Predictive Multiscale Modeling for Decision Support in ... · III. Extreme value property estimates...

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 George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering

2

Any opinions, findings, and conclusions or recommendations expressed here are those of the authors and do not necessarily reflect the views of the National Science Foundation.

• NSF PSU-GT Center for Computational Materials Design

• NSF CMMI

• AFOSR, ARL • QuesTek, NAVAIR • DOE NEAMS

• Current Students: Shuozhi Xu, Paul Kern, Aaron Tallman

Former students and post docs • Ryan Austin and Jeff Lloyd, ARL • Craig Przybyla and Bill Musinski,

AFRL • Gustavo Castelluccio, Sandia • Conor Hennessey

Evolutionary responses (properties): Nonequilibrium, metastable

Essential for (i) mechanism ID, (ii) validation

The Mesoscale Gap in Modeling

Dislocations in Metallic Systems

Length and time scales are both involved

Thermodynamics and near equilibrium kinetics


3

Common Combined Strategy

Bottom-Up limited but increasing

Top-Down

Objective

Mechanisms, Validation

Scale Specific


4

A More General Perspective on

Crystalline Plasticity

DDD, PFM

Grain scale crystal plasticity

Microscopic phase field models

Generalized continua

Various problems demand a suite of models

Dislocation field mechanics

Coarse-grained atomistics


5

What are the Elements of

Crystalline Plasticity?

• 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


6

Uncertainty in Multiscale Modeling

Uncertainty in Models

at a Given Scale

• Assumed mechanism(s)

• Form of model/equation

• Model parameters

• Numerical algorithm and

implementation

• Solution convergence

• Sample sets analyzed and

spatial scales of simulation

• Randomness of structure

Uncertainty in Scale

Linking Algorithms

• Model reduction (reduction of

order)

• Configuration of information

passing (e.g., handshaking vs.

direct parameter estimation)

• Type of coupling – different

parameter spaces, discrete vs

continuum, dynamic vs

thermodynamic, etc.

• Lack of scale separation (time,

space)

• Forms of linking strategy

• Parameters passed

Not much attention in literature

Panchal, J.H., Kalidindi, S.R., and McDowell, D.L., Computer-Aided Design, Vol. 45, No. 1, 2013, pp. 4–25.


7

Scale Bridging Methods – Mesoplasticity

Length

Scale

Time Scale Models Examples of Scale Bridging

Approaches

Primary Sources of

Uncertainty

2 nm NA/ ground state First principles, e.g., Density

Functional Theory (DFT)

Assumptions in DFT method,

placement of atoms

Quantum MD

200 nm 10 ns Molecular dynamics (MD) Interatomic potential, cutoff,

thermostat and ensemble

Domain decomposition, coupled atomistics

discrete dislocation (CADD), coarse

grained MD, kinetic Monte Carlo

Attenuation due to abrupt interfaces of

models, passing defects, coarse

graining defects

2 mm

s

Discrete dislocation dynamics

Discretization of dislocation lines,

cores, reactions and junctions, grain

boundaries

Multiscale crystal plasticity

Averaging methods for defect kinetics

and lattice rotation

20 mm

1000 s

Crystal plasticity, including generalized

continuum models (gradient,

micropolar, micromorphic)

Kinetics, slip system hardening (self

and latent) relations, cross slip,

obstacle interactions, increasing #

adjustable parameters

RVE simulations, polycrystal/composite

homogenization

RVE size, initial and boundary

conditions, eigenstrain fields, self-

consistency

200 mm Days Heterogeneous FE with simplified

constitutive relations

Mesh refinement, convergence, model

reduction

Substructuring, variable fidelity, adaptive

remeshing, multigrid

Loss of information, remeshing error,

boundary conditions

>2 mm Years Structural FE Low order models, meshing, geometric

modeling

Panchal, Kalidindi, McDowell, Computer-Aided Design, 2013

These are hierarchical two-scale transitions


8

Material Selection

High Degree of Uncertainty

Structure

Properties

Performance

Goals/means (in

ductive)

Cause and effect (

deductive)

Processing

Structure

Properties

Performance

Goals/means (in

ductive)

Cause and effect (

deductive)

Processing

Limitation in Inverse problem

G.B. Olson, Science, 29 Aug., 1997, Vol. 277

Multilevel Design & Development:

Conceptualization

Integrated materials & product design

Part

System

Assembly

Continuum

Quantum

Mesoscale

Atomistic


9

Shift to Concurrent Product-Process-Material

System Design

System

Subsystems

Components

Parts

Materials

System

Specifications

Meso

Macro

Molecular

Quantum

Material

Specifications

Match the time

frame

Penn State- GT CCMD NSF I/UCRC 2005-2013


10

Mappings in Multilevel Design

Composition,

initial

microstructure

a; To,to

Composition,

actual

microstructure,

A,T,t,Ri

Microstructure

Attributes, A’,T,t,Ri

* dist functions

* explicit

Properties,

overlay on

A,T,t,Ri

Properties,

overlay on

A’,T,t,Ri

M Performance

Requirements

Dimension of space:

M + NA’’ or M + NP PS

SP

PP

Properties

P (NP) Typical

Materials

Selection

Emphasis on

Materials

Selection

Typical Ashby Maps

Ranged sets of performance requirements and Pareto-optimal solutions

Structure

Properties

Performance

Goals/means (in

ductive)

Cause and effect (

deductive)

Processing

Structure

Properties

Performance

Goals/means (in

ductive)

Cause and effect (

deductive)

Processing


11

Multiscale Modeling Issues in Support of

Multilevel Materials Design

Structure

Properties

Performance

Goals/means (in

ductive)

Cause and effect (

deductive)

Processing

Structure

Properties

Performance

Goals/means (in

ductive)

Cause and effect (

deductive)

Processing

Some Key Issues:

Properties are scale specific; the challenge is how to tailor at various scales of hierarchy (length and time) in the presence of scale coupling. Multiscale modeling can assist in addressing these questions.

• Modeling at selective scales of hierarchy to provide decision support for materials development

• Uncertainties of models at various scales and multiscale transitions are prevalent

• Uncertainties in initial conditions and process history effects are ubiquitous

• Sensitivity of responses to microstructure


12

Y

X Type I, II, III Robust Solution

Upper Limit

Lower Limit

Response

Function

Deviation at Optimal Solution

Deviation at Type I, II Robust Solution

Deviation at Type I, II, III Robust Solution

Design Variable

Type I, II Robust Solution

Optimal Solution

Decision-Making with Uncertainty

H. Choi et al, 2005.

McDowell, D.L., Panchal, J.H., Choi, H.-J., Seepersad, C.C., Allen, J.K. and Mistree, F., Integrated Design of Multiscale, Multifunctional Materials and Products, Elsevier, October 2009 (392 pages), ISBN-13: 978-1-85617-662-0

• Ranged sets of performance requirements • Ranged sets of solutions, Pareto optimal character • Use set theory to facilitate top-down design based on bottom-up simulation (IDEM)

• Type I: System variable (noise) uncertainty

• Type II: Design variable uncertainty

• Type III: Model parameter/structure uncertainty

• Multi-level design: IDEM


13

Key Enabling Elements: Multilevel Materials

Design & Development under Uncertainty

• Approximate Inverse methods for property-structure, structure-process relations based on data sciences and metamodeling

• High throughput strategies to accelerate exploration and steer towards interesting potential solutions

• VVUQ for decision support • Robustness– insensitivity to process variation and

material variability • Addressing missing physics in many-body

problems (e.g., mesoscale) via learning techniques, e.g., Bayesian updating


14

Uncertainty Examples in Today’s Talk

I. Challenging prevailing understanding and

interpretation of mesoscale experiments

based on high fidelity modeling

II. Model form/structure uncertainty at

mesoscales

III. Extreme value property estimates and MSC

fatigue crack growth

IV. Combined bottom-up and top-down

strategies for model parameter estimation


15

I. Shock Physics: Experimental Uncertainty

• Dislocation velocity Thermally activated

Drag dominated

Relativistic damping

/ exp / 1

S

S f G

h

c h

cv

N v G k

aa

a a a a

2

0

1

2

S

eff

h

B c

b

a a a

aa

a a

Mean dislocation velocity as a function of shear stress

Mechanical threshold stress Athermal

threshold

Austin, R.A. and McDowell, D.L., Int. J. Plasticity, Vol. 27, No. 1, 2011, pp. 1-24. Austin, R.A. and McDowell, D.L., Int. J. Plasticity, Vol.32-33, 2012, pp. 134-154.


16

Dislocation-Based Crystal Plasticity

tot m im

m hom het mult ann trap

im trap hom1

m hom hom

N N

N N N N N N

N N N

v N x

N

b bN

a a a

a a a a a a

a a a

a a a

(1) Austin and McDowell, Int. Journ. Plast., 2011 (2) Austin and McDowell, Int. Journ. Plast., 2012

3

,0

0

,0

exp 1hom

hom

hom

g bN N

k

m

het hetN fa

N dislocation density

Reflect dislocation substructure evolution

Length scales down to sub 100 nm, time scales less than 1 ms


17

Dislocation Substructure Evolution Rates

and Nonequilbrium Stress

Steady wave analysis

Dynamic shear stress

Highly nonequilibrium!


18

Shock in polycrystal Al

• Elastic precursor decay rate is

much more rapid for polycrystal

than for single crystal

• Shock broadening due to

orientation spread

More plastic dissipation Elastic Precursor

200 μm thick vapor-deposited Al samples, 4 GPa shock strength, Gupta et al.,JAP, 2009

Direct ablation experiments 0.72 μm thick vapor-deposited sample, Crowhurst et al., PRL, 2011 (40 GPa shock strength)

Lloyd, Clayton, Austin, McDowell, D.L., JMPS, 69, 2014, 14-32. Lloyd, Clayton, Becker, McDowell, D.L., Int. J. Plast. 60, 2014, 118-144.

Single wave structure is not real, but an artifact of the experiment


19

II. Model Form Uncertainty:

Dislocation-GB Interactions

Shen et al., Scripta Mater. 1986

Lee et al., Met. Trans. 1990

Slip transmission criteria (Lee-Robertson-Birnbaum criteria) Lee et al., Scripta Mater., 1989

• Geometric condition The angle 𝜃 between the lines of intersection of the incoming and outgoing slip planes with GB should be minimized.

• Resolved shear stress (RSS) condition The RSS acting on the outgoing slip system from the incoming dislocation should be maximized.

• Residual GB dislocation condition The magnitude of the Burgers of the residual dislocation 𝒃𝑟 should be minimized.

Abuzaid et al., JMPS, 2012


20

Ex Situ Hi Res DIC and EBSD

Abuzaid et al., JMPS 60(6) 2012, 1201

Hastelloy X

What about uncertainty of progressive buildup of slip fields within grains? Ex situ experiments don’t give such information… 4D information regarding increments of slip transfer would be helpful

Ex situ Hi Res DIC and EBSD


21

Model Form Uncertainty

Possible reactions The dislocation-GB interaction is a complex process, which depends on • Materials (FCC, BCC, HCP, different

stacking fault energy) • Temperature • Strain rate • Resolved shear stress • Type of dislocation (edge, screw, mixed) • Type of GB (twin boundary, symmetric,

asymmetric, tilt, twist, etc) and misorientation, asymmetry

• Prior reactions with residual Burgers vector

• Incoming gliding plane • etc.


22

Generalized Stacking Fault Energy

Illustration of 1NN and 2NN elements in CAC simulations (integration points (solid blue) and slave nodes (open blue). 1NN has 27 integration points and 2NN has 125.

Xu, S., Che, R., Xiong, L., Chen, Y. and McDowell, D.L., “A Quasistatic Implementation of the Concurrent Atomistic-Continuum Method for FCC Crystals,” International Journal of Plasticity 72 (2015) 91-126.

• Sequential conjugate gradient energy minimization, 0K

• Avoids overdriven MD results • Can add quenched dynamics to

improve efficiency for evolving defects


23

CAC Simulations: Slip Transfer of Mixed Character

Dislocations across Σ𝟑 CTB in Cu and Al

Dislocation multiplication: Frank-Read source

For Cu With Shuozhi Xu et al. – in progress

Quasistatic CAC: Xu et al., Int. J. Plast., 2015

Quenched Dynamics: Sheppard et al., J. Chem. Phys., 2008


24

Scale and Geometry Dependent CTB Reactions

𝜎appl𝑖𝑒𝑑 = 2GPa 𝐿𝑥 = 260𝑏 = 74.47 nm (Al)

Dislocation recombination at CTB

𝑥[110]

𝑦[1 12]

𝑧[11 1]

Wide specimen, free surfaces

Plane view

Leading and trailing partials recombine at CTB, then split into two CTB partials and glide in the same direction on the CTB out of the free surface

Leading and trailing partials recombine at CTB, then split into two partials exiting from the point of constriction into the adjacent grain (note: strictly not direct transmission but indiscernible via TEM)


25

Unresolved: Reduced Order Descriptions

Etc… (including migration, initial conditions, etc.)

Extended LRB criteria Mantle-Core

• Many potential variants of GB structure • Single dislocations versus pileup – sequence of slip transfer

reactions • 3D character of GBs • Add to this multicomponent systems, impurities, segregants

– very high dimensional • Can’t be solved without data sciences along with high

throughput experiments/many observations and modeling

?


26

III. Uncertainty in Extreme Value

Property Estimates and MSC Growth in Fatigue

2. Identify EV response of SVEs via simulation

3. Characterize EV distributions of key response

parameters

0.0001 0.001 0.01

.01

.1

1

51020305070809095

99

99.9

99.99

Simulated Extreme Value FIP

CD

F

Strain=0.5%

Strain=0.7%

4. Characterize correlated microstructure attributes

coincident with the EV response (EV marked correlation functions)

1. Generate multiple SVEs based on predefined distributions of key

microstructure attributes

5. Identify extreme value correlated attributes key to response and rank

microstructures 6(b). Select top candidates for experimental

evaluation

1 1, , , n 1 1, , , n

a

Experimental Calibration/Validation

6(a). Iterate materials design

Groeber et al. 2007, IN100

C. Przybyla, GT, 2010


27

Microstructure-Sensitive Fatigue Problems

Min. Length Scale, L O(10-10 m) O(10-8 m) O(10-7 m) O(10-5 m) O (10-3 m)

Atomistic Discrete Dislocation Polycrystal Macroscale dislocations patterns plasticity plasticity

Statistical theories

Sub-micron

Specimens; SEM

MEMs regime Mech. Testing

Lab scaleTEM

“TOP DOWN”

Vacancies and Dislocation Slip banding and

dislocation reactions substructures embryonic cracks

FIPsCrack nucleation and

damage process zone

This Proposal

Mechanisms and validation

Mesoscale DPZ


28

Example of (a) the specimen notch and FE model, and (b) monotonic and cyclic plasticity for a four-point bending experiment on a polycrystalline ferritic steel. Sweeny … Dunne, J. Mech. Phys Solids 61 (2013) 1224-1240.

Experiment-Simulation Connectivity: Crack Formation and Early Growth


29

Modeling Crack Formation and Early Growth:

Fatigue Indicator Parameters

Crack formation due to intense

shear along the slip band of Ti-

6Al-4V (Le Biavant, et. al, 2001).

Slip band impingement on grain

boundary of polycrystalline nickel

(Morrison and Moosbrugger, 1997).

p max

net nn

y

1 k2

p max*max n

y

1 k2

cyc cyc

1p pij ij

V V

dVV

O(10-100) mm3,

depending on

characteristic GS

DPZ


30

Crystal Plasticity Model for Ti-6Al-4V

Drag stress 0Da

e pF F F Nsys

p p p k k k

k

ˆ

1

0 0

1

L F F s n

M

k k k

k k k

0 ksgn

D

k k k k

Dh h yk k

skd

k k k

s s m

yk k k k k

CRSS sk

(0) D (0) Dd

Mayeur, Zhang, Bridier (2005-2009)

1500

1000

500

0

-500

-1000

Str

ess,

MP

a

0.080.060.040.020.00

Strain

Simulation Experiment

940

920

900

880

860

840

820

Yie

ld S

tre

ss,

,

MP

a

0.80.60.40.20.0

Volume fraction of primary a phase

Simulation

Experiment


31

Validation of Fatigue Cracking

• Experiments are expensive for model calibration

• Few statistically significant datasets exist for distribution of local slip to validate localization predictions

We assume transgranular slip/failure modes here; GB dominated slip transfer is alternative approach (cf. Sangid et al., Acta Mater. 2011; JMPS, 2011).

Bridier et al., IJP, 2009


32

Extreme Value Statistics for Ti-6Al-4V

• Details of FE (ABAQUS) models: Ti-6Al-4V crystal plasticity model by Bridier et

al. 2008

Ellipsoid based microstructure generator

Cycled at 0.6% strain at 0.2% s-1

0.400 mm x 0.400 mm 0.400 mm microstructure block

100 instantiations for each microstructure

Ten cycles in uniaxial tension (R=0)

Periodic boundary conditions

ODF with Random Texture

Microstructures Assumed Mean and St. Dev.

for Grain Size Distributions

α+β Colony Primary α

Micro Name Transformed

β Size (μm)

Primary α

Size (μm)

Vol %

Primary

α

μ σ μ σ

A Fine bi-modal low α 50 10-50 30% 50 5 25 10

B Fine bi-modal high α 50 10-50 70% 50 5 25 10

C Coarse bi-modal low α 80 40-60 30% 80 10 50 5

D Coarse bi-modal high α 80 40-60 70% 80 10 50 5

Random Texture


33

Extreme Value Fatigue Indicator Parameter

Distributions in Duplex Ti-6Al-4V

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

5.00

6.00

0.00E+00 1.00E-10 2.00E-10 3.00E-10 4.00E-10

ln(1

/ln

(1/p

))

Extreme Value FS FIP

A

B

C

D

A Fine bi-modal low α

B Fine bi-modal high α

C Coarse bi-modal low α

D Coarse bi-modal high α

Gumbel Distribution (Type I):

exp n n n

n

y u

Y nF y ea

Ellipsoid based microstructure generator

Cycled at 0.6% strain at 0.2% s-1, R = 0, 19 cycles, PBCs

0.400 mm x 0.400 mm 0.400 mm SVE

100 instantiations for each microstructure

ODF with Random Texture

Przybyla and McDowell, 2010


34

mg=0.45 to 0.5 (Basal, primary α)

mg’=0.45 to 0.5 (Basal, primary α) mg=0.45 to 0.5 (Basal, primary α)

mg’=0.45 to 0.5 (Prismatic, primary α)


mg’=0.45 to 0.5 (Pyramidal <a>, primary α)


mg’=0.45 to 0.5 (Pyramidal <a+c>, primary α)

Validation of Extreme Value Failure Modes:

Ti-6Al-4V, Random Texture

Cluster of similarly oriented equiaxed α for easy basal or

prismatic slip

Equiaxed α oriented for easy basal or prismatic

Equiaxed α oriented for hard <c+a> slip

Easy slip region

a

*S. K. Jha, J. M. Larsen, VHCF-4, pp. 385-396, 2007

34


35

Epistemic Uncertainty

Fine scale (bottom-up) • Slip system activation and hardening relations

• GB Interfaces – unstructured vs structured meshing – slip transfer

relations

• Heterogeneous slip localization, dislocation substructure and

mechanisms for slip irreversibilitySecond phase particle cracking,

debonding

• Numerical implementation strategy (elements, meshing, order of

integration, and averaging domain for FPZ, etc.)

Coarse Scale (top-down) • FIP definition

• Microstructure representation

Grain size, shape and orientation distribution

Grain boundary character distribution


36

DPZ Band Averaging of FIPs

For transgranular MSC growth, FIPs are averaged along bands aligned

with active slip planes.

FIP (FIP )meso Avga a per band

3D MSC Growth Modeling

Castelluccio, G.M., and McDowell, D.L., “A Mesoscale Approach for Growth of 3D Microstructurally Small Fatigue Cracks in Polycrystals,” Int. J. Damage Mechanics, 23(6), 2014, 791-818. Castelluccio, G.M., and McDowell, D.L., "Mesoscale Modeling of Microstructurally Small Fatigue Cracks in Metallic Polycrystals," Mat. Sci. Eng. A, Vol. 598, No. 26, 2014, pp. 34-55.

RR 1000 Ni-base superalloy


37

2

0

FIP1 a

FIP gP

Initial value for band in next uncracked grain

Renormalized Sub-Grain FIP Evolution

FIP evolution during crack growth

Crack size based on equivalent area, as per Murakami, i.e.,

a A


38

Apply a few loading cycles

Apply a few loading cycles, redistribute cyclic stress and

plastic strain fields

Extend the crack along the band with shortest MSC life

along intersecting slip systems in adjacent grain

Crack the band with shortest nucleation life

1st grain (Nucleation/Incubation)

2g

inc 0

gr

N FIPd

a a

a

Subsequent grains (MSC) (analytical projection)

ni i

gr st nd

i

d D D

Crack Growth Algorithm

1 2MSC gr Hist

11 2

c1N tanh d N

cc c

a a

2 ref

gr gr

0Ac

2d

F

d

IPa2

1 gr 2 thc 2d c CTD

gr

2o

d

MSC Hist

oth

1FIP A CTD1 a

2

daN N

a

a a

2

0 th= .2FIP (1 0.5(a ) ) CTD

ni i

st nd

iitrans iref

msc gr

D Dda

ddN

a

a


39

Validation: Physical Consistency with Observed Trends

1=da

c adN

This is characteristic of our findings…

Note: we have not imposed anything remotely close to this law in simulations


40

C. H. Wang, K. J. Miller. Fat. Frac. of Eng. Mat. & Struc. 16, 181–198, 1993

Mean Stress Effect on Crack Nucleation – Uniaxial Loading

0 exp( ) C

m aN A B

Differs from Morrow or Smith-Watson-Topper (SWT)

2g

inc 0

gr

N FIPd

a a

a

Validation: Physical Consistency with Observed Trends


41

Co

st/I

mp

reci

sio

n

Model Refinement

Model utility based on Improvement Potential

Model development and execution cost

Model imprecision; Epistemic uncertainty

Now Eventual

A Note on Model Refinement

Includes: • DPZ definition/size • Subscale nucleation/growth models • Unstructured meshing and mesh

refinement


42

Top-Down

1

nsN

cr i i

i

aa a

0 exp 1 ;

0;

qp

g f a

f

t

f

F sfor s

kT s

for s

a a

a a

aa

a a

Patra, Zhu, McDowell IJP, doi10.1016/j.ijplas.2014.03.016.

Bottom-Up

Narayanan, McDowell, Zhu, JMPS 65, 2014

IV. Fusing Bottom-Up and Top-Down

Information

bcc Fe


43

Parameters form Structural Bridge

1. Pre-exponential factor

2. Activation energy of

dislocation glide at zero

external stress

3. Shape factor p

4. Shape factor q

5. Thermal slip resistance at 0 K

1. Temperature

2. Driving stress

3. Athermal slip

resistance

Reinterpretation of parameters!

Calibration Inputs

Configuration Inputs

Aaron Tallman, PhD work in progress

1. Thermal kink-based

reference strain rate

2. Kinkpair activation energy

at zero ext. stress

3. Both p, q describe stress

4. dependence of kinkpair

activation energy

5. Thermal slip resistance at

0 K

Aaron Tallman, PhD Work in progress


44

θ→x Squared Euclidean Distance

Loss function values Bottom up (x) Top down MLE (𝜽 )

Using Prior density

function 0.792 1.032

Using Posterior density

function 0.776 0.846

decrease in Bregman

Divergence 2% 18%

Before data After data

These are the

results for the

test for

requirement iii Column 1: Agreement & Identifiability

Column 2: Identifiability Only

2

max min

-space

|i

i i

i i

xLoss P Data d

θθ

x θ θ


45

Multiscale Bayesian Calibration

, , , : Calibration Inputs

, , , : Configuration Inputs

, : Model Responses

, : Experimental Data

: Missing Physics Coefficients

, : Missing Physics Functions

i i

i i

m m

e e

m

x w

X Y

X Y

f X

θ φ

x w


46

Accumulation of Data

• Calibration applies data in a per datum formulation

• As new data are gathered, each new point can be

included in a new calibration

22old data new data

1 1exp, exp,

,,1exp

2

m em ej ji i

i ji j

Y YY YObj C

x θ xx θ x

θ

exp,

, : Calibration Inputs

, : Configuration Inputs

: Model Responses

: Experimental Data

: Standardizing Factor

: std. dev. of exp. datum i

i

i

m

e

i

x

Y

Y

C

θ

x


47

Recent TMS Study

On behalf of National Institute of Standards (NIST) Material Measurement Laboratory

John Ågren, KTH, Sweden Raymundo Arróyave, Texas A&M University Mark Asta, UC-Berkeley Corbett Battaile, Sandia Carelyn Campbell, NIST James Guest, Johns Hopkins Paul Krajewksi, GM Alexis Lewis, NSF Wing Kam Liu, Northwestern University David McDowell, Georgia Tech Tony Rollett, Carnegie Mellon University Dallas Trinkle, University of Illionis Peter Voorhees, Northwestern University

http://www.tms.org/multiscalestudy/


48

Technical/Scientific Recommendations

• Recommendation T1: Develop initiatives that address uncertainty

quantification and propagation (UQ/UP) across multiple models

describing a range of material length and time scales

• Recommendation T2: Develop strong coupling methods that allow

bidirectional communication between deformation and microstructural

evolution models (i.e., methodologies to account for the co-evolution of

microstructure and deformation)

• Recommendation T3: Devise methods and protocols for taking into

account rare events and extreme value statistical distributions

• Recommendation T4: Develop multi-resolution (or multiscale) multi-

physics free energy functions (and associated kinetic parameters)

involving microstructure evolution, defect formation, and life prediction

• Recommendation T5: Develop and execute focused research efforts

addressing interfacial properties and nucleation effects, with particular

emphasis on carrying out more systematic studies that couple theory,

experiments, and simulations across length and time scales

• T6-T9…


49

• Current Students: Shuozhi Xu, Paul Kern, Aaron Tallman

Former students and post docs • Ryan Austin and Jeff Lloyd, ARL • Craig Przybyla and Bill Musinski,

AFRL • Gustavo Castelluccio, Sandia • Conor Hennessey

Any opinions, findings, and conclusions or recommendations expressed here are those of the authors and do not necessarily reflect the views of the National Science Foundation.

• NSF PSU-GT Center for Computational Materials Design

• NSF CMMI

• AFOSR, ARL • QuesTek, NAVAIR • DOE NEAMS

Thanks

Predictive Multiscale Modeling for Decision Support in ... · III. Extreme value property estimates...

Documents

Transcript of Predictive Multiscale Modeling for Decision Support in ... · III. Extreme value property estimates...