Numerical study of the liquid-solid interface properties for binary alloys using phase-field crystal approach

2013 ◽  
Vol 1535 ◽  
Author(s):  
Muhammad Ajmal Choudhary ◽  
Julia Kundin ◽  
Heike Emmerich
Keyword(s):  
Phase Field ◽  
Solid Phase ◽  
Numerical Study ◽  
Liquid Droplet ◽  
Alloy System ◽  
Model Parameters ◽  
Systematic Analysis ◽  
Solid Interface ◽  
The Impact ◽  
Phase Field Crystal

ABSTRACTThe phase-field crystal (PFC) method has emerged as a promising technique to simulate the evolution of crystalline patterns with atomistic resolution on mesoscopic time scales. We use a 2D PFC model based on Elder et al. [Phy. Rev. B 75, 064107 (2007)] to perform a systematic analysis of a liquid-solid interface for a binary alloy system. We propose the method of determining interfacial energies for a curved liquid-solid interface by stabilizing the circular solid seed in the surrounding liquid phase and the liquid droplet in the solid phase for various seed sizes in a finite system. We also investigate the impact of model parameters on the resulting interface energies. The interface energies are computed with various system sizes in order to study the system size effects. In particular, we compare the simulation results in the form of the interface energy as a function of radius with the existing theories.

A Sensitivity Study of the Porcine Head Subjected to Bump Impact

2016 ◽  
Author(s):  
Kimberly A. Thompson ◽  
Adam C. Sokolow ◽  
Juliana Ivancik ◽  
Timothy G. Zhang ◽  
William H. Mermagen ◽  
...  
Keyword(s):  
Human Brain ◽  
3D Model ◽  
Porcine Model ◽  
Load Transfer ◽  
Numerical Study ◽  
Sensitivity Study ◽  
Complex Problem ◽  
Model Parameters ◽  
Skin Thickness ◽  
The Impact

Understanding load transfer to the human brain is a complex problem that has been a key subject of recent investigations [4–6]. Because the porcine is a gyrencephalic species, having greater structural and functional similarities to the human brain than other lower species outlined in the literature, it is commonly chosen as a surrogate for human brain studies [7]. Consequently, we have chosen to use a porcine model in this work. To understand stress wave transfer to and through the brain, it is important to fully characterize the nature of the impact (i.e. source, location, and speed) as well as the response of the constituent tissues under such impact. We suspect the material and topology of these tissues play an important role in their response. In this paper, we report on a numerical study assessing the sensitivity of model parameters for a 6-month old Gottingen mini-pig model, under bump loading. In this study, 2D models are used for computational simplicity. While a 3D model is more realistic in nature, a 2D representation is still valuable in that it can provide trends on parameter sensitivity that can help steer the development of the 3D model. In this work, we investigate the variation of skull and skin thickness, evaluate material variability of the skull, and consider the effects of nasal cavities on load transfer. Eighty simulations are computed in LS-DYNA and analyzed in MATLAB. The results of this study will provide useful knowledge on the necessary components and parameters of the porcine model and therefore provide more confidence in the analysis. This is an essential first step as we look toward bridging the gap between correlates of injury in animal and human models.

A regularized isothermal phase-field model of two-phase solid–fluid mixture and its spatial dissipative discretization equations

2021 ◽  
Vol 36 (4) ◽  
pp. 197-217
Author(s):  
Vladislav Balashov
Keyword(s):  
Phase Field ◽  
Solid Phase ◽  
Numerical Study ◽  
Strain Tensor ◽  
Phase Field Model ◽  
Evolutionary Equation ◽  
Two Phase ◽  
Fluid Mixture ◽  
Component Mixture ◽  
Eulerian Description

Abstract The present paper is devoted to a model describing a two-phase isothermal mixture, in which one of the phases obeys solid-like (namely, elastic) rheology. A fully Eulerian description is considered. To describe the stress–strain behaviour of the solid phase the elastic energy term is added to the Helmholtz free energy. The term depends on Almansi strain tensor. In its turn, the strain tensor is defined as the solution of the corresponding evolutionary equation. Considered model belongs to the phase field family. Formally it describes two-component mixture and uses mass densities of the components as order parameters. A distinctive feature of the considered model is its preliminary regularization according to the quasi-hydrodynamic framework. The dissipativity in total energy is proved when periodic boundary conditions are imposed. A spatial dissipative semi-discrete (continuous in time and discrete in space) scheme based on staggered grids is suggested. The theoretical results remain valid in the absence of the regularization. The results of a numerical study in a 2D setting are presented.

Numerical study of the melting and resolidification of the substrate during the impact of a ceramic droplet in a plasma spraying process

2019 ◽  
Vol 88 (2) ◽  
pp. 20901 ◽  
Author(s):  
Mouloud Driouche ◽  
Tahar Rezoug ◽  
Mohammed El Ganaoui
Keyword(s):  
Numerical Model ◽  
Phase Change ◽  
Solid Phase ◽  
Numerical Study ◽  
Solid Substrate ◽  
Navier Stokes ◽  
Droplet Spreading ◽  
Substrate Melting ◽  
Volume Method ◽  
The Impact

The substrate melting can significantly improve the properties of plasma spray coatings. Indeed the adhesion of the projected particles to the substrate can be ameliorated by the substrate melting. In this article, a numerical model is developed to study the dynamics of fluids and heat transfer with liquid/solid phase change during impact of a fully melted alumina particle on an aluminum solid substrate, taking into account of the substrate melting. The model is based on solving the Navier-Stokes and energy equations with liquid / solid phase change. These equations are coupled with the fluid of volume method (VOF), to follow the free surface of the particle during its spreading and solidification. The finite volume method is used to discretize the equations in a 2D axisymmetric domain. A comparison with the published experimental results was carried out to validate this numerical model. Simulations were performed for different initial droplet diameters to study its effect on droplet spreading as well as on substrate melting. It has been observed that the substrate melting begins before the droplet spreads completely; the substrate melting reaches its maximum when the droplet is close to its total solidification. Droplet spreading and substrate melting are more important for large sizes droplets.

Numerical study for the impact of liquid droplets on solid surfaces

2007 ◽  
Vol 221 (3) ◽  
pp. 293-301 ◽  
Author(s):  
A-S Yang ◽  
M-T Yang ◽  
M-C Hong
Keyword(s):  
Indium Tin Oxide ◽  
Numerical Study ◽  
Liquid Droplet ◽  
Solid Surfaces ◽  
Stainless Steel Surface ◽  
Force Model ◽  
Liquid Droplets ◽  
Construction Technique ◽  
Practical Applications ◽  
The Impact

The impinging behaviour of liquid droplets on solid surfaces is studied using a computational approach. The analysis comprises the unsteady three-dimensional conservation equations of mass and momentum, with the surface tension effect treated by the continuous surface force model. Gas-liquid interfacial motions are simulated by the volume-of-fluid method in conjunction with the piecewise linear interface construction technique. In the computer code validation for a water droplet impacting on a polished stainless steel surface, computer-generated images of the time evolution of the droplet impingement dispersal shape are compared with magnified photographs by Pasandideh-Fard et al. The flow and transport phenomena in the impingement flowfield are further examined in detail. In order to respond to the need for its use in practical applications, the study is extended to explore the spreading progression to achieve a better understanding of the interaction of a 30 μm diameter polyethylenedioxy thiophene liquid droplet with a 50 × 50 μm indium tin oxide-coating square cavity at an impact velocity of 6 m/s.

scholarly journals Phase-Field Model for the Simulation of Brittle-Anisotropic and Ductile Crack Propagation in Composite Materials

2021 ◽  
Author(s):  
Christoph Herrmann ◽  
Daniel Schneider ◽  
Ephraim Schoof ◽  
Felix Schwab ◽  
Britta Nestler
Keyword(s):  
Crack Propagation ◽  
Phase Field ◽  
Field Model ◽  
Solid Phase ◽  
Compressive Load ◽  
Phase Field Model ◽  
Model Parameters ◽  
Ductile Crack ◽  
Critical Energy Release Rate ◽  
Compression Load

In this work, a small-strain phase-field model is presented, which is able to predict crack propagation in systems with anisotropic brittle and ductile constituents. To model the anisotropic brittle crack propagation, an anisotropic critical energy release rate is used. The brittle constituents behave linear-elastically, in a transversely isotropic manner. Ductile crack growth is realised by a special crack degradation function, depending on the accumulated plastic strain, which is calculated by following the J2-plasticity theory. The mechanical jump conditions are applied in solid-solid phase transition regions. The influence of the relevant model parameters on a crack, propagating through a planar brittle-ductile interface, and furthermore a crack developing in a domain with a single anisotropic brittle ellipsoid, embedded in a ductile matrix, is investigated. We demonstrate that important properties, concerning the mechanical behaviour of grey cast iron, such as the favoured growth of cracks along the graphite lamellae and the tension-compression load asymmetry of the stress-strain response, are covered by the model. The behaviour is analysed on basis of a simulation domain consisting of three differently oriented elliptical inclusions, embedded in a ductile matrix, which is subjected to tensile and compressive load. The used material parameters correspond to graphite lamellae and pearlite.

scholarly journals A unified phase-field model of fracture in viscoelastic materials

2021 ◽  
Author(s):  
Franz Dammaß ◽  
Marreddy Ambati ◽  
Markus Kästner
Keyword(s):  
Free Energy ◽  
Phase Field ◽  
Field Model ◽  
Numerical Study ◽  
Phase Field Model ◽  
Energy Functional ◽  
Internal Variables ◽  
Model Parameters ◽  
Rate Dependency ◽  
Viscoelastic Materials

AbstractThe phase-field approach has proven to be a powerful tool for the prediction of crack phenomena. When it is applied to inelastic materials, it is crucial to adequately account for the coupling between dissipative mechanisms present in the bulk and fracture. In this contribution, we propose a unified phase-field model for fracture of viscoelastic materials. The formulation is characterized by the pseudo-energy functional which consists of free energy and dissipation due to fracture. The free energy includes a contribution which is related to viscous dissipation that plays an essential role in coupling the phase-field and the viscous internal variables. The governing equations for the phase-field and the viscous internal variables are deduced in a consistent thermodynamic manner from the pseudo-energy functional. The resulting model establishes a two-way coupling between crack phase-field and relaxation mechanisms, i.e. viscous internal variables explicitly enter the evolution of phase-field and vice versa. Depending on the specific choice of the model parameters, it has flexibility in capturing the possible coupled responses, and the approaches of recently published formulations are obtained as limiting cases. By means of a numerical study of monotonically increasing load, creep and relaxation phenomena, rate-dependency of failure in viscoelastic materials is analysed and modelling assumptions of the present formulation are discussed.

scholarly journals Investigation of Viscoelastic-Creep and Mechanical-Hysteresis Behaviors of Hydrostatically Stressed Crystal Using the Phase Field Crystal Method

2020 ◽  
Vol 2020 ◽  
pp. 1-20
Author(s):  
J. Em-Udom ◽  
N. Pisutha-Arnond
Keyword(s):  
Phase Field ◽  
Density Functional ◽  
Applied Pressure ◽  
Pressure Oscillation ◽  
Complex Moduli ◽  
Viscoelastic Creep ◽  
Mechanical Hysteresis ◽  
Deformation Problem ◽  
The Impact ◽  
Phase Field Crystal

The phase field crystal (PFC) method is a density-functional-type model with atomistic resolution and operating on diffusive time scales which has been proven to be an efficient tool for predicting numerous material phenomena. In this work, we first propose a method to predict viscoelastic-creep and mechanical-hysteresis behaviors in a body-centered-cubic (BCC) solid using a PFC method that is incorporated with a pressure-controlled dynamic equation which enables convenient control of deformation by specifying external pressure. To achieve our objective, we use constant pressure for the viscoelastic-creep study and sinusoidal pressure oscillation for the mechanical-hysteresis study. The parametric studies show that the relaxation time in the viscoelastic-creep phenomena is proportional to temperature. Also, mechanical-hysteresis behavior and the complex moduli predicted by the model are consistent with those of the standard linear solid model in a low-frequency pressure oscillation. Moreover, the impact of temperature on complex moduli is also investigated within the solid-stabilizing range. These results qualitatively agree with experimental and theoretical observations reported in the previous literature. We believe that our work should contribute to extending the capability of the PFC method to investigate the deformation problem when the externally applied pressure is required.

scholarly journals Phase-Field Model for the Simulation of Brittle-Anisotropic and Ductile Crack Propagation in Composite Materials

Materials ◽  
2021 ◽  
Vol 14 (17) ◽  
pp. 4956
Author(s):  
Christoph Herrmann ◽  
Daniel Schneider ◽  
Ephraim Schoof ◽  
Felix Schwab ◽  
Britta Nestler
Keyword(s):  
Crack Propagation ◽  
Phase Field ◽  
Field Model ◽  
Solid Phase ◽  
Compressive Load ◽  
Phase Field Model ◽  
Model Parameters ◽  
Ductile Crack ◽  
Critical Energy Release Rate ◽  
Compression Load

In this work, a small-strain phase-field model is presented, which is able to predict crack propagation in systems with anisotropic brittle and ductile constituents. To model the anisotropic brittle crack propagation, an anisotropic critical energy release rate is used. The brittle constituents behave linear-elastically in a transversely isotropic manner. Ductile crack growth is realised by a special crack degradation function, depending on the accumulated plastic strain, which is calculated by following the J2-plasticity theory. The mechanical jump conditions are applied in solid-solid phase transition regions. The influence of the relevant model parameters on a crack propagating through a planar brittle-ductile interface, and furthermore a crack developing in a domain with a single anisotropic brittle ellipsoid, embedded in a ductile matrix, is investigated. We demonstrate that important properties concerning the mechanical behaviour of grey cast iron, such as the favoured growth of cracks along the graphite lamellae and the tension–compression load asymmetry of the stress–strain response, are covered by the model. The behaviour is analysed on the basis of a simulation domain consisting of three differently oriented elliptical inclusions, embedded in a ductile matrix, which is subjected to tensile and compressive load. The material parameters used correspond to graphite lamellae and pearlite.

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