Multiphysics Foundations for Material State Change Prognosis in Material Systems UNIVERSITY OF SOUTH CAROLINA “Forward Projected State Awareness” Form

Multiphysics Foundations for Material State Multiphysics Foundations for Material State Change Prognosis in Material SystemsChange Prognosis in Material Systems

UNIVERSITY OF SOUTH CAROLINA

Ken Reifsnider, NAE Educational Foundation University Professor of Mechanical Engineering Director, Solid Oxide Fuel Cell Program www.engr.sc.edu/SOFC University of South Carolina, Columbia, SC 29208 (803)777-0084 [email protected]

“Forward Projected State Awareness”

Form relates to function +

Substance relates to performance

What something is determines what it does -and what it will do

“The material is the sensor”

Acknowledgements:

“Foundations for Mechanical Prognosis of Nano-Structured Membranes,” AFOSR, Victor Giurgiutiu

Constitutive Modeling for Mechanical Response of Ionomer-Based Nano-Phased Composite Laminates,” Sponsor: NSF

Strength Concepts for Large Nonlinear Deformations of Woven Strength Concepts for Large Nonlinear Deformations of Woven Composites at Different Strain RatesComposites at Different Strain Rates , ONR / GD Electric Boat


Material Systems Material Systems Distributed Distributed Properties (e.g. ‘damage’)Properties (e.g. ‘damage’)

Material Systems Material Systems Distributed Distributed Properties (e.g. ‘damage’)Properties (e.g. ‘damage’)


“Damage Tolerance and Durability ofMaterial Systems”

Kenneth Reifsnider &Scott CaseJohn Wiley, 2003

Ken Reifsnider

Distributed Damage Distributed Damage Reliability ~ Reliability ~ conditional probabilityconditional probability

Distributed Damage Distributed Damage Reliability ~ Reliability ~ conditional probabilityconditional probability


Ken Reifsnider

Q t1 t 1R t1 R t( )

1

R

dR

dt dt

1

R

dR

dt

R t1 exp t t( )

d

Risk analysis specifiesan exponential relibility

Then “collecting” damage:

0 2 4 6 8 100

1

2

3

4

5

ss st( )

st0 2 4 6 8 10

0

2

4

6

8

ss st( )

st

a = 4 a = 12

Distributed Damage Distributed Damage Nonlinear stress Nonlinear stress strain behaviorstrain behavior

Distributed Damage Distributed Damage Nonlinear stress Nonlinear stress strain behaviorstrain behavior


0

20000

40000

60000

80000

100000

120000

0. 0% 0. 5% 1. 0% 1. 5% 2. 0% 2. 5% 3. 0% 3. 5% 4. 0% 4. 5%Eff ecti ve Strai n(i n)

Effec

tive

Str

ess(

Psi)

15 Degree

30 Degree

60 Degree

45 degree

)(2

1

ll h

E

w

2

)()()(2

nn

n hh

222

41

42 cossinsincos)( cchl

Elastic:Plastic:

h():

Elastic-plastic analysis:

Single master curve

Large deformation ~distributed damage:

Liqun XingKen Reifsnider

15o

30o45o

60o

90o

0o

Constitutive Models Constitutive Models

Related literature:

1. Weeks C.A. and Sun C.T.; Design and Characterization of Multi-core Composite Laminates, 38 th International SAMPE Symposium, May 10-13, pp. 1736-1750, 1993

2. Sun, C.T. and Potti S.V., A simple model to predict residual velocities of thick composite laminates subjected to high velocity impact, Int. J. Impact Engg, V. 18, No. 3 pp-339-353, 1996

3. Sun C.T. and Chen, J.L., Composite Materials, 23, 1009-11020, 1989

4. Tamuzs, V.m, Dzelzitis, K. and Reifsnider, K.L., Applied Composite Materials, Vol.11 No.5, 259-279, 2004

5. Tamuzs, V.m, Dzelzitis, K. and Reifsnider, K.L., Applied Composite Materials, Vol.11 No.5, 281-293, 2004

6. Ogihara, S. and Reifsnider, K.L., Applied Composite Materials, Vol.9, 249-263, 2002

Constitutive equations representing that progressive damage were constructed, and generalized for ABAQUS:

captures strain-rate dependence

only one time dependent parameter

-50.6

-50.4

-50.2

-50

-49.8

-49.6

-49.4

-10 -8 -6 -4 -2 0

Log (Strain Rate)

LogA

0

20000

40000

60000

80000

100000

120000

0. 0% 0. 5% 1. 0% 1. 5% 2. 0% 2. 5% 3. 0% 3. 5% 4. 0% 4. 5% 5. 0%

Eff ecti ve Pl asti c Strai n

Effec

tive

Str

ess

(Psi

)

0. 0001/ s

0. 002/ s

0. 01/ s

'p

A ' n A

t '

pd

d

m

0

15

30

45

Finite Element Verification & Validation:

Failure surfaces

Contour of failure index


Liqun XingKen Reifsnider

Micro-cracking Micro-cracking Strain to break Strain to breakMicro-cracking Micro-cracking Strain to break Strain to break

Models of specific local material state changes can be used to correctly estimate limits of behavior

4 5 De g re e S tre s s -S tra in

0

5 00 0

1 00 00

1 50 00

2 00 00

2 50 00

3 00 00

3 50 00

4 00 00

0 % 3 % 5 % 8 % 1 0% 1 3% 1 5% 1 8% 2 0% 2 3% 2 5%

S tra in (in )

Stress(Psi)

Strain (%) (percent)

Strain to Break

I II III IV

15 degree30 degree

45 degree

elastic strain under changed G12 3.81% 7.64% 8.51%

plastic strain due to fiber shearing 1.95% 4.65% 8.34%

Total strain to break -calculated 5.76% 12.29% 16.85%

Total strain to break - observed 5.35% 15.1% 19.8%

15 degree15 degree30 degree30 degree

45 degree45 degree

elastic strain under changed G12elastic strain under changed G12 3.81%3.81% 7.64%7.64% 8.51%8.51%

plastic strain due to fiber shearingplastic strain due to fiber shearing 1.95%1.95% 4.65%4.65% 8.34%8.34%

Total strain to break -calculatedTotal strain to break -calculated 5.76%5.76% 12.29%12.29% 16.85%16.85%

Total strain to break - observedTotal strain to break - observed 5.35%5.35% 15.1%15.1% 19.8%19.8%

How can we relate the other How can we relate the other specific events that control specific events that control the state of the material to the state of the material to real-time measurements to real-time measurements to create state awareness that create state awareness that specifies mechanical state specifies mechanical state variables like stiffness, variables like stiffness, strength, and life?strength, and life?

Mass Balance

Charge Transfer Balance

Species Diffusion

Momentum

Energy Balance

Stress-Strain

Temperature dependent properties: conductivity, exchange current density, species diffusion, polarizations, thermal stress, capacitance…

Results: Material system response coupled to material state,

in real time?

Heat Transfer:Sources- overpotentials, entropy changesSink- heat conduction, convection and radiationGoverning Equations

Physics

Multiphysics representation of response Multiphysics representation of response in terms of material state:in terms of material state:

(the material is the sensor)(the material is the sensor)

Multiphysics representation of response Multiphysics representation of response in terms of material state:in terms of material state:

(the material is the sensor)(the material is the sensor)Ken Reifsnider

Material state = set of all physical Material state = set of all physical variables variables neededneeded to define system to define system

performanceperformance

Material state = set of all physical Material state = set of all physical variables variables neededneeded to define system to define system

performanceperformance

Conductivity – by using a cyclic excitation voltage in our simulation, we were able to predict the impedance behavior of an actual microstructure, which compares very well with the observed results for the bulk material

of that type microstructure becomes a multiphysics indicator of material state

Local Integrated Current

tieU 0

Local Integrated Current

tieU 0


Ken Reifsnider

Surface1, BC1

Surface2, BC2

Electrochemical ImpedanceSpectroscopy provides data that relate to microstructure

AC Simulation

Impedance spectra calculated by finite element method and corresponding measured

result for as-received and as-aged 10ScSZ1550.

Microstructure changes correctly predictEIS results a measure of local conduction paths, geometry, and micro-constituent properties

Ken Reifsnider, Gang Ju

Impedance / conductivity –

requires a path reflects material properties, properties, geometry, interfaces

at the local level in a fundamental way dynamic measurements are sensitive to transport, chemical

or electrochemical activity, microstructural integrity, interfaces, …

distributed sensor / detector technology is out there we can model the physics (good foundation in the literature)


Ken Reifsnider

0

inf

0

inf

68,228102.2 exp 1 exp

1 exp

41,710572.5 exp

c c

c c

c cE

c c

k k t

k k RT

E E tC

E E

RT

References: Zhu Dongming and Miller Robert A 2000 MRS Bulletin 25 n7 43--47

State changes :

• porosity / tortuosity• Ohmic resistance• interface phase formation• impurity migration• microcracking / delamination• conductivity (T, i)• stiffness• strength• ….

Rate equations :

Multiphysics analysis :

• balance equations• constitutive equations• boundary conditions• extensive variables as functions of time

Predicted specific power density as function ofhistory of operation, design, manufacturing :

Mechanical performance,failure prediction :

Durability – a general multiphysics-based approach:

Foundations for Durability of Fuel Cells and Fuel Cell Systems

Ken Reifsnider

Mechanical condition can be measured by EIS methods:


Ken ReifsniderLiqun Xing, Paul Fazzino

0 5 10 15

x 104

0

1

2

3

4

5

6x 10

4

Z - Real (Ohms)

-Z -

Im

agin

ary

(O

hm

s)

100

101

102

103

104

105

106

0

0.5

1

1.5

2x 10

5

Frequency (Hz)

|Z| (

Ohm

s)

100

101

102

103

104

105

106

-80

-60

-40

-20

0

Frequency (Hz)

Pha

se (

Deg

rees

)

Fractured Glass Fiber Composite:

EIS data:

0 5 10 15

x 105

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10

5

Z - Real (Ohms)

-Z -

Im

agin

ary

(O

hm

s)

Non Damaged

Partially DamagedDamaged

100

101

102

103

104

105

106

0

1

2

x 106

Frequency (Hz)

|Z| (

Ohm

s)

Non Damaged

Partially DamagedDamaged

100

101

102

103

104

105

106

-80

-60

-40

-20

0

Frequency (Hz)

Phas

e (D

egre

es)

Mechanical degradation can be measured by EIS methods:


Ken ReifsniderLiqun Xing, Paul Fazzino


Ken Reifsnider

Measurements:Impedance spectroscopy

Interpretation:Multiphysics

Material mechanical state:Composite mechanics

Performance:Remaining stiffness, strength and life as afunction of expected operation environment

Science AdvanceScience Advance multiphysics multiphysics

material statematerial state

Technical AdvanceTechnical Advance material state material state

mechanical performance mechanical performance methodologiesmethodologies

Science AdvanceScience Advance multiphysics multiphysics

material statematerial state

Technical AdvanceTechnical Advance material state material state

mechanical performance mechanical performance methodologiesmethodologies

ELECTRONICSTD WORK

A

B

D E

F

C

G

AA

BB

DD EE

FF

CC

GG

INTEGRATEDINTO ELECTRONICPROCESS MAPS & ASSOCIATED WITH WORKINSTRUCTIONS

ELECTRONICIPD

A

B

D E

F

C

G

IPT 1

IPT 2

IPT 3

WORK FLOWMANAGEMENT

COLLABORATIVEENGINEERING

SECURE B2B

DESIGNAUTOMATION

A

B

D E

F

C

G

SYSTEMOPTIMIZER

OP

TIM

IZE

R

OP

TIM

IZE

R

IPT 1&2

IPT 3

AUTOMATEITERATION

SATISFY CRITERIA

GRID COMPUTING

LIBRARY OF“WRAPPED” TOOLS

A

B

C

B

CG

ACCURATE

VALIDATED

CERTIFIED

CONTROLLED

Proprietary tools

INTEGRATIONFRAMEWORK

C

GB

D

F

H

INTEGRATETHIRD PARTY& LEGACY TOOLS

INDUSTRYACCEPTED

COMMERCIAL

Commercial of the shelf (COTS)Available FIPER, CO, ModelCenter

Internal PWStandard Work& IPD Process

Center for eDesign, Airforce ACD&D,

CAD PDMs

COTS: iSIGHT

45

What do we do with such foundations?


46

We must provide representations and models of material systems that can be used to design and manufacture engineering structures.




Material models Material models Nonlinear stress Nonlinear stress strain behaviorstrain behavior

Material models Material models Nonlinear stress Nonlinear stress strain behaviorstrain behavior

1

( / )

( , )

E V

E

V V

E

E

f

Elastic- viscoplastic analysis:

Large deformation, material modelscan represent such behavior, but not specific events or types of damage

( )1( ) ( ) (1 ) atb E c E e t k

Liqun Xing

Documents

Multiphysics Foundations for Material State Change Prognosis in Material Systems UNIVERSITY OF SOUTH CAROLINA “Forward Projected State Awareness” Form