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

Integrated Computational

Materials Engineering (ICME) for Metals

Reinvigorating Design with Science and Engineering

Dr. Mark F. Horstemeyer ([email protected])CAVS Chair Professor

ASME, ASM, SAE, AAAS Fellow

Acknowledgments: DOE, DoD, and CAVS

Process-Structure-Property Modeling and the Associated History

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

0

200

400

600

800

1000

1200

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

ST

RE

SS

(M

Pa

)

STRAIN

20C

800C

20C reload

304L SS

25% wrong answerif history is not considered!!

History is important to predict the future!!

Macroscale InternalState Variable Theory

MultiscaleModeling

MaterialHeterogeneities

BVP

MetalsPolymersCeramicsCompositesBiological materials

Solving Complex Engineering Problems

MSUDMG

model

Macroscale MSU ISV/MSF Models Implementation/Use

Finite Element

Code(ABAQUS)

boundary conditionsloadstemperaturestrain ratehistory

initial microstructure-inclusion content

mesh

failure

Note: model canbe implemented in other FE codes

MultiscaleMaterialsModeling

Physics ValidationAnd

Numerical Verification

Design

, , s e fMSUMSF

ModelLife

ISV=Internal State VariableMSF=MultiStage Fatigue

Note: the ISV and MSFmodels give a 95% correctanswer where current modelsin codes give a 50% answer

Lightweightingfor less emissionsand better gas mileage

Cost savings

safety

ICMEneed

HPC

Social, Economical, and Political Driving Forces for ICME

• 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 222nd fastest computer in the world and the 14th fastest computer in US academia

• Based on the November 2009 Green500 list, Talon is equivalent to the 8th most energy-efficient supercomputer in the world

High Performance Computing

Development Phase

Resolution Cost per problem

Concept Design

Detail Design

Proto-typing

Evaluation

Production Ramp-Up

Full Production

Development Phase

Number of Problem

Resolutions Design Change Cost

1 X 10 X

100 X

1000 X

20000+ X

Design Change Cost

Conventional Design, Build, Test

Design Change Cost

Digital Engineering

Design Change Cost

Upfront EngineeringSimulation Driven Development

Source: ITI (GE Aircraft Engines)

Lead Time Reduction Simulation Based Design

Lead Time Reduction

Lead Time Reduction Simulation Based Design Cost Savings

1. Requirements

Integrated Computational Materials Engineering (ICME)

1. Requirements


2. D

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Req

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1. Requirements


2. D

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3. U

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1. Requirements

4. Process-Structure-Property Modeling


2. D

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Crashworthiness and Safety

Macroscale ISV Continuum

Bridge 1 = Interfacial Energy, Elasticity

Atomistics(EAM,MEAM,MD,M

S,

NmBridge 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

DislocationDynamics (Micro-3D)

100’s Nm

ElectronicsPrinciples

(DFT)

Å

Crystal Plasticity(ISV + FEA)10-100

µm

Crystal Plasticity(ISV + FEA)µm

CrystalPlasticity

(ISV + FEA)

100-500µm

Bridge 6 =

Elastic Moduli

Bridge 7 =High Rate Mechanis

ms

Bridge 8 =

Dislocation

Motion

Bridge 9 =

Void \ Crack

Nucleation

Bridge 10 =Void \ Crack

Growth


Multiscale Modeling

Multiscale Experiments

IVS ModelVoid Growth

Void/Void CoalescenceVoid/Particle Coalescence

Fem AnalysisIdealized Geometry

Realistic RVE GeometryMonotonic/Cyclic Loads

Crystal Plasticity

ExperimentFracture of SiliconGrowth of Holes

ExperimentUniaxial/torsionNotch Tensile

Fatigue Crack GrowthCyclic Plasticity

FEM AnalysisTorsion/Comp

TensionMonotonic/Cyclic

Continuum ModelCyclic Plasticity

Damage

Structural Scale

Experiments FEM

ModelCohesive Energy

Critical Stress

AnalysisFracture

Interface Debonding

Nanoscale

ExperimentSEM

Optical methods

ISV ModelVoid Nucleation

FEM AnalysisIdealized GeometryRealistic Geometry

Microscale

Mesoscale

Macroscale

ISV ModelVoid Growth

Void/Crack Nucleation

ExperimentTEM

1. Exploratory exps2. Model correlation exps3. Model validation exps

OptimalProductProcess

Environment(loads,

boundary conditions)

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 )

Design Objective

& Constraints

Preference & Risk Attitude

Optimization under Uncertainty

Design Optimization

CyberInfrastructure

Engineering tools (CAD, CAE, etc.)

Conceptual design process(user-friendly interfaces)

IT technologies(hidden from the engineer)


Bridge 1 = Energy, Elasticity


S,

NmBridge 2 = Dislocation Mobilities


Bridge 12 = FEA


100’s Nm

Electronics

Principles (DFT)

Å

Crystal Plasticity(ISV + FEA)

µm

Bridge 9 =

polycrystal stress-

strain behavior


Bridge 6 =

Elastic Moduli


ms

Bridge 8 =dislocation density and yield

Can I create a formedcomponentwithout anexperiment?with multiscalemodeling?

QuantifyPerformanceParametersFirst!!!

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


(nm)(100 nm)

(Å)

(mm-m)

(mm)

Start with the End in Mind: What do I need for the Macroscale

Internal State Variable Plasticity-Damage Model to address

the performance and manufacturing?

Bridge

downscaling:

energiesand

elasticmoduli

of Al

needed

upscaling:

energiesand

elasticmoduli

of Al

given

Electronics Scale: DFT simulations of Al (0.1-10 nm)

Nanoscale: MD simulations ofAl (10-100 nm)

2

2

dt

xdmaF

x),( txF

om)(tx

dt

dxv

dt

dva

)(tx)(tx

)(xV

x

VF

mvp 2

2

1mvT

(1) Classical mechanics:

maF

Initial conditions:

00 )0(,)0( xxvv

)(xV

Classical mechanics Quantum mechanics

The Schrödinger Equation (1926)

(2) Quantum mechanics

)(tx ),( tx Wave function

maF

Vxmt

i2

22

2

xm

)(xV

sJh

3410054572.12

)0,(x ),( tx)(tx)0(x)0(v

Schrödinger Equation

/ 22

1

1( ) ( )

2

eN

s i ii

T

r r

Basis for theDensity FunctionalTheorem (DFT)

Bridge 1 = Interfacial Energy, Elasticity

Atomistic Simulations

(EAM,MEAM,MD,MS)

Nm

Bridge 2 = dislocation mobilites

ElectronicsPrinciples (DFT)

Bridge 7=High Rate

MechanismsDislocation

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

ij

ijij

i ij

ijii rrFE )(2

1)(

)(

1. Molecular Dynamics (f=ma, finite temperatures)2. Molecular Statics (rate independent, absolute zero)3. Monte Carlo Simulations (quasi-static, finite temperatures)

Energy: Embedded Atom Method (EAM)

Energy (U)

Radius (r) distance betweenatoms

e

Repulsion

1/r12

1/r6

Attraction

r

r

electrons

core

atoms

E F 12 r

f E

ij 1

V m vi

v j 1

2V ri f j

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:

free surfaces shear crystal asymmetry

Determination of Atomic Stress Tensor(Daw and Baskes, 1984, Phys. Rev)

name DFT result Mishin EAM [2002]

Mendelev EAM [2009]

Jelinek MEAM [2010]

Horstemeyer MEAM [ICME Book]

Lattice constant

4.049 4.066 4.060 4.046 4.046

Bulk modulus

79.4 93.3 83.7 77.8 66.8

Cohesive energy (eV)

-3.36 -3.36 -3.41 -3.35 -3.35

Vacancy energy (eV)

0.72 1.67 1.84 1.40 1.16

Surface Formation Energy 100

(mJ/m2)

1212 1007 508 1033 1010


(mJ/m2)

1349 1115 629 1083 1055


(mJ/m2)

988 960 481 758 731

Stacking fault

energy (intrinsic)

133 85 148 160 164

Stacking fault

energy (extrinsic)

133 86 151 162 165

Stacking fault

energy (twin)

61.0 43.9 77.6 82.2 83.7

Elastic modulus

C44 (GPa)

31.6 79.4 30.1 28.1 18.4

Elastic modulus

C11 (GPa)

114 136 110 111 93

Elastic modulus

C12 (GPa)

61.9 72.2 70.9 61.2 53.6

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

Comparison of DFT and MEAM calculations for Aluminum illustrating the Bridging Results

Comparison of DFT with EAM and MEAM potential results for the

Generalized Stacking Fault Energy Curves

Bridge

downscaling:

dislocationmobilityvalues

upscaling:

edge and screwdislocation

dragcoefficients

Nanoscale: MD simulations ofAl (10-100 nm)

Mesoscale: forest hardening from DD simulations of Al (100 nm-1 mm)

Dislocation moving in Al to quantify the velocity for DD sims

v *b

B drag coefficientdislocati

onvelocity

Atomistic Simulations of Aluminum with an Edge Dislocation

Bridge 2 = Dislocation Mobilities


Dislocation Dynamics

Simulationsµm

Bridge 8= dislocation

density and yield

Atomistic Simulations

Crystal Plasticity Simulations

Macroscale ISV Constitutive Equations

b f

dislocation junctionstrength

dislocation hardening

DD simulation result of the dislocation junction strength, α

Bridge

downscaling:

single crystal

hardening rule

upscaling:

constantsfor

hardeningrule

Microscale: DD simulations ofAl (100 nm- 1 mm)

Mesoscale: crystal plasticity polycrystalline Al simulations (1-200 mm)

s ( s 0) exp h0

s 0

Ct

Voce Hardening Eqtn

Plastic shearrate determinedfrom DD sims

hardening constants determined from DD sims

DD results for the hardening rule to be used in Crystal Plasticity (CP)


Crystal Plasticity Simulations

Dislocation Dynamics

Simulations


stress-strain behavior

Macroscale ISV Constitutive Equations

µm

CP single crystal simulation of Al using the DD hardening constants

uncertaintyband

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)

Bridgedownscaling:

Stress-strain

behavior

upscaling:

PolycrystalStress-Straincurves

Microscale: Crystal Plasticity (1-20 mm)

Note: s-e curve without an exp!!!

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


stress-strain

behavior


(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 (1st Law of Thermo)

What is a constitutive relation? A mathematical description of material behaviorTo 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 relations2nd Law of Thermo

materials science

mechanics

Governing Equations

0expz

coal CTDCSc C v v C T DCS

De D Din

Din f T sinh ' R Y T 1 D

V T 1 D

' '

02

3

zo

e e in ind s

DCSW W h T D r T D r T

DCS

2 02

3

zin in

d s

DCSR H T D R T D R T R

DCS

Dislocation-plasticity internal state variables

Damage internal state variables

particles pores particles poresD c c

particles v v

1 223 3 1

1 333 22 22

4exp

27in T

IC

J J Id CD a b c TJ JK f J

3 31 1 0.4319

2 2

Y TV T

inH

vm

V T V Tv v D

Y T Y T

2 2 111 sinh

1 2 1

inHpores poresm

vmpores

V TY T D

V TY T

Particle size

Particle Volume fraction

Nearest neighbor distance Dimensionless grain size

Grain sizeDimensionless grain size

Damage

Damage rate

1 2 11

e e e e DW W D tr D I D D

D

Macroscale Internal State Variable Plasticity-Damage Microstructure-Property Model Equations

Average Lower Bound Upper Bound

Young’s Modulus 68970 68970 68970

Poisson’s Ration 0.33 0.33 0.33

c01 0. 0. 0.

c02 1. 1. 1.

c03 9.12 8. 9.12

c04 161.7 161.7 161.7

c05 0.00001 0.00001 0.00001

c06 1. 1. 1.

c07 1. 1. 1.

c08 0. 0. 0.

c09 0. 0. 0.

c10 0. 0. 0.

c11 0. 0. 0.

c12 0. 0. 0.

c13 0.0136 0.012 0.0136

c14 0.08855 0.08855 0.08855

c15 193 188 225

c16 0. 0. 0.

c17 0. 0. 0.

c18 0. 0. 0.

c19 0. 0. 0.

c20 0. 0. 0.

c21 0. 0. 0.

Macroscale ISV DMG-Plasticity Parameters

uncertaintybands

Macroscale ISV Model calibrated with Mesoscale Crystal Plasticity Results

Structural Scale: FEA of forming (m)

Macroscale (mm)

Bridgedownscaling:

materialmodel

upscaling:

validatedand

verifiedmaterialmodel

(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


S,

NmBridge 2 = Dislocation Mobilities


Bridge 12 = FEA


100’s Nm

Electronics

Principles (DFT)

Å

Crystal Plasticity(ISV + FEA)

µm

Bridge 9 =

polycrystal stress-

strain behavior


Bridge 6 =

Elastic Moduli


ms

Bridge 8 =dislocation density and yield

Can I create aformedcomponentwithout anexperiment?with multiscalemodeling?

YES&

YES!!

Requirements

Process-Structure-Property Modeling


Dow

nsc

ali

ng

Req

uir

em

en

ts

Up

scali

ng

Reu

ltss

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

Documents

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