scholarly journals Progress and opportunities in modelling environmentally assisted cracking

2021 ◽  
Vol 6 ◽  
pp. 70-77
Author(s):  
Emilio Martínez Pañeda
Keyword(s):  
Phase Field ◽  
Hydrogen Uptake ◽  
Field Variable ◽  
Field Methods ◽  
Phase Field Models ◽  
Deformation And Fracture ◽  
Environmentally Assisted Cracking ◽  
Material Environment ◽  
Recent Developments ◽  
New Generation

Environmentally assisted cracking phenomena are widespread across the transport, defence, energy and construction sectors. However, predicting environmentally assisted fractures is a highly cross-disciplinary endeavour that requires resolving the multiple material-environment interactions taking place. In this manuscript, an overview is given of recent breakthroughs in the modelling of environmentally assisted cracking. The focus is on the opportunities created by two recent developments: phase field and multi-physics modelling. The possibilities enabled by the confluence of phase field methods and electro-chemo-mechanics modelling are discussed in the context of three environmental assisted cracking phenomena of particular engineering interest: hydrogen embrittlement, localised corrosion and corrosion fatigue. Mechanical processes such as deformation and fracture can be coupled with chemical phenomena like local reactions, ionic transport and hydrogen uptake and diffusion. Moreover, these can be combined with the prediction of an evolving interface, such as a growing pit or a crack, as dictated by a phase field variable that evolves based on thermodynamics and local kinetics. Suitable for both microstructural and continuum length scales, this new generation of simulation-based, multi-physics phase field models can open new modelling horizons and enable Virtual Testing in harmful environments. 

scholarly journals Keeping it together: A phase-field version of path-connectedness and its implementation

2021 ◽  
Vol 15 ◽  
pp. 174830262110543
Author(s):  
Patrick Dondl ◽  
Stephan Wojtowytsch
Keyword(s):  
Phase Field ◽  
Geodesic Distance ◽  
Weighted Graph ◽  
Field Variable ◽  
Connected Components ◽  
Spontaneous Curvature ◽  
Graph Structure ◽  
Topological Constraint ◽  
Phase Field Models ◽  
Path Connectedness

We describe the implementation of a topological constraint in finite-element simulations of phase-field models, which ensures path-connectedness of preimages of intervals in the phase-field variable. The constraint takes the form of an energetic penalty for a suitable geodesic distance between all pairs of points in the domain. The main application of our method presented here is a discrete steepest descent of a phase-field version of a bending energy with spontaneous curvature and additional surface area penalty. This leads to disconnected surfaces without our topological constraint but connected surfaces with the constraint. Numerically, our constraint is treated by first transforming the double integral over all pairs of points in the domain to a weighted graph structure and then using Dijkstra’s algorithm to calculate the distance between discrete connected components.

Application of Coupled Lattice Boltzmann and Phase-Field Methods for Multiphase Flow Simulations

2013 ◽  
Author(s):  
Kannan N. Premnath ◽  
D. V. Patil ◽  
Sanjoy Banerjee
Keyword(s):  
Multiphase Flow ◽  
Phase Field ◽  
Lattice Boltzmann ◽  
Multiphase Flows ◽  
Field Variable ◽  
Field Methods ◽  
Flow Problems ◽  
Acceleration Techniques ◽  
Local Relaxation ◽  
Phase Field Methods

Coupling of lattice Boltzmann (LB) and phase-field (PF) methods is discussed for simulation of a range of multiphase flow problems. The local relaxation and shifting operators make the LB method an attractive candidate for the simulation of the single-phase as well as multiphase flows. For simulating interface dynamics, LB methods require to be coupled with an appropriate scheme representing interfacial dynamics. To this end, we have used a model based on the order parameter, which could be either an index function or a phase-field variable, and coupled it with a LB solver for the simulation of various classes of complex multi-physics and multiphase flows. The LB method is used to compute the flow-field, and, in the case of electrodeposition process modeling, the electro-static potential-field. The application of such a coupled LB-PF is illustrated by the solution of a variety of examples. Finally, fast simulation of such a coupled algorithm is achieved using the state-of-art numerical solution acceleration techniques involving preconditioning and multigrid approaches.

scholarly journals Phase-Field Models for Multi-Component Fluid Flows

2012 ◽  
Vol 12 (3) ◽  
pp. 613-661 ◽  
Author(s):  
Junseok Kim
Keyword(s):  
Phase Field ◽  
Fluid Flows ◽  
Surface Tension Force ◽  
Immiscible Fluids ◽  
Phase Field Method ◽  
Finite Width ◽  
Field Methods ◽  
Practical Applications ◽  
Phase Field Models ◽  
Advection Term

AbstractIn this paper, we review the recent development of phase-field models and their numerical methods for multi-component fluid flows with interfacial phenomena. The models consist of a Navier-Stokes system coupled with a multi-component Cahn-Hilliard system through a phase-field dependent surface tension force, variable density and viscosity, and the advection term. The classical infinitely thin boundary of separation between two immiscible fluids is replaced by a transition region of a small but finite width, across which the composition of the mixture changes continuously. A constant level set of the phase-field is used to capture the interface between two immiscible fluids. Phase-field methods are capable of computing topological changes such as splitting and merging, and thus have been applied successfully to multi-component fluid flows involving large interface deformations. Practical applications are provided to illustrate the usefulness of using a phase-field method. Computational results of various experiments show the accuracy and effectiveness of phase-field models.

Coupled microstructural-compositional evolution informed by a thermodynamic database using the hybrid Potts-phase field model

2013 ◽  
Vol 1524 ◽  
Author(s):  
Jordan J. Cox ◽  
Eric R. Homer ◽  
Veena Tikare
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Field Method ◽  
Phase Field Method ◽  
Field Methods ◽  
Energy Functionals ◽  
Compositional Evolution ◽  
Recent Developments ◽  
Phase Field Methods

ABSTRACTA recently introduced hybrid Potts-phase field method has demonstrated the ability to evolve microstructures in conjunction with compositional fields tied to different phases. In this approach, Monte Carlo Potts methods are used to evolve the microstructure while phase field methods are used to evolve the composition, and the two fields are coupled through free energy functionals. Recent developments of the model allow different multi-component alloy systems to be simulated by using thermodynamic databases and kinetic quantities to dictate the behavior. An example of the method using the aluminum-silicon binary system is demonstrated.

scholarly journals Irreversibility and alternate minimization in phase field fracture: a viscosity approach

2020 ◽  
Vol 71 (4) ◽  
Author(s):  
Stefano Almi
Keyword(s):  
Phase Field ◽  
Field Variable ◽  
Minimization Algorithm ◽  
Vanishing Viscosity ◽  
Vanishing Viscosity Limit ◽  
Phase Field Models ◽  
Iterative Minimization ◽  
Viscosity Limit

Abstract This work is devoted to the analysis of convergence of an alternate (staggered) minimization algorithm in the framework of phase field models of fracture. The energy of the system is characterized by a nonlinear splitting of tensile and compressive strains, featuring non-interpenetration of the fracture lips. The alternating scheme is coupled with an $$L^{2}$$ L 2 -penalization in the phase field variable, driven by a viscous parameter $$\delta >0$$ δ > 0 , and with an irreversibility constraint, forcing the monotonicity of the phase field only w.r.t. time, but not along the whole iterative minimization. We show first the convergence of such a scheme to a viscous evolution for $$\delta >0$$ δ > 0 and then consider the vanishing viscosity limit $$\delta \rightarrow 0$$ δ → 0 .

Recent developments in phase-field models of solidification

1995 ◽  
Vol 16 (7) ◽  
pp. 163-172 ◽  
Author(s):  
A.A Wheeler ◽  
N.A Ahmad ◽  
W.J Boettinger ◽  
R.J Braun ◽  
G.B McFadden ◽  
...  
Keyword(s):  
Phase Field ◽  
Phase Field Models ◽  
Recent Developments

MULTISCALE MODELING OF SOLIDIFICATION: PHASE-FIELD METHODS TO ADAPTIVE MESH REFINEMENT

2005 ◽  
Vol 19 (31) ◽  
pp. 4525-4565 ◽  
Author(s):  
NIKOLAS PROVATAS ◽  
MICHAEL GREENWOOD ◽  
BADRINARAYAN ATHREYA ◽  
NIGEL GOLDENFELD ◽  
JONATHAN DANTZIG
Keyword(s):  
Asymptotic Analysis ◽  
Phase Field ◽  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Field Equations ◽  
Field Methods ◽  
Dendritic Spacing ◽  
Phase Field Models ◽  
Phase Field Methods

We review the use of phase field methods in solidification modeling, describing their fundamental connection to the physics of phase transformations. The inherent challenges associated with simulating phase field models across multiple length and time scales are discussed, as well as how these challenges have been addressed in recent years. Specifically, we discuss new asymptotic analysis methods that enable phase field equations to emulate the sharp interface limit even in the case of quite diffuse phase-field interfaces, an aspect that greatly reduces computation times. We then review recent dynamic adaptive mesh refinement algorithms that have enabled a dramatic increase in the scale of microstructures that can be simulated using phase-field models, at significantly reduced simulation times. Combined with new methods of asymptotic analysis, the adaptive mesh approach provides a truly multi-scale capability for simulating solidification microstructures from nanometers up to centimeters. Finally, we present recent results on 2D and 3D dendritic growth and dendritic spacing selection, which have been made using phase-field models solved with adaptive mesh refinement.

scholarly journals Simulating Pitting Corrosion in AM 316L Microstructures Through Phase Field Methods and Computational Modeling

2022 ◽  
Author(s):  
Patrick Brewick
Keyword(s):  
Pitting Corrosion ◽  
Phase Field ◽  
Stress Responses ◽  
Corrosion Process ◽  
Computational Simulations ◽  
Stress Concentrations ◽  
Field Methods ◽  
Phase Field Models ◽  
Circular Model ◽  
Phase Field Methods

Abstract This work investigates how the crystallographic features of additive manufactured (AM) microstructures impact the pitting corrosion process through computational simulations of phase field models. Crystallographic influence is explored by introducing orientation dependencies into the corrosion potentials and elastic constants of the model through microstructural data provided from AM 316L samples. Comparisons of evolved pit morphologies and stress responses are made to a standard homogeneous, semi-circular model to better highlight how the complexity of AM microstructures affects pit evolution and stress concentrations. The results illustrate that AM-informed modeling cases produce larger, deeper pits with numerous locations of elevated stress concentrations along the pit front.

Recent developments in low-voltage SEM of polymers

1993 ◽  
Vol 51 ◽  
pp. 866-867
Author(s):  
S.J. Krause ◽  
W.W. Adams
Keyword(s):  
Low Voltage ◽  
Chromatic Aberration ◽  
Thermal Electron ◽  
Analytical Technique ◽  
Recent Developments ◽  
Beam Currents ◽  
New Generation ◽  
First Time ◽  
Voltage Scanning ◽  
Beam Damage

Over the past decade low voltage scanning electron microscopy (LVSEM) of polymers has evolved from an interesting curiosity to a powerful analytical technique. This development has been driven by improved instrumentation and in particular, reliable field emission gun (FEG) SEMs. The usefulness of LVSEM has also grown because of an improved theoretical and experimental understanding of sample-beam interactions and by advances in sample preparation and operating techniques. This paper will review progress in polymer LVSEM and present recent results and developments in the field.In the early 1980s a new generation of SEMs produced beam currents that were sufficient to allow imaging at low voltages from 5keV to 0.5 keV. Thus, for the first time, it became possible to routinely image uncoated polymers at voltages below their negative charging threshold, the "second crossover", E2 (Fig. 1). LVSEM also improved contrast and reduced beam damage in sputter metal coated polymers. Unfortunately, resolution was limited to a few tenths of a micron due to the low brightness and chromatic aberration of thermal electron emission sources.

scholarly journals Phase-field model of precipitation processes with coherency loss

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Tian-Le Cheng ◽  
You-Hai Wen
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Ostwald Ripening ◽  
Phase Field Model ◽  
Energy Criterion ◽  
Field Variable ◽  
Ginzburg Landau ◽  
Underlying Mechanisms ◽  
Flood Fill ◽  
Coherency Loss

AbstractA phase-field model is proposed to simulate coherency loss coupled with microstructure evolution. A special field variable is employed to describe the degree of coherency loss of each particle and its evolution is governed by a Ginzburg-Landau type kinetic equation. For the sake of computational efficiency, a flood-fill algorithm is introduced that can drastically reduce the required number of field variables, which allows the model to efficiently simulate a large number of particles sufficient for characterizing their statistical features during Ostwald ripening. The model can incorporate size dependence of coherency loss, metastability of coherent particles, and effectively incorporate the underlying mechanisms of coherency loss by introducing a so-called differential energy criterion. The model is applied to simulate coarsening of Al3Sc precipitates in aluminum alloy and comprehensively compared with experiments. Our results clearly show how the particle size distribution is changed during coherency loss and affects the coarsening rate.

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