requires: 1. theory, 2. computations, and 3. experiments
TRANSCRIPT
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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
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Process-Structure-Property Modeling and the Associated History
Requires: 1. theory, 2. computations, and 3. experiments
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0
200
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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!!
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Macroscale InternalState Variable Theory
MultiscaleModeling
MaterialHeterogeneities
BVP
MetalsPolymersCeramicsCompositesBiological materials
Solving Complex Engineering Problems
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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
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Lightweightingfor less emissionsand better gas mileage
Cost savings
safety
ICMEneed
HPC
Social, Economical, and Political Driving Forces for ICME
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• 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
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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
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Lead Time Reduction
Lead Time Reduction Simulation Based Design Cost Savings
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1. Requirements
Integrated Computational Materials Engineering (ICME)
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1. Requirements
Integrated Computational Materials Engineering (ICME)
2. D
ow
nsc
ali
ng
Req
uir
em
en
ts
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1. Requirements
Integrated Computational Materials Engineering (ICME)
2. D
ow
nsc
ali
ng
Req
uir
em
en
ts
3. U
psc
ali
ng
Reu
ltss
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1. Requirements
4. Process-Structure-Property Modeling
Integrated Computational Materials Engineering (ICME)
2. D
ow
nsc
ali
ng
Req
uir
em
en
ts
3. U
psc
ali
ng
Reu
ltss
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Crashworthiness and Safety
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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
Macroscale ISV Continuum
Multiscale Modeling
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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
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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
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CyberInfrastructure
Engineering tools (CAD, CAE, etc.)
Conceptual design process(user-friendly interfaces)
IT technologies(hidden from the engineer)
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Macroscale ISV Continuum
Bridge 1 = Energy, Elasticity
Atomistics(EAM,MEAM,MD,M
S,
NmBridge 2 = Dislocation Mobilities
Bridge 3 = Hardening Rules
Bridge 12 = FEA
DislocationDynamics (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 Mechanis
ms
Bridge 8 =dislocation density and yield
Can I create a formedcomponentwithout anexperiment?with multiscalemodeling?
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QuantifyPerformanceParametersFirst!!!
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Plasticity/Ductility
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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)
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?
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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)
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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)
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(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
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/ 22
1
1( ) ( )
2
eN
s i ii
T
r r
Basis for theDensity FunctionalTheorem (DFT)
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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
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• 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)
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Energy (U)
Radius (r) distance betweenatoms
e
Repulsion
1/r12
1/r6
Attraction
r
r
electrons
core
atoms
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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)
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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
Surface Formation Energy 110
(mJ/m2)
1349 1115 629 1083 1055
Surface Formation Energy 111
(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.
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•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
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Comparison of DFT with EAM and MEAM potential results for the
Generalized Stacking Fault Energy Curves
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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)
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Dislocation moving in Al to quantify the velocity for DD sims
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v *b
B drag coefficientdislocati
onvelocity
Atomistic Simulations of Aluminum with an Edge Dislocation
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Bridge 2 = Dislocation Mobilities
Bridge 3 = Hardening Rules
Dislocation Dynamics
Simulationsµm
Bridge 8= dislocation
density and yield
Atomistic Simulations
Crystal Plasticity Simulations
Macroscale ISV Constitutive Equations
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b f
dislocation junctionstrength
dislocation hardening
DD simulation result of the dislocation junction strength, α
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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)
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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)
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Bridge 3 = Hardening Rules
Crystal Plasticity Simulations
Dislocation Dynamics
Simulations
Bridge 9 =Polycrystal
stress-strain behavior
Macroscale ISV Constitutive Equations
µm
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CP single crystal simulation of Al using the DD hardening constants
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uncertaintyband
experiment
CP Stress-Strain Behavior of Single Crystal Al using four sets of DD constants
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Comparison of Experimental and CP simulation results for a single crystal
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Macroscale: Continuum Point (mm)
Bridgedownscaling:
Stress-strain
behavior
upscaling:
PolycrystalStress-Straincurves
Microscale: Crystal Plasticity (1-20 mm)
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Note: s-e curve without an exp!!!
Polycrystalline CP calculations with 180 grains with the four DD constant sets using the volume average
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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
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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
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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
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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
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uncertaintybands
Macroscale ISV Model calibrated with Mesoscale Crystal Plasticity Results
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Structural Scale: FEA of forming (m)
Macroscale (mm)
Bridgedownscaling:
materialmodel
upscaling:
validatedand
verifiedmaterialmodel
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(Aluminum)
Finite Element Analysis of Forming : Set Up
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Structural Scale Finite Element Simulations of Forming Using the Macroscale ISV Model from the Multiscale Analysis showing the thickness changes
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Structural Scale Finite Element Simulations of Forming Using the Macroscale ISV Model from the Multiscale Analysis showing the plastic strains
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Structural Scale Finite Element Simulations of Forming Using the Macroscale ISV Model from the Multiscale Analysis showing the damage
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Bridge 1 = Energy, Elasticity
Atomistics(EAM,MEAM,MD,M
S,
NmBridge 2 = Dislocation Mobilities
Bridge 3 = Hardening Rules
Bridge 12 = FEA
DislocationDynamics (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 Mechanis
ms
Bridge 8 =dislocation density and yield
Can I create aformedcomponentwithout anexperiment?with multiscalemodeling?
YES&
YES!!
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Requirements
Process-Structure-Property Modeling
Integrated Computational Materials Engineering (ICME)
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