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The Witness Sample Approach to Prognosis

The Witness Sample Approach to Prognosis. A. F. (Skip) Grandt School of Aeronautics and Astronautics Purdue University Currently USAF Academy Department of Engineering Mechanics AFOSR Workshop on Prognosis of Aircraft and Space Devices, Components, and Systems

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The Witness Sample Approach to Prognosis

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  1. The Witness Sample Approach to Prognosis A. F. (Skip) Grandt School of Aeronautics and Astronautics Purdue 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. Outline Objective: Review simple technique to evaluate structural usage in context of potential for fatigue/corrosion damage  Describe “serial number” tracking concept Topics: Overview witness sample approach Review 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

  5. The Witness Sample Approach to Prognosis or “It Takes One to Know One!”

  6. Structure crack Gage Crack 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”

  7. Failure (structure) Structure Crack Length as Now Gage Crack Length ag 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

  8. 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. Without Overload Overload Applied Stresss Crack Length (a) With Overload Time Elapsed Cycle (N) Fatigue Crack Retardation (Load Sequence Effect) Note: Peak tensile load can increase life Fig. 7.5

  10. Fatigue Crack Retardation/Sequence (2024-T3 Al – Schijve) Ds = 50 Mpa; smean = 80 Mpa; R = 55/105Mpa = 0.52 speak = +200/-40 MPa Fig. 7.7 Reference: Schijve, ASM V 19, 1996

  11. S 0 – 20 ksi S A. t 230,000 reversals = life 12 in 2 in dia S Fatigue Nucleation Load Sequence Effects (Crews data) Constant amplitude fatigue tests with 2024-T3 aluminum plates with open holes

  12. S S +/- 40 ksi 0 – 20 ksi 0 – 20 ksi B. A. t t 230,000 reversals 126,000 reversals change S 20 reversals +/- 40 ksi change 0 – 20 ksi C. t 920,000 reversals 19 reversals Example Load Sequence Effects: Crews data Note: sequence changed life from 126,000 to 920,000 reversals

  13. 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

  14. Crack Gage Theory • Structural and gage cracks see same number of cycles N • Assume: • da/dN = F(K)

  15. Theory Continued Assume power law for crack growth Assume gage/structure stress related sg= fss (f depends on geometry, attachment, etc.)

  16. Theory Concluded If structure Paris exponent, ms, equals the gage exponent, mg = m • Solve for as versus ag • Relation depends on f, ai’s, b’s, materials . . . • But independent of Stress!!

  17. Structure crack Gage Crack 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

  18. Gage Cracks Structure Cracks 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

  19. Edge-Crack Gage Results(Transfer Function) • Plot structure vs gage crack length • Independent of stress • Agrees with model

  20. 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

  21. Crack 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

  22. 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 B/BN = 4.0

  23. Crack length (mm) Thousands of Cycles 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

  24. 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

  25. 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”

  26. 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

  27. 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

  28. Side-Groove Gage Transfer Function (note scale difference) 0.2 4 constant amplitude fatigue tests 0.0 2.0

  29. Structure crack as (inch) Gage crack ag (inch) Experiment Vs. Predictive Model

  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

  32. Gage 1 Gage 2 Double-Gage Theory Compute “effective” stress Compute structure crack Reference: A. Dumanis and A. F. Grandt, 15th ICAF, 1989

  33. 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  Gage measures severity of structural loads (fatigue damage potential)

  34. 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

  35. 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

  36. 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. Ps L W T a Crack Gage G L u Structural Member a S Adhesive 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” Ps

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

  39. No overload With overload Fatigue Crack Retardation (7075-T6 aluminum) smax /smin = 18.3/55.2 Mpa smax = 99.3 Mpa 1/4001 cycle block Reference: Bucci, EFM, v 12, No. 3, 1979 Fig. 7.6

  40. Alon Dumanis-Modan Evaluation of the Crack Gage as an Advanced Individual Tracking Concept, Ph. D. Thesis, Purdue University, Dec. 1982

  41. Matthew D. Gates A Crack Gage Approach to Monitoring Fatigue Damage Potential in Aircraft, M.S. Thesis, Purdue University, May 1997.

  42. Joseph A. Ori Experimental Evaluation of a Single Edge Crack Crack Growth Gage for Monitoring Aircraft Structures, M.S. Thesis, Air Force Institute of Technology, Dec 1977.

  43. Thousands of delay cycles Specimen Thickness BN (mm) Side-Grooves Promote “Thick Section” Crack Retardation

  44. Fatigue Crack Retardation/Sequence (2024-T3 Al – Schijve) Ds = 6.6 Mpa; smean = 8.2 Mpa; R = 4.9/11.5Mpa = 0.43 smax = +19.2 MPa , smin = -2.9 MPa Fig. 10.10 Reference: Broek

  45. Load Sequence Effects e t s s e t Mean stress Hi-lo strain  sequence results in compressive mean stress  when last large  peak is tension  increases life

  46. e t s s e Mean stress t Load Sequence Effects Hi-lo strain  sequence results in tensile mean stress  when last large  peak was compression as shown here  decreases life!

  47. Number of exceedances/unit time 0 Load Factor n 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

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