Predictive Multiscale Modeling for Decision Support in Design of - PowerPoint PPT Presentation

Predictive Multiscale Modeling for Decision Support in Design of Hierarchical Alloy Systems David L. McDowell Woodruff School of Mechanical Engineering School of Materials Science & Engineering Georgia Institute of Technology Atlanta, GA USA Predictive Multiscale Materials Modeling Isaac Newton Institute, Cambridge University December 2, 2015

The Mesoscale Gap in Modeling Dislocations in Metallic Systems The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering Thermodynamics and Essential for (i) mechanism ID, (ii) validation near equilibrium kinetics • Current Students: Shuozhi Xu, • NSF PSU-GT Center for Paul Kern, Aaron Tallman Computational Materials Design • NSF CMMI Any opinions, findings, and conclusions or recommendations expressed here are those Former students and post docs of the authors and do not necessarily reflect the views of the National Science Foundation. • Ryan Austin and Jeff Lloyd, ARL • AFOSR, ARL • Craig Przybyla and Bill Musinski, • QuesTek, NAVAIR AFRL • DOE NEAMS • Gustavo Castelluccio, Sandia • Conor Hennessey Evolutionary responses (properties): Nonequilibrium, Length and time scales are both involved metastable 2

Common Combined Strategy The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering Mechanisms, Validation Scale Specific Objective Bottom-Up Top-Down limited but increasing 3

A More General Perspective on Crystalline Plasticity The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering Dislocation field mechanics Coarse-grained atomistics Various problems DDD, PFM demand a suite of Microscopic phase Generalized continua models field models Grain scale crystal plasticity 4

What are the Elements of Crystalline Plasticity? The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering • Plastic anisotropy via slip • Elastic anisotropy • Slip system interaction • Multiplication and recovery (implicit or explicit) • Thermally activated flow • Lattice rotation via skew symmetric plastic velocity gradient • Mixed character 3D dislocations (implicit or explicit) • Dislocation core effects • Crystal connection for elastic and plastic incompatibilities at multi-resolution • Long range elastic dislocation interactions • Distinct nucleation, multiplication, and annihilation • Junction formation and short range interactions • Cross slip, climb 5

Uncertainty in Multiscale Modeling The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering Uncertainty in Models at a Given Scale • Assumed mechanism(s) • Form of model/equation Uncertainty in Scale • Model parameters Linking Algorithms • Numerical algorithm and implementation • Model reduction (reduction of • Solution convergence order) • Sample sets analyzed and • Configuration of information spatial scales of simulation Not much passing (e.g., handshaking vs. • Randomness of structure direct parameter estimation) attention in • Type of coupling – different literature parameter spaces, discrete vs continuum, dynamic vs Panchal, J.H., Kalidindi, S.R., and thermodynamic, etc. McDowell, D.L., Computer-Aided • Lack of scale separation (time, Design, Vol. 45, No. 1, 2013, pp. 4 – 25. space) • Forms of linking strategy • Parameters passed 6

Scale Bridging Methods – Mesoplasticity The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering Panchal, Kalidindi, McDowell, Computer-Aided Design, 2013 Length Time Scale Models Examples of Scale Bridging Primary Sources of Scale Approaches Uncertainty 2 nm NA/ ground state First principles, e.g., Density Assumptions in DFT method, Functional Theory (DFT) placement of atoms Quantum MD 10 ns Molecular dynamics (MD) Interatomic potential, cutoff, 200 nm thermostat and ensemble These are Domain decomposition, coupled atomistics Attenuation due to abrupt interfaces of discrete dislocation (CADD), coarse models, passing defects, coarse hierarchical two- grained MD, kinetic Monte Carlo graining defects Discretization of dislocation lines, scale transitions cores, reactions and junctions, grain 2 m m s Discrete dislocation dynamics boundaries Averaging methods for defect kinetics and lattice rotation Multiscale crystal plasticity Crystal plasticity, including generalized Kinetics, slip system hardening (self continuum models (gradient, and latent) relations, cross slip, micropolar, micromorphic) obstacle interactions, increasing # 1000 s adjustable parameters 20 m m RVE simulations, polycrystal/composite RVE size, initial and boundary homogenization conditions, eigenstrain fields, self- consistency 200 m m Days Heterogeneous FE with simplified Mesh refinement, convergence, model constitutive relations reduction 7 Substructuring, variable fidelity, adaptive Loss of information, remeshing error,

Multilevel Design & Development: Conceptualization The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering ) ) Limitation in e e v v i i t t c c u u Inverse problem d d n n i i ( ( Performance Performance s s n n a a e e m m / / s s l l a a o o System G G Properties Properties High Degree of ) ) e e Structure Structure v v i i Assembly Uncertainty t t c c u u d d e e d d ( ( t t c c e e f f f f Processing Processing e e d d n n a a Part e e s s u u a a C C G.B. Olson, Science , 29 Aug., 1997, Vol. 277 Continuum Mesoscale Material Selection Atomistic Quantum Integrated materials & product design 8

Shift to Concurrent Product-Process-Material System Design The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering System Specifications System Subsystems Components Match Parts the time Materials Material frame Specifications Macro Meso Molecular Quantum Penn State- GT CCMD NSF I/UCRC 2005-2013 9

Mappings in Multilevel Design The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering Goals/means (inductive) Goals/means (inductive) Properties Performance Performance P (N P ) Typical Materials Properties Properties Selection ) ) e e Structure Structure v v i i t t c c u u SP d d e e d d M Performance ( ( Properties, t t c c e e f f Processing Processing f f Requirements e e overlay on d d n n a a e e s s A’,T,t,R i u u a a Dimension of space: C C M + N A’’ or M + N P PS Typical Ashby Maps Microstructure Properties, Attributes, A’,T,t,R i overlay on * dist functions PP A,T,t,R i * explicit Emphasis on Materials Composition, Composition, actual Selection initial microstructure, microstructure A,T,t,R i a ; T o ,t o Ranged sets of performance requirements and Pareto-optimal solutions 10

Multiscale Modeling Issues in Support of Multilevel Materials Design The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering  Goals/means (inductive) Goals/means (inductive) Performance Performance Properties Properties ) ) e e Structure Structure v v i i t t c c u u d d e e d d ( ( t t c c e e f f Processing Processing f f e e d d n n a a e e s s u u Some Key Issues: a a C C • Modeling at selective scales of hierarchy to Properties are scale specific; the challenge provide decision support for materials development is how to tailor at various scales of • Uncertainties of models at various scales and hierarchy (length and time) in the multiscale transitions are prevalent presence of scale coupling. Multiscale modeling can assist in addressing these • Uncertainties in initial conditions and process questions. history effects are ubiquitous • Sensitivity of responses to microstructure 11

Decision-Making with Uncertainty The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering H. Choi et al, 2005. Deviation at Optimal Y Upper Limit • Type I: System variable Solution (noise) uncertainty Deviation at Type I, II • Type II: Design variable Response Robust Solution uncertainty Function • Type III: Model parameter/structure uncertainty Lower Limit • Multi-level design: IDEM Deviation at Type I, II, III Robust Solution Design Optimal Type I, II, III X Type I, II Variable Solution Robust Robust Solution Solution McDowell, D.L., Panchal, J.H., Choi, H.-J., Seepersad, C.C., Allen, J.K. and Mistree, F., • Ranged sets of performance requirements Integrated Design of Multiscale, • Ranged sets of solutions, Pareto optimal Multifunctional Materials and Products, character Elsevier, October 2009 (392 pages), ISBN-13: • Use set theory to facilitate top-down design 978-1-85617-662-0 based on bottom-up simulation (IDEM) 12