Quantifying uncertainty in the process-structure relationship for Al–Cu solidification

Tran, Anh; Liu, Dehao; Tran, Hoang A.; Wang, Yan

doi:10.1088/1361-651X/ab2690

Title: Quantifying uncertainty in the process-structure relationship for Al–Cu solidification

Abstract

Phase field method (PFM) is a simulation tool to predict microstructural evolution during solidification and is helpful to establish the process-structure relationship for alloys. The robustness of the relationship however is affected by model-form and parameter uncertainties in PFM. In this paper, the uncertainty associated with the thermodynamic and process parameters of PFM is studied and quantified. Surrogate modeling is used to interpolate four quantities of interests (QoIs), including dendritic perimeter, area, primary arm length, and solute segregation, as functions of thermodynamic and process parameters. A sparse grid approach is applied to mitigate the curse-of-dimensionality computational burden in uncertainty quantification. Polynomial chaos expansion is employed to obtain the probability density functions of the QoIs. The effect of parameter uncertainty on the Al–Cu dendritic growth during solidification simulation are investigated. Here, the results show that the dendritic morphology varies significantly with respect to the interface mobility and the initial temperature.

Authors:

^[1];

^[2];

^[1]

Georgia Inst. of Technology, Atlanta, GA (United States)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Publication Date:: 2019-06-19

Research Org.:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1559610

Grant/Contract Number:: AC05-00OR22725

Resource Type:: Accepted Manuscript

Journal Name:: Modelling and Simulation in Materials Science and Engineering

Additional Journal Information:: Journal Volume: 27; Journal Issue: 6; Journal ID: ISSN 0965-0393

Publisher:: IOP Publishing

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE; uncertainty quantification; phasefield method; solidification; sparse grid; polynomial chaos expansion

Citation Formats


                    Tran, Anh, Liu, Dehao, Tran, Hoang A., and Wang, Yan. Quantifying uncertainty in the process-structure relationship for Al–Cu solidification.  United States: N. p., 2019. 
Web.  doi:10.1088/1361-651X/ab2690.

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                    Tran, Anh, Liu, Dehao, Tran, Hoang A., & Wang, Yan. Quantifying uncertainty in the process-structure relationship for Al–Cu solidification.  United States.  https://doi.org/10.1088/1361-651X/ab2690

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                    Tran, Anh, Liu, Dehao, Tran, Hoang A., and Wang, Yan. Wed .  
"Quantifying uncertainty in the process-structure relationship for Al–Cu solidification".  United States.  https://doi.org/10.1088/1361-651X/ab2690.  https://www.osti.gov/servlets/purl/1559610.

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@article{osti_1559610,

  title        = {Quantifying uncertainty in the process-structure relationship for Al–Cu solidification},

  author       = {Tran, Anh and Liu, Dehao and Tran, Hoang A. and Wang, Yan},

  abstractNote = {Phase field method (PFM) is a simulation tool to predict microstructural evolution during solidification and is helpful to establish the process-structure relationship for alloys. The robustness of the relationship however is affected by model-form and parameter uncertainties in PFM. In this paper, the uncertainty associated with the thermodynamic and process parameters of PFM is studied and quantified. Surrogate modeling is used to interpolate four quantities of interests (QoIs), including dendritic perimeter, area, primary arm length, and solute segregation, as functions of thermodynamic and process parameters. A sparse grid approach is applied to mitigate the curse-of-dimensionality computational burden in uncertainty quantification. Polynomial chaos expansion is employed to obtain the probability density functions of the QoIs. The effect of parameter uncertainty on the Al–Cu dendritic growth during solidification simulation are investigated. Here, the results show that the dendritic morphology varies significantly with respect to the interface mobility and the initial temperature.},

  doi          = {10.1088/1361-651X/ab2690},

  journal      = {Modelling and Simulation in Materials Science and Engineering},

  number       = 6,

  volume       = 27,

  place        = {United States},

  year         = {2019},

  month        = {6}

}

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Title: Quantifying uncertainty in the process-structure relationship for Al–Cu solidification

Abstract

Citation Formats

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Phase-field-lattice Boltzmann studies for dendritic growth with natural convection journal, September 2017

Uncertainty Quantification in MD Simulations. Part I: Forward Propagation journal, January 2012

Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics journal, January 2009

Reliable kinetic Monte Carlo simulation based on random set sampling journal, February 2013

The multiphase-field model with an integrated concept for modelling solute diffusion journal, April 1998

Computational microstructure characterization and reconstruction for stochastic multiscale material design journal, January 2013

Bayesian Error Estimation in Density-Functional Theory journal, November 2005

Statistical approaches to forcefield calibration and prediction uncertainty in molecular simulation journal, February 2011

Multiscale Uncertainty Quantification Based on a Generalized Hidden Markov Model journal, March 2011

Sparse grids journal, May 2004

A dynamically adaptive sparse grids method for quasi-optimal interpolation of multidimensional functions journal, June 2016

Growth competition of columnar dendritic grains: A phase-field study journal, January 2015

Morphological Stability of a Particle Growing by Diffusion or Heat Flow journal, February 1963

Uncertainty quantification in modelling equiaxed alloy solidification journal, August 2016

Review of Structure Representation and Reconstruction on Mesoscale and Microscale journal, January 2014

How Short Is Too Short for the Interactions of a Water Potential? Exploring the Parameter Space of a Coarse-Grained Water Model Using Uncertainty Quantification journal, March 2014

Quantification of Epistemic Uncertainty in Grain Attachment Models for Equiaxed Solidification journal, February 2017

A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data journal, January 2008

The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations journal, January 2002

Uncertainty Quantification in MD Simulations. Part II: Bayesian Inference of Force-Field Parameters journal, January 2012

A Stochastic Projection Method for Fluid Flow journal, September 2002

Error correction in multi-fidelity molecular dynamics simulations using functional uncertainty quantification journal, April 2017

Parallel multiphase field simulations with OpenPhase journal, June 2017

Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes journal, January 2004

Reliable Molecular Dynamics: Uncertainty quantification using interval analysis in molecular dynamics simulation journal, February 2017

A phase-field model with antitrapping current for multicomponent alloys with arbitrary thermodynamic properties journal, August 2007

Stability of a Planar Interface During Solidification of a Dilute Binary Alloy journal, February 1964

Instabilities and pattern formation in crystal growth journal, January 1980

Phase-field models in materials science journal, July 2009

Uncertainty Quantification of Modelling of Equiaxed Solidification journal, July 2016

Error Estimates for Solid-State Density-Functional Theory Predictions: An Overview by Means of the Ground-State Elemental Crystals journal, October 2013

Scaling laws governing the growth and interaction of equiaxed Al-Cu dendrites: A study combining experiments with phase-field simulations journal, September 2018

A Stability Function for Explicit Evaluation of the Mullins‐Sekerka Interface Stability Criterion journal, January 1965

Multiphase-field approach for multicomponent alloys with extrapolation scheme for numerical application journal, June 2006

A method for numerical integration on an automatic computer journal, December 1960

Simulating Mobile Dendrites in a Flow journal, January 2013

Uncertainty quantification in reacting-flow simulations through non-intrusive spectral projection journal, February 2003

Simple Cubature Formulas with High Polynomial Exactness
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Quantitative phase-field modeling of dendritic growth in two and three dimensions
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Topological structural analysis of digitized binary images by border following
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Quantifying Parameter Sensitivity and Uncertainty for Interatomic Potential Design: Application to Saturated Hydrocarbons
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Front fluctuations for the stochastic Cahn–Hilliard equation
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Uncertainty analysis and estimation of robust AIREBO parameters for graphene
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Phase-Field Formulation for Quantitative Modeling of Alloy Solidification
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Uncertainty Quantification in Modeling Metal Alloy Solidification
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Uncertainty Quantification in Solidification Modelling
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Effect of interface anisotropy on spacing selection in constrained dendrite growth
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Generation of 3D representative volume elements for heterogeneous materials: A review
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An Efficient Saddle Point Search Method Using Kriging Metamodels
conference, January 2016

A review of dendritic growth during solidification: Mathematical modeling and numerical simulations
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Stochastic Cahn–Hilliard Equation with Fractional Noise
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An Efficient First-Principles Saddle Point Searching Method Based on Distributed Kriging Metamodels
journal, September 2017

Computational microstructure characterization and reconstruction: Review of the state-of-the-art techniques
journal, June 2018

Modeling of coupled motion and growth interaction of equiaxed dendritic crystals in a binary alloy during solidification
journal, March 2017

Orientation Dependence of Columnar Dendritic Growth with Sidebranching Behaviors in Directional Solidification: Insights from Phase-Field Simulations
journal, April 2018

Explicit Cost Bounds of Algorithms for Multivariate Tensor Product Problems
journal, March 1995

Mesoscale multi-physics simulation of rapid solidification of Ti-6Al-4V alloy
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Uncertainty quantification in molecular dynamics studies of the glass transition temperature
journal, March 2016

Uncertainty Quantification in Multiscale Simulation of Materials: A Prospective
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Prediction Uncertainty of Density Functional Approximations for Properties of Crystals with Cubic Symmetry
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Sensitivity analysis and uncertainty calculation for dispersion corrected density functional theory
journal, February 2011

Evidence for a universal law of dendritic growth rates
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Theory of dendritic growth—I. Elements of a stability analysis
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Model-Form Calibration in Drift-Diffusion Simulation Using Fractional Derivatives
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Reconciled Top-Down and Bottom-Up Hierarchical Multiscale Calibration of bcc fe Crystal Plasticity
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Special Issue on Uncertainty Quantification in Multiscale System Design and Simulation
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Data Driven, Predictive Molecular Dynamics for Nanoscale Flow Simulations under Uncertainty
journal, November 2013

Measurements of microhardness during transient horizontal directional solidification of Al-Rich Al-Cu alloys: Effect of thermal parameters, primary dendrite arm spacing and Al2Cu intermetallic phase
journal, May 2015

Phase-field-lattice Boltzmann studies for dendritic growth with natural convection
journal, September 2017

Uncertainty Quantification in MD Simulations. Part I: Forward Propagation
journal, January 2012

Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics
journal, January 2009

Reliable kinetic Monte Carlo simulation based on random set sampling
journal, February 2013

The multiphase-field model with an integrated concept for modelling solute diffusion
journal, April 1998

Computational microstructure characterization and reconstruction for stochastic multiscale material design
journal, January 2013

Bayesian Error Estimation in Density-Functional Theory
journal, November 2005

Statistical approaches to forcefield calibration and prediction uncertainty in molecular simulation
journal, February 2011

Multiscale Uncertainty Quantification Based on a Generalized Hidden Markov Model
journal, March 2011

Sparse grids
journal, May 2004

A dynamically adaptive sparse grids method for quasi-optimal interpolation of multidimensional functions
journal, June 2016

Growth competition of columnar dendritic grains: A phase-field study
journal, January 2015

Morphological Stability of a Particle Growing by Diffusion or Heat Flow
journal, February 1963

Uncertainty quantification in modelling equiaxed alloy solidification
journal, August 2016

Review of Structure Representation and Reconstruction on Mesoscale and Microscale
journal, January 2014

How Short Is Too Short for the Interactions of a Water Potential? Exploring the Parameter Space of a Coarse-Grained Water Model Using Uncertainty Quantification
journal, March 2014

Quantification of Epistemic Uncertainty in Grain Attachment Models for Equiaxed Solidification
journal, February 2017

A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
journal, January 2008

The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
journal, January 2002

Uncertainty Quantification in MD Simulations. Part II: Bayesian Inference of Force-Field Parameters
journal, January 2012

A Stochastic Projection Method for Fluid Flow
journal, September 2002

Error correction in multi-fidelity molecular dynamics simulations using functional uncertainty quantification
journal, April 2017

Parallel multiphase field simulations with OpenPhase
journal, June 2017

Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes
journal, January 2004

Reliable Molecular Dynamics: Uncertainty quantification using interval analysis in molecular dynamics simulation
journal, February 2017

A phase-field model with antitrapping current for multicomponent alloys with arbitrary thermodynamic properties
journal, August 2007

Stability of a Planar Interface During Solidification of a Dilute Binary Alloy
journal, February 1964

Instabilities and pattern formation in crystal growth
journal, January 1980

Phase-field models in materials science
journal, July 2009

Uncertainty Quantification of Modelling of Equiaxed Solidification
journal, July 2016

Error Estimates for Solid-State Density-Functional Theory Predictions: An Overview by Means of the Ground-State Elemental Crystals
journal, October 2013

Scaling laws governing the growth and interaction of equiaxed Al-Cu dendrites: A study combining experiments with phase-field simulations
journal, September 2018

A Stability Function for Explicit Evaluation of the Mullins‐Sekerka Interface Stability Criterion
journal, January 1965

Multiphase-field approach for multicomponent alloys with extrapolation scheme for numerical application
journal, June 2006

A method for numerical integration on an automatic computer
journal, December 1960

Simulating Mobile Dendrites in a Flow
journal, January 2013

Uncertainty quantification in reacting-flow simulations through non-intrusive spectral projection
journal, February 2003