A systematic investigation is presented into the microstructural and micromechanical influences on ductile damage nucleation with an emphasis on grain boundaries in polycrystals. Microstructures obtained from experiments on copper polycrystals are characterized using Electron Backscatter Diffraction (EBSD) and near-field High-Energy Diffraction Microscopy (nf-HEDM) and the occurrence of damage is compared with micromechanical values obtained using an elasto-viscoplastic model based on the Fast- Fourier Transform (EVPFFT). The model produces full-field solutions for the stress and strain in voxelized polycrystalline microstructures. In order to resolve the fields onto interfaces, local Cartesian moments of the polycrystalline grain structure are used to extract the normals of grain boundaries and the tangents of triple junctions directly from the voxelized microstructure. Thus projecting the stress yields a parameter with potential significance, i.e. the grain boundary surface tractions. We identify “traction hotspots”, i.e. regions with tractions that are significantly above the mean, for the case of uniaxial tension. These show correlations with the angle between the grain boundary normal and the loading axis, a trend that some experiments also show when boundaries that nucleated voids are analyzed using EBSD, though differences present between the simulation and experiment hint that further criteria are needed. Nf-HEDM was used to record microstructure images of a polycrystalline sample before and after it undergoes damage. The damage locations in the post-shocked image are mapped onto the pre-shocked image, allowing stress and strain values from the EVPFFT model in the regions that eventually nucleated damage to be correlated with the locations of the void. The unexpected result was that differences in plastic work across boundaries correlated with voids, whereas vi quantities such as triaxiality and normal forces across boundaries did not.

Partial differential equations having diffusive, convective and reactive terms appear naturally in the modeling of a large variety of processes of practical interest in several branches of science such as biology, chemistry, economics, physics, physiology and materials science. Moreover, in some instances several species or components interact with each other requiring to solve strongly coupled systems of convection-diffusion-reaction equations. Of special interest for us is the numerical treatment of the advection dominated continuum dislocation transport equations used to describe the plastic behavior of crystalline materials.Analytical solutions for such equations are extremely scarce and practically limited to linear equations with homogeneous coefficients and simple initial and boundary conditions. Therefore, resorting to numerical approximations is the most affordable and often the only viable strategy to deal with such models. However, when classical numerical methods are used to approximate the solutions of such equations, even in the simplest one dimensional case in the steady state regime for a single equation, instabilities in the form of node to node spurious oscillations are found when the convective or reactive terms dominate over the diffusive term.To address such issues, stabilization techniques have been developed over the years in order to handle such transport equations by numerical means, overcoming the stability difficulties. However, such stabilization techniques are most often suited for particular problems. For instance the Streamline Upwind Petrov-Galerkin method, to name only one of the most well-known, successfully eliminates spurious oscillations for single advection-diffusion equations when its advective form is discretized, but have been shown useless if the divergence form is used instead. Additionally, no extensive work has been carried out for systems of coupled equations. The reason for this immaturity is the lack of a maximum principle when going from a single transport equation towards systems of coupled equations.The main aim of this work is to present a stabilization technique for systems of coupled multidimensional convection-diffusion-reaction equations based on coefficient perturbations. These perturbations are optimally chosen in such a way that certain compatibility conditions analogous to a maximum principle are satisfied. Once the computed perturbations are injected in the classical Bubnov-Galerkin finite element method, they provide smooth and stable numerical approximations.Such a stabilization technique is first developed for the single one-dimensional convection-diffusion-reaction equation. Rigorous proof of its effectiveness in rendering unconditionally stable numerical approximations with respect to the space discretization is provided for the convection-diffusion case via the fulfillment of the discrete maximum principle. It is also demonstrated and confirmed by numerical assessments that the stabilized solution is consistent with the discretized partial differential equation, since it converges to the classical Bubnov-Galerkin solution if the mesh Peclet number is small enough. The corresponding proofs for the diffusion-reaction and the general convection-diffusion-reaction cases can be obtained in a similar manner. Furthermore, it is demonstrated that this stabilization technique is applicable irrespective of whether the advective or the divergence form is used for the spatial discretization, making it highly flexible and general. Subsequently the stabilization technique is extended to the one-dimensional multiple equations case by using the superposition principle, a well-known strategy used when solving non-homogeneous second order ordinary differential equations. Finally, the stabilization technique is applied to mutually perpendicular spatial dimensions in order to deal with multidimensional problems.Applications to several prototypical linear coupled systems of partial differential equations, of interest in several scientific disciplines, are presented. Subsequently the stabilization technique is applied to the continuum dislocation transport equations, involving their non-linearity, their strongly coupled character and the special boundary conditions used in this context; a combination of additional difficulties which most traditional stabilization techniques are unable to deal with. The proposed stabilization scheme has been successfully applied to these equations. Its effectiveness in stabilizing the classical Bubnov-Galerkin scheme and being consistent with the discretized partial differential equation are both demonstrated in the numerical simulations performed. Such effectiveness remains unaffected when different types of dislocation transport models with constant or variable length scales are used.These results allow envisioning the use of the developed technique for simulating systems of strongly coupled convection-diffusion-reaction equations with an affordable computational effort. In particular, the above mentioned crystal plasticity models can now be handled with reasonable computation times without the use of extraordinary computational power, but still being able to render accurate and physically meaningful numerical approximations. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

A machining process is one of the most common techniques used to remove material in order to create a final product. Most studies on mechanisms of cutting are performed under the assumption that the studied material is isotropic, homogeneous and continuous. One important feature of material- its anisotropyis linked to its crystallographic nature, which is usually ignored in machining studies. A crystallographic orientation of a workpiece material exerts a great influence on the chip-formation mechanism. Thus, there is a need for developing fundamental understanding of material's behaviour and material removal processes. While the effect of crystallographic orientation on cutting-force variation is extensively reported in the literature, the development of the single crystal machining models is somewhat limited.

abstract: Shock loading is a complex phenomenon that can lead to failure mechanisms such as strain localization, void nucleation and growth, and eventually spall fracture. Studying incipient stages of spall damage is of paramount importance to accurately determine initiation sites in the material microstructure where damage will nucleate and grow and to formulate continuum models that account for the variability of the damage process due to microstructural heterogeneity. The length scale of damage with respect to that of the surrounding microstructure has proven to be a key aspect in determining sites of failure initiation. Correlations have been found between the damage sites and the surrounding microstructure to determine the preferred sites of spall damage, since it tends to localize at and around the regions of intrinsic defects such as grain boundaries and triple points. However, considerable amount of work still has to be done in this regard to determine the physics driving the damage at these intrinsic weak sites in the microstructure. The main focus of this research work is to understand the physical mechanisms behind the damage localization at these preferred sites. A crystal plasticity constitutive model is implemented with different damage criteria to study the effects of stress concentration and strain localization at the grain boundaries. A cohesive zone modeling technique is used to include the intrinsic strength of the grain boundaries in the simulations. The constitutive model is verified using single elements tests, calibrated using single crystal impact experiments and validated using bicrystal and multicrystal impact experiments. The results indicate that strain localization is the predominant driving force for damage initiation and evolution. The microstructural effects on theses damage sites are studied to attribute the extent of damage to microstructural features such as grain orientation, misorientation, Taylor factor and the grain boundary planes. The finite element simulations show good correlation with the experimental results and can be used as the preliminary step in developing accurate probabilistic models for damage nucleation. / Dissertation/Thesis / Ph.D. Mechanical Engineering 2013

This work explores the processing-microstructure-property relationships in two-phase titanium alloys such as Ti-6Al-4V and Ti-5Al-5V-5Mo-3Cr that are used for aerospace applications. For this purpose, an Integrated Computational Materials Engineering approach is used. Microstructure and texture of titanium alloys are characterized using optical microscopy, electron backscatter diffraction and x-ray diffraction. To model their properties, threedimensional synthetic digital microstructures are generated based on experimental characterization data. An open source software package, DREAM.3D, is used to create heterogeneous two-phase microstructures that are statistically representative of two-phase titanium alloys. Both mean-field and full-field crystal plasticity models are used for simulating uniaxial compression at different loading conditions. A viscoplastic self-consistent model is used to match the stress-strain response of the Ti-5553 alloy based on uniaxial compression tests. A physically-based Mechanical Threshold Stress (MTS) model is designed to cover wide ranges of deformation conditions. Uncertainties in the parameters of the MTS model are quantified using canonical correlation analysis, a multivariate global sensitivity analysis technique. An elastoviscoplastic full-field model based on the fast Fourier transform algorithm was used to used to simulate the deformation response at both microscopic and continuum level. The probability distribution of stresses and strains for both the phases in the two-phase material is examined statistically. The effect of changing HCP phase volume fraction and morphology has been explored with the intent of explaining the ow softening behavior in titanium alloys.

Aircraft engine components can be subjected to a large number of thermo-mechanical loading cycles and to long dwell times at high temperatures. In particular, the understanding of creep in single crystal superalloy turbine blades is of importance for designing more reliable and fuel efficient aircraft engines. Creep tests on single crystal superalloy specimens have shown greater creep strain rates for thinner specimens than predicted by current theories. Therefore, it is necessary to develop a more predictive description of creep processes in these materials for them to be used effectively. Experimental observations have shown that the crystals have an initial porosity and that the progressive growth of these voids plays a major role in limiting creep life. In order to understand void growth under creep in single crystals, we have analyzed the creep response of three dimensional unit cells with a single spherical void under different types of isothermal creep loading. The growth behavior of the void is simulated using a three dimensional rate dependent crystal plasticity constitutive relation in a quasi-static finite element analysis. The aim of the present work is to analyze the effect of stress traixiality and Lode parameter on void growth under both constant true stress and constant engineering stress isothermal creep loading.

HCP materials are exceedingly being used as alloys and composites in several high strength light weight applications such as aerospace and aeronautical structures, deep sea maritime applications, and as biocompatible materials. To understand the deformation of HCP materials, reliable tools and techniques are required. One such technique is the Elasto-Plastic Self Consistency (EPSC) model. ESPC models use Eshelby’s Inclusion Theory as their basic formulation to model the strain experienced by a grain within a strained material sample. One of the oldest approximations (or models) used to model the grain’s strain within a strained sample is the Taylor’s Assumption (TA). TA assumes that each grain is strained to the same average value. EPSC models are different from the TA model since each grain modelled by the EPSC model would be strained to a different value. This is possible and obtained by solving an infinite domain boundary value problem. This key advantage of the EPSC model can therefore predict localized weak spots within material samples.EPSC models use the concept of eigen strain where the inhomogeneous grain is replaced with an equivalent inclusion. The technique proposed in this research is used to simulate uniaxial tension of rolled textured Magnesium. The number of deformation modes used in this research is seven. Both slipping systems and twinning systems are included in the simulation. The hardening phenomenon is described as a function of self-hardening as well as latent-hardening. As stated in (S. Kweon, 2020), modelling the interactive hardening requires a more robust numerical iterative technique. An improved robust iterative numerical technique is explained in (Daniel Raja, 2021) and (Soondo Kweon D. S., 2021). This research implements the equivalent inclusion theory in combination with the numerical iterative technique developed in the aforementioned papers.The report begins with the need for this research and advocates for the same. Then, the conceptional theories and the imaginary thought experiment performed by John D. Eshelby is presented. The concept of “Eigen Strain” which serves as the base work needed to understand and formulate the Equivalent Inclusion Theory is described in detail. The Equivalent Inclusion is then presented and developed. The concept of Green’s Function is presented and explained. These concepts serve as the building block for the derivation and calculation of the Eshelby Tensor which relates the concepts of eigen strain and constrained strain. The report concludes the theory section with the amalgamation of the ideas of the Green’s Function and Eigen Strain to develop the Eshelby Tensor for an Isotropic material as well as Anisotropic materials. In the following section, the unit cell accompanied with the deformation modes within the unit cell of an HCP material that are used in these simulations are presented. Following unit cell model, the crystal plasticity model which includes plastic deformation, hardening laws, and elastic deformation is elaborated. The results obtained from the simulation are presented and salient features are highlighted that are observed in the results. Lastly, the report concludes by pointing out key “take aways” from this research and identifies possible avenues for future research.Additionally, ten appendices are included towards the end of this report to enhance understanding of complicated derivations and solutions. Lastly, the author’s vita is included at the end of the report.

Methods designed for incorporation into multiscale modeling polycrystals are presented in this work in two tasks. This work contains mesoscale methods for capturing the effects of both the interactions of slip dislocations encountering twin grain boundaries and the simultaneous growth of multiple twin grain volume fractions on mechanical hardening and texture evolution. These are implemented in a crystal plasticity framework using the Los Alamos visco-plastic self consistent code, VPSC-7. Presented here, the effects of simultaneous growth in multiple twin variants on textural evolution is tracked using a Kalidindi-type twin volume transfer scheme. In Task 1, the implementation of this scheme in order to simulate the texture of Twinning Induced Plasticity steels (TWIP) subjected to Equal Channel Angular Pressing (ECAP) are summarized. In Task 2, the hardening effects of two types of interactions between slip dislocations and encountered twin grain boundaries, namely dislocation transmutation and dissociation, are captured by way of modifying the dislocation density based hardening model of [14]. Interactions of the first type are presented in a constitutive relation calculating the amount of dislocation density apportioned to a given slip system contained within the encountered twin volume fraction from each interacting slip system in the parent volume fraction. The amount transmuted from each interacting slip system described using the Correspondence Method, an onto mapping of slip systems in a parent grain to slip systems in considered twin grains. Interactions of the second type are then introduced into this constitutive relation as a disassociation parameter, the value of which is established by observations gleaned from the results of the molecular dynamics simulations of [11] and [36]. These methods are implanted to simulate the anisotropic hardening behavior of HCP magnesium under multiple load paths.

This thesis discusses plasticity-induced crack closure based finite element simulations of small fatigue cracks in three dimensions utilizing crystal plasticity theory. Previously, modeling has been performed in two dimensions using a double-slip crystal plasticity material model. The goal of this work is to extend that research using a full three-dimensional FCC crystal plasticity material model implementation that accounts for all twelve FCC slip systems. Discussions of Python scripts that were written to perform analyses with the commercial finite element code ABAQUS are given. A detailed description of the modeling methodology is presented along with results for single crystals and bicrystals. The results are compared with finite element and experimental results from the literature. A discussion of preliminary work for the analysis of crack growth around an intermetallic particle is also presented.

This thesis focuses on the effects of slip-slip, slip-twin, and slip-precipitates interactions on strain hardening, with the intent of developing comprehensive modelling capabilities enabling to investigate unit processes and their collective effects up to the macroscopic response. To this end, the modelling strategy adopted in this work relies on a two-way exchange of information between predictions obtained by discrete dislocation dynamics (DDD) simulations and crystal plasticity laws informed by DDD. At the scale of lattice defects, a DDD tool enabling simulations on any crystalline structure is developed to model dislocation-dislocation, dislocation-twin and dislocation-particles interactions. The tool is first used to quantify the collective effect and strength of dislocation-dislocation interactions on latent-hardening, especially in the case of pure Mg. With regards to slip-twin interactions, a transmission mechanism is implemented in the DDD framework so as to investigate the collective effects of dislocation transmission across a twin-boundary. With respect to slip-particles interactions, an efficient novel DDD approach based on a Fast Fourier Transform (FFT) technique is developed to include the field fluctuations related to elastic heterogeneities giving rise to image forces on dislocation lines. In addition, the DDD-FFT approach allows for the efficient treatment of anisotropic elasticity, thereby paving the way towards performing DDD simulations in low-symmetry polycrystals. The information extracted from the collective dislocation interactions are then passed to a series of constitutive models, and later used to quantify their effects at the scale of the polycrystal. For such purpose, a constitutive framework capable of receiving information from lower scales and establishing a direct connection with DDD simulations is notably developed.