The Witness Sample Approach to Prognosis
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Transcript of The Witness Sample Approach to Prognosis
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The Witness Sample Approach to Prognosis
A. F. (Skip) GrandtSchool of Aeronautics and
AstronauticsPurdue University
Currently USAF Academy Department of Engineering Mechanics
AFOSR Workshop on Prognosis of Aircraft and Space Devices, Components, and Systems
Cincinnati, OH, 19-20 February 2008
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OutlineObjective: Review simple technique to evaluate
structural usage in context of potential for fatigue/corrosion damage
Describe “serial number” tracking concept
Topics:Overview witness sample approachReview prior work
• Uniform thickness gages• Side-groove gages• Multiple gages
Summarize status/needs
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AcknowledgementsColleagues: Joe Gallagher, Bob Crane, Noel Ashbaugh, Joe
Ori, Alon Dumanis-Modan, Matt GatesSponsors:• Air Force Materials Laboratory (~ 1976-79)• Air Force Institute of Technology (~1977)• Air Force Flight Dynamics Laboratory/University
of Dayton Research Institute (1980-82)• Air Force Office of Scientific Research (1995-97)
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Objective and Approach• Mount cracked coupon (witness
sample) to structure• Monitor crack extension in sample• Interpret coupon crack growth as
potential for fatigue in parent structure
Adhesive
aS
Crack GageL
a
u
G
Structural Member
LT W
Ps
Ps Adhesive
aS
Crack GageL
a
u
G
Structural Member
LT W
Ps
Adhesive
aS
Crack GageL
a
u
G
Structural Member
LT W
Ps
Adhesive
aS
Crack GageL
a
u
G
Adhesive
aS
Crack GageL
a
u
G
Structural Member
LT W
Ps
Structural Member
LT W
Ps
LT W
Ps
Ps Gage Crack Length agStru
ctur
e Cr
ack
Leng
th a
sNow
Failure (structure)
Gage Crack Length agStru
ctur
e Cr
ack
Leng
th a
sNow
Gage Crack Length agStru
ctur
e Cr
ack
Leng
th a
s
Gage Crack Length agStru
ctur
e Cr
ack
Leng
th a
sNow
Failure (structure)
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The Witness Sample Approach to Prognosis
or
“It Takes One to Know One!”
Witness Sample Overview• Crack gage is “analog computer” that
measures/evaluates severity of structural loading
• Growth of gage crack gives potential for structural crack growth
• Crack gage is a “prognosis sensor”
Structure crackGage Crack
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Transfer Function(Relate gage/structure cracks)
• Gage crack and assumed structure crack growth are related
• Can “design” gage for desired response
• Material• Shape• Initial crack sizes• Ease of
measurement• Independent of load
history under certain conditions
Stru
ctur
e Cr
ack
Leng
th a
s
Gage Crack Length ag
Now
Failure (structure)
Why Witness Samples?• Simpler than current tracking methods
– Flight load recorders, accelerometers, . . – Expensive, extensive effort, complicated
• Witness sample advantages– Simple cracked coupon– Transfer functions determine potential for structural
crack growth– Can be “designed” for given response– Damage potential immediately quantified- Sensitive to same parameters as crack
- Load sequence- Environment
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Time
App
lied
Stre
ss
Overload
Fig. 7.5
Fatigue Crack Retardation(Load Sequence Effect)
Note: Peak tensile load can increase life
Without Overload
With Overload
Cra
ck L
engt
h (a
)Elapsed Cycle (N)
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Fig. 7.7
Fatigue Crack Retardation/Sequence(2024-T3 Al – Schijve)
s = 50 Mpa; mean = 80 Mpa; R = 55/105Mpa = 0.52 peak = +200/-40 MPa
Reference: Schijve, ASM V 19, 1996
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Fatigue Nucleation Load Sequence Effects (Crews data)
230,000 reversals = life t
S
0 – 20 ksi
A.
Constant amplitude fatigue tests with 2024-T3 aluminum plates with open holes
2 in dia
12 in
S
S
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Example Load Sequence Effects: Crews data
Note: sequence changed life from 126,000 to 920,000
reversals
126,000 reversals
20 reversals
t
S +/- 40 ksi0 – 20 ksiB.
change
230,000 reversals t
S0 – 20 ksi
A.
19 reversals
920,000 reversalst
S +/- 40 ksi0 – 20 ksi
C.
change
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Load Sequence is ImportantNote:• Order in which loads are applied can
have tremendous influence on fatigue life
• Introduces mean stresses that can be tensile or positive
• Most pronounced for spectra with many small loads and a few large loads
• Sequence effect must be accounted for on prognosis data – complicates traditional load monitoring schemes
Crack Gage Theory
• Structural and gage cracks see same number of cycles N
• Assume: • da/dN = F(K)
s
Adhesive
P
aS
Crack GageL
Member
a
u
G
Structural
LT W
Ps
s
Adhesive
P
aS
Crack GageL
Member
a
u
G
Adhesive
P
aS
Crack GageL
Member
a
u
G
Structural
LT W
Ps
Structural
LT W
Ps
LT W
Ps
N = daF
daFs g
aa
aa
igg
iss
( ) ( )K K
Theory ContinuedAssume power law for crack growth
Assume gage/structure stress related(a)a=K where
F(K)KCdNda m
g= fs (f depends on geometry, attachment, etc.)
s
is
g
ig gs
a
a
a
a mgsg
msss )af(C
da)a(C
da
Theory Concluded If structure Paris exponent, ms, equals
the gage exponent, mg = m
• Solve for as versus ag
• Relation depends on f, ai’s, ’s, materials . . .• But independent of Stress!!
daC a
daC f as s
mg g
ma
a
a
a
ig
g
is
s
( ) ( )
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Uniform Thickness Gages(with J. A. Ori and N. E. Ashbaugh)
Gages: • edge or center cracks• 2024-T3, 2219-T851, 7075-T6• 0.03 inch thick• 1.5, 2 inch length (unbond)
Structure: • Cracked hole• 2219-T851 • 0.24 or 0.525 inch
thick
Structure crackGage Crack
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Edge-Crack Gage Results(Crack Length vs Cycles)
• Constant amplitude stress• 10.5 ksi• 13.3 ksi
• Crack growth depends on stress
Ref: J. A. Ori & A. F. Grandt, ASTM 1979
Gage Cracks StructureCracks
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Edge-Crack Gage Results(Transfer Function)
• Plot structure vs gage crack length
• Independent of stress
• Agrees with model
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Center-Crack GageDesign Parameters
Transfer function depends on:
• Initial crack sizes• Gage/structure material• Unbond length• Gage geometry
• Thickness, width• Crack configuration
• Potential to “design” gage for desired response
Ref: N. E. Ashbaugh & A. F. Grandt, ASTM 1979
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Side-Grooved Crack Gage(A. Dumanis-Modan and M. Gates)
Goal:• Promote plane strain
in thin crack gage Similar fatigue crack
retardation in thin gage and thick structure
• Gage provides better estimate of structural crack growth
Crack
Side-Grooved Gage Results ( A. Dumanis-Modan)
Found that “deep double side-grooved” gages resulted in repeatable gage behavior, and fatigue retardation consistent with thick structure
2.0"
0.125"
0.031"
0.375
"4.1
"
Adhesive
0.187
5 "B/BN = 4.0
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Side-Grooves Promote “Thick Section” Crack Growth
• 7075-T6 alloy• 2.0 overload
ratio• 0.63 mm
thickness• Uniform• Side-groove
Ref: J. P. Hess, A. Grandt, and A. Dumanis, IJFEMS, 1983 Thousands of Cycles
Crac
k le
ngth
(m
m)
Side-Grooved Gage Results (Alon Dumanis-Modan)
• 17 tests with side-grooved gages
• 9 load histories• Constant amplitude (R = -0.1, 0.1, 0.3)• 50% overload (R = - 0.1, 0.1, 0.3)• Variable amplitude T-38
spectrum – mild – Baseline– severe)
Ref: Dumanis-Modan & Grandt, EFM 1987
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Side-Groove Gage Results• Scatter in data
• Associated with initial crack lengths
• Inherent to fatigue crack growth
• Load independent model gives reasonable prediction
• Curve “too steep”• “Gage crack grows
too slow”
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Side-Grooved Gage 2 (Matt Gates)
Objective: Improve side-groove gage• Decrease slope of transfer function
• Make gage crack grow faster than structural crack
• Increase unbond length• Reduce scatter in fatigue lives
• Tighten tolerances in gage dimensions• Relieve side-groove residual stresses
Ref. M. D. Gates & A. F. Grandt, Jr., SEM 1997
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Results: Side-Groove Gage 2
• Gage response made more sensitive by increasing length (unbond) of gage• Gage growth rate 12 x structure
crack growth rate• Machining of side-grooves can
introduce residual stresses >> inconsistent behavior• Stress relieve of gages potential
solution, but must be done carefully
Side-Groove Gage Transfer Function (note scale difference)
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Gage Crack Length (in)
Stru
ctur
e C
rack
Len
gth
(in)
E060E073E080E072
Struc
ture
cra
ck a
s(in
ch)
Gage crack ag (inch)
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Gage Crack Length (in)
Stru
ctur
e C
rack
Len
gth
(in)
E060E073E080E072
Struc
ture
cra
ck a
s(in
ch)
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Gage Crack Length (in)
Stru
ctur
e C
rack
Len
gth
(in)
E060E073E080E072
Struc
ture
cra
ck a
s(in
ch)
Gage crack ag (inch)
4 constant amplitude
fatigue tests
2.0
0.2
0.0
Experiment Vs. Predictive Model
0
0.05
0.1
0.15
0.2
0.25
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Gage Crack Length (in)
Stru
ctur
e Cr
ack
Leng
th (i
n)
E060
E073
E080
E072
Prediction E060
Prediction E073
Prediction E080
Prediction E072
Gage crack ag (inch)
Stru
ctur
e cr
ack
a s
(inc
h)
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Multiple Gages Describe load dependent transfer function
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Multiple Gages
Concept: • Second crack gage provides
additional information• Allows one to determine “effective”
stress• Allows more sophisticated fatigue
crack growth models• Model not limited to Paris equation• Does involve more detailed analysis
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Double-Gage Theory
g
ig
a
ag )K(Fda=N Gage 1
g
ig
a
ag )K(Fda=N Gage 2
Compute “effective” stress
Compute structure crack
N = daF
daFs g
aa
aa
igg
iss
( ) ( )K K
Reference: A. Dumanis and A. F. Grandt, 15th ICAF, 1989
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Summary: Current Status• Fundamental basis for gage
and structure crack relation• Experimentally verified
• Uniform thickness• Side-groove gage• Double gage
• “Design” gage for desired response s
Adhesive
P
a S
Crack GageL
Member
a
u
G
Structural
LT W
Ps
s
Adhesive
P
a S
Crack GageL
Member
a
u
G
Structural
LT W
Ps
s
Adhesive
P
a S
Crack GageL
Member
a
u
G
Adhesive
P
a S
Crack GageL
Member
a
u
G
Structural
LT W
Ps
Structural
LT W
Ps
LT W
Ps
Gage measures severity of structural loads (fatigue damage
potential)
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Summary: Research Needs• Gage attachment
• Develop/evaluate attachment for long term performance
• Side-groove consistency • Control machining and/or stress relief
• “Tweak” design parameters• Remote measurement of gage crack length
• Develop/evaluate inspection method
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Summary• Other potential prognosis applications
• Corrosion monitoring feasible• Potential for fatigue crack “nucleation”
and/or total life applications
• Key idea: actual damage (fatigue, corrosion, creep . . .) in redundant component can tell much about severity of parent structural usage
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References J. P. Gallagher, A. F. Grandt, Jr., and R. L. Crane, “Tracking Crack Growth Damage in US Air
Force Aircraft,” Journal of Aircraft, Vol. 15, No. 7, July 1978, pp. 435-442. N. E. Ashbaugh and A. F. Grandt, Jr., “Evaluation of a Crack-Growth Gage for Monitoring
Possible Structural Fatigue Crack Growth,” Service Fatigue Loads Monitoring, Simulation and Analysis, ASTM Special Technical Publication 671, pp. 94-117, 1979. Also published as AFML-TR-77-233, February 1978.
R. L. Crane, A. F. Grandt, Jr., and J. P. Gallagher, "Assessment of Flaw Growth Potential in Structural Components," United States Patent No. 4,107,980, August 22, 1978.
J. A. Ori and A. F. Grandt, Jr., “Single-Edge-Cracked Crack Growth Gage,” Fracture Mechanics, ASTM Special Technical Publication 677, 533-549, 1979.
J. P. Hess, A. F. Grandt, Jr., and A. Dumanis, “Effects of Side-Grooves on Fatigue Crack Retardation,” International Journal of Fatigue of Engineering Materials and Structures, Vol. 6, No. 2, 1983, pp. 189-199.
Dumanis and A. F. Grandt, Jr., “Development of a Side-Grooved Crack Gage for Fleet Tracking of Fatigue Damage,” Engineering Fracture Mechanics, Vol. 26, No. 1, 1987, pp. 95-104.
A. Dumanis and A. F. Grandt, Jr., “Development of a Double Crack Growth Gage Algorithm for Application to Fleet Tracking of Fatigue Damage,” Proceedings International Committee on Aeronautical Fatigue 21st Conference, 15th Symposium, Jerusalem, Israel, June 1989.
M. D. Gates and A. F. Grandt, Jr., “Crack Gage Approach to Monitoring Fatigue Damage Potential in Aircraft,” 1997 Society for Experimental Mechanics Spring Conference on Experimental and Applied Mechanics, June 2-4, 1997, Bellevue, Washington (2 pages). Extended version of paper (7 double-column pages) also accepted for publication in the 1997 SEM Spring Post-conference Proceedings, 1998.
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Crack Gage Overview• Crack gage is an “analog computer” that
measures/evaluates severity of structural loading
• Growth of gage crack gives potential for structural crack growth
• Crack gage is a “prognosis sensor”
Adhesive
a S
Crack GageL
a
u
G
Structural Member
LT W
Ps
Ps
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U. S. Patent 4,107,980August 22, 1978
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42Fig. 7.6
Fatigue Crack Retardation(7075-T6 aluminum)
max /min = 18.3/55.2 Mpa max = 99.3 Mpa 1/4001 cycle block
Reference: Bucci, EFM, v 12, No. 3, 1979
No overload
With overload
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Alon Dumanis-ModanEvaluation of the Crack Gage as an Advanced Individual
Tracking Concept, Ph. D. Thesis, Purdue University, Dec. 1982
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Matthew D. Gates A Crack Gage Approach to Monitoring Fatigue
Damage Potential in Aircraft, M.S. Thesis, Purdue University, May 1997.
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Joseph A. OriExperimental Evaluation of a Single Edge Crack Crack
Growth Gage for Monitoring Aircraft Structures, M.S. Thesis, Air Force Institute of Technology, Dec 1977.
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Side-Grooves Promote “Thick Section” Crack Retardation
Thou
sand
s of
del
ay c
ycle
s
Specimen Thickness BN (mm)
47Fig. 10.10
Fatigue Crack Retardation/Sequence(2024-T3 Al – Schijve)
s = 6.6 Mpa; mean = 8.2 Mpa; R = 4.9/11.5Mpa = 0.43 max = +19.2 MPa , min = -2.9 MPa
Reference: Broek
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Load Sequence Effects
Hi-lo strain sequence results in compressive mean stress when last large peak is tension
increases life
t
t
Mean stress
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Load Sequence Effects Hi-lo strain
sequence results in tensile mean stress when last large peak was compression as shown here
decreases life!
t
t
Mean stress
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Num
ber o
f ex
ceed
ance
s/un
it tim
e
Load Factor n0
Schematic Exceedance Curve (Fig. 16.4)
• Gives the number of times given load factor exceeded in unit of time
• Does not show sequence or order of applied loads