Dr. Mark HorstemeyerCAVS Chair Professor

ASME FellowMississippi State Universitymfhorst@me.msstate.edu

662.325.5449

Multiscale Modeling:An Overview

Outline1) Modeling Philosophy Overview2) MSU Internal State Variable Plasticity-Damage Model (MSU DMG 1.0) Theory

1) Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000

2) Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993.

3) Image Analysis Tool 1.0 User’s Tutorial4) DMGfit 1.0 User’s Tutorial5) MSU MultiStage Fatigue Model (MSU MSF 1.0) Theory

1) McDowell, D.L., Gall, K., Horstemeyer, M.F., and Fan, J., “Microstructure-Based Fatigue Modeling of Cast A356-T6 Alloy,” Engineering Fracture Mechanics, Vol. 70, pp.49-80, 2003.

6) MSFfit 1.0 User’s Tutorial7) MSU ISV Thermoplastic Model (MSU TP 1.0) Theory

1) J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variable Model for Amorphous Glassy Polymers,” submitted to Acta Mechanica

8) TPfit 1.0 User’s Tutorial

Computational Manufacturing and Design

Mission: We couple multidisciplinary research of solid mechanics, materials, physics, and applied mathematics in three synergistic areas: theoretical modeling, experimentation, and large scale parallel computational simulation to optimize design and manufacturing processes.

Macroscale ISV Continuum

Bridge 1 = Interfacial Energy, Elasticity

Atomistics(EAM,MEAM,MD,MS,

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

Mechanisms

Bridge 8 =Dislocation

Motion

Bridge 9 =Void \ Crack Nucleation

Bridge 10 =Void \ Crack

Growth

Macroscale ISV Continuum

Multiscale Modeling

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

Multiscale Experiments1. 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

Model

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

Engineering tools (CAD, CAE, etc.)

Conceptual design process(user-friendly interfaces)

IT technologies(hidden from the engineer)

CyberInfrastructure

D

CB

A

E

Standard FEAStress

(from highest to lowest)

DAC E B

Inclusion (from most severe

to less severe)BEADC

Damage (from most severe

to less severe)ADECB

initial failure site

(a)

(b)

Region 3Region 1model

experiment

0

10000

20000

30000

40000

50000

60000

70000

80000

0 5 10 15 20 25

app

lied

load

(N

ewto

ns)

applied displacement (mm)

before CRADA workpeak design load =48000 N

after CRADA workpeak design load=72000 N

15000

20000

25000

30000

35000

40000

10 100 1000 104 105

app

lied

lo

ad (

New

ton

s)

cycles

after CRADA work

before CRADA work

Result: To optimize a redesign such that 25% weight saved

50% increase in load-bearing capacity100% increase in fatigue life

$2 less per part

GM CADILLAC CONTROL ARM LIGHTWEIGHT DESIGN

(2000)Objective: To employ multiscale material modeling

to reduce the weight of components

Truth!Wrong!

System

Subsystem

Component

Internal State Variable Plasticity-Damage

Simulation

StructuresPore sizeNearest Neighbor DistanceDendrite Cell SizePorosity

Boundary ConditionsPanic brakePothole strikeForcesMoments

GM Corvette Cradle Magnesium Design (2005)

ED

BA

C

F Mises Stress

Initial Porosity

Damage

Highest D C EB F BE E DA D AF B F

Lowest C A C

Cradle Load-to-Failure Simulation Results

Modern FEA answer

Modern Materials Science answer True answer

Powder Metal FC0205 Steel (2008)Compaction, Sintering, and Performance

failure predicted by damage model under performance with distribution of initial porosity

experiment

model

maximum von Mises Stress

Note: standard FEA wouldhave given the wrong location

I – Compaction Modeling (Validation)Main Bearing Cap – Green Density Distribution- after Springback (g/cc)

FEA ModelGeometry and Material Solution imported from ABAQUS/ Explicit to

ABAQUS/Standard for Elastic Springback Analysis

ExperimentX-ray CT

2D X-Ray CT

FEA 205Q

Image Analysis

9

1 32

4

57 8

10

11

6

1213

1615

1718

14

19 20

1 32

4

57 8

10

11

6

1213

1615

1718

14

19 20

9

Density Immersion

Density (g/cc)

+7.00

+6.90+6.85+6.80+6.75+6.70+6.65+6.60+6.55

+6.95

+6.50+6.45+6.40

+7.05

ExperimentImmersion and Image Analysis Densities

by Zone

Volume grows 0.6%after springback

density

Cyberinfrastructure Design FrameworkFEAsimulation

Optimization

CAD

Model calibration

Materialpropertiesrepository

Inputdeck

Material

Geometry

FEAoutputs

FEA setup

Validation

Computeplatformsettings

Material models andconstants

Mesh

Boundaryconditions/loading

Post-processingdirectives

Design objectives/requirements

Experimentaldata

MSF

MSU Multiscale Modeling

• Vision: In 5-10 years, we are internationally recognized as the premiere material modeling group in world for our validated and verified research and production models

• Mission: systemize our multiscale modeling capability so that the cyberinfrastructure easily admits each different aspect of the modeling characteristics (codes, materials info, mechanical properties tests, multiscale models, etc)

Modeling History and Overview• Started in thermonuclear weapons design at Sandia

(no underground systems level testing)• Populate the space of systems levels with simulations

(simulation based design and multiscale modeling to get correct physics)

• Used for many different metal alloys in materials processing and life-performance analysis

• Tech transfer to Navy, Army, and automotive applications

• Notion of history modeling with internal state variables

FEA Simulations and Timeline Using Internal State Variable Model

• Early 1980’s: steel alloys for weapon laydown event (highlight: front cover of Science) plasticity, damage, and fracture

• Mid 1980’s-1990’s: forging process: rex• Late 1980’s: analysis of various components:

plasticity and failure• Early 1990’s: Navy submarines lethality, welding• Mid 1990’s: forming, extrusion, heat treatment• Late 1990’s: automotive castings• Early 2000’s: everything automotive• Mid 2000’s: Army vehicle component designs• Late 2000’s: polymers and powder metals

Metals Modeled by Macroscale DMG ISV Plasticity-Damage Model 1.0

• Steel Alloys (15)– A286, AF, C1008, S7tool, 1020, 10b22, 4140, 4340, 210SS, 304LSS, 319SS,

HY80, HY100, HY130, FC0205• Aluminum Alloys(16)

– 1100, 2024T0, 2024T35, 2024T4, 5083, 5086, 6061T0, 6022, 6050, 6061T0, 6061T6, 7039, 7075T0, 7075T6, A319, A356

• Magnesium Alloys (7)– AM20, AM30, AM50, AM60, AZ31, AZ91, AE44

• Titanium Alloys (4)– Ti7Al4Mo, Ti8Al1Mo1V, Ti0Al6V4, Ti6Al6V2Sn

• Uranium Alloys (2)– D38, D380075Ti

• Nickel (2)– 99.99% pure, In718

• Brass (1)– 99% pure

70 metal alloys to date!

Phenomena N=Model 1

Phenomena 1=Model 1

Phenomena 2=Model 2

Phenomena 3=Model 3

Phenomena N=Model N

.

.

.

.

Classical Modeling Paradigm MSU CAVS Modeling Paradigm

MSU CAVS CMD Material Modeling Philosophy

Phenomena 1=Model 1

Phenomena 2=Model 1+few additional constants

Phenomena 3=Model 1+few additional constants

.

.

.

.

.

Note: with every new phenomena the modelmoves back to a general abstraction so if the newconstants are zero the original model results

Note: with each new model, many moreconstants are introduced with the newmodel

Phenomena N=Model 1

Creep=Nabarro-Herring Model

Plasticity=Ramberg-Osgood

Damage=Johnson-Cook

Phenomena N=Model N

.

.

.

.

Classical Modeling Paradigm MSU CAVS Modeling Paradigm

Example of Philosophies with Creep and Plasticity

Creep=Garafalo flow rule

Plasticity=Garafalo + dislocation density ISVs

Damage=Garafalo+disl ISVs+Damage ISVs

.

.

.

.

.

Note: with every new phenomena the modelmoves back to a general abstraction so if the newconstants are zero the original model results

Note: with each new model, many moreconstants are introduced with the addednew model

Macroscale Research and Production ModelsNote 1: Production models/codes must have a documented citable journal article for each version of the code

a. makes impact factor greaterb. makes it easier for next graduate student to add incremental improvements

Note 2: Production models/codes must build on the previous worka. helps systemize and synergize our efforts in terms of research and fundingb. clears up confusion to outsider customers and industryc. helps user base

Note 3: Production models/codes must have a theoretical and user’s manuala. absolute necessity for new graduate students and new user’sb. helps the broad usage of the model over timec. this alone may lead the greatest impact over time

Note 4: Only a Production model/code can go into the cyberinfrastructure

Journal Article History and MSU CAVS R&D Modeling Plan

Bammann (1990) temperature and strain rate dependent unified-creep plasticity model (Bammann Model)

Bammann et al. (1993) applications of Bammann model with damage (no formal name)BCJ (1995) formalization of model (really mod of 1993 paper: BCJ)Horstemeyer et al. (2000) microstructure with damage (DMG model)

MSU CAVS DMG ISV Model 1.0

Version 1.1

ProductionResearch

EMMI

AnisotropicDamage (Solanki)

PressureDep yield(Hammi)

Coalescence(Allison,Oglesby)

Version 1.2

Version 1.3

Elastic moddamage(Allison)

Version 1.4

Recrystallization/grain growth

?

Add more materials with quantifying the structure-property relations

V&V

V&V

MSU CAVS R&D Modeling Plan (cont)

MSU CAVS DMG ISV Model 1.0

Version 1.5

ProductionResearch

EMMI

Plastic spin(Najafi)

High rateStress stateDep(Tucker)

Version 1.6

Version 1.7

Hardeningchange(Bammann)

Version 2.0 (new setof constants required

for all materials)

Twinning(Oppedal,Bammann,Horstemeyer,Marin)

Version 1.8

Subscalestudies

V&V

MSU CAVS R&D Modeling Plan (cont)

MSU CAVS ND DMG ISV Model 2.0

Version 2.1

ProductionResearch

Phase Transform(LWang)

Nonlocaldamage(Solanki)

Version 2.2

Version 2.3

PPT morphology(El Kadiri)

Solidification(Felicelli,LWang)

New name??

Subscalestudies

Validation and Verification (V&V)

Research FE CodesTahoeRamaswamy code (nonlocal damage, implicit)Winters code (coupled thermomechanical)ABAQUS

Production FE CodesABAQUSLS DynaESI PamcrashESI PamstampMD Nastran

model Fitting algorithm(Carino)

Modelverification

Model implementation

Metals Modeled by MultiStage Fatigue Model 1.0

• Steel Alloys (3)– 4140, 319SS, FC0205

• Aluminum Alloys(5)– 2024T0, 7075T6, A319, A356, A380

• Magnesium Alloys (7)– AM30, AM50, AM60, AZ31, AZ61, AZ91, AE44

15 metal alloys to date!

Polymers Modeled by MultiStage Fatigue Model 1.0• Polyurethane (2)

– Pure, carbon nanotube polyurethane• Elastomer (2)

– SBR, track rubber• Polycarbonate (1)

Journal Article History and MSU CAVS R&D Modeling Plan

McDowell et al (2003) microstructure-sensitive MultiStage Fatigue (MSF)Xue et al (2007) grain size and texture effectsJordon et al (2008) nearest neighbor distance and elastic moduli effect on porosity

MSU CAVS MSF Model 1.0

Version 1.1

ProductionResearch

Thermomechanical(???)

SymptoticExpansionsISVs (???)

Corrosion(???)

Version 1.2

Version 1.3

Polymers(Bouvard,Brown)

Version 1.4

Add more materials with quantifying the structure-property relations

V&V

Polymers Modeled by Macroscale ISV ViscoElastic-ViscoPlasticity-Damage Model 1.0

• Polycarbonate (1)• Polypropylene (1)• Polyurethane (1)• ABS• Elastomer (3-Santoprene, natural rubber, SBR)• Nylon (4)

– Nylon 6.6, Nylon 4.4, E-glass+Nylon, S-glass+Nylon• Kevlar• Brain• Liver• Tendon• Placenta

12 polymers to date!

Journal Article History and ISV Polymer Modeling Plan

Bammann (1990) temperature and strain rate dependent unified-creep plasticity modelBammann et al. (1993) applications of Bammann model with damageBCJ (1995) formalization of modelHorstemeyer et al. (2000) microstructure with damage

MSU CAVS Poly DMG ISV Model 1.0

Version 1.1

ProductionResearch

viscoelasticity(Prabhu)

?Add more materials with quantifying the structure-property relations

V&V

Boyce-ArrudaAnand

rubbers(Brown) Version 1.2

nanocomposites(Lacy, Shi, Zhang,Pittman, Toghiani)

Version 1.3

Model calibration tools developmentCMD Theoreticians

RLCarino

THaupt/CCG

Model evaluationroutine(Fortran, MATLAB)

Computationalbackendfor model(MATLAB)

DMG

ImageAnalyzer

MSF

BB->VEP

EMMI

PQplot

MSC

Piecewise lines->DSR

DMG UMAT+Uncertainty

DMG VUMAT+Nucleation data

VPSC

MSF+amplitude loading

(Fung->Biomaterial?)

Dislocation ANN GUI

ImageStitcher

RPTpostprocessorStand-aloneexecutable

Webservice

Tool & Status

Web-based

Users

PC-based

Feedback

Production codes

Model code, Providers, UsersDMG

ImageAnalyzer

MSF

BB->VEP

EMMI

PQplot

MSC

Piecewise curves->DSR

DMG UMAT+Uncertainty

DMG VUMAT+Nucl. data

VPSC

MSF+amplitude loading

(Fung->Biomaterial?)

Dislocation ANN GUI

ImageStitcher

RPTpostprocessor

mfhorst

tnw7

mfhorst, bjordan

jeanluc

ebmarin

yhammi

yhammi

(jeanluc)

kns3

kns3

aoppedal, haitham

Mfhorst,bjordan

(lwilliams)

ElKadiri

(bjordon)

(axue)

(various), S.Agnew, Y.Guo

(various)

yhammi, bjordon, paul, adrian

jeanluc, jef83

jcrapps

(USAMP-PM?)

(USAMP-PM?)

sponder

kns3

kns3

aoppedal

(NGC?)

?

osama, (haitham’s student)

(axue’s student)

Production codes

Computational Manufacturing and Design

Mission: We couple multidisciplinary research of solid mechanics, materials, physics, and applied mathematics in three synergistic areas: theoretical modeling, experimentation, and large scale parallel computational simulation to optimize design and manufacturing processes.