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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
UNIVERSITY OF SOUTH CAROLINA
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’)
UNIVERSITY OF SOUTH CAROLINA
“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
UNIVERSITY OF SOUTH CAROLINA
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
UNIVERSITY OF SOUTH CAROLINA
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
UNIVERSITY OF SOUTH CAROLINA
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
UNIVERSITY OF SOUTH CAROLINA
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)
UNIVERSITY OF SOUTH CAROLINA
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:
UNIVERSITY OF SOUTH CAROLINA
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:
UNIVERSITY OF SOUTH CAROLINA
Ken ReifsniderLiqun Xing, Paul Fazzino
UNIVERSITY OF SOUTH CAROLINA
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
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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
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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?
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.
What do we do with such foundations?
What do we do with such foundations?
UNIVERSITY OF SOUTH CAROLINA
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