Monday 8:00 AM

March 14, 2022

Room: Materials Design

Location: On-Demand Room

Can atomistic simulations tell us their corresponding evolution equations in the continuum limit? Can a non-equilibrium process be interpreted as an equilibrium one? In this talk, various coarse-graining strategies will be discussed to elucidate these questions, and provide important connections between atomistic and continuum models.

A phase-field model is a numerical model that is widely employed for simulating material microstructure evolution because it exhibits higher accuracy than other models. However, lack of material parameters is the primary issue that needs to be addressed in phase-field studies. Presently, there are no effective methods for determining such material parameters both through experiments and simulations. A solution for addressing this issue is to conduct phase-field simulation by simultaneously performing the experiments or molecular dynamics simulations. To this end, data assimilation is a promising technique that integrates the aforementioned two methods. Furthermore, application of data assimilation has become possible owing to the recent advancements in computer performance, such as computing using graphics processing units. In this presentation, I will demonstrate our current approach for determining material parameters by utilizing both high-performance phase-field simulation and data assimilation.

Phase-field is now a standard approach for modeling solidification fronts. When used in the context of additive manufacturing, computational requirements can be quite demanding in 3D, with many grains of different orientations, multiple alloying species, and high velocity moving solidification fronts. The addition of a coupled evolving temperature field can make the equations very stiff, in which case an implicit time stepping approach can be beneficial. In this talk, we will discuss some of these issues, and how recent developments in high-performance computers with GPU accelerators provide both challenges and opportunities for these models. More specifically, we will discuss and show results using the Kim-Kim-Suzuki model of coexistent phases coupled with CALPHAD databases.This research was supported by the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration.

Hydrogen Cottrell atmosphere prescribes elevated hydrogen concentrations near dislocations which can contribute to hydrogen embrittlement. Traditional atomistic simulations of Cottrell atmosphere can only be achieved using Monte Carlo methods where smooth concentration profiles are averaged over millions or more configurations. These methods preclude the effects of important phenomena including dislocation thermal vibration, solute-solute dynamic interaction, and dislocation migration under applied stresses. Molecular dynamics methods do not have these limitations, but they deal only with one configuration which cannot yield smooth concentration profiles. Here we demonstrate that for a fast diffusion solute like hydrogen, time and ensemble averaged molecular dynamics methods also enable averages of millions or more distinct configurations, resulting in smooth calculations of Cottrell atmosphere. We have performed such molecular dynamics simulations to study hydrogen Cottrell atmospheres around edge dislocations in aluminum and stainless steel alloys revealing important insights of Cottrell atmosphere formation not known in the past.

The grain topology of polycrystalline microstructures has a critical influence on mechanical properties, but its mathematical quantification remains a challenge due to the complexity of grain shapes. This work develops a universal descriptor that quantifies 2D and 3D grain shapes of microstructures. In particular, it is derived by the eigenvalues that are the functions of Hu moments, which are invariant to shape transformations. The descriptor is also integrated into a novel uncertainty quantification (UQ) methodology to capture the uncertainty in grain shapes of additively manufactured microstructures and model their propagation on mechanical properties. To generate sufficient statistics, Markov Random Field (MRF) is applied to build the synthetic microstructure data for the aerospace alloy, Titanium-7wt%- Aluminum (Ti-7Al) using small-scale experimental data. The UQ formulation is used to predict the variations in the texture and grain shapes of the microstructures, as well as the elasto-plastic material properties computed by crystal plasticity simulations.

ExaCA, an exascale-capable cellular automata application, is a grain-scale microstructure modeling tool designed to simulate as-solidified alloys during additive manufacturing (AM). As part of the Exascale Computing Project (ECP) and ExaAM workflow, ExaCA must leverage new node architectures (e.g. GPUs) for high performance computing. We will show how CA is implemented with the performance portable Kokkos library and compare performance across parallel backends for AM test problems. Additionally, we will discuss the “sparse” and “extended” input data formats for time-temperature history from the process model, which result in computational cost – accuracy tradeoffs. Simulated microstructures with varying levels of model approximations will be compared to those characterized from AM benchmark experiments. Continuing work will involve analysis of the simplifying assumptions of the process-microstructure modeling approach, with identification of needs for more rigorous modeling, additional input data, as well as performance considerations necessitated by these model improvements. Supported by ECP (17-SC-20-SC).

Data assimilation is a mathematical technique to estimate model states and parameters by integrating a simulation model with experimental data. We developed an adjoint model to integrate a phase-field model for spinodal decomposition with time-series measurement data of compositional field maps to estimate six material parameters (Gibbs energy parameters etc.) in the phase-field model. To confirm the effectiveness of the developed adjoint model, numerical tests called “twin experiments” were conducted using synthetic measurement data prepared in advance through phase-field simulation. In the twin experiments, the optimum estimates of six model parameters of interest were shown to coincide with true values. Furthermore, the effects of the standard deviation of measurement noise and the time interval of measurements on the uncertainties of optimum estimates of parameters were successfully quantified by the twin experiments.

Modeling diffusion from the atomic scale is necessary because experimental studies are only feasible at high temperatures and in most systems, the full Onsager matrix cannot be measured. The problem is mostly solved in pure and dilute alloys but remains a challenge in concentrated alloys due to the vastness and complexity of the configuration space. In this work, we aim to extend the kinetic cluster expansion formalism in order to get an efficient evaluation of transport coefficients in concentrated alloys based on atomic-scale data. Our formalism relies on the Self-Consistent Mean Field Theory and is implemented in the KineCluE code. We treat the configuration exactly in the vicinity of the diffusing species, while further away atoms are replaced by a homogeneous mean-field. We compare our model’s performance to previous studies and provide a detailed study of the diffusion properties of model Fe-Cr alloys.

KineCluE is a recently developed open-source software for calculating Onsager transport coefficients of small defect-solute clusters based on self-consistent mean field theory (SCMF). Using this tool requires the input of a few to over thousands of energy levels for the relevant configurations and saddle-points. We developed an interface to automate the calculation of the required energy levels of vacancy-solute clusters using NEB and interatomic potentials in LAMMPS. We combine this with a low-temperature expansion approximation of cluster concentrations to describe multi-cluster transport coefficients for an FCC Cu-Ag system and a BCC Fe-Cu system. Both systems demonstrate the importance of including appropriate clusters to model the full transport behavior. We also compare Fe-Cu cluster diffusivity calculated by KineCluE with results calculated from KMC simulations parameterized with the same interatomic potential. They show good agreement, and we confirm and quantify the prediction that tri-vacancy-solute clusters can contribute significantly to solute diffusion.

Solidification during additive manufacturing has several relevant length scales. Overlap between these scales calls into question scale separation assumptions in many multiscale modeling methods. We present a new approach to examine the interplay of phenomena at the melt pool, grain, and dendrite scales and whether it is captured in a multiscale model. 2D, GPU-accelerated, polycrystalline, dendrite-resolved, melt-pool-scale phase-field simulations are used as reference solutions. The multiscale model consists of a melt-pool-scale thermal model (macroscale model) and phase-field simulations of a few dendrite arms growing epitaxially from a base plate grain (microscale model). Most microstructural features are accurately represented in the multiscale model, except the primary dendrite arm spacing. We discuss the impact of these findings on multiscale modeling of additive manufacturing, including for optimally controling the heat source for a target microstructure. This abstract has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy.

While density functional theory (DFT) is a critical tool in predictive understanding of materials and widely applicable, it is relatively slow and computationally expensive. As an attractive alternative, graph convolutional neural networks (GCNN) have demonstrated significant predictive power as surrogate models for atomistic properties. Despite their success, large network sizes and computational complexity make the training of the GCNNs challenging and potentially unstable. In this work, we develop an accelerated and stable GCNN application built for effective use of heterogeneous hardware and with physical constraints-based regularization. Specifically, we develop a GCNN with a focus on distributed, GPU-capable training and prediction, for ultimate use on the Summit and upcoming exascale Frontier supercomputers, which is based on PyTorch with multiple graph interaction models and multi-headed network architectures. We will present GCNN predictions for open source DFT data sets, contrasting accuracy, stability, and computational cost.

An interatomic potential for CrFeMnNi quaternary alloys focusing on plasticity has been developed with the embedded atomic method (EAM) termed EAM-21. The newly developed interatomic potential was based on a tested previously developed potential of FeNiCr ternary alloys and pure Mn. The potential parameters were determined by fitting to experimental, density functional theory and other existing EAM data, including elastic constants and stacking fault energy. Other properties of the potential include structural stability, the potential predict face-centered cubic (fcc) structure stability under shear strain at elevated temperature. The potential applicability was tested on 1⁄2[110] edge dislocation core structure for pure Ni, equiatomic alloy of CrFeMnNi and its subsystems at different temperature. The stable glide of edge dislocation and fcc phase stability at different temperature range was confirmed. This study demonstrates the suitability of EAM-21 potential for plasticity mechanismand mechanical properties of CrFeMnNi system.

A dislocation-density based multiple slip crystalline plasticity formulation and a microstructurally-based fracture methodology have been used in conjunction with a new statistical framework to develop a representation of failure probabilities for hydrided Zircalloy-4 materials. Using a genetic learning algorithm and Bayes’ rule, an extreme value theory (EVT) of fracture was obtained for a stochastic representation of crack nucleation and propagation. This resulting validated model of crack probability can be applied either topographically to generate contours of crack likelihood on a representative material or applied directly to the input parameters to provide a library of fracture probabilities for a broad range of microstructural characteristics and mechanisms. The proposed framework can provide a framework for understanding material failure, and how fundamental material mechanisms can be used to inform predictions at the microstructural scale.

Melt pool scale models of additive manufacturing (AM) processes can help elucidate process-structure-property relationships for AM parts. However, the predictive capability of these models is limited by uncertainties in experimental conditions and model parameters. Here, a method is proposed to calibrate uncertain parameters used in a continuum model for powder bed fusion AM. Two different model fidelities are examined: a higher fidelity version that considers fluid flow in the melt pool and a lower fidelity version that neglects fluid flow. The Tasmanian package was used for automated surrogate construction and calibration of melt pool width and depth to within 10% of the NIST AMB2018-02 dataset melt pool geometries. It is demonstrated that the heat source dimensions in the lower fidelity model can be calibrated to approximate the effects of fluid flow in the melt pool. This work was supported by the Exascale Computing Project.

Machine learning techniques using rapid artificial neural networks (RANN) have proven to be effective tools to rapidly mimic first principles calculations. New neural network potentials are capable of accurately modeling the transformations between the \alpha,\beta\ and\ \omega phases of titanium and zirconium including accurate prediction of the equilibrium phase diagram. These potentials show remarkable accuracy beyond their first principle dataset, indicating that they reliably parameterize the underlying physics. Transitions between each of the phase pairs are observed in dynamic simulation using calculations of the Gibbs free energy. The calculated triple points are 8.67 GPa, 1058 K for Ti and 5.04 GPa, 988.35 K for Zr, close to their experimentally observed values. The success of the RANN potentials with single element phase transitions suggests the potential of this method to make robust alloy phase diagram calculations such as for TiAl. This can augment or anticipate experiments to accelerate materials discovery.

Recent computational and experimental studies on copper/graphene nanocomposites indicate the potential for graphene additions to improve upon the conductive properties of polycrystalline copper. In order to ascertain the effect of these additions and disambiguate their contribution with respect to microstructure on their ultimate conductivity, we have developed a finite difference-based calculation of electrical conductivity as a function of microstructure. To this end, the effects of grain size, texture, dislocation density, and graphene content on the conductivity of the Cu-Graphene nanocomposites were evaluated. Additionally, a parameter study was performed to evaluate the effect of graphene on the Cu grain boundaries on the associated change in grain boundary conductivity. Our calculations indicate a range of grain size, grain boundary coverage, and change in grain boundary properties that would likely result in an improvement upon bulk Cu conductivity.

Phase field approaches have been recently used to model dislocation motion and interaction in many systems including FCC, BCC, HCP metals, and also multi-principal element alloys (MPEAs). While many interesting features about dislocation motion can be captured, phase field approaches applied to dislocation motion and interaction typically do not account for thermally activated motion. In this work, a kinetic Monte Carlo (kMC) scheme is integrated into a phase field dislocation dynamics (PFDD) model to account for thermal activation using Gillespie’s Stochastic Simulation Algorithm. While the implementation is general and could be applied to many different thermally activated processes, we apply the model to simulate a dislocation transmitting through an interface.

A major challenge in simulating the thermal behavior of an entire part made by additive manufacturing processes is the disparate length and time scales between transport phenomena occurring in the melt pool and the component. A common approach for the concurrent solution of partial differential equations on multiple computational resources is spatial parallelization by means on mesh decomposition. Ideally, the speed up from spatial parallelization would be linear, however, communication between resources eventually limits the speed up to a constant value, known as the strong scaling limit. Once spatial parallelization becomes saturated, additional parallelism by means of time-domain decomposition is needed to take advantage of high performance computing (HPC) resources. In this talk, a time-parallel method is proposed to improve the computational scalability of additive manufacturing simulations on HPC systems. Example results are shown for the NIST AM benchmark, and the tradeoff between accuracy and speedup is investigated.

Here we report the development and results of a computationally-efficient 3-dimensional multiphase Monte Carlo approach for microstructure-scale formation and evolution of “line compound” materials systems such as SiC-Diamond composite materials from carbon and silicon precursors, the selected example. This new model is capable of considering long-range interactions between components or phases as a system evolves, enabling simulation of processes such as diffusion-limited phase transformations concurrently with traditionally-modeled microstructure evolution processes such as grain growth or allotropic phase change. This model has been parameterized for the formation of SiC-Diamond composites using Si and C precursor materials in conjunction with recent experimental efforts, including formation of SiC, as well as growth of graphitic layers at interfaces and thermal behavior during processing. The results are evaluated with phase field model to test the mechanical perfomance of resultant Si-SiC-C microstructures to optimize the precursor configuration and processing conditions.

Titanium alloys find diverse aerospace applications owing to their superior combination of lightweight, mechanical properties, corrosion resistance, and so forth. We analyzed the available data, in the literature, of the titanium alloys for two critical applications: landing gear beams and aeroengines. We applied fundamental statistical analysis (FSA), principal component analysis (PCA), and multiple-attribute decision making (MADM) to unearth the voice of the data. The ranks assigned by several MADMs, including ARAS (additive ratio assessment method)), MEW (multiplicative exponent weighing) and ROVM (range of value method) were consistent. FSA and PCA consolidated the MADM ranks of the alloys and identified similar top-ranked alloys. The investigations highlight similarities (and differences) across several grades/variants of the alloys, suggest potential replacement or substitute for the existing alloys, weed-out some of the heavier alloys and consequently help in reducing the weight, and provide possible directions for improvement and/or development of these alloys.