Integr grate ted C Computa tatio tional Ma l Materia ials ls - - PowerPoint PPT Presentation

Integr grate ted C Computa tatio tional Ma l Materia ials ls Sc Science & & Engineering ( (IC ICMSE SE ) ) Appr pproache hes t to Problems wi with h Evolving D Domai mains

Worksho shop o

• n C

Compu puta tati tional M Methods ds for P r Prob roblems w with Evolv lvin ing Do Domain ins an and Dis Discontin inuit itie ies AHP AHPCRC, S , Stanfor

• rd U

Univers rsity, C y, CA Decem ecember er 4 4-5, 5, 2013 2013

Somnat nath G h Ghosh

De Depar artments of C Civ ivil il & Me Mechanic ical l Engin gineerin ing Johns H Hopkins U Univers rsity Baltimore, Maryland USA

Integ egrated ated M Materi terials als S Scien ence & e & Engine neering ( (ICMSE) SE) P Paradi digm

• J. Allison, D. Backman, and L. Christodoulou, "Integrated Computational Materials

Engineering: A new paradigm for the global materials profession," JOM, pp. 25-27, 2006.

ICMSE SE philoso sophy phy “entails i integra ration

• n o
• f i

inform

• rmation
• n a

acros

• ss le

lengt gth an and t tim ime s scale ales for all all rele levan ant m mat ateria ials ls p phenomena an a and enable ables concurrent an analy alysis o

• f man

anuf ufac acturin ing, d design ign, an and mat aterial ials w wit ithin in a a holis listic ic s system” ”

Two C Cas ase S Studies i in t the I e ICMSE E Parad radig igm

1.

• 1. Multi

ti-scale le m model f l for ductile ile failu ilure in hete terogeneous m meta tallic mate terials

• 2. Im

. Image-ba based m modelin ling of fatig igue ue f failu ilure in m metall llic ic allo loys

Ductile F e Failure o ure of H Hetero erogen eneous us Metall allic ic M Mater erial ials

Automotive Engine Block Microstructure: Cast Aluminum Alloy with Si Particulates and Intermetallics Evolving Ductile Failure in Aluminum Microstructure

Stress-Strain plot showing ductility

• Ductile failure in heterogeneous materials typically initiates with

particle cracking or interfacial debonding.

• Voids grow near nucleated regions with deformation, and

subsequently coalesce with neighboring voids to result in localized matrix failure.

• Evolution of matrix failure causes stress and strain redistribution

in the microstructure that leads to ductile fracture at other sites.

• Eventually, the phenomena leads to catastrophic failure of the

microstructure.

Fat Fatigue i in Aerosp space E Engine Mat aterials s

9 times during hold (2 min) 20 times during cycle

Stress time

1 sec 1 sec

Stress time

50 times during one cycle 9 times during hold (2 min) 20 times during cycle

Stress time

1 sec 1 sec

Stress time

50 times during one cycle

Dwell fatigue Regular fatigue

• Crack initiation site is sub-surface
• Initiation location depends on local microstructure
• Initiation area is faceted with limited evidence of plasticity
• Away from initiation site, crack growth is ‘normal’, i.e. striations
• 2 min. dwell can lead to 2-10 x reduction in fatigue life

Effect of microstructure important in predicting fatigue life: e.g. nucleation at location of extreme values of grain morphology,

• rientation and misorientation, micro-texturing.

Structur cture-Materi erial Inte teracti tion Chal hallenges

• Mo

Modelin ling at at the macros roscopic s scales cannot

• t

prov rovide a accura rate estim imates o

• f d

duc uctilit ility an and fat atigu igue lif life

• Lac

acks ap appropriat iate lo local ge al geometric ic an and thermo-mechan anical al in information o

• f the in

incip ipie ient d dam amage age s sit ites

• Mo

Modelin ling at at the micros

• stru

ructura ral s scales is comput utat atio ional ally ly i intractabl ble

• Need a

approp ropri riate mult ulti-scale le t techniq ique ues in in spat atia ial an l and temporal l domai ains that at w will ill up uphold ld t the e effic icie iency o

• f sim

imula ulations, w while ile not compro romising t the require red r resol

• lution
• ns

Adapt daptive Multi Spat Spatial-Sca cale le Mo Modelin ling o g of Ductile Fr Frac acture i in Heterogeneous M Metal allic Ma Materia ials ls Case ase St Study dy 1

• S. Ghosh, “Micromechanical Analysis and Multi-Scale Modeling Using the Voronoi Cell Finite

Element Method”, CRC Press/Taylor & Francis, 2011, 729 pages.

• S. Ghosh and D. Paquet, “Adaptive Multi-Level Model for Multi-Scale Analysis of Ductile Fracture

in Heterogeneous Aluminum Alloys”, Mechanics of Materials, (in press), 2013.

• S. Ghosh, J. Bai and D. Paquet, Jour. Mech. Physics Solids, Vol. 57, 2009.
• C. Hu, J. Bai and S. Ghosh, Modeling and Simulation in Materials Science and Engineering, Vol. 15,
• pp. S377-S392, 2007

Two-Wa Way C y Couple led Adap Adaptive Conc

• ncurrent

t Multi ti-Scal Scale Mode del

Modeling Error

Introduce multiple-level hierarchy

Discretization Error

Increase DOF e.g. by h-p-adaptation

RVE Homogenization

Level-0

B O T T O M U P T O P D O W N

Localization

Level-1 Level-2

Physics-Based Reduced Ordered Models Homogenization Theory- Based Swing Region for Error Analysis Micromechanical Analysis in Critical Regions

Fra ramew ework rk f for C

• r Conc
• ncurren

ent M Multi-Sc Scal aling

1.

• 1. Mult

Multi-Sc Scal ale C Characterizat atio ion: : Morpholo logy gy-bas based D Domai ain P Partitio ionin ing g an and RV RVE Id Identifi fication

2304 µm 48

µm

A

' ' '

( ', ') ( ', ') ( ', ')

g g g hrsm wvlt diff

I x y I x y I x y = +

High Resolu

• lutio

ion Dom

• main

Recon construct uctio ion Step 1. Wavelet interpolation

• f low res. images

Step 2. Correlation-based enhancement from limited high res. images Recur cursiv ive R Refin inement based d

• n
• n Mor
• rph

phol

• log
• gica

cal l Cha haract cteristic c Fun unct ctions

Frame mework for C Concur urrent M Mult ulti-Scal cales

2.

• 2. Micromechan

anic ical al Analy alysis is: Voron

• noi
• i Cell

ll FEM f M for Duc Ductile ile Fractur ure

Optical micrograph VCFEM

• S. Ghosh, “Micromechanical Analysis and Multi-Scale Modeling Using the Voronoi Cell Finite

Element Method”, CRC Press/Taylor & Francis, 2011, 729 pages.

VCFEM for undamaged particle VCFEM for damaged particle VCFEM for Matrix Cracking

( ) ( ) ( )

( )

( )

, , : '

m c m c e tm c

e e m m c c c

d d d d d

+ +

Ω Ω ∂Ω Γ ∂Ω

∆ ∆ = − ∆ ∆ Ω − ∆ Ω + + ∆ ⋅ ⋅∆ ∂Ω − + ∆ ⋅∆ Γ − + ∆ − − ∆ ⋅ ⋅∆ ∂Ω

∏ ∫ ∫ ∫ ∫ ∫

σ u B σ σ ε σ σ σ n u t t u σ σ σ σ n u

( )

cr

c c cr

d

∂Ω

′′ − + ∆ ⋅ ⋅∆ ∂Ω

∫

σ σ n u

( )

( )

, :

s s s

s s s s s s

d d d

Ω Ω ∂Ω

+ ∆ ∆ Ω + ∆ Ω − + ∆ ⋅ ⋅∆ ∂Ω

∫ ∫ ∫

A σ ε σ ε σ σ n u

VCFEM for damaged particle VCFEM for Matrix Cracking Stress function:

/ m m m c poly rec

Φ = Φ + Φ

c c poly

Φ = Φ

/ m cr rec

+Φ

/ c cr rec

+Φ

Vor

• ron
• noi C

Cell FE FEM M For Formulation for

• r

Partic icle le a and Matrix ix Crac

acking

VCFEM for undamaged particle

For local softening in stress-strain response: Higher-order displacement interpolated regions is embedded in the stress-interpolated VCFEM domain

• C. Hu and S. Ghosh, IJNME, 2008.

Assumed Stress-Hybrid FEM

Non

• n-lo

loca cal void

• id grow
• wth

h rate

Particle Cracking Nucleation: Weibull distribution based crack initiation criterion

Microstruc uctur ural P Partic icle le a and Matrix ix Cra racking

Matrix Cracking Nucleation:

Gurson-Tvergaard-Needleman (GTN) type Models ( )

2 * *2 2 1 3

3 2 cosh 1 2 σ σ     Φ = + − − +         q p q q f q f

( )

(1 )

p p p nucleation growth kk

df df df A d f d ε ε ε = + = + −

( )

* * c u c c c c F c

f for f f f f f f f f for f f f f ≤   = −  + − >  − 

( ) ( ) ( ) ( )

1

local v

f f w dV W = −

∫

x x x x x     

( ) ( )

( )

2 2 1 1 2

3 2 cosh 1 2 φ   Σ Σ   = + − − =     

eq hyd f p f p

Q f Q f Y W Y W

( ) ( )

1

p kk

f f e A e e = − +    ( )( ) ( )(

)

( )( ) ( )

2 2 2 2 2 eq p yy zz p zz xx p xx yy p xy

F W G W H W C W Σ = Σ − Σ + Σ − Σ + Σ − Σ + Σ

Anisotropic yield surface in the GTN model

1 1

; (1 ) = Σ = Σ + Σ + Σ − 

hyd xx yy zz inclusion

Q Q f

F, G, H and C: Anisotropic YS parameters calibrated from homogenization of micromechanics in principal material-damage coordinates

( ) ( ) ( ) ( )

1

local v

f f w dV W = −

∫

x x x x x     

3.

• 3. Macros

roscopic Mo Modelin ling: : Hom Homogenized C Con

• ntinuum M

Mod

• del f

for

• r

Plas lastic icit ity an and Dam Damage age E Evolu lution wit ith H Heteroge geneit itie ies

Frame mework for C Concur urrent M Mult ulti-Scal cales

Val Validation o

• f Mac

acroscopic H HCPD M Mode del

Str Stres ess–strain n respons nse b by HC HCPD mode

• del

l and micr icromech chanica cal solut

• lutio

ions for

• r non
• n-prop
• por
• rtio

ional loa loadi ding.

Evol

• lution
• n o
• f a

anisot

• tro

ropy parameters rs F, , G, H , H for R RVE wi with th 40 40 in inclus lusions

Frame mework for C Concur urrent M Mult ulti-Scal caling

3.

• 3. Macros

roscopic Mo Modelin ling: : Hom Homogenized C Con

• ntinuum M

Mod

• del f

for

• r

Plas lastic icit ity an and Dam Damage age E Evolu lution wit ith H Heteroge geneit itie ies u

RVE1 RVE2 RVE3 RVE4 RVE5

xx

Σ

(GPa)

Void volume fraction

1 1 1 1 1 1 1 2 int

δ δ δ δ δ δ

+ + + + + + Ω Ω Ω Ω Γ

Π = Π + Π + Π + Π + Π =

n n n n n n het lo l l tr

Level-0 RVE Level-1 Level-2/tr

Coupling microscopic and macroscopic sub-domains using Relaxed Constraint method.

Frame mework for C Concur urrent M Mult ulti-Scal caling

4. . Adap aptiv ive Mult Multi-Level Mo l Modelin ling: : For C Couplin ling Mult Multip iple le Sc Scale ales in in Sim Simulat ulatin ing Failur ailure

,

Obtained from LE-VCFEM.

,

Obtained from the FEM implementation of the HCPD model.

Micromechanics simulation Adaptive multi-scale simulation Horizontal normal stress component σxx (GPa)

Adapt daptive M Multi-le level Mo l Model l

Evolution of adaptive multi-level mesh

Uy=0.0μm Uy=7.8μm Uy=13.0μm Uy=13.7μm

Underlying microstructure and microscopic stress σyy (GPa)

Uy=13.0μm

Level-2/tr Level-0 Level-1 Sealed

Adapti tive M Multi ti-level M Model

Te Tensile ile De Deformation o

• f Mic

Micro-speci cimen en

Image-Bas ased d Mode deling an and d Multi-Ti Time me Scaling f for

• r Fatigue Prob

Problems in in T Ti i an and M d Mg Alloys s Case ase St Study dy 2 2

• S. Ghosh and D. Dimiduk , “Computational Methods for Microstructure-Property

Relations”, Springer NY, 2011, 790 pages.

• S. Ghosh and P. Chakraborty, Int. Jour. Fatigue, Vol. 48, pp. 231-246, 2013.
• M. Anahid, M. Samal and S. Ghosh, Jour. Mech. Physics Solids, Vol. 59, 2011.
• G. Venkatramani, S. Ghosh and M.J. Mills, Acta Materialia, Vol. 55, 2007.
• D. Deka, D.S. Joseph, S. Ghosh, and M.J. Mills, Met. Mater. Trans. A, 2006.

• Ima

mage B Based C Crys ysta tal P l Pla lasti ticit ity F y FEM with ith Experime ment ntal Val alidat ation

• 3D Polycrysta

stallin line M Microst structu ture Si Simu mulat ation

• Fat

atigue C Crac ack I k Initiat ation i in Dwell St Studies

• Multi

ulti-time Sc Scal ale Models in Cryst stal al P Plast asticity

Impo Important St Steps

1. . Rate te De Dependent t Crystal P Plasticity

e

= S E C

2 2

2( )

β β α αβ β β α α β β

α γ λ γ

• =

+ −

∑ ∑

    

SSD GND

k G b g q h g g

0 1

1

r s s

g g h h sign g g

β β β β β β

  = − −    

( )

2 s s a s s

h h h h sech h h

β β β β β β β β

γ τ τ     − = + −     −      

* p

= F F F

Kinematics Constitutive Relations Flow rule Slip System Deformation Resistance Self Hardening Evolution (hcp) Self Hardening Evolution (bcc)

, ( S)

eT e eff kin α α α α

τ τ τ τ = − ≡ ⊗ :m n

α α

F F

1 m eff

sign g

α α α α

τ γ γ τ

• =

/

( ) 

α α α α kin kin

τ cγ - d τ γ    =

Back-stress Evolution

sα mα sα mα

Fp F* F

α α α

= +

• K

g g D

Grain size effect on Deformation Resistance

Acharya and Beaudoin, 2000

Experimental Data Processing

(ii) ii) St Stat atis istic icall ally E Equiv uivale lent

Distribution and Correlation Functions

• 2. Methods o
• f Virtua

ual M l Microstructur ure Simula mulatio ion

(i) C ) CAD AD-Ba Based

Adaptive Non-Uniform Rational B- Spline (NURBS) functions for GB Bhandari, Ghosh et, al. 2007 Groeber, Ghosh et. al, 2008

1-3. Im . Image-Base sed C Cryst stal Pl Plast sticity F FEM EM Mod Model f for

• r T

Ti-62 6242 M 42 Microstructu ture

Schmid Factor along a section Local stress along a section

Defor

• rmati

tion Twi winning i g in Mag agnesium:

Initiat ation an and Evo volution

Crack initiated from twin-grain boundary intersection. Zigzag crack propagation at twin-twin interactions crack propagation along twin boundaries

Micro-crack formation along twin boundaries

SEM observation of twin boundary cracking in fatigue test of Mg.

Twinning accumulation in fatigue test

(D.K. Xu, E.H. Han, Scripta. Mat. 2013)

𝟐𝟐𝟔 cycles 𝟐𝟐𝟕 cycles

(Q. Yu et al, Mat. Sci. Eng. A, 2011)

Micro-crack formation was observed in fatigue samples in both twin-grain boundary intersection and inside grains along twin boundaries.

𝐹𝑗𝑗𝑗 → 𝐹𝑢𝑢 + 𝐹𝑠 + 𝐹𝑗𝑗𝑢 + 𝐹

𝑔𝑔𝑔𝑔𝑢 − 𝑋 𝑓𝑓𝑢(𝜐)

Nucleation criteria: 𝐹𝑡𝑢𝑔𝑡𝑔𝑓 < 𝐹𝑗𝑗𝑗; 𝑒𝑡𝑢𝑔𝑡𝑔𝑓 > 2𝑠

𝛿̇𝑢𝑢 = 𝜍𝑢𝑢𝑐𝑢𝑢𝑚𝑢𝑢𝑔exp ∆𝐺 − 𝜐𝑊∗ 𝐿𝐶𝑈

Twin dislocation propagation rate: Energetic criteria of dislocation dissociation for twin nucleation

Modelin ling D Deforma matio ion Twin innin ing

Model for twin nucleation & propagation CPFE simulation results Twin formation mechanism

twin formation layer-by- layer twinning dislocations

Lo Load ad She Shedd dding Le Leadi ading t to Fatigue Crack ck Initia iatio tion

Soft grain (High h Pris ism Schm chmid id fact ctor

• r)

Dislocation pile up near the boundary

• f hard and soft

grains Hard grain (Low Prism Schmid factor) Stress concentration in near boundary

3. . A N Nonl

• nloc
• cal Crac

ack N Nucl cleat ation n Mod Model

2

8 (1 )

s

G c B π υ γ = −

2 2

β π = + ≥ ⇒

c eff n t

K T T T c

= ≥

eff c

R T c R

/ π =

c c

R K

Single parameter to be calibrated

Models relating crack length c and opening B

• Mic

icro-cr crack ack in in hard gr grain in du due to to dis islo locatio ion pile ileup in in so soft grain in

• Crack

ack openin ning dis ispla lacement corre rresponds to to th the closure re failure ure alo long a Burg urger’s ’s ci circu cuit surr rroun unding th the pile iled-up up dis islo locations ns

• Tractio

tion acro ross th the mic icro-cr crack tip ip in in hard gr grain

• pens up

up th the cr crac ack.

Slip plane

c

Grain boundary B= nb

T

t

T

n

Pile up length

Stroh (1964)

Experime mental l Calib libratio ion & & Valid lidatio ions

Dw Dwell ll fat atigu igue t tests o

• n Ti

Ti-6242 6242

Test No

• No. of cycles to

crack initiation (experiments)

• No. of cycles to crack

initiation (simulation) % Relative error Calibrated at 80% life Calibrated at 80% life I 550 cycles 620 cycles 12.7%

Micros roscop

• pic f

feature res of p predicte ted d lo locat ation o

• f crac

ack in init itiat iation

Experimentally

• bserved

Sample 1 Sample 2 ‘c’ axis orientation 0 - 30o 38.5o 25.2o Prism Schmid factor 0 - 0.1 0.17 0.09 Basal Schmid factor 0.3 - 0.45 0.48 0.38

Cra rack P Pro ropagation i in Cry rystalline M Mat aterials f fro rom MD S Simulati tion

• ns
• 1. C

Char arac acterizat zation an and Quan antificat ation o

• f M

Mechan anisms s in Molecular ar Si Simulat ation

Dis islo locatio ion Extrac action ( (DXA) A)

Deformation g gradie ient for

• r twi

wins Crack surface

Dislocation DXA Dislocation density, Burgers vector Twin Deformation gradient Twin volume fraction Crack surface Equivalent ellipse Crack length, opening

Dislocation segments colored by magnitude of Burgers vector

• Dis

islo locatio ion m motio ion blunts crack t k tip

• Cros
• ss s

slip ob p observed

• Dislocat

ation f from m diffe ferent slip s systems ms interac act f formi ming immobile le j junctio ions (s (stair-rod d dislocat ation) )

Dislocation Evolution

St Stra rain-Strai rain Respons nse w with M h Mechani hanisms Evolut lutio ion

Energy Balance: 𝒆𝒆 = 𝒆𝑽𝐟𝐟 + 𝒆𝑽𝐣𝐣𝐟𝐟 + 𝒆𝒆 𝒆𝒆: work done by applied force 𝒆𝒆 : generated heat 𝒆𝑽𝐟𝐟 : elastic strain energy that can be recovered by unloading 𝒆𝑽𝐣𝐣𝐟𝐟: inelastic strain energy not recoverable, related to defect energy Crack Evolution

• 4. M

Mult ulti-Time Sc Scal ale M Modeling f for r Fatigue ue A Analys lysis is

Nf = 11,718 Nf = 43,180 Nf = 20,141 Nf = 24,241

Fp F Fe

sα mα sα mα

Computational requirements for cycle by cycle complete polycrystalline microstructural fatigue analysis is prohibitive Extrapolation (often pursued) is grossly inaccurate Field Data on Fatigue Life

Wavelet Decomposition of Nodal Displacements

( , ) ( ) ( )

k k k

u N c N τ ψ τ =∑

Coefficients of wavelet basis

• Depends on coarse cycle scale (N)
• Independent of fine scale.

Wavelet basis function

• Fine scale (τ) behavior
• Independent of coarse scale (N)

Wavele let T Transfo forma matio ion Based M Mult ulti- Time Sc Scal aling g Methodology (WATMU

MUS) S)

Haar Wavelet

Dilation Translation

Multi-resolution basis functions: Translation and Dilation

• Com
• mpa

pact S Supp pport : : No spurious oscillations from truncation, e.g. Gibbs's instabilities

• Orthog
• gon
• nal: Daubechies family
• Multiresolution t

transfo format mation: Space of basis functions for a resolution is well defined and finite. Reduced number of coefficients to characterize a waveform

• No

Non-pe periodi dic:

• Wor

Works f for

• r R

R=-1.

Properties and Advantages

{ }

2 1 1

...... ... ( )

m

V V V L R

− +

⊂ ⊂ ⊂ ⊂

Higher Resolution Lower Resolution

Wav avelets a and M nd Multi-resol

• luti

tion

• n

2 1

• 1

m,n m n

..... V V V ....... L ( ) with span{ } V

−

⊂ ⊂ ⊂ ⊂ ⊂ φ = ฀

Projection to Vm : Approximation of function at m-th resolution

2 ,

2 (2 )

m m m n

n φ φ τ = −

Scaling Function

Dilation Translation Orthogonal Basis for Wm (through translation) : ψ(τ) :mother wavelet

2

2 (2 )

m m mn

n ψ ψ τ = −

Detail space Wm : Orthogonal difference between resolutions m & m+1

1 m m m

V V W

+ =

⊕

( )

, ,

( )

m n m n m n

f C τ φ τ =∑∑

Scaling Function Mother Wavelet Daube Daubechie ies-4 W 4 Wav avele let, N=4 =4

Basis functions: Square integrable functions projected into nested subspaces of varying resolution Vm

• Evolution of State Variable
• Change of State Variable in a Cycle:
• Cycle Rate of Change of Cycle Scale

State Variable (Coarse Scale Derivative): (independent of τ)

Coarse Scale Evolutionary Constitutive Equations: (Integration Point)

( ) ( , ) ( ) ( , ( ), ) ( ( ), ( )) ε τ τ ε = − = =

∫

T k k

dy N y N T y N dN f y N d Y y N N

• Wavelet transformed of nodal displacements:
• Deformaton gradient

( , ) ( ) ( )

k i i k k

u N c N

α α

τ ψ τ =∑

( , )

m k ij ij m i k j T T

N F F t d c d X

α α α

τ ψ τ ψ τ ∂ = = ∂

∑ ∑ ∫ ∫ Element Level:

Wave avelet Tr Tran ansf sformed M d Multi-Sc Scal ale Methodol dolog

• gy

( , ( )) ( , ( ), )

k

y f y t f y N ε ε τ = = 

( , , , )

p acc

F gα

α

χ γ

( , ) ( ) ( , ( ), )

τ

τ ε τ τ = +∫

k

y N y N f y N d

Adaptivity ty i in n th the WATMUS US Algor

• rith

thm

2 Errors Sources

• 1. Truncation of higher order terms O(∆N3) in the numerical

integration of coarse scale equations (ε0

p , g0)

3 2 3 3 3 2

1 ( 1) ( 1) 6 ( 1) 1

prev

N d y r r N r dN r N ∆ + − + = ∆ = + − ∆ 

2 3 3 3 2 3

1 ( 1) ( 1) , max 6 ( 1) 1

el

po k k T trunc trunc trunc po el V

d r r d F f N dV dF r dN σ + − + ≤ ∆ = + −

∫

  B

Truncation Error from Residual in Equilibrium Equation due to Constitutive Integration

1 3

max η

∈

  ∆ =      





evol

trunc step k trunc k

f N

• 2. Ignore slowly varying displacement coefficients to reduce size

| / |

k

dc dN η ≥

• evol

evol add non evol evol −

= ∪ =      

Solve the element equilibrium residual components for evolving coefficients

Fp

,22

Fp

0,22 at a material point

Fp

0,22 in the microstructure

WATMUS S – Coar arse an and Fine Sc Scal ale Resp esponse se

σ22 at 300000th cycle Evolution of stress along a material line with cycles

Summar mary

• Conventionally implemented phenomenological models lack

robust underlying physics-based mechanisms with little relation to actual micromechanical features.

• Coupled with advanced modeling capabilities, provide the

foundations for predictive science and technology with consequences in material design and processing to endure demanding mission profiles with improved reliability.

• Comprehensive approaches, taking advantage of the emerging

frontiers in computational and experimental science and engineering, are necessary for addressing this critical challenge.