Requires: 1. theory, 2. computations, and 3. experiments

304L SS 25% wrong answer if history is not considered!!

Macroscale Internal State Variable Theory Multiscale Modeling Material Heterogeneities BVP Metals Polymers Ceramics Composites Biological materials

MSU DMG model Macroscale MSU ISV/MSF Models Implementation/Use Finite Element Code (ABAQUS) boundary conditions loads temperature strain rate history initial microstructure- inclusion content mesh failure Note: model can be implemented in other FE codes Multiscale Materials Modeling Physics Validation And Numerical Verification Design  MSU MSF Model Life ISV=Internal State Variable MSF=MultiStage Fatigue Note: the ISV and MSF models give a 95% correct answer where current models in codes give a 50% answer

Lightweighting for less emissions and better gas mileage Cost savings safety ICME need HPC

High-Performance computing systems  Talon: 3072 processors, 6 TB RAM  Raptor: 2048 processors, 4 TB RAM  Matador: 512 processors, 512 GB RAM  Maverick: 384 processors, 480 GB RAM Storage  250 TB of high-speed disk storage  2 PB of near-line storage Based on the November 2009 TOP500 list, Talon is equivalent to the 222 nd fastest computer in the world and the 14 th fastest computer in US academia Based on the November 2009 Green500 list, Talon is equivalent to the 8 th most energy-efficient supercomputer in the world

Developmen t Phase Resolution Cost per problem Concept Desig n Detail Desig n Proto- typing Evaluatio n Production Ramp- Up Full Productio n Developmen t Phase Number of Problem Resolutions Design Change Cost 1 X10 X 100 X 1000 X X Design Change Cost Conventional Design, Build, Test Design Change Cost Digital Engineering Design Change Cost Upfront Engineering Simulation Driven Development Source: ITI (GE Aircraft Engines)

Lead Time Reduction

1. Requirements

2. Downscaling Requirements

1. Requirements 2. Downscaling Requirements 3. Upscaling Reultss

1. Requirements 4. Process-Structure-Property Modeling 2. Downscaling Requirements 3. Upscaling Reultss

Macroscale ISV Continuum Bridge 1 = Interfacial Energy, Elasticity Atomistics (EAM,MEAM,MD,MS, Nm Bridge 2 = Mobility Bridge 3 = Hardening Rules Bridge 4 = Particle Interactions Bridge 5 = Particle- Void Interactions Void \ Crack Interactions Bridge 11 = FEA ISV Bridge 12 = FEA Dislocation Dynamics (Micro-3D) 100’s Nm Electronics Principles (DFT) Å Crystal Plasticity (ISV + FEA) µm Crystal Plasticity (ISV + FEA) µm Crystal Plasticity (ISV + FEA) µm Bridge 6 = Elastic Moduli Bridge 7 = High Rate Mechanisms Bridge 8 = Dislocation Motion Bridge 9 = Void \ Crack Nucleation Bridge 10 = Void \ Crack Growth Macroscale ISV Continuum Multiscale Modeling

IVS Model Void Growth Void/Void Coalescence Void/Particle Coalescence Fem Analysis Idealized Geometry Realistic RVE Geometry Monotonic/Cyclic Loads Crystal Plasticity Experiment Fracture of Silicon Growth of Holes Experiment Uniaxial/torsion Notch Tensile Fatigue Crack Growth Cyclic Plasticity FEM Analysis Torsion/Comp Tension Monotonic/Cyclic Continuum Model Cyclic Plasticity Damage Structural Scale Experiments FEM Model Cohesive Energy Critical Stress Analysis Fracture Interface Debonding Nanoscale Experiment SEM Optical methods ISV Model Void Nucleation FEM Analysis Idealized Geometry Realistic Geometry Microscale Mesoscale Macroscale ISV Model Void Growth Void/Crack Nucleation Experiment TEM 1.Exploratory exps 2.Model correlation exps 3.Model validation exps

Optimal Product Process Optimal Product Process Environment (loads, boundary conditions) Environment (loads, boundary conditions) Product (material, shape, topology) Product (material, shape, topology) Process (method, settings, tooling) Design Options Cost Analysis Modeling FEM Analysis Experiment Multiscales Analysis Product & Process Performance (strength, reliability, weight, cost, manufactur- ability ) Product & Process Performance (strength, reliability, weight, cost, manufactur- ability ) Design Objective & Constraints Preference & Risk Attitude Optimization under Uncertainty

Engineering tools (CAD, CAE, etc.) Conceptual design process (user-friendly interfaces) IT technologies (hidden from the engineer)

Macroscale ISV Continuum Bridge 1 = Energy, Elasticity Atomistics (EAM,MEAM,MD,MS, Nm Bridge 2 = Dislocation Mobilities Bridge 3 = Hardening Rules Bridge 12 = FEA Dislocation Dynamics (Micro-3D) 100’s Nm Electronics Principles (DFT) Å Crystal Plasticity (ISV + FEA) µm Bridge 9 = polycrystal stress- strain behavior Macroscale ISV Continuum Bridge 6 = Elastic Moduli Bridge 7 = High Rate Mechanisms Bridge 8 = dislocation density and yield Can I create a formed component without an experiment? with multiscale modeling?

Quantify Performance Parameters First!!!

Plasticity/Ductility

Bridge 12 = material model Bridge 6 = Elastic Moduli Bridge 7 = High Rate Mechanisms Bridge 8= Dislocation Density and Yield Bridge 9 = Polycrystal stress-strain behavior Macroscale ISV Continuum (nm) (100 nm) (Å) (mm-m) (mm)

Bridge down scaling: energies and elastic moduli of Al needed up scaling: energies and elastic moduli of Al given Electronics Scale: DFT simulations of Al ( nm) Nanoscale: MD simulations of Al ( nm)

(1) Classical mechanics: Initial conditions: Classical mechanicsQuantum mechanics The Schrödinger Equation (1926)

(2) Quantum mechanics Wave function Schrödinge r Equation

Basis for the Density Functional Theorem (DFT)

Bridge 1 = Interfacial Energy, Elasticity Atomistic Simulations (EAM,MEAM,MD,M S) Nm Bridge 2 = dislocation mobilites Electronics Principles (DFT) Bridge 7= High Rate Mechanisms Dislocation Dynamics (DD) Macroscale ISV Constitutive Equation

Total energy E F i : embedding energy of atom i  i : electronic density of atom i r ij : separation distance between atom i and j  ij : pair potential of atom i and j 1.Molecular Dynamics (f=ma, finite temperatures) 2.Molecular Statics (rate independent, absolute zero) 3.Monte Carlo Simulations (quasi-static, finite temperatures)

Energy (U) Radius (r) distance between atoms e Repulsio n 1/r 12 1/r 6 Attractio n r r electron s core atoms

Embedded Atom Method (EAM) and Modified Embedded Atom Method (MEAM) potentials Local force determined from energy Dipole Force Tensor (virial stress) is determined from local forces Note: the difference between EAM and MEAM is an added degree of angular rotations that affect the electron density cloud. For EAM, this quantity is simply a scalar, but for MEAM it includes three terms that are physically motivated:

Summary of values for the constants for aluminum for the EAM/MEAM potentials.

MEAM found fcc to have lowest energy MEAM equilibrium volumes are close to ab-initio DFT results

Bridge down scaling: dislocation mobility values up scaling: edge and screw dislocation drag coefficients Nanoscale: MD simulations of Al ( nm) Mesoscale: forest hardening from DD simulations of Al (100 nm-1 mm)

drag coefficient dislocation velocity

Bridge 2 = Dislocation Mobilities Bridge 3 = Hardening Rules Dislocation Dynamics Simulations µm Bridge 8= dislocation density and yield Atomistic Simulations Crystal Plasticity Simulations Macroscale ISV Constitutive Equations

dislocation junction strength dislocation hardening

Bridge down scaling: single crystal hardening rule up scaling: constants for hardening rule Microscale: DD simulations of Al (100 nm- 1 mm) Mesoscale: crystal plasticity polycrystalline Al simulations (1-200 mm)

Voce Hardening Eqtn Plastic shear rate determined from DD sims hardening constants determined from DD sims DD results for the hardening rule to be used in Crystal Plasticity (CP)

Bridge 3 = Hardening Rules Crystal Plasticity Simulations Dislocation Dynamics Simulations Bridge 9 = Polycrystal stress- strain behavior Macroscale ISV Constitutive Equations µm

CP single crystal simulation of Al using the DD hardening constants

uncertainty band experiment CP Stress-Strain Behavior of Single Crystal Al using four sets of DD constants

Comparison of Experimental and CP simulation results for a single crystal

Macroscale: Continuum Point (mm) Bridge down scaling: Stress- strain behavior up scaling: Polycrystal Stress- Strain curves Microscale: Crystal Plasticity (1-20 mm)

Note: - curve without an exp!!! Polycrystalline CP calculations with 180 grains with the four DD constant sets using the volume average Polycrystalline CP calculations with 180 grains with the four DD constant sets using the volume average

Bridge 12 = material model Bridge 6 = Elastic Moduli Bridge 7 = High Rate Mechanisms Bridge 8= Dislocation Density and Yield Bridge 9 = Polycrystal stress-strain behavior Macroscale ISV Continuum (nm) (100 nm) (Å) (mm-m) (mm) Macroscale Internal State Variable Plasticity-Damage Model Downscaling Requirements

Equilibrium Conservation of Mass Balance of Momentum (angular and linear) Balance of Energy (1 st Law of Thermo) What is a constitutive relation? A mathematical description of material behavior To satisfy continuum theory relating stress and strain (in a solid mechanics sense) Too many unknowns for the number of equations, need another equation Constitutive relation Internal state variable theory Microstructure-property relations 2 nd Law of Thermo materials science mechanics Governing Equations

Dislocation-plasticity internal state variables Damage internal state variables Particle size Particle Volume fraction Nearest neighbor distance Dimensionless grain size Grain size Dimensionless grain size Damage Damage rate Macroscale Internal State Variable Plasticity-Damage Microstructure-Property Model Equations

AverageLower BoundUpper Bound Young’s Modulus68970 Poisson’s Ration0.33 c010. c021. c c c c061. c071. c080. c090. c100. c110. c120. c c c c160. c170. c180. c190. c200. c210. Macroscale ISV DMG-Plasticity Parameters

uncertainty bands Macroscale ISV Model calibrated with Mesoscale Crystal Plasticity Results Macroscale ISV Model calibrated with Mesoscale Crystal Plasticity Results

Structural Scale: FEA of forming (m) Macroscal e (mm) Bridge down scaling: material model up scaling: validated and verified material model

(Aluminum) Finite Element Analysis of Forming : Set Up

Structural Scale Finite Element Simulations of Forming Using the Macroscale ISV Model from the Multiscale Analysis showing the thickness changes

Structural Scale Finite Element Simulations of Forming Using the Macroscale ISV Model from the Multiscale Analysis showing the plastic strains

Structural Scale Finite Element Simulations of Forming Using the Macroscale ISV Model from the Multiscale Analysis showing the damage

Bridge 1 = Energy, Elasticity Atomistics (EAM,MEAM,MD,MS, Nm Bridge 2 = Dislocation Mobilities Bridge 3 = Hardening Rules Bridge 12 = FEA Dislocation Dynamics (Micro-3D) 100’s Nm Electronics Principles (DFT) Å Crystal Plasticity (ISV + FEA) µm Bridge 9 = polycrystal stress- strain behavior Macroscale ISV Continuum Bridge 6 = Elastic Moduli Bridge 7 = High Rate Mechanisms Bridge 8 = dislocation density and yield Can I create a formed component without an experiment? with multiscale modeling? Can I create a formed component without an experiment? with multiscale modeling? YES & YES!!

Requirements Process-Structure-Property Modeling Downscaling Requirements Upscaling Reultss