1,720,992 research outputs found
Phase field modeling of grain growth in porous polycrystalline solids
Get PDFThe concurrent evolution of grain size and porosity in porous polycrystalline solids is a technically important problem. All the physical properties of such materials depend strongly on pore fraction and pore and grain sizes and distributions. Theoretical models for the pore-grain boundary interactions during grain growth usually employ restrictive, unrealistic assumptions on the pore and grain shapes and motions to render the problem tractable. However, these assumptions limit the models to be only of qualitative nature and hence cannot be used for predictions. This has motivated us to develop a novel phase field model to investigate the process of grain growth in porous polycrystalline solids. Based on a dynamical system of coupled Cahn-Hilliard and All en-Cahn equations, the model couples the curvature-driven grain boundary motion and the migration of pores via surface diffusion. As such, the model accounts for all possible interactions between the pore and grain boundary, which highly influence the grain growth kinetics. Through a formal asymptotic analysis, the current work demonstrates that the phase field model recovers the corresponding sharp-interface dynamics of the co-evolution of grain boundaries and pores; this analysis also fixes the model kinetic parameters in terms of real materials properties. The model was used to investigate the effect of porosity on the kinetics of grain growth in UO2 and CeO2 in 2D and 3D. It is shown that the model captures the phenomenon of pore breakaway often observed in experiments. Pores on three- and four- grain junctions were found to transform to edge pores (pores on two-grain junction) before complete separation. The simulations demonstrated that inhomogeneous distribution of pores and pore breakaway lead to abnormal grain growth. The simulations also showed that grain growth kinetics in these materials changes from boundary-controlled to pore-controlled as the amount of porosity increases. The kinetic growth parameters such as the growth exponent and the rate constant (or equivalently the activation energy) were found to depend strongly on the precise amount and distribution of porosity, which reconciles the different experimental results reported for grain growth in such materials
Development of a multiscale atomistic code to investigate self-organized pattern formation induced by ion irradiation
Get PDFVarious self-organized patterns including ripples and quantum dots can be induced by ion beam sputtering (IBS). For the past decades, the understanding of such phenomenon has been mainly relied on the Bradley-Harper theory that attributes the formation of self-organized patterns to the interplay between roughening by curvature dependence of erosion and smoothening by surface diffusion. Recently, the development of the crater function theory has overturned this erosion-based paradigm to a redistribution-based paradigm. The theory has proved that erosion is irrelevant and negligible in the pattern formation at low and intermediate incidence angles. Despite the success, there are still some questions open to discuss. The role of erosion for the ripple formation at glancing angles is still unclear. Furthermore, the current application of the crater function theory is limited in the linear regime. The applicability in the nonlinear regime is unknown. In this work, a hybrid MD/kMC (Molecular Dynamics/kinetic Monte Carlo) multiscale atomistic model is developed to elucidate these unknown issues. This model uses the crater functions, which are obtained by MD simulations, to model the prompt mass redistribution due to single-ion impacts. Defect migration, which is missing in previous models using crater functions, is treated by a kMC Arrhenius model. Using this model, a systematic study was performed for silicon bombarded by Ar+ ions of various energies (100 eV, 250 eV, 500 eV, 700 eV and 1000 eV) at incidence angles of 0° to 80° with fluence up to 1018 ions/cm 2 to cover both the linear and nonlinear regimes. The simulation results are in very good agreement with the experimental findings and the moment-description continuum theory in many features of surface evolution, namely, the phase diagram, wavelength dependence of ion energy and incidence angle, and the nonlinear evolution of surface roughness. The simulations elucidate that erosion plays the dominant role in the pattern formation at glancing angles. In the nonlinear regimes, the ripples first undergo coarsening and then reach saturation state. The surface roughness obeys the scaling theory and yields the growth exponent β=0.358, which is very close to the experimental finding. Ion irradiation with simultaneous sample rotation is also simulated, resulting in the formation of arrays of squared ordered dots. The patterns with sample rotation are found to be strongly correlated to the rotation speed and the pattern types formed without sample rotation
The Statistical Foundations of Line Bundle Continuum Dislocation Dynamics
No full textA first-principles theory of plasticity in metals currently does not exist. While many plasticity models make reference to rules based on heuristic arguments regarding dislocations (the fundamental mediators of plastic deformation in crystals), the scientific community still does not have a theory of dislocation dynamics which can recover even basic features of plasticity theory. Discrete dislocation dynamics, though a valuable tool for understanding fundamentals topics in dislocation plasticity, becomes unusable beyond 1.5% strain due to the line length multiplication inherent in deformation. As a result, it is necessary to develop continuum theories of dislocation dynamics which treat dislocation densities rather than individual dislocations. This thesis examines the foundations of one such continuum theory: line bundle continuum dislocation dynamics, which assumes that dislocations are roughly parallel at every point. First, this assumption is given definite meaning and it is shown from discrete dislocation dynamics data that to be appropriate when modelling dislocation densities on fine length scales (resolving densities on lengths less than 100 nm). Second, it is found that an additional driving force, the correlation stress, emerges from coarse-graining the line bundle dynamics. This correction to the dislocation interactions is dependent on tensorial dislocation correlation functions describing the short-range errors in the products of dislocation densities lying on two slip systems. The full set of these dislocation correlation functions are evaluated from discrete density data with the aid of a novel left-and-right handed classification of slip system interactions in FCC crystals. Lastly, a study of the correlation stress in a representative dislocation system suggests that these stresses are roughly one tenth the magnitude of the mean-field dislocation interaction stress. Taken together, this thesis bridges discrete and continuum models of dislocation dynamics and provides a foundation for future work on a first-principles theory of metal plasticity
Computational Modelling of Thermal Transport Using Spectral Phonon Boltzmann Transport Equation
Get PDFLattice vibration is the main microscopic mechanism for thermal transport in dielectric materials. The convenience of the analysis of atomic vibrations in the reciprocal space, motivated by the pioneering work of Debye and Peirels, made phonon transport theory is one of the standard paradigms adequate to study the microstructure and stoichiometry effects on thermal transport phenomena at mesoscale. UO2 is of theoretical as well as technological importance. The characteristic thermal transport phenomena at short length-scale (∼ nanometer) and time-scale (∼ picosecond) associated with radiation dictate close examination of available theoretical models and solution methods for thermal conductivity prediction, in addition to the validity of introduced approximations. By the virtue of INS experimental technique with powerful resolution, a direct benchmarking of simulated phonon properties results has been made possible. This provides by far a more accurate assessment criteria than thermal conductivity, and pave the way for founding sophisticated models of radiation effects on thermal transport with theoretical supports, beyond the currently available empirical or phenomenological models that succeed to reproduce the right macroscopic behavior in many cases just because of error cancellations and/or the use of adjustable parameters. Within time dependent perturbation theory (Fermi golden rule) framework, to represent the collision term of the semi-classical phonon Boltzmann Transport Equation, the bottleneck of the employed approach is to calculate intrinsic and extrinsic scattering rates of phonon modes. Being a highly correlated system with 5f electrons and magnetic phase transition at very low temperature, there are several challenges facing first-principle methods to leverage accurate phonon properties at finite temperature and imperfect structure that still need to be overcome. Moreover, it is common that using 3-phonon processes alone in other dielectrics overestimates lattice thermal conductivity at high temperatures (due to ignoring higher order phonon-phonon interactions), however, previous computational studies predicted values for UO2 conductivity lower than experiment by a factor of two about one third of the melting temperature. These observations assert the necessity of firstly investigating the impact of different introduced approximations for the calculation of intrinsic lattice thermal conductivity, to analyze the crucial parameters and to better understand this anomalous prediction. In this investigation, we present a critical assessment of several common approximations for the calculations of lattice thermal conductivity using spectral phonon Boltzmann Transport Equations. These approximations pertain to dispersion anisotropy and relations, Brillouin zone structure, and the coupling between the scattering rates of phonon normal modes. By employing harmonic approximation—perturbation theory to describe the scattering rates of a model system, FCC argon, our calculations show that widely spread approximations such as isotropic continuum and Single Mode Relaxation Time (SMRT) are not reliable, even for the case of cubic systems with their high symmetry properties. The success of these approximations is demonstrated to be a direct result of error cancellations. In addition, we show the essential importance of considering coupling terms at phonon mode level, and not in a statistical average sense as, for example, Callaway’s model does. By taking into account the coupling terms, the results evidence the crossover between the heat diffusion mediated by particle-like phonons (incoherent scattering) and the wave-like heat propagation due to phonon coherent scattering. Furthermore, this made possible revealing thermal conductivity anisotropy in cubic crystals. Finally, sensitivity of conductivity prediction to phonon spectrum is found to change over temperature. On the other hand, we challenge the widespread consensus that phonon-phonon interactions are inactive in the low temperature regime, which, in past investigations, led to the belief that the peak in lattice thermal conductivity (versus temperature) occurs because of two competing scattering mechanisms, umklapp and defect scattering mechanisms, dominant above and below the peak temperature, respectively. To the contrary, our study demonstrates that peak thermal conductivity, versus temperature, can still be obtained solely based upon phonon-phonon processes. This finding has been aided by considering the inelastic nature of 3-phonon scattering through applying energy conservation rule in a statistical average sense. Among the different statistical distributions examined to represent the regularized Dirac delta function appearing in Fermi Golden Rule, adopting Lorentz distribution, in analogy with phonon normal mode eigenenergy broadening due to the leading term of crystal anharmonicity, can uniquely reproduce the attained behavior in the low temperature limit. Simulation results, based on our adjustable-parameter-free model, evidence that the heavy tail of the Lorentz distribution is the key. Unlike other models that similarly employ harmonic approximation—perturbation theory to describe the 3-phonon scattering rates, a maximum in the intrinsic thermal conductivity at finite temperature was strikingly obtained in our investigation, without the need to consider multi-step or higher order phonon interactions. (Abstract shortened by ProQuest.
A discrete dislocation approach to grain boundary diffusion
No full textStresses, and their relaxation, in thin films at size scales on the order of (sub)micrometers are critical to the mechanical reliability of small devices. In this study we present a discrete dislocation dynamics framework to describe diffusional stress relaxation. We find a nearly linear relationship between the relaxed, residual tensile stress and grain size. The origin lies in the amount of diffused material and the opening profile along the grain boundary.</p
Continuum Dislocation Dynamics Modeling of Mesoscale Crystal Plasticity at Finite Deformation
No full textOver the past two decade, there have been renewed interests in the use of continuum models of dislocation to predict the plastic strength of metals from basic properties of dislocations. Such interests have been motivated by the unique self-organized dislocation microstructures that develop during plastic deformation of metals and the need to understand their origin and connection with strength of metals. This thesis effort focuses on the theoretical development of a vector-density based representation of dislocation dynamics on the mesoscale accounting for the kinematics of finite deformation. This model consists of two parts, the first is the development of the transport-reaction equations governing dislocation dynamics within the finite deformation setting, and the second focuses on the computational solution of the resulting model. The transport-reaction equations come in the form of a set of hyperbolic curl type transport equations, with reaction terms that nonlinearly couple these equations. The equations are also geometrically non-linear due to finite deformation kinematics and by their constitutive closure. The solution of the resulting model consists of two parts that are coupled in a staggered fashion, the crystal mechanics equations are lumped in the stress equilibrium equations, and the dislocation transport-reactions equations. The two sets of equations are solved by the Galerkin and First-Order System Least-Squares (FOSLS) finite element methods. A special attention is given to the accurate modeling of glissile dislocation junctions using de Rahm currents and graph theory ideas. The introduction of these measures requires the derivation of further transport relations. Using homogenization theory, we specialize the proposed model to a mean deformation gradient driven bulk plasticity model. Lastly, we simulate bulk plasticity behavior and compare our results against experiments
Computational Modeling of Dislocation Microstructure Patterns at Small Strains Using Continuum Dislocation Dynamics
No full textSelf-organized dislocation structures in deforming metals have a strong influence on the mechanical response of metals. However, accurate prediction of these patterns remains a challenge due to the complex dynamic and multiscale nature of the underlying process. This dissertation focuses on the development of a theoretical framework for continuum dislocation dynamics (CDD) models to predict dislocation microstructure formation at small strains, along with corresponding numerical simulation results. CDD models have the capability to incorporate plasticity physics spanning different time and length scales while capturing the dislocation motion explicitly within reasonable computational time. A typical model consists of two components: crystal mechanics, formulated as an eigenstrain problem, and dislocation dynamics, treated as a transport-reaction problem. In the first part of the thesis, a novel framework is introduced to solve the dislocation transport by decoupling the system of transport-reaction equations and enforcing the dislocation continuity constraint on individual slip systems. The results obtained from this framework demonstrate high accuracy and computational efficiency, significantly enhancing the predictive capabilities of the model. Building upon the framework, a statistical analysis of stress fluctuations in discrete dislocation dynamics (DDD) simulations is conducted to understand the relationship between coarse-grained average stress and local stress states. This analysis is motivated by the need to accurately capture dislocation reactions, such as cross-slip, which strongly depend on the local stress state, using the coarse-grained approach in CDD. The results revealed that the difference between the local and the coarse-grained states can be characterized using a Cauchy distribution. Consequently, a novel strategy is proposed to incorporate these statistical characteristics into the CDD model, yielding cross-slip rate predictions that align well with DDD results. In the final part of the study, the developed framework is applied to investigate the dislocation pattern formation during the early stages of cyclic loading. The simulation results successfully capture the formation of dislocation vein like structure and provide insights regarding the formation of labyrinth structure observed in experiments during cyclic loading at saturated state
A discrete dislocation approach to grain boundary diffusion
No full textStresses, and their relaxation, in thin films at size scales on the order of (sub)micrometers are critical to the mechanical reliability of small devices. In this study we present a discrete dislocation dynamics framework to describe diffusional stress relaxation. We find a nearly linear relationship between the relaxed, residual tensile stress and grain size. The origin lies in the amount of diffused material and the opening profile along the grain boundary.</p
STATISTICAL MECHANICS MODELING OF MESOSCALE DEFORMATION IN METALS
Get PDFThe research under this project focused on a theoretical and computational modeling of dislocation dynamics of mesoscale deformation of metal single crystals. Specifically, the work aimed to implement a continuum statistical theory of dislocations to understand strain hardening and cell structure formation under monotonic loading. These aspects of crystal deformation are manifestations of the evolution of the underlying dislocation system under mechanical loading. The project had three research tasks: 1) Investigating the statistical characteristics of dislocation systems in deformed crystals. 2) Formulating kinetic equations of dislocations and coupling these kinetics equations and crystal mechanics. 3) Computational solution of coupled crystal mechanics and dislocation kinetics. Comparison of dislocation dynamics predictions with experimental results in the area of statistical properties of dislocations and their field was also a part of the proposed effort. In the first research task, the dislocation dynamics simulation method was used to investigate the spatial, orientation, velocity, and temporal statistics of dynamical dislocation systems, and on the use of the results from this investigation to complete the kinetic description of dislocations. The second task focused on completing the formulation of a kinetic theory of dislocations that respects the discrete nature of crystallographic slip and the physics of dislocation motion and dislocation interaction in the crystal. Part of this effort also targeted the theoretical basis for establishing the connection between discrete and continuum representation of dislocations and the analysis of discrete dislocation simulation results within the continuum framework. This part of the research enables the enrichment of the kinetic description with information representing the discrete dislocation systems behavior. The third task focused on the development of physics-inspired numerical methods of solution of the coupled dislocation kinetics and crystal mechanics framework. To a large extent, this task has also been successfully started. We have developed a custom finite-element approach with mesh points being a subset of the underlying crystal structure. When used to predict the evolution of the dislocation system, the planar motion of dislocations is naturally captured for all slip systems, thus minimizing numerical errors and providing simple ways to investigate cross slip and dislocation reactions. Preliminary results in this direction show that we are closer than ever in building a predictive framework for dislocation dynamics and mesoscale plasticity based on the first principles of dislocation dynamics. The rest of the report gives and overview of the research performed under this project and highlights the key results and open questions left for future investigations
Multiscale Simulation of Thermo-mechanical Processes in Irradiated Fission-reactor Materials
Get PDFThis report contains a summary of progress made on the subtask area on phase field model development for microstructure evolution in irradiated materials, which was a part of the Computational Materials Science Network (CMSN) project entitled: Multiscale Simulation of Thermo-mechanical Processes in Irradiated Fission-reactor Materials. The model problem chosen has been that of void nucleation and growth under irradiation conditions in single component systems
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