Algorithm Development in Materials Science and Engineering: Nano and Micro Scale Algorithms and Their Applications
Sponsored by: TMS Materials Processing and Manufacturing Division, TMS: Computational Materials Science and Engineering Committee, TMS: Integrated Computational Materials Engineering Committee, TMS: Phase Transformations Committee, TMS: Solidification Committee
Program Organizers: Mohsen Asle Zaeem, Colorado School of Mines; Mikhail Mendelev, NASA ARC; Garritt Tucker, Colorado School of Mines; Ebrahim Asadi, University of Memphis; Bryan Wong, University of California, Riverside; Sam Reeve, Oak Ridge National Laboratory; Enrique Martinez Saez, Clemson University; Adrian Sabau, Oak Ridge National Laboratory
Monday 2:00 PM
February 28, 2022
Room: 253A
Location: Anaheim Convention Center
Session Chair: Mohsen Asle Zaeem, Colorado School of Mines; Sam Reeve, Oak Ridge National Laboratory
2:00 PM
Combining Discrete and Continuous in Time Stochastic Simulations in a Solid-solid Phase Field Simulation: Nicholas Julian1; Enrique Martinez Saez2; Jaime Marian1; 1University of California Los Angeles; 2Clemson University
Models driven by stochastic processes capture fluctuations found in natural systems which are absent in the solution of ordinary and partial differential equations. However, due to disparities between the characteristics of discrete and continuous-in-time stochastic processes, models are often restricted to quantities which are exclusively either discrete or continuous in time, such as the Poisson processes of kinetic Monte Carlo or the Brownian motion of fluctuation hydrodynamics. In addition to having distinct probability distributions, discrete and continuous in time processes impose different restrictions on the numerical integration schemes applied to them, e.g. the Stratonovich numerical integration scheme typically applied to multiplicative Gaussian white noise does not preserve the chain rule of differentiation when applied to multiplicative Poisson noise. In this presentation we explore the difference in distributions of stochastic processes driven by both Gaussian and Poisson multiplicative noises through an application of Marcus canonical integral to a solid-solid phase transformation.
2:20 PM
An Orientation-field Phase Field Model for Anisotropic Grain Growth: Philip Staublin1; Peter Voorhees1; James Warren2; Arnab Mukherjee1; 1Northwestern University; 2National Institute of Standards and Technology
Grain boundary properties are a function of the misorientation and inclination of the boundary, or the five macroscopic degrees of freedom. Existing multi-order parameter models of grain growth that include these five degrees of freedom can lead to spontaneous grain formation at boundaries, involve many order parameters, and may not correctly reproduce the kinetics at triple junctions. A potential solution is to employ an orientation-field phase field model that uses a single scalar or vector field to track the local crystal orientation. An extension of the Henry-Mellenthin-Plapp orientation-field model is presented for simulations of anisotropic grain growth, allowing the grain boundary energy and mobility to vary with all five crystallographic degrees of freedom. The model correctly reproduces analytical equilibrium dihedral angles and steady state velocities for triple junctions, showing promise for use in large scale simulations of grain coarsening.
2:40 PM
Digital Representation and Quantification of Discrete Dislocation Structures: Andreas Robertson1; Surya Kalidindi1; 1Georgia Institute of Technology
Discrete dislocation structures and their evolution are known to control the mechanical properties of metal samples. Specifically, the spatial arrangement of these defect structures plays a fundamental role in this linkage. Although the optimal design of many extreme environment engineering materials requires the careful study and design of these defect systems, the lack of computationally efficient and statistically rigorous descriptors for such defect systems has hindered researchers’ ability to effectively perform these studies. In this presentation, we describe a computational framework for the efficient, rigorous statistical quantification and low-dimensional representation of dislocation structures using the formalism of two-point statistics along with principal component analysis. We also discuss the usefulness of this basic framework for comparing and observing dislocation structures by using the framework to perform an supervised classification of a dislocation structure dataset.
3:00 PM
Line Free 3D Dislocation Dynamics in Finite Domains: Aitor Cruzado1; Pilar Ariza2; Alan Needleman1; Michael Ortiz3; Amine Benzerga1; 1Texas A&M University; 2University of Seville; 3California Institute of Technology
We develop a method for three-dimensional discrete dislocation plasticity in finite domains. The method is based on the line-free framework of monopoles, in which dislocation events are considered as a transportation map problem. Long-range interactions are accounted for through linear elasticity and a core regularization procedure. Monopole motion is governed by an appropriate expression of the Peach-Koehler force and a drag-type relation. General boundary-value problem solutions are obtained by superposition of the infinite medium solution for the dislocations and a complementary finite-element solution that enforces boundary conditions. A computationally efficient approach, based on the principle of virtual work, is used to formulate and solve the image problem. Special attention is given to the interaction of curved dislocations with arbitrary domain boundaries and free surfaces. For illustration, calculations are carried out to investigate size effects that may arise in the compression of pillars and torsion of wires.
3:20 PM Break
3:40 PM
Statistics of the Lattice Distortion of Dislocated Crystals: Joseph Anderson1; Anter El-Azab1; 1Purdue University
How are the internal statistics of lattice distortions related to the underlying defect configuration? This complex relationship lies at the heart of modern characterization methods of crystal plasticity, e.g. electron back-scatter diffraction, high-energy x-ray diffraction, etc. While the forward problem, from the dislocation configuration to the internal lattice distortion field, is well understood, the inverse relationship is poorly understood. The present study will focus on dimensionality reduction of the relationship between the dislocation density autocorrelation functions and the internal elastic distortion distribution. The purpose of this work is to search for a low-dimensional subspace of the 9-dimensional distortion tensor space which accounts for the majority of variation in the distortion field. Following identification of such a subspace, linkages from these internal elastic distortion features to the dislocation density autocorrelation functions are established.