critical shape and a steady-state dSFW was reached. The evolution of the stacking faults during the FR dislocation loop expansion is due to the different energetic barriers to glide that governs each partial dislocation. Directional dependency is also noticed for the FR source simulations of the pyramidal II plane, as the energetic barriers (e.g. from the asymmetric GSFE profile) associated with the leading and the trailing partial are ”assigned” based on the directionality of the applied shear stress. All of the simulations up to now are deterministic and carried out under an assumed temperature of 0K. However, the pyramidal planes are suspected to be temperature dependent more so than the other slip planes and many material processes and applications occur at or above room temperature. So in order to truly understand pyramidal II dislocation behavior we need to explore the temperature dependency of pyramidal slip. This necessitates the extension of the PFDD formulation to account for thermal activation. In our final PFDD development we derive the Langevin force equations for the phase field framework to account for thermal fluctuations at variable temperatures. This produces a stochastic thermal noise term that we can add to the energy minimization equation in the PFDD model. This advanced PFDD model with thermal capabilities is then used to explore how temperature affects the time to dislocation loop formation from a Frank-Read FR source. We study Mg, Ti, and Zr over various temperatures T ranging from 0 ≤ T /Tm ≤ 0.5, where Tm is the melting temperature for each material. We also look at the velocity of infinitely long screw and edge type dislocations as they glide under the same shear stress we apply in the FR simulations. We find the leading partial for the screw dislocation ”breaks away” at a greater velocity than the trailing partial at higher temperatures T /Tm > 0.2 creating a continuously growing stacking fault. We find that when we decrease the applied shear stress the leading screw partial does not breakaway at higher temperatures. This breakaway is not observed for the temperatures and stresses applied to edge dislocations. In the FR source simulations this results in the screw portions ”smearing” out at higher temperatures. This breakaway phenomenon observed on the pyramidal II plane is both dislocation character type, stress and temperature dependent.

The impact of voids on structural metal performance has been investigated in the context of two case studies: nanovoids as strengtheners in irradiated materials, and void growth size effects during ductile failure.

Nanovoid Strengthening: When nanoscale in diameter, voids can act as obstacles to dislocation motion, resulting in strengthening reminiscent of precipitation hardening. This is especially relevant to irradiated metals in applications such as nuclear power plants. Local regions of very highly concentrated nanovoid defect clusters within irradiated metals are observed to cause material strengthening, meaning bulk yielding behavior is altered from what is expected in the original material design. However, it is not yet possible to reliably predict the consequence of nanovoids in metals with existing models, as they are not informed by the fundamental mechanisms behind this response. To address this, the meso-scale simulation technique Phase Field Dislocation Dynamics (PFDD) is applied to the problem in Chapter 2. This technique is an energetic framework within which rigorous discrete dislocation physics is applied, and which allows for larger simulation cell sizes than are commonly available to lower-length-scale methods.

Surprisingly, the critical stress is found to scale linearly with the ratio of the intrinsic to unstable stacking fault energies, and to scale directly with the linear void fraction. This novel empirical strengthening model is named the Linear Fraction (LF) Model, and is thought to be driven by the dynamic constriction and extension of the stacking fault width as the two dissociated partials of an fcc dislocation bow around a nanovoid obtacle. This deviates from the expected line-tension-approximation mechanism due to bowing around an obstacle, which has until now been used to inform analytical predictive models. Remarkably, this new strengthening trend holds for the vast majority of fcc metals and void size arrays tested, and in Chapter 3 it is discovered to fit compellingly with a number of MD studies as well as for nano-precipitates in PFDD. The boundaries of when the LF model will apply to nano-obstacle strengthening has only briefly been investigated, and the extent to which PFDD results will agree with other atomistic techniques such as MD is still an open question. With this in mind, a number of future work directions are discussed in Chapter 5, Sections 5.1 and 5.2.

Meso-Scale Void Growth: Voids are present in more than just irradiated structural metals, and evidence exists that nanovoids can also be found in large quantities during plastic deformation. While some of these may strengthen at the nanoscale, some may also grow during plastic deformation. It is still an open question which voids will grow and which will not, but growth into the hundreds of nanometers and beyond increase the likelihood that the presence of these voids will degrade the structural performance of the metal and possibly lead to part failure. Given the severity of the consequences, an understanding of this void growth behavior is of significant interest. A novel in-situ testing method is discussed next in Chapter 4, which was designed to target a specific gap in experimental void growth evidence at these lower, transitional length scales.

The design of this experiment was meant to be as versatile as possible while also providing as much control as possible over material, void size, void-void interactions, and void/grain size interactions. Two primary goals of this approach were to 1) directly observe the evolution of voids at length scales below what has been achieved in literature, and 2) to fabricate these intentional void defects within tensile specimen without the use of FIB which is known to damage film surfaces. For these goals moderate success was achieved, and this technique was deployed for the problem of void growth size effects at sub-micron void sizes. Existing literature on fundamental size effects are limited to computational theories for very simplified model systems. When applied to the two defected specimen for this work, the fundamental size effect theories proved elusive because of the dominance of a third size effect consideration: the ratio of the void size to the thin film grain size. As such, promising future work avenues to push the boundaries of what is currently known experimentally for void growth are provided in Chapter 5, Section 5.3.