Finite element model of primary recrystallization in polycrystalline aggregates using a level set framework

International audienceThe paper describes a robust finite element model of interface motion in media with multiple domains and junctions, as is the case in polycrystalline materials. The adopted level set framework describes each domain (grain) with a single level set function, while avoiding the creation of overlap or vacuum between these domains. The finite element mesh provides information on stored energies, calculated from a previous deformation step. Nucleation and growth of new grains are modelled by inserting additional level set functions around chosen nodes of the mesh. The kinetics and topological evolutions induced by primary recrystallization are discussed from simple test cases to more complex configurations and compared with the Johnson-Mehl-Avrami-Kolmogorov theory

Three-dimensional Finite Element model for Dynamics of the Earth\u27s Mantle using an Internal State Variable Constitutive Model

This dissertation presents a numerical model constructed to investigate the dynamics and structures of the Earth’s mantle. Deformation of the Earth’s mantle, which is composed of solid silicate minerals, is strongly governed by the constitutive relation-ship among multiple length-scale structures and properties. To explain the realistic consti-tutive behavior of the silicate mantle, an Internal State Variable (ISV) theory that is an advanced and novel constitutive approach for history-dependent elastoviscoplasticity was applied. The ISV constitutive model was, in turn, implemented into a three-dimensional geodynamic code, TERRA3D, which uses the Finite Element method developed for the mantle convection problem. The sequential studies performed in this dissertation are presented in the follow-ing order: i) a comprehensive summary of the mantle material structures (compositions and microstructural features) and its mechanical properties (elasticity and rheology), ii) a development of a recrystallization and grain size dependent ISV constitutive model for the polycrystalline materials such as minerals and metals, which explains comprehensive mineral physics occurring under the conditions of pressure, temperature, and strain rate within the mantle and their history dependence, and iii) an application of the recrystalli-zation and grain size dependent ISV model to the Earth’s mantle convection problem us-ing the TERRA3D for an investigation of the grain size and dynamic recrystallization efect on the mantle dynamics. The applied ISV constitutive model within the TERRA3D Finite Element frame-work captures the subscale dynamics (dislocation density evolution, dynamic and static recrystallization, grain growth, and grain refinement) and their effect on the large-scale rheology and dynamics of the Earth’s mantle. The numerical investigations reveal that the potential for the mechanical instability and weakening within the mantle arises from the kinetics of grain size and recrystallization and their rheological effect. This mechanical instability leads to the mantle convection entering the episodic overturn regime. The TERRA3D-ISV mantle convection model herein also provides some insightful discover-ies regarding the dynamics and structures within the mantle, explaining its complex rhe-ology caused by the kinetics of recrystallization, grain size, hardening, dislocation recov-ery, and diffusion in the geological settings

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

A modified level set approach to 2D modeling of dynamic recrystallization

The macroscopic properties of metallic materials depend on the state of the grain microstructure. Recrystallization acts as one of the most important mechanisms in the evolution of the microstructure and hence also of the macroscopic properties. This paper presents a mesoscale model of microstructure evolution due to recrystallization, based on a level set formulation employed in a finite element setting. The use of level sets to represent grains and grain boundaries in polycrystal microstructures is a relatively recent development in computational materials science and the present contribution suggests new methodologies such as interface reconstruction, allowing for example boundary conditions to be prescribed along grain boundary interfaces and distinct localization and representation of grain boundary junctions. Polycrystal plasticity is modeled by considering the evolution of dislocation density in the individual crystals. The influence of grain boundaries on dislocation accumulation is captured in the model, causing the formation of dislocation density gradients within the grains. The model is used in simulations of dynamic recrystallization, taking pure copper as example material. It is shown that the proposed model captures the salient features of dynamic recrystallization during thermomechanical materials processing

Multi-Scale Modeling of Dynamic Recrystallization in Metals Undergoing Thermo-Mechanical Processing

This study focuses on devising a unified multi-scale numerical framework to predict the grain size evolution by dynamic recrystallization in metals and alloys for an array of severe plastic thermo-mechanical deformation conditions. The model is developed to predict the temporal and spatial grain size evolution of the material subjected to high strain rate and temperature dependent deformation. Dynamic recrystallization evolves by either a continuous grain refinement mechanism around room temperatures or by a discontinuous grain nucleation and growth mechanism at elevated temperatures. The multi-scale model bridges a dislocation density-based constitutive framework with microscale physics-based recrystallization laws to predict both the types of recrystallization phenomena simultaneously. The simulations are conducted within an integrated probabilistic cellular automata-finite element framework to capture the physics of the recrystallization mechanisms. High strain rate loading experiments in conjunction with microstructural characterization tests are conducted for pure copper to characterize the dynamic grain size evolution in the material and evaluated against the model predictions. Synchrotron X-rays are integrated with a modified Kolsky tension bar to conduct in situ temporal characterization of the grain refinement mechanism operating during the dynamic deformation of copper and evaluated against the developed model kinetics. Finally, the model is implemented to predict the grain size evolution developed during the friction stir spot welding of Al 6061-T6 for varying tool rotational speeds. The experiments show that the original microstructure is completely replaced by a recrystallized fine-grained microstructure with the final average grain size and morphology dependent on the process parameters. The model accurately predicts the process temperature rise with increasing tool rotational speeds, which results in a higher rate of grain coarsening during the dynamic recrystallization phenomenon

Multi-Scale Modeling of Dynamic Recrystallization in Metals Undergoing Thermo-Mechanical Processing

This study focuses on devising a unified multi-scale numerical framework to predict the grain size evolution by dynamic recrystallization in metals and alloys for an array of severe plastic thermo-mechanical deformation conditions. The model is developed to predict the temporal and spatial grain size evolution of the material subjected to high strain rate and temperature dependent deformation. Dynamic recrystallization evolves by either a continuous grain refinement mechanism around room temperatures or by a discontinuous grain nucleation and growth mechanism at elevated temperatures. The multi-scale model bridges a dislocation density-based constitutive framework with microscale physics-based recrystallization laws to predict both the types of recrystallization phenomena simultaneously. The simulations are conducted within an integrated probabilistic cellular automata-finite element framework to capture the physics of the recrystallization mechanisms. High strain rate loading experiments in conjunction with microstructural characterization tests are conducted for pure copper to characterize the dynamic grain size evolution in the material and evaluated against the model predictions. Synchrotron X-rays are integrated with a modified Kolsky tension bar to conduct in situ temporal characterization of the grain refinement mechanism operating during the dynamic deformation of copper and evaluated against the developed model kinetics. Finally, the model is implemented to predict the grain size evolution developed during the friction stir spot welding of Al 6061-T6 for varying tool rotational speeds. The experiments show that the original microstructure is completely replaced by a recrystallized fine-grained microstructure with the final average grain size and morphology dependent on the process parameters. The model accurately predicts the process temperature rise with increasing tool rotational speeds, which results in a higher rate of grain coarsening during the dynamic recrystallization phenomenon

Phase-field modeling of unidirectionally solidified microstructures under diffusive-convective regime

Moderne Werkstoffe zeichnen sich oft durch ein breites Spektrum an maßgeschneiderten mechanischen, magnetischen, elektronischen oder thermophysikalischen Eigenschaften aus. In Verbindung mit der ihnen zugrundeliegenden Mikrostruktur kann das Verhalten der meisten technischen Werkstoffe durch genaue Modellierung der neuartigen Eigenschaften mit maßgeschneiderten Morphologien vorhergesagt werden. Im Allgemeinen wird die Bildung von Erstarrungsmikrostrukturen durch das Wechselspiel zwischen Kapillarität und Diffusion bestimmt. Das Vorhandensein von Schmelzekonvektion spielt eine bedeutende Rolle für die endgültigen Gefügeeigenschaften von Gusslegierungen und wird aufgrund seiner Komplexität oft vernachlässigt. Da die Kontrolle der Mikrostruktur für jede Verarbeitungsaktivität von wesentlicher Bedeutung ist, wird in dieser Dissertation ein Phasenfeldmodell mit Flüssigphasenkonvektion verwendet, in dem die Wechselwirkung von diffusiv-konvektiven Feldern und deren Auswirkung auf die Gefügeentwicklung untersucht wird. Im folgenden Teil werden die numerischen Ergebnisse unter einem diffusionskonvektiven Regime von den Korngrenzen bis zu den Säulendendriten diskutiert. Zunächst wird ein Phasenfeldmodell verwendet, um das Phänomen des Korngrenzenrillens unter Gleichgewichtsbedingungen zu untersuchen. Das Modell wird validiert, indem die Rillenkinetik mit der volumendiffusionsgesteuerten Rillentheorie verglichen wird. In Form der Schmelzkonvektion wird erstmals die Rolle eines zusätzlichen konvektiven Transportmechanismus auf Korngrenzenrillen eingehend untersucht. Die simulierten Rillen zeigen eine hervorragende Übereinstimmung mit früheren experimentellen Theorien sowie mit der Theorie der scharfen Grenzflächen. Daneben wird auch die Wanderung der Fest-Fest-Korngrenze erfasst, wobei das Auftreten asymmetrischer Grate die seitliche Drift der Rillenwurzel entlang der stromabwärtigen Richtung fördert. Darüber hinaus wird die Initiierung von Mikrostrukturmustern für energetisch isotrope Grenzflächen vorgestellt, wobei die Vorhersage der Spitzenaufteilungsposition anhand eines analytischen Kriteriums diskutiert wird. Infolge von krümmungsgetriebenen Flüssen wird die fundamentale und sich wiederholende Einheit von Mikrostrukturen mit Spitzenspaltung durch einen direkten Vergleich zwischen dem Phasenfeld und der Position der scharfen Grenzflächenspitze analysiert. Im Gegensatz zu den vorhandenen Studien sagt das vorgeschlagene Kriterium die Verzweigungsposition in einem erstarrenden Muster erfolgreich voraus. Anschließend wird der Einfluss anderer Parameter wie der Grenzflächenanisotropie, der Schmelzkonvektion und der Oberflächenenergien auf den strukturellen Übergang von Mikrostrukturen mit Spitzenspaltung ermittelt. Während für ein isotropes Kristallwachstum eine Morphologie der Spitzenaufspaltung beobachtet wird, wird für anisotrope Grenzflächen das Auftreten von richtungsabhängigen säulenförmigen Dendriten demonstriert. Anschließend wird die Vorhersage des interdendritischen Armabstands bei vorhandener Schmelzkonvektion untersucht. In Übereinstimmung mit früheren experimentellen Studien wird gezeigt, dass der Selektionsmechanismus von Primärarmen durch das Eintauchen von Dendriten in das Diffusionsregime zum Überwachsen von Tertiärarmen im Diffusionskonvektionsregime führt. Darüber hinaus zeigt sich, dass die Vorhersage des primä}ren Dendritenarmabstands aufgrund des Vorhandenseins eines konvektiven Transports im interdendritischen Bereich modifiziert ist. Danach werden Phasenfeldsimulationen durchgeführt, um die Wachstumskonkurrenz von Säulendendriten vorherzusagen, die an der Korngrenze konvergieren. Während der Herstellung von Einkristall-Turbinenschaufeln häufig untersucht, wird das Überwuchsverhalten von falsch ausgerichteten Dendriten an der Korngrenze erfasst und analysiert. Zum ersten Mal wird gezeigt, dass das Vorhandensein eines zusätzlichen Massentransports in der flüssigen Massenphase die gelösten dendritischen Spitzen fördert, was wiederum denÜberwuchsmechanismus an der Korngrenze modifiziert. Durch mikrostrukturelle Auswahlkarten wird auch gezeigt, dass Parameter wie der Fehlorientierungswinkel und die Grenzflächenanisotropie dieÜberwuchsdynamik an der Korngrenze weitgehend steuern