arXiv subjects

Britta Nestler

Publications and source records attributed to Britta Nestler.

35 records · Page 2Linked to original sources

arXiv2020

Morphological stability of three-dimensional cementite rods in polycrystalline system: A phase-field analysis

Transformations accompanying shape-instability govern the morphological configuration and distribution of the phases in a microstructure. Owing to the influence of the microstructure on the properties of a material, the stability of three-dimensional rods in a representative polycrystalline system is extensively analysed. A multiphase-field model, which recovers the physical laws and sharp-interface relations, and includes grain boundary diffusion, is adopted to investigate the morphological evolution of the precipitate. Moreover, the efficiency of the numerical approach is ensured by establishing the volume-preserving chemical equilibrium through the incorporation TCFe8 (CALPHAD) data and solving phase-field evolution in the Allen-Cahn framework. The morphological evolution of the rod in the multiphase system exhibits a unique transformation mechanism which is significantly different from the evolution of an isolated finite-structure. It is realised that, in a polycrystalline arrangement, irrespective of the initial rod-size , the shape-change begins with the energy-minimising events at the triple junctions. This early transformation renders a characteristic morphology at the longitudinal ends of the structure, which introduces sufficient driving-force through the curvature-difference for the subsequent morphological changes. The continued mass transfer to the terminations, ultimately, breaks-off the rod into separate entities that are entangled in the grain boundary. With increasing aspect ratio of the rod, it is identified that the source of mass transfer, which turns into the ovulation site, shifts from the centre. This increases the number of fragmentation events and introduces satellite particle. A comprehensive understanding of the transformation kinetics and mechanism governing the morphological evolution of the rods in a polycrystalline system is rendered in this work.

cs.CE↗

arXiv2020

Influence of stress-free transformation strain on the autocatalytic growth of bainite: A multiphase-field analysis

Analytical treatments, formulated to predict the rate of the bainite transformation, define autocatalysis as the growth of the subunits at the bainite-austenite interface. Furthermore, the role of the stress-free transformation strain is often translated to a thermodynamic criterion that needs to be fulfilled for the growth of the subunits. In the present work, an elastic phase-field model, which elegantly recovers the sharp-interface relations, is employed to comprehensively explicate the effect of the elastic energy on the evolution of the subunits. The primary finding of the current analysis is that the role of eigenstrains in the bainite transformation is apparently complicated to be directly quantified as the thermodynamic constraint. It is realized that the inhomogeneous stress state, induced by the growth of the primary subunit, renders a spatially dependent ill- and well-favored condition for the growth of the secondary subunits. A favorability contour, which encloses the sections that facilitate the elastically preferred growth, is postulated based on the elastic interaction. Through the numerical analyses, the enhanced growth of the subunits within the favorability-contour is verified. Current investigations show that the morphology and size of the elastically preferred region respectively changes and increases with the progressive growth of the subunits.

cond-mat.mtrl-sci↗

arXiv2018

Phase-field analysis of quenching and partitioning in a polycrystalline Fe-C system under constrained-carbon equilibrium condition

Mechanical properties of steels are significantly enhanced by retained austenite. Particularly, it has been shown that a recently developed heat-treatment technique called Quenching and Partitioning (Q\&P) stabilises austenite effectively. In the present work, the phase-field approach is adopted to simulate the phase transformation and carbon diffusion, which respectively accompanies the quenching and partitioning process of the polycrystalline Fe-C system. By incorporating the chemical driving-force from the CALPHAD database, the elastic phase-field model, which recovers the sharp-interface solutions, simulates the martensite (alpha') transformation at three different quenching temperatures. The resulting martensite volume-fractions are in complete agreement with the analytical predictions. For the first time, in this study, the constrained carbon equilibrium (CCE) condition is introduced in the polycrystalline set-up to yield the predicted partitioning endpoints. Under the CCE condition, the carbon partitioning in two alloys of varying composition is analysed through the phase-field model which employs chemical potential as the dynamic variable. The volume fraction and distribution of retained austenite is determined from the carbon distribution and its temporal evolution during the partitioning is investigated. It is identified that in the initial stages of partitioning carbon gets accumulated in the austenite ($γ$) along the $γα'$-interface, owing to the substantial difference in the diffusivities and CCE endpoints. This accumulation stabilises the austenite adjacent to the interface. However, depending on the martensite volume-fraction and the alloy composition, the evolution of the stabilised austenite varies. Furthermore, the influence of the phase distribution on the kinetics of the temporal evolution of retained austenite is elucidated.

cond-mat.mtrl-sci↗

arXiv2018

Breakup of liquid jets and the formation of satellite and subsatellite droplets

A spontaneous breakup of a liquid jet results in the formation of a chain of droplets, which is a daily observed phenomenon, such as in the raining process and under an open water-faucet. We here report inkjet printing experiments for the formation of droplets which are inconsistent with existing theories and thereafter propose a novel concept of surface area minimization to address the droplet-formation condition. The novel concept is also capable of predicting the formation of satellite and subsatellite droplets, which cannot be comprehended by the classic Rayleigh theory for the formation of droplets. We also present a new evolution behavior of liquid jets not yet reported before that the jet initially transforms into droplets and then becomes a uniform-radius jet again. The current results can be applied to a variety of disciplines where liquid jets are present.

physics.flu-dyn↗

arXiv2018

Experience Report: Formal Methods in Material Science

Increased demands in the field of scientific computation require that algorithms be more efficiently implemented. Maintaining correctness in addition to efficiency is a challenge that software engineers in the field have to face. In this report we share our first impressions and experiences on the applicability of formal methods to such design challenges arising in the development of scientific computation software in the field of material science. We investigated two different algorithms, one for load distribution and one for the computation of convex hulls, and demonstrate how formal methods have been used to discover counterexamples to the correctness of the existing implementations as well as proving the correctness of a revised algorithm. The techniques employed for this include SMT solvers, and automatic and interactive verification tools.

cs.SE↗

arXiv2018

A Scalable and Extensible Checkpointing Scheme for Massively Parallel Simulations

Realistic simulations in engineering or in the materials sciences can consume enormous computing resources and thus require the use of massively parallel supercomputers. The probability of a failure increases both with the runtime and with the number of system components. For future exascale systems it is therefore considered critical that strategies are developed to make software resilient against failures. In this article, we present a scalable, distributed, diskless, and resilient checkpointing scheme that can create and recover snapshots of a partitioned simulation domain. We demonstrate the efficiency and scalability of the checkpoint strategy for simulations with up to $40$ billion computational cells executing on more than $400$ billion floating point values. A checkpoint creation is shown to require only a few seconds and the new checkpointing scheme scales almost perfectly up to more than $260\,000$ ($2^{18}$) processes. To recover from a diskless checkpoint during runtime, we realize the recovery algorithms using ULFM MPI. The checkpointing mechanism is fully integrated in a state-of-the-art high-performance multi-physics simulation framework. We demonstrate the efficiency and robustness of the method with a realistic phase-field simulation originating in the material sciences and with a lattice Boltzmann method implementation.

cs.DC↗

arXiv2016

Influence of substrate interaction and confinement on electric field induced transition in symmetric block copolymer thin films

In the present work, we study morphologies arising due to competing substrate interaction, electric field and confinement effects on a symmetric diblock copolymer. We employ a coarse grained non-local Cahn-Hilliard phenomenological model taking into account the appropriate contributions of substrate interaction and electrostatic field. The proposed model couples the Ohta-Kawasaki functional with Maxwell equation of electrostatics, thus alleviating the need for any approximate solution used in previous studies. We calculate the phase diagram in electric field-substrate strength space for different film thicknesses. In addition to identifying the presence of parallel, perpendicular and mixed lamellae phases similar to analytical calculations, we also find a region in the phase diagram where hybrid morphologies (combination of two phases) coexist. These hybrid morphologies arise either solely due to substrate affinity and confinement or are induced due to the applied electric field. The dependence of the critical fields for transition between the various phases on substrate strength, film thickness and dielectric contrast is discussed. Some preliminary 3D results are also presented to corroborate the presence of hybrid morphologies.

cond-mat.mtrl-sci↗

arXiv2015

Compound droplets on fibers

Droplets on fibers have been extensively studied in the recent years. Although the equilibrium shapes of simple droplets on fibers are well established, the situation becomes more complex for compound fluidic systems. Through experimental and numerical investigations, we show herein that compound droplets can be formed on fibers and that they adopt specific geometries. We focus on the various contact lines formed at the meeting of the different phases and we study their equilibrium state. It appears that, depending on the surface tensions, the triple contact lines can remain separate or merge together and form quadruple lines. The nature of the contact lines influences the behavior of the compound droplets on fibers. Indeed, both experimental and numerical results show that, during the detachment process, depending on whether the contact lines are triple or quadruple, the characteristic length is the inner droplet radius or the fiber radius.

physics.flu-dyn↗

arXiv2015

Massively Parallel Phase-Field Simulations for Ternary Eutectic Directional Solidification

Microstructures forming during ternary eutectic directional solidification processes have significant influence on the macroscopic mechanical properties of metal alloys. For a realistic simulation, we use the well established thermodynamically consistent phase-field method and improve it with a new grand potential formulation to couple the concentration evolution. This extension is very compute intensive due to a temperature dependent diffusive concentration. We significantly extend previous simulations that have used simpler phase-field models or were performed on smaller domain sizes. The new method has been implemented within the massively parallel HPC framework waLBerla that is designed to exploit current supercomputers efficiently. We apply various optimization techniques, including buffering techniques, explicit SIMD kernel vectorization, and communication hiding. Simulations utilizing up to 262,144 cores have been run on three different supercomputing architectures and weak scalability results are shown. Additionally, a hierarchical, mesh-based data reduction strategy is developed to keep the I/O problem manageable at scale.

cs.DC↗

arXiv2014

Deviations from cooperative growth mode during eutectoid transformation: insights from phase-field approach

The non-cooperative eutectoid transformation relies on the presence of pre-existing cementite particles in the parent austenitic phase and yields a product, popularly known as the divorced eutectoid. In isothermal conditions, two of the important parameters, which influence the transformation mechanism and determine the final morphology are undercooling (below A1 temperature) and inter-particle spacing. Although, the criteria which governs the morphological transition from lamellar to divorced is experimentally well established, numerical studies that give a detailed exposition of the non-cooperative transformation mechanism, have not been reported extensively. In the present work, we employ a multiphase-field model, that uses the thermodynamic information from the CALPHAD database, to numerically simulate the pulling-away of the advancing ferrite-austenite interface from cementite, which results in a transition from lamellar to divorced eutectoid morphology in Fe-C alloy. We also identify the onset of a concurrent growth and coarsening regime at small inter-particle spacing and low undercooling. We analyze the simulation results to unravel the essential physics behind this complex spacial and temporal evolution pathway and amend the existing criteria by constructing a Lamellar-Divorced-Coarsening (LDC) map.

cond-mat.mtrl-sci↗

arXiv2013

Three-dimensional phase-field study of crack-seal microstructures - Insights from innovative post-processing techniques

Numerical simulations of vein evolution contribute to a better understanding of processes involved in their formation and possess the potential to provide invaluable insights into the rock deformation history and fluid flow pathways. The primary aim of the present article is to investigate the influence of a realistic boundary condition, i.e. an algorithmically generated fractal surface, on the vein evolution in 3-D using a thermodynamically consistent approach, while explaining the benefits of accounting for an extra dimensionality. The 3-D simulation results are supplemented by innovative numerical post-processing and advanced visualization techniques. The new methodologies to measure the tracking efficiency demonstrate the importance of accounting the temporal evolution; no such information is usually accessible in field studies and notoriously difficult to obtain from laboratory experiments as well. The grain growth statistics obtained by numerically post-processing the 3-D computational microstructures explain the pinning mechanism which leads to arrest of grain boundaries/multi-junctions by crack peaks, thereby, enhancing the tracking behavior.

physics.geo-ph↗

arXiv2013

Phase-field study of grain boundary tracking behavior in crack-seal microstructures

In order to address the growth of crystals in veins, a multiphase-field model is used to capture the dynamics of crystals precipitating from a super-saturated solution. To gain a detailed understanding of the polycrystal growth phenomena in veins, we investigate the influence of various boundary conditions on crystal growth. In particular, we analyze the formation of vein microstructures resulting from the free growth of crystals as well as crack-sealing processes. We define the crystal symmetry by considering the anisotropy in surface energy to simulate crystals with flat facets and sharp corners. The resulting growth competition of crystals with different orientations is studied to deduce a consistent orientation selection rule in the free-growth regime. Using crack-sealing simulations, we correlate the grain boundary tracking behavior depending on the relative rate of crack opening, opening trajectory, initial grain size and wall roughness. Further, we illustrate how these parameters induce the microstructural transition between blocky (crystals growing anisotropically) to fibrous morphology (isotropic) and formation of grain boundaries. The phase-field simulations of crystals in the free-growth regime (in 2D and 3D) indicate that the growth or consumption of a crystal is dependent on the orientation difference with neighboring crystals. The crack-sealing simulation results (in 2D and 3D) reveal that crystals grow isotropically and grain boundaries track the opening trajectory if the wall roughness is high, opening increments are small and crystals touch the wall before the next crack increment starts. Further, we find that within the complete crack-seal regime, anisotropy in surface energy results in the formation of curved/oscillating grain boundaries (instead of straight) when the crack opening velocity is increased and wall roughness is not sufficiently high.

physics.geo-ph↗

arXiv2013

Theoretical and numerical study of lamellar eutectoid growth influenced by volume diffusion

We investigate the lamellar growth of pearlite at the expense of austenite during the eutectoid transformation in steel. To begin with, we extend the Jackson-Hunt-type calculation (previously used to analyze eutectic transformation) to eutectoid transformation by accounting for diffusion in all the phases. Our principal finding is that the growth rates in presence of diffusion in all the phases is different as compared to the case when diffusion in growing phases is absent. The difference in the dynamics is described by a factor 'ρ' which comprises of the ratio of the diffusivities of the bulk and the growing phases, along with the ratios of the slopes of the phase co-existence lines. Thereafter, we perform phase-field simulations, the results of which are in agreement with analytical predictions. The phase-field simulations also reveal that diffusion in austenite as well as ferrite leads to the formation of tapered cementite along with an overall increase in the transformation kinetics as compared to diffusion in austenite (only). Finally, it is worth noting that the aim of present work is not to consider the pearlitic transformation in totality, rather it is to isolate and thereby investigate the influence of diffusivity in the growing phases on the front velocity.

cond-mat.mtrl-sci↗

arXiv2011

Theoretical and numerical study of lamellar eutectic three-phase growth in ternary alloys

We investigate lamellar three-phase patterns that form during the directional solidification of ternary eutectic alloys in thin samples. A distinctive feature of this system is that many different geometric arrangements of the three phases are possible, contrary to the widely studied two-phase patterns in binary eutectics. Here, we first analyze the case of stable lamellar coupled growth of a symmetric model ternary eutectic alloy, using a Jackson-Hunt type calculation in thin film morphology, for arbitrary configurations, and derive expressions for the front undercooling as a function of velocity and spacing. Next, we carry out phase-field simulations to test our analytic predictions and to study the instabilities of the simplest periodic lamellar arrays. For large spacings, we observe different oscillatory modes that are similar to those found previously for binary eutectics and that can be classified using the symmetry elements of the steady-state pattern. For small spacings, we observe a new instability that leads to a change in the sequence of the phases. Its onset can be well predicted by our analytic calculations. Finally, some preliminary phase-field simulations of three-dimensional growth structures are also presented.

cond-mat.mtrl-sci↗

arXiv2006

Phase-field modelling of solute trapping during rapid solidification of a Si-As alloy

The effect of nonequilibrium solute trapping by a growing solid under rapid solidification conditions is studied using a phase-field model. Considering a continuous steady-state concentration profile across the diffuse solid-liquid interface, a new definition of the nonequilibrium partition coefficient in the phase-field context is introduced. This definition leads, in particular for high growth velocities, to a better description of the available experimental data in comparison with other diffuse interface and sharp-interface predictions.

cond-mat.mtrl-sci↗

arXiv2005

Dendritic to globular morphology transition in ternary alloy solidification

The evolution of solidification microstructures in ternary metallic alloys is investigated by adaptive finite element simulations of a general multicomponent phase-field model. A morphological transition from dendritic to globular growth is found by varying the alloy composition at a fixed undercooling. The dependence of the growth velocity and of the impurity segregation in the solid phase on the composition is analyzed and indicates a smooth type of transition between the dendritic and globular growth structures.

cond-mat.mtrl-sci↗

arXiv2004

Phase-field simulations of solidification in binary and ternary systems using a finite element method

We present adaptive finite element simulations of dendritic and eutectic solidification in binary and ternary alloys. The computations are based on a recently formulated phase-field model that is especially appropriate for modelling non-isothermal solidification in multicomponent multiphase systems. In this approach, a set of governing equations for the phase-field variables, for the concentrations of the alloy components and for the temperature has to be solved numerically, ensuring local entropy production and the conservation of mass and inner energy. To efficiently perform numerical simulations, we developed a numerical scheme to solve the governing equations using a finite element method on an adaptive non-uniform mesh with highest resolution in the regions of the phase boundaries. Simulation results of the solidification in ternary Ni$_{60}$Cu$_{40-x}$Cr$_{x}$ alloys are presented investigating the influence of the alloy composition on the growth morphology and on the growth velocity. A morphology diagram is obtained that shows a transition from a dendritic to a globular structure with increasing Cr concentrations. Furthermore, we comment on 2D and 3D simulations of binary eutectic phase transformations. Regular oscillatory growth structures are observed combined with a topological change of the matrix phase in 3D. An outlook for the application of our methods to describe AlCu eutectics is given.

cond-mat.mtrl-sci↗