1

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

2

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

3

Acknowledgements

Colleagues: Joe Gallagher, Bob Crane, Noel Ashbaugh, Joe

Ori, Alon Dumanis-Modan, Matt Gates

Sponsors:• 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)

4

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

PsAdhesive

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 ag

Stru

ctu

re C

rack

Length

as

Now

Failure (structure)

Gage Crack Length ag

Stru

ctu

re C

rack

Length

as

Now

Gage Crack Length ag

Stru

ctu

re C

rack

Length

as

Gage Crack Length ag

Stru

ctu

re C

rack

Length

as

Now

Failure (structure)

5

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 crack

Gage Crack

7

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

Str

uctu

re C

rack

Len

gth

as

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

9

Time

Ap

pli

ed S

tres

s

Overload

Fig. 7.5

Fatigue Crack Retardation(Load Sequence Effect)

Note: Peak tensile load can increase life

Without Overload

With Overload

Cra

ck L

eng

th (

a)

Elapsed Cycle (N)

10

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

11

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

12

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

S

0 – 20 ksi

A.

19 reversals

920,000 reversalst

S +/- 40 ksi0 – 20 ksi

C.

change

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Load Sequence is Important

Note:• 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 Gage

L

Member

a

u

G

Structural

LT W

Ps

s

Adhesive

P

aS

Crack Gage

L

Member

a

u

G

Adhesive

P

aS

Crack Gage

L

Member

a

u

G

Structural

LT W

Ps

Structural

LT W

Ps

LT W

Ps

N =da

F

da

Fs gaa

aa

igg

iss

( ) ( )K K

Theory ContinuedAssume power law for crack growth

Assume gage/structure stress related

(a)a=K where

F(K)KCdN

da m

g= fs (f depends on geometry, attachment, etc.)

s

is

g

iggs

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!!

da

C a

da

C f as sm

g gma

a

a

a

ig

g

is

s

( ) ( )

17

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 crack

Gage 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

Cra

ck len

gth

(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)

Str

uc

ture

Cra

ck

Le

ng

th (

in)

E060

E073

E080

E072

Stru

ctu

re c

rack

as

(inch)

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)

Str

uc

ture

Cra

ck

Le

ng

th (

in)

E060

E073

E080

E072

Stru

ctu

re c

rack

as

(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)

Str

uc

ture

Cra

ck

Le

ng

th (

in)

E060

E073

E080

E072

Stru

ctu

re c

rack

as

(inch)

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)

Str

uctu

re C

rack L

en

gth

(in

)

E060

E073

E080

E072

Prediction E060

Prediction E073

Prediction E080

Prediction E072

Gage crack ag (inch)

Str

uct

ure

cra

ck a

s

(in

ch

)

30

Multiple Gages

Describe load dependent transfer function

31

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(F

da=N Gage 1

g

ig

a

ag )K(F

da=N Gage 2

Compute “effective” stress

Compute structure crack

N =da

F

da

Fs gaa

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 Gage

L

Member

a

u

G

Structural

LT W

Ps

s

Adhesive

P

a S

Crack Gage

L

Member

a

u

G

Structural

LT W

Ps

s

Adhesive

P

a S

Crack Gage

L

Member

a

u

G

Adhesive

P

a S

Crack Gage

L

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.

37

38

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

40

U. S. Patent 4,107,980August 22, 1978

41

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

43

Alon Dumanis-ModanEvaluation of the Crack Gage as an Advanced Individual

Tracking Concept, Ph. D. Thesis, Purdue University, Dec. 1982

44

Matthew D. Gates A Crack Gage Approach to Monitoring Fatigue

Damage Potential in Aircraft, M.S. Thesis, Purdue University, May 1997.

45

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.

46

Side-Grooves Promote “Thick Section” Crack Retardation

Th

ou

san

ds o

f d

ela

y 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

48

Load Sequence Effects

Hi-lo strain sequence results in compressive mean stress when last large peak is tension

increases life

t

t

Mean stress

49

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

50

Nu

mb

er o

f ex

ceed

ance

s/u

nit

tim

e

Load Factor n

0

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