predictive modeling and simulation ofpredictive modeling ...predictive modeling and simulation...

Predictive Modeling and Simulation ofPredictive Modeling and Simulation of the Dynamic Response of Materials at

CaltechCaltech

Michael OrtizBeijing University of Aeronautics and Astronautics (BUAA)

School of Jet PropulsionSchool of Jet Propulsion Beijing, March 14, 2011

PSAAP: Predictive Science Academic Alliance Program

Michael OrtizBUAA 3/14/11 - 1

Caltech & Jet Propulsion Lab (JPL)



DoE - ASC/PSAAP Centers



Overarching objectives – QMU

• Aim: Quantify performance Margin & Uncertainty (QMU) in the behavior of complex physical/engineered systems

• Example: Short-term weather prediction,– Old: Prediction that tomorrow will rain in Beijing…

New: Guarantee same with 99% confidence– New: Guarantee same with 99% confidence…

• QMU is important for achieving confidence in high-consequence decisions, designs (e.g., aircraft safety)

• Paradigm shift in experimental science, modeling and simulation, scientific computing (predictive science):

Deterministic Non deterministic systems– Deterministic → Non-deterministic systems– Mean performance → Mean performance + uncertainties– Tight integration of experiments, theory and simulation


– Robust design: Design systems to minimize uncertainty– Resource allocation: Eliminate main uncertainty sources Michael Ortiz

BUAA 3/14/11- 4

Application: Hypervelocity impact

Challenge: Predict hypervelocity impact phenomena (10Km/s ) with quantified margins and uncertainties

NASA Ames Research Center E fl h f h l it t tEnergy flash from hypervelocity test

at 7.9 Km/s


Hypervelocity impact test bumper shield(Ernst-Mach Institut, Freiburg Germany)

Michael OrtizBUAA 3/14/11- 5

Annual UQ campaigns

April 15 2008

UQ campaign timelineTarget Ballistic (SBGG)April 15, 2008

Center startsPlate

Ballistic (SBGG)

•Aluminum plates•Steel impactor (50g)•Thickness: 0.125-0.5”

Target Plate

Ballistic (SPHIR)

•Steel/Ta plates

Target Plate

Hypervelocity (SPHIR)

•Aluminum plates

•Velocity: 0.4-1 Km/s

Target Plate

Ballistic (SPHIR)

•Aluminum plates•Steel/Ta plates•Steel impactor•Thick.: 50-105 mils•Obliquity: 0-30°

•Aluminum plates•Nylon impactor•Thick.: 10-105 mils•Obliquity: 0-80°

•Aluminum plates•Steel impactor•Thick.: 50-105 mils•Obliquity: 0-30°

Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q1Q1 Q2 Q3 Q4 Q1 Q2 QQ4

•Velocity: 2-3 Km/s •Velocity: 3-10 Km/s•Velocity: 2-3 Km/s



Hypervelocity impact as system

performance measures:

response function(black box)

system inputs: measures:(black box)inputs:

• Random • Observablesvariables

• Known or k df

• Observables• Subject to

performance unknown pdfs

• Controllable• Uncontrollable

specifications• Random (due to

randomness in• Uncontrollable• Unknown-

unknowns (Z)

randomness in inputs, system)

• Noisy (unknown Probability of



unknowns)y

Failure?

Center’s assets

Experimental Science Simulation codes

SPHIRPhysics models UQ tools

VTF EurekaHSRTPhysics models UQ tools



Plasma/EoS Probability/CoM UQ pipelineStrength

Center’s assets







Hypervelocity impact at Caltech



Caltech’s Small Particle Hypervelocity Impact Range facility(Prof. A.J. Rosakis, Director)


BREECH PUMP TUBE

LAUNCH TUBE

FLIGHT TUBE

TARGET TANK

Front Spall Cloud

Debris Cloud

Witness Plate

STAGE 1 STAGE 2

Impactor

TargetWitness Plate

aluminum witness plates replaced by capture media

Target Materials•SteelAluminum Ø 71 mil (1x10-3 in)

by capture media

• Impact Speeds: 2 to 10 km/sI t Obli iti 0 t 80 d

•Aluminum•Tantalum

Impactor Materials•Steel

Ø 71 mil (1x10 3 in) launch tube bore

PSAAP: Predictive Science Academic Alliance Program 11

• Impact Obliquities: 0 to 80 degrees• Impactor Mass: 1 to 50 mg

Steel•Nylon


SPHIR – A reconfigurable facility

A il 15 2008

SPHIR configuration timeline

April 15, 2008

Center starts

Target Ballistic impactTarget Plate

Hypervel. impact

•Al/Steel multi platesPlatea s c pac

•Steel/Al plates•Steel/nylon impactor

•Al/Steel multi-plates•nylon impactor

Target Hypervel. impactTarget Plate

Ballistic impact

•Steel plates•Steel impactor

Target Plate

Ballistic/Hypervel.

•Al plates•Steel/nylon impactor

Plateype e pact

•Al/Steel/Ta bi-plates•nylon impactor•Soft-gel capture

Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q1Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q1Q4 Q1 Q2 Q3 Q4Q4




April 15 2008

Diagnostic deployment timeline

VelocimetryApril 15, 2008

Center starts

Perforation areaProfilometry

Optimet

Velocimetry

Valyn Multi-Beam VISAR

Real-time CGSFull-field

surface slopesPerforation area

Olympus SZ61 Microscope

OptimetMiniConoscan

3000

surface slopes

Backlighting

Real time

Spectrometry

Real-time

Z

YX

Real-time shadowgraph

imagingspectra


Y



SPHIR – Inputs and Metrics

System Outputs (Y)System inputs (X)

Diagnostics

Conoscope

MetricsProfilometry

Perforation area Slope

Projectile velocity

Projectile mass Conoscope

Backlighting shadowgraph

Perforation area, Slope Contour Area

Real-time back-surface bulge and ejecta/debris

cloud formation

Projectile mass

Number of target plates shadowgraph

VISAR

cloud formation

Real-time, back-surface velocimetry

R l ti f ll fi ld

plates

Plate thicknesses

CGS

Spectro-

Real-time, full-field back-surface deformation

Impact flash, debris and spall clouds spectra

Plate obliquities

Projectile/plate


Michael Ortiz

pphotometer spall clouds, spectra

over IR to UV range

j pmaterials

BUAA 3/14/11- 14

SPHIR - Sample data

• Added challenges:– Experimental

!10

11

12

Plot assumes average of obliquities (a) for all targets tested of a given thickness (h)

Vbl = Ho*( h/Dp)^n / (cos a)^sA = if V<Vbl, 0, K*Dp^2 * {(h/Dp)^p} * {[cos(a)]^u} * {tanh[(V/Vbl)-1]}^m

A = perforation area (mm^2)) scatter!– Impact velocity

uncontrollable!7

8

9

ea (m

m)

A = perforation area (mm 2)h = target thickness (mm)a = imapct obliquity (rad)V = impact speed (km/s)Dp = imactor diameter (mm)Ho, K, n, s, p, u, m are curve fit parametersre

a (m

m2 )

Distribution of Speeds Obtained

0 8

0.9

1

peed

Fit Errors: Uniform = 0.32 Gaussian = 0.08

GaussianMean = 2.49StDev = 0.25

Measured speed distribution

bilit

y

4

5

6

Perfo

ratio

n A

re

1.9mm Data

2.3mm Data

2 6mm Datarfora

tion

a

0.4

0.5

0.6

0.7

0.8

roba

bilit

y of

Low

er S

pat

ive

prob

ab

1

2

32.6mm Data

1.9mm Model

2.3mm Model

2.6mm Model

Impactor area

Per

0

0.1

0.2

0.3

0.4

Cum

ulat

ive

PrC

umul

a

01.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3

Impact Speed (km/s)Impact speed (km/s)Experimental ballistic curves (SPHIR)



1.6 1.8 2 2.2 2.4 2.6 2.8 3

Impact Speed (km/sImpact speed (km/s)Experimental ballistic curves (SPHIR)

440 C Steel spherical projectiles304 Stainless Steel plate targets

Ballistic impact – GALCIT Small Bore Gas Gun (SBGG) facility( ) y

Barrel Pressure Gun

Light detectorsdetectors(velocity )

Data recorder LeCroy



Caltech’s Small Bore Gas Gun (SBGG) facility(Prof. G. Ravichandran, Director)

Ballistic impact – SBGG

System inputs (X) System Outputs (Y)

Projectile velocity

Plate thickness

Diagnostics

Conoscope

MetricsProfilometry Plate thickness

Projectile/plate materials

Conoscope yPerforation area

materials



Ballistic impact - Sample data

350

400

m/s)

50

60

2)

200

250

300

not perforated

perforated

Velocity

(m

30

40

d area

(mm

2

32 milli‐inch

40 milli‐inchOptimet

MiniConoscan

100

150

200

Projectile

0

10

20

Perforated 50 milli‐inch

63 milli‐inch

MiniConoscan3000

30 40 50 60 70Plate thickness (milli‐inch)

0 100 200 300 400

Impact Velocity (m/s)

Perforation area vs impact velocity Perforation/non perforationPerforation area vs. impact velocity(note small data scatter!)

Perforation/non-perforationboundary

Experimental ballistic curves (SBGG)


Michael Ortiz

p ( )S2 Steel spherical projectiles

Al 6061 plate targetsBUAA 3/14/11- 18

High Strain-Rate Testing (HSRT)

1 2(1 )peq eq

Pk kDt

d

Stress:

3peq

dkh

Strain:

S li H ki

Shear Compression Specimen (SCS)

Split Hokinson (Kolsky) pressure bar

Strength Dissipation

Measure )t(and)t(),t(

p

Full field imaging


Michael Ortiz

Full-field imaging,Sub-grain resolution

BUAA 3/14/11- 19

Caltech’s High Strain-Rate Testing (HSRT) facility(Prof. G. Ravichandran, Director)

Conventional validation - Examples

Shear compression specimen Power-law work hardening

Pa)

Pa)

Power-law strain-rate sensitivity

Stre

ss (M

P

Stre

ss (M

P

ent S

hear

S

ent S

hear

S

Equ

ival

e

Equ

ival

e

M. Vural, D. Rittel and G. Ravichandran, “Large strain mechanical behavior of 1018 cold rolled steel over a wide range of strain rates ”

Equivalent Shear Strain Equivalent Shear Strain


behavior of 1018 cold-rolled steel over a wide range of strain rates, Metallurgical and Materials Transactions A, Vol. 34A (2003) p. 2873.


Conventional validation - Examples

Power-law strain-rate sensitivity

)re

ss (M

Pa Experimental

Model

She

ar S

trE

quiv

alen

t E

Equivalent Shear Strain Rate (1/s)


M. Vural, D. Rittel and G. Ravichandran, “Large strain mechanical behavior of 1018 cold-rolled steel over a wide range of strain rates,” Metallurgical and Materials Transactions A, Vol. 34A (2003) p. 2873. Michael Ortiz

BUAA 3/14/11 - 21

High Strain-Rate Testing (HSRT)

250Incident Shock

Ideal Mach State

Al Impactor at 1 km/s


Tantalum Hugoniot

Us2 > Us1

Reflected Shocksteel

200

Simulated Mach StateTa Impactor at 1 km/s

Ta Impactor at 2 km/sUs1

Mach

Mach Disk

150

P (G

Pa) 3.1x

(4.7 km/s)

Mach Stem

Impactorp (G

Pa) steel

50

100

P

3.6x(2.9 km/s)

4x(5 5 k / )



Mach-Lens Test

p

0

50

4.5x(3.4 km/s)

(2.9 km/s)(5.5 km/s)

Ta Impactor at 1 km/s

Ta Impactor at 2 km/s



Michael Ortiz

0 0.5 1 1.5 2 2.5

Up (km/s)Up (km/s)BUAA 3/14/11- 22

Experimental data at Caltech

• The Caltech center has its own in-house experimental facilities:– Small Particle Hypervelocity Impact Range– Small Bore Gas Gun Facility (ballistics)– High-Strain Rate Facility (constitutive characterization)High Strain Rate Facility (constitutive characterization)

• Experimental facilities are reconfigurable and may be regarded as black boxes mapping inputs to outputs

• Experimental facilities supply specific instances of systems to be modeled, tested and certified

• Experimental facilities supply data in for purposes of• Experimental facilities supply data in for purposes of Uncertainty Quantification– Integral ‘data on demand’ at fixed inputs



– Integral legacy data (by accumulation)– Component data (e.g., constitutive data)

Center’s assets







Focus simulation - Roadmap

Simulation roadmapTargetE k OTMTargetL i VTF TargetE l i VTFA il 15 2008

TargetABAQUS Explicit

Target Plate

Eureka OTM

•Update-Lagrange•Optimal transport•Meshfree/MPM

Target Plate

Lagrangian VTF

•Lagrangian FEM•Explicit dynamics•Proxy ball contact

Target Plate

Eulerian VTF

•Eulerian AMR•FD/WENO•EoS/strength

April 15, 2008

Center starts

Target Plate

ABAQUS Explicit

•Lagrangian FEM•Explicit dynamics•Explicit contact

•Meshfree/MPM•Variational dyns•Seizing contact•Erosion/fracture

•Proxy-ball contact•Element erosion•Engr. Models/EoS•Massively parallel

•EoS/strength•Multiphase/BC•Ghost fluid•Massive parallelExplicit contact

•Element erosion•Engr. Models•Serial

•Multiscale models

Serial Parallel




Center’s assets







Multiscale models - Strength

Full-scalecalculations

ms

calculationsDirect numerical simulation of polycrystals, effective models

µs

Subgrain structures:Hall-Petch scaling,martensite…

Dislocation dynamics: Forest hardening, cross slip…

ns

MD: Core energies, kink mobilities…

QM: Multiphase EoS, transport, plasma…



mmnm µm

n QM: Multiphase EoS, transport, plasma…

Multiscale Modeling - Strength

Ballistic impact

Polycrystalplasticity

Void-growth

Single-crystal

plasticity

Equilibrium properties Dissipation

EoS Elastic moduli Viscosity Hardening


Michael Ortiz

Heat capacity

Rate sensitivity

BUAA 3/14/11 - 30

Multiscale Modeling - EoS

Ballistic impact


Void-growth

Single-crystal

plasticity




Michael Ortiz

Heat capacity

Rate sensitivity

BUAA 3/14/11 - 31

Multiscale Modeling – Computed EoS

bcc

a

bcc Fe hcp

GP

a

Pressure (GPa)

100

12050 500

A)

20

40

60

80

100

0K 250K500K

10

20

30

40

P(G

Pa)

2000 K200

300

400

P(G

Pa)

bcc Fe

hcp Fe bcc V

ssur

e (G

PA

0.7 0.8 0.9 1.0 1.1 1.2-40

-20

0

20

V/V0

500K 1000K 1500K 2000K 2500K 3000K

0.90 0.95 1.00 1.05 1.10 1.15 1.20

-20

-10

0

0 K

V/V0

2000 K

40 45 50 55 60 65 70 75 80

0

100

0 K

V (bohr3)

3000 KPre

s

Volume Volume Volume


Michael Ortiz

0( )Volume Volume VolumeFirst-principles EoS, heat capacity, elastic moduli

(Wasserman, Stixrude and Cohen, PRB 53, 8296, 1996)BUAA 3/14/11 - 32

Multiscale Modeling - Viscosity

Ballistic impact


Void-growth

Single-crystal

plasticity



Viscosity vs (p,T) for liquid Ta,


Michael Ortiz

Heat capacity

Rate sensitivity

y (p ) qFe, from shear stress autocorr. function (Axel van de Walle)

BUAA 3/14/11 - 33

Multiscale Modeling - Transport

Ballistic impact


Void-growth

Single-crystal

plasticity




Michael Ortiz

Heat capacity

Rate sensitivity

BUAA 3/14/11 - 34

Multiscale Modeling – Rate sensitivity

1/2<111> screw dislocation1/2<111> screw dislocationSingle Kinks (<112> kink)Kink

Negative core (n)Positive core (p)Positive core (p)

• From kink dynamics (MD): – Formation energies– Migration energy barriers

• From thermal activation theory:


Michael Ortiz

– Dislocation mobility– Rate sensitivity

BUAA 3/14/11 - 35

Multiscale Modeling - Hardening

Ballistic impact


Void-growth

Single-crystal

plasticity




Michael Ortiz

Heat capacity

Rate sensitivity

BUAA 3/14/11 - 36

Multiscale Modeling – Hardening

Ta

• From dislocation dynamics:From dislocation dynamics: – Anisotropic line tension– Secondary dislocations– Dislocation multiplication


Michael Ortiz

• Percolation analysis (Kocks):– Hardening relations (analytical)

BUAA 3/14/11 - 37

Multiscale models – Ductile fracture

Material point erosion:Fracture & fragmentation

ms

Space-filling hollow spheres:Void growth & coalescence

Fracture & fragmentation

µs Q i ti

Void growth & coalescence

Quasicontinuum: Nanovoid cavitation

ns

QM: Vacancies, binding & migration energies

KMC: Nanovoid nucleation rates



38mmnm µm

g g g

Multiscale Modeling – Fracture (FE2)

Ballistic impact


Void-growth

Single-crystal

Void nucleation(not implemented)

plasticity




Michael Ortiz

Heat capacity

Rate sensitivity

BUAA 3/14/11 - 39

Multiscale Modeling - Polycrystal

Ballistic impact


Void-growth

Single-crystal

plasticity




Michael Ortiz

Heat capacity

Rate sensitivity

BUAA 3/14/11 - 40

Multiscale Modeling - Polycrystal

• Multiscale models integrated into full-scale simulations!

OTM i l ti h h t i l i t C li d t iki


OTM simulation where each material point represents a randomly oriented crystal

Copper cylinder striking frictionless rigid wall at 227m/s


Center’s assets







Development of UQ methodology

April 15 2008

UQ methodology timelineApril 15, 2008

Center starts

Data on Demand Data on Demand Legacy DataData-on-DemandProtocol (I)

McDiarmidInequality

Data-on-DemandProtocol (II)

McDiarmidinequality

Legacy-DataProtocol

McDiarmidinequalityInequality

Noiseless dataControllable

inputs

inequalityNoisy data

Uncontrollable inputs

inequalityLipschitzconstantsNoisy data




The data-on-Demand UQ protocol

ModelinggError

SystemUncertainty


The Annual Assessment CycleMichael Ortiz

BUAA 3/14/11 - 44

The data-on-Demand UQ Protocol

UQ

Modeling d

ExperimentalS i



andSimulation

Science

Tightly-integrated simulations and experiments!

Caltech’s UQ pipeline - CSE OTMEffort led by Caltech’s

Center for AdvancedComputing Research

Challenge: Develop Computational Scienceand Engineering (CSE) i f t t f t i t

Mystic optimizer SPHIR

infrastructure for uncertainty quantification (UQ) analysis.

Mystic optimizer SPHIR


Michael OrtizLANL’s coyoteBUAA 3/14/11 - 46

UQ orchestrates all activities

Computational Fluid

D iDynamics

Computational Science and E i i

Probability and Statistics Engineeringand Statistics

UQExperimental

ScienceMaterials

Models and

UQScience

Computational Solid

Properties


Michael Ortiz

Dynamics

BUAA 3/14/11 - 47

Our vision for Predictive Science…

A Walk through PS Evolution must lid t

mustcertifyA Walk through PS Evolution

must computefast, big…

must havephysics…

validate… certify…

g p y

circa 1995 circa 1998 circa 2002

• QMU is the next logical step in the evolution of PS• Articulating QMU in precise, rigorous and quantitative

terms is a grand challenge of our time!


terms is a grand challenge of our time!Michael Ortiz

BUAA 3/14/11 - 48

Overview

Thank you!y



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