<div>The service life of aircraft structure, primarily composed of aluminum alloys, is markedly lower when galvanic corrosion is present due to early crack initiation at localized pitting, with the likelihood of cracking being higher at pits spanning several microns. To understand the joint effect that the mechanical and chemical behavior of AA7050-T7451 have on the evolution of corrosion prior and until its transition to cracking, the microstructure, constituent particles, mechanical strains, and the corrosion morphology were experimentally characterized using high-resolution methods and the mechanical stresses are computationally modeled at the micrometer level using a FFT-based crystal plasticity framework. </div><div><br></div><div>The material was corroded under both mechanically loaded and unloaded conditions under different corrosion intervals to properly capture the evolution of corrosion before, during, and after particle fallout. For the events prior to cracking, statistical cross-correlations between the mechanical state of the material and the corrosion morphology were performed to understand the mechanisms driving corrosion at its various stages. For the cracking event and its subsequent growth, the joint analysis of strains and stresses obtained from 3D crystal plasticity models were used to calculate Fatigue Indicator Parameters (FIPs) that can quantitatively give an insight of the major mechanisms driving crack initiation and growth in pre-corroded materials. The development of micromechanical models that account for both the environmental degradation and the microstructure in the material allowed to accurately predict the location of crack initiation arising from pits, which has been a longstanding problem in the field of corrosion. It is concluded that both corrosion growth and its transition to cracking are multivariable events, where corrosion growth is jointly driven by the local chemistry and the micromechanics, and crack initiation is driven by the coupled interaction between the corrosion geometry and the micromechanics.</div><div><br></div>

La compréhension des mécanismes de déformation dans les matériaux polycristallins est un problème important, qui conditionne notre capacité à concevoir et à produire des pièces de structure plus sures et avec un impact environnemental moindre. Cette compréhension est aujourd'hui limitée par notre capacité à observer à la fois la microstructure du matériau et ses mécanismes de déformation en trois dimensions (3D) aux petites échelles, et à informer les simulations mécaniques à partir des mécanismes physique de déformations du réseau cristallin. Des progrès considérables ont été faits dans les dernières décennies avec les observations de surfaces (i.e. technique EBSD associée a de la corrélation d’image) qui a permis de nombreuses études combinant des observations expérimentales à des simulations, à partir de la surface de la microstructure. Cependant, une comparaison précise sans connaitre la microstructure sous-jacente reste un défi. Dans ce travail, nous proposons une nouvelle méthodologie basée d'une part sur des mesures couplant la tomographie et la diffraction des rayons X, et d'autre part sur des simulations mécaniques de platicité cristalline. Cette approche permet une comparaison quantitative en volume entre les mécanismes de déformation, l’évolution de la courbure du réseau cristallin et les champs mécaniques simulés.Pour ce faire, une machine de traction dédiée aux expériences 4D d’imagerie par diffraction sur grands instruments a été conçue, et utilisée pour déformer en tension un échantillon d’Aluminium Lithium. La cartographie 3D de la microstructure a été obtenue par tomographie par contraste de diffraction, et un agrégat de trois grains dans le volume de l’échantillon a été choisi comme région d’intérêt pour des observation 4D par topotomographie. L’apparition des premières bandes de glissement en volume et leur évolution au cours du chargement ont été observées le long de plans cristallographiques bien définis. Les trois grains ont montré une activité plastique le long de deux familles de plans différents, pas toujours en accord avec une analyse macroscopique du facteur de Schmid, ce qui est attribué à l'influence du voisinage sur l'activation des systèmes de glissement. Les changements d’amplitude et d’orientation de la courbure moyenne des grains ont été mesures avec un niveau de détail sans précédent, par une analyse tridimensionnelle des courbes de reflexions.En parallèle, des simulations de la plasticité cristalline par éléments finis (CPFE) ont été menées utilisant la cartographie tridimensionnelle de la microstructure mesurée expérimentalement. Un chargement uniaxial de traction a été applique pour reproduire numériquement l’expérience, et comparer grain par grain l’activité plastique. L’activité des systèmes de glissement prédite par le modèle est conforme aux observations expérimentales d’une activité plastique le long de deux plans. Un cadre mathématique pour prédire l’angle de Bragg local en fonction des déformations et des rotations du réseau cristallin a été formulé. Un post-traitement des champs intragranulaires de déformation à partir des résultats des simulations CPFE a montré une excellente concordance avec les résultats expérimentaux. Ce résultat confirme que la topotomographie in-situ aux rayons X est un outil prometteur pour l’étude des premiers stades de la plasticité cristalline en volume. / Understanding the intimate details of plastic deformation in polycrystalline materials is an important issue to improve material design and ultimately produce safer structural parts with less impact on the environment. This understanding is presently limited by our ability to observe both the microstructure of the material and the deformation processes in three dimensions (3D) at small length scales and inform mechanical simulations with physical deformation mechanisms of the crystal lattice. Considerable progress has been made in the last decade with surface observation (eg EBSD coupled to digital image correlation) which led to numerous studies combining experimental observations and simulations from the surface microstructure. However, an accurate comparison without knowing the underlying microstructure remain challenging. In this work, we propose a new methodology which allows a quantitative comparison between the observation of deformation mechanisms, the evolution of the grain lattice curvature and the simulated mechanical fields.For that purpose, a mechanical stress rig dedicated for synchrotron 4D diffraction imaging experiments has been designed, and used to deform an Aluminium-Lithium specimen under tension. The 3D grain map has been obtained by diffraction contrast tomography analysis, and a cluster of three grains within the bulk has been selected to be the region of interest of the 4D observation by X-ray topotomography. The appearance and evolution of 3D crystalline defects as a function of the applied load has been observed to be located along well defined crystallographic planes. All three grains showed plastic activity on along two different set of planes, which is not always coherent with a macroscopic Schmid Factor analysis. The change of the amplitude and the orientation of the average grain curvature has been measured with an unprecedented level of detail by means of 3D rocking curve analysis.In parallel, crystal plasticity finite element (CPFE) simulations have been carried using the 3D grain map measured experimentally. Tension loading was applied to reproduce the experiment numerically and compare the plastic activity on a grain by grain basis. The slip system activity predicted by the model matches in most cases the observed two slip system scenario. A mathematical framework to predict the local Bragg angle based on the stretch and rotation of the crystal lattice by the elastic strain tensor was derived. Post-processing the intragranular strains fields from the CPFE results allowed to simulate 3D rocking curves, showing excellent agreement with the experimental measurements. This result confirms that in situ X-ray topotomography is a promising tool to study the early stage of polycrystal plasticity within the bulk of millimetric material specimens.

<p>This report is a review on aspects of constitutive modelling of high strength steels. Aspects that have been presented are basic crystallography of steel, martensite transformation, thermodynamics and plasticity from a phenomenological point of view. The phenomenon called mechanical twinning is reviewed and the properties of a new material type called TWIP-steel have been briefly presented. Focus has been given on phenomenological models and methods, but an overview over multiscale methods has also been given.</p>

This report is a review on aspects of constitutive modelling of high strength steels. Aspects that have been presented are basic crystallography of steel, martensite transformation, thermodynamics and plasticity from a phenomenological point of view. The phenomenon called mechanical twinning is reviewed and the properties of a new material type called TWIP-steel have been briefly presented. Focus has been given on phenomenological models and methods, but an overview over multiscale methods has also been given.

Magnesium, with a Hexagonal Close-Packed (HCP) structure, is the eighth most abundant element in the earth’s crust and the third most plentiful element dissolved in the seawater. Magnesium alloys exhibit the attractive characteristics of low densities and high strength-to-weight ratios along with good castability, recyclability, and machinability. Replacing the steel and/or aluminum sheet parts with magnesium sheet parts in vehicles is a great way of reducing the vehicles weight, which results in great savings on fuel consumption. The lack of magnesium sheet components in vehicle assemblies is due to magnesium’s poor room-temperature formability. In order to successfully form the sheets of magnesium at room temperature, it is necessary to understand the formability of magnesium at room temperature controlled by various plastic deformation mechanisms. The plastic deformation mechanisms in pure magnesium and some of its alloys at room temperature are crystallographic slip and deformation twinning. The slip systems in magnesium at room temperature are classified into primary (first generation), secondary (second generation), and tertiary (third generation) slip systems. The twinning systems in magnesium at room temperature are classified into primary (first generation) and secondary (second generation, or double) twinning systems. A new comprehensive rate-dependent elastic-viscoplastic Crystal Plasticity Constitutive Model (CPCM) that accounts for all these plastic deformation mechanisms in magnesium was proposed. The proposed model individually simulates slip-induced shear in the parent as well as in the primary and secondary twinned regions, and twinning-induced shear in the primary and secondary twinned regions. The model also tracks the texture evolution in the parent, primary and secondary twinned regions. Separate resistance evolution functions for the primary, secondary, and tertiary slip systems, as well as primary and secondary twinning systems were considered in the formulation. In the resistance evolution functions, the interactions between various slip and twinning systems were accounted for. The CPCM was calibrated using the experimental data reported in the literature for pure magnesium single crystals at room temperature, but needs further experimental data for full calibration. The partially calibrated model was used to assess the contributions of various plastic deformation mechanisms in the material stress-strain response. The results showed that neglecting secondary slip and secondary twinning while simulating plastic deformation of magnesium alloys by crystal plasticity approach can lead to erroneous results. This indicates that all the plastic deformation mechanisms have to be accounted for when modelling the plastic deformation in magnesium alloys. Also, the CPCM in conjunction with the Marciniak–Kuczynski (M–K) framework were used to assess the formability of a magnesium single crystal sheet at room temperature by predicting the Forming Limit Diagrams (FLDs). Sheet necking was initiated from an initial imperfection in terms of a narrow band. A homogeneous deformation field was assumed inside and outside the band, and conditions of compatibility and equilibrium were enforced across the band interfaces. Thus, the CPCM only needs to be applied to two regions, one inside and one outside the band. The FLDs were simulated under two conditions: a) the plastic deformation mechanisms are primary slip systems alone, and b) the plastic deformation mechanisms are primary slip and primary twinning systems. The FLDs were computed for two grain orientations. In the first orientation, primary extension twinning systems had favourable orientation for activation. In the second orientation, primary contraction twinning systems had favourable orientation for activation. The effects of shear strain outside the necking band, rate sensitivity, and c/a ratio on the simulated FLDs in the two grain orientations were individually explored.

The goal of this research work is to further the understanding of crystal plasticity, particularly at reduced structural and material length scales. Fundamental understanding of plasticity is central to various challenges facing design and manufacturing of materials for structural and electronic device applications. The development of microstructurally tailored advanced metallic materials with enhanced mechanical properties that can withstand extremes in stress, strain, and temperature, will aid in increasing the efficiency of power generating systems by allowing them to work at higher temperatures and pressures. High specific strength materials can lead to low fuel consumption in transport vehicles. Experiments have shown that enhanced mechanical properties can be obtained in materials by constraining their size, microstructure (e.g. grain size), or both for various applications. For the successful design of these materials, it is necessary to have a thorough understanding of the influence of different length scales and evolving microstructure on the overall behavior. In this study, distinction is made between the effect of structural and material length scale on the mechanical behavior of materials. A length scale associated with an underlying physical mechanism influencing the mechanical behavior can overlap with either structural length scales or material length scales. If it overlaps with structural length scales, then the material is said to be dimensionally constrained. On the other hand, if it overlaps with material length scales, for example grain size, then the material is said to be microstructurally constrained. The objectives of this research work are: (1) to investigate scale and size effects due to dimensional constraints; (2) to investigate size effects due to microstructural constraints; and (3) to develop a size dependent hardening model through coarse graining of dislocation dynamics. A discrete dislocation dynamics (DDD) framework where the scale of analysis is intermediate between a fully discretized (e.g. atomistic) and fully continuum is used for this study. This mesoscale tool allows to address all the stated objectives of this study within a single framework. Within this framework, the effect of structural and the material length scales are naturally accounted for in the simulations and need not be specified in an ad hoc manner, as in some continuum models. It holds the promise of connecting the evolution of the defect microstructure to the effective response of the crystal. Further, it provides useful information to develop physically motivated continuum models to model size effects in materials. The contributions of this study are: (a) provides a new interpretation of mechanical size effect due to only dimensional constraint using DDD; (b) a development of an experimentally validated DDD simulation methodology to model Cu micropillars; (c) a coarse graining technique using DDD to develop a phenomenological model to capture size effect on strain hardening; and (d) a development of a DDD framework for polycrystals to investigate grain size effect on yield strength and strain hardening.

The objective of this dissertation is to further the understanding of inelastic behavior in metallic materials. Despite the increasing use of polymeric composites in aircraft structures, high specific strength metals continue to be used in key components such as airframe, fuselage, wings, landing gear and hot engine parts. Design of metallic structures subjected to thermomechanical extremes in aerospace, automotive and nuclear applications requires consideration of the plasticity, creep and fracture behavior of these materials. Consideration of inelasticity and damage processes is also important in the design of metallic components used in functional applications such as thin films, flexible electronics and micro electro mechanical systems. Fracture mechanics has been largely successful in modeling damage and failure phenomena in a host of engineering materials. In the context of ductile metals, the Gurson void growth model remains one of the most successful and widely used models. However, some well documented limitations of the model in quantitative prediction of the fracture strains and failure modes at low triaxialities may be traceable to the limited representation of the damage microstructure in the model. In the first part of this dissertation, we develop an extended continuum model of void growth that takes into account details of the material microstructure such as the texture of the plastically deforming matrix and the evolution of the void shape. The need for such an extension is motivated by a detailed investigation of the effects of the two types of anisotropy on the materials' effective response using finite element analysis. The model is derived using the Hill-Mandel homogenization theory and an approximate limit analysis of a porous representative volume element. Comparisons with several numerical studies are presented towards a partial validation of the analytical model. Inelastic phenomena such as plasticity and creep result from the collective behavior of a large number of nano and micro scale defects such as dislocations, vacancies and grain boundaries. Continuum models relate macroscopically observable quantities such as stress and strain by coarse graining the discrete defect microstructure. While continuum models provide a good approximation for the effective behavior of bulk materials, several deviations have been observed in experiments at small scales such as an intrinsic size dependence of the material strength. Discrete dislocation dynamics (DD) is a mesoscale method for obtaining the mechanical response of a material by direct simulation of the motion and interactions of dislocations. The model incorporates an intrinsic length scale in the dislocation Burgers vector and potentially allows for size dependent mechanical behavior to emerge naturally from the dynamics of the dislocation ensemble. In the second part of this dissertation, a simplified two dimensional DD model is employed to study several phenomena of practical interest such as strain hardening under homogeneous deformation, growth of microvoids in a crystalline matrix and creep of single crystals at elevated temperatures. These studies have been enabled by several recent enhancements to the existing two-dimensional DD framework described in Chapter V. The main contributions from this research are: (i) development of a fully anisotropic continuum model of void growth for use in ductile fracture simulations and (ii) enhancing the capabilities of an existing two-dimensional DD framework for large scale simulations in complex domains and at elevated temperatures.

Magnesium, with a Hexagonal Close-Packed (HCP) structure, is the eighth most abundant element in the earth’s crust and the third most plentiful element dissolved in the seawater. Magnesium alloys exhibit the attractive characteristics of low densities and high strength-to-weight ratios along with good castability, recyclability, and machinability. Replacing the steel and/or aluminum sheet parts with magnesium sheet parts in vehicles is a great way of reducing the vehicles weight, which results in great savings on fuel consumption. The lack of magnesium sheet components in vehicle assemblies is due to magnesium’s poor room-temperature formability. In order to successfully form the sheets of magnesium at room temperature, it is necessary to understand the formability of magnesium at room temperature controlled by various plastic deformation mechanisms. The plastic deformation mechanisms in pure magnesium and some of its alloys at room temperature are crystallographic slip and deformation twinning. The slip systems in magnesium at room temperature are classified into primary (first generation), secondary (second generation), and tertiary (third generation) slip systems. The twinning systems in magnesium at room temperature are classified into primary (first generation) and secondary (second generation, or double) twinning systems. A new comprehensive rate-dependent elastic-viscoplastic Crystal Plasticity Constitutive Model (CPCM) that accounts for all these plastic deformation mechanisms in magnesium was proposed. The proposed model individually simulates slip-induced shear in the parent as well as in the primary and secondary twinned regions, and twinning-induced shear in the primary and secondary twinned regions. The model also tracks the texture evolution in the parent, primary and secondary twinned regions. Separate resistance evolution functions for the primary, secondary, and tertiary slip systems, as well as primary and secondary twinning systems were considered in the formulation. In the resistance evolution functions, the interactions between various slip and twinning systems were accounted for. The CPCM was calibrated using the experimental data reported in the literature for pure magnesium single crystals at room temperature, but needs further experimental data for full calibration. The partially calibrated model was used to assess the contributions of various plastic deformation mechanisms in the material stress-strain response. The results showed that neglecting secondary slip and secondary twinning while simulating plastic deformation of magnesium alloys by crystal plasticity approach can lead to erroneous results. This indicates that all the plastic deformation mechanisms have to be accounted for when modelling the plastic deformation in magnesium alloys. Also, the CPCM in conjunction with the Marciniak–Kuczynski (M–K) framework were used to assess the formability of a magnesium single crystal sheet at room temperature by predicting the Forming Limit Diagrams (FLDs). Sheet necking was initiated from an initial imperfection in terms of a narrow band. A homogeneous deformation field was assumed inside and outside the band, and conditions of compatibility and equilibrium were enforced across the band interfaces. Thus, the CPCM only needs to be applied to two regions, one inside and one outside the band. The FLDs were simulated under two conditions: a) the plastic deformation mechanisms are primary slip systems alone, and b) the plastic deformation mechanisms are primary slip and primary twinning systems. The FLDs were computed for two grain orientations. In the first orientation, primary extension twinning systems had favourable orientation for activation. In the second orientation, primary contraction twinning systems had favourable orientation for activation. The effects of shear strain outside the necking band, rate sensitivity, and c/a ratio on the simulated FLDs in the two grain orientations were individually explored.

This thesis examines the qualitative and quantitative variation in local plastic deformation and surface roughening due to crystallographic texture in body-centered cubic materials, specifically interstitial-free steel sheet and molybdenum foil and sheet. Complex forming operations currently used in industrial manufacturing lead to high material failure rates, due in part to the severity of the applied strain path. A multi-scale model was developed to examine the contribution of mesoscopic and local microscopic behaviour to the macroscopic constitutive response of bcc metals during deformation. The model integrated a dislocation-based hardening scheme and a Taylor-based crystal-plasticity formulation into the subroutine of an explicit dynamic FEM code, LS-DYNA. Numerical analyses using this model were able to predict not only correct grain rotation during deformation, but variations in plastic anisotropy due to initial crystallographic orientation. Simulations of molybdenum foil under uniaxial tension supported the existence of bending due to local variations in plastic anisotropy, confirmed with good quantitative agreement by experimental measurements of surface roughening. A series of two-stage strain-path tests were performed, revealing a prestrain-dependent softening of both the steel and molybdenum samples when an orthogonal secondary strain path is applied. Numerical analyses of these tests overestimate macroscopic hardening during complex loading, due in part to the dynamic nature of the FEM code used. / Thesis (Ph.D, Mechanical and Materials Engineering) -- Queen's University, 2009-04-15 11:51:04.518

Zirconium and its alloys have been extensively used in both heavy and light water nuclear reactors. Like other Hexagonal Close-Packed (HCP) materials, e.g. magnesium, zirconium alloys develop different textures during manufacturing process which result in highly anisotropic materials with different responses under different loading conditions. Slip and twinning are two major deformation mechanisms during plastic deformation of zirconium. This dissertation uses various experimental techniques and a crystal plasticity scheme in the finite element framework to study deformation mechanisms in HCP materials with an emphasis on twinning in Zircaloy-2. The current study is presented as a manuscript format dissertation comprised of four manuscript chapters. After a literature review in Chapter 2, Chapter 3 reports steps in developing a crystal plasticity finite element user material subroutine for modeling deformation in Zircaloy-2 at room temperature. It is shown in Chapter 3 that the developed rate dependent equations are capable of capturing evolution of key features, e.g., texture, lattice strains, and twin volume fractions, during deformation by twinning and slip. Chapter 4 reports various assumptions and approaches in modeling twinning where results are compared against neutron diffraction measurements from the literature. It is shown in Chapter 4 that the predominant twin reorientation scheme can explain texture development more precisely than the other schemes discussed. Chapter 5 and 6 are two connected chapters where in the first one the formation of twins is studied statistically and in the second one, local inception and propagation of twins is studied. Numerical results of these two chapters are compared with 2D electron backscattered diffraction measurements, both carried out by the author and from the literature. Results from these two connected chapters emphasize the important role of grain boundary geometry and stress concentration sites on twin nucleation and growth. The four manuscript chapters are followed by summarizing conclusions and suggestions for future work in Chapter 7. / Thesis (Ph.D, Mechanical and Materials Engineering) -- Queen's University, 2012-04-23 11:50:33.751