Experimental Mechanics

, Volume 59, Issue 2, pp 263–276 | Cite as

Enhanced Pre-Strain Application for Goodman Data Generated with Vibration-Based Testing

  • K. KnappEmail author
  • A. Palazotto
  • O. Scott-Emuakpor
  • C. Holycross


Imparting residual stress is an essential step in the generation of Goodman data via Air Force Research Laboratory’s vibration-based fatigue test. Conventional Goodman data is constructed through uniaxial fatigue testing at a rate of 40 Hz, while the vibration-based testing excites stresses at 1,600 Hz in a stress state similar to those of gas turbine engine (GTE) airfoils in service. Fully reversed oscillating fatigue loads are combined with a steady residual stress imparted by a preliminary plastic straining procedure, and a finite element model (FEM) is used to predict the residual stress distribution at the fatigue zone of the sample. The goal of this work is enhancing the Pre-strain procedure that imparts residual stresses to develop a less conservative design approach that captures GTE phenomena on a modified Goodman line. Improvements were made to the FEM by more effectively incorporating empirical tensile stress-strain behavior, in addition to more accurately representing the pressures and forces acting on the specimen during monotonic loading. Results are demonstrated on Aluminum 6061-T6 by comparing strain field results from digital image correlation to FEM analysis. The converged FEM solution had a standard deviation in εyy of 2,557 microstrain and predicted a residual σyy of 73.91 MPa, while the optimized solution had a standard deviation in εyy of 495.2 microstrain (akin to the experimental variation of 376.1 microstrain) and predicted a residual σyy of 31.03 MPa.


Plastic deformation Residual stress Digital image correlation Finite element modeling Fatigue life approximation 




\(\varepsilon ^{peak}_{tot}\)

Total strain at peak load

\(\varepsilon ^{zero}_{tot}\)

Total strain at zero

\(\varepsilon ^{rec}_{tot}\)

Total strain recovered


Plastic strain

\(\varepsilon ^{res}_{e}\)

Elastic residual strain


Stress at peak load


Residual stress


Poisson’s ratio


Young’s modulus

\(R=\frac {\sigma _{min}}{\sigma _{max}}\)

Stress ratio


Stress amplitude at failure


Cycles to failure during last step


Stress amplitude during previous step


Specified dwell fatigue cycles


Stress amplitude for failure at Nstep

\(\varepsilon _{_{FEM}}\)

Total strain predicted by FEM

\(\varepsilon _{_{DIC}}\)

Total strain measured by DIC



The authors would like to thank the Air Force Research Laboratories (AFRL), specifically the Turbine Engine Fatigue Facility (TEFF) for their financial support, facility and equipment access, and encouragement of this research.


  1. 1.
    Nicholas T (2006) High cycle fatigue - a mechanics of materials perspective. Elsevier, OxfordGoogle Scholar
  2. 2.
    (2002) Engine Structural Integrity Program (ENSIP), MIL-HDBK-1783B (USAF)Google Scholar
  3. 3.
    (2007) American Society for Testing and Materials, E466-07: Standard practice for conducting force controlled constant amplitude axial fatigue tests of metallic materials. ASTM book of standards. ASTM International, West Conshohocken, PAGoogle Scholar
  4. 4.
    George T, Seidt J, Shen M-HH, Cross C, Nicholas T (2004) Development of a novel Vibration-Based fatigue testing methodology. Int J Fatigue 26(5):477–486CrossRefGoogle Scholar
  5. 5.
    Yun GJ, Abdullah ABM, Binienda W (2012) Development of a Closed-Loop High-Cycle resonant fatigue testing system. Journal of Experimental Mechanics 52:275–288CrossRefGoogle Scholar
  6. 6.
    Mohanty S, Chattopadhyay A, Peralta P, Das S (2011) Bayesian statistic based multivariate gaussian process approach for Offline/Online fatigue crack growth prediction. Journal of Experimental Mechanics 51:833–843CrossRefGoogle Scholar
  7. 7.
    George T, Shen M-HH, Cross C, Nicholas T (2006) A new multiaxial fatigue testing method for variable amplitude loading and stress ratio. J Eng Gas Turbines Power 128:857–864CrossRefGoogle Scholar
  8. 8.
    Goodman J (1899) Mechanics applied to engineering, longmans. Green, and Co., LondonzbMATHGoogle Scholar
  9. 9.
    Froustey C, Lambert M, Charles JL, Lataillade JL (2007) Design of an impact loading machine based on a flywheel device: application to the fatigue resistance of the high rate pre-straining sensitivity of aluminium alloys. Journal of Experimental Mechanics 47:709–721CrossRefGoogle Scholar
  10. 10.
    George T, Shen M-HH, Scott-Emuakpor O, Nicholas T, Cross C, Calcaterra J (2005) Goodman diagram via Vibration-Based fatigue testing. J Eng Mater Technol 127(1):58–64CrossRefGoogle Scholar
  11. 11.
    Olson MD, DeWald AT, Prime MB, Hill MR (2015) Estimation of uncertainty for contour method residual stress measurements. Journal of Experimental Mechanics 55:577–585CrossRefGoogle Scholar
  12. 12.
    Schuster S, Steinzig M, Gibmeier J (2017) Incremental hole drilling for residual stress analysis of thin walled components with regard to plasticity effects. Journal of Experimental Mechanics 57:1457–1467CrossRefGoogle Scholar
  13. 13.
    Winiarski B, Benedetti M, Fontanari V, Allahkarami M, Hanan JC, Withers PJ (2016) High spatial resolution evaluation of residual stresses in shot peened specimens containing sharp and blunt notches by micro-hole drilling, micro-slot cutting and Micro-X-ray diffraction method. Journal of Experimental Mechanics 56:1449–1463CrossRefGoogle Scholar
  14. 14.
    Olson MD, Hill MR (2015) A new mechanical method for biaxial residual stress mapping. Journal of Experimental Mechanics 55:1139–1150CrossRefGoogle Scholar
  15. 15.
    Kim HK, Coules HE, Pavier MJ, Shterenlikht A (2015) Measurement of highly Non-Uniform residual stress fields with reduced plastic error. Journal of Experimental Mechanics 55:1211–1224CrossRefGoogle Scholar
  16. 16.
    Zuccarello B, Menda F, Scafidi F (2016) Error and uncertainty analysis of Non-Uniform residual stress evaluation by using the Ring-Core method. Journal of Experimental Mechanics 56:1531–1546CrossRefGoogle Scholar
  17. 17.
    Levieil B, Bridier F, Doudard C, Thevenet D, Calloch S (2016) User influence on two complementary residual stress determination methods: Contour method and incremental X-Ray diffraction. Journal of Experimental Mechanics 56:1641–1652CrossRefGoogle Scholar
  18. 18.
    Lee Z, Radmilovic V, Ahn B, Lavernia EJ, Nutt SR (2009) Tensile deformation and fracture mechanism of bulk bimodal Ultrafine-Grained Al-Mg alloy. Journal of Metallurgical and Materials Transactions 41A:795–801Google Scholar
  19. 19.
    Xue L, Zhimin Y, Bo N, Li Z, Qinglin P, Feng J (2007) High cycle fatigue characteristics of 2124-T851 aluminum alloy. Journal of Frontiers of Materials Science in China 1:168–172CrossRefGoogle Scholar
  20. 20.
    Liu Y, Yang C, Chen W, Zhu D, Li Y (2014) Effects of particle size and properties on the microstructures, mechanical properties, and fracture mechanisms of 7075 Al hybrid composites prepared by squeeze casting. Journal of Experimental Mechanics 49:7855–7863Google Scholar
  21. 21.
    Lee WM, Zikry MA (2010) Microstructural characterization of a High-Strength aluminum alloy subjected to high Strain-Rate impact. Journal of Metallurgical and Materials Transactions 42A:1215–1221Google Scholar
  22. 22.
    Hertzberg R (1995) Deformation and fracture mechanics of engineering materials, 4th edn. Wiley, New YorkGoogle Scholar
  23. 23.
    Li XJ, Tan MJ (2003) A study of the strength of P/M 6061Al and composites during high strain rate superplastic deformation. J Mater Sci 38:2505–2510CrossRefGoogle Scholar
  24. 24.
    Bigger R, Carpenter A, Scoot N, Dannemann K, Chocron S, Williams C (2018) Dynamic response of aluminum 5083 during taylor impact using digital image correlation. Journal of Experimental Mechanics 58:951–961CrossRefGoogle Scholar
  25. 25.
    Mylonas GI, Labeas GN (2014) Mechanical characterisation of aluminium alloy 7449-T7651 at high strain rates and elevated temperatures using split hopkinson bar testing. Journal of Experimental Techniques 38:26–34CrossRefGoogle Scholar
  26. 26.
    Salem HG, Lee WM, Bodelot L, Ravichandran G, Zikry MA (2012) Quasi-Static And High-Strain-Rate experimental microstructural investigation of a High-Strength aluminum alloy. Journal of Metallurgical and Materials Transactions 43A:1895–1901CrossRefGoogle Scholar
  27. 27.
    Scott-Emuakpor O, Schwartz J, George T, Holycross C, Slater J (2015) Bending fatigue life characterisation of direct metal laser sintering nickel alloy 718. Journal of Fatigue & Fracture of Engineering Materials & Structures 38:1105–1117CrossRefGoogle Scholar
  28. 28.
    Scott-Emuakpor O, Beck J, George T, Holycross C (2015) Regression study to standardize piezoelectric axial fatigue testing. In: AIAA Science and technology forum and exposition, 5-9 january 2015, paper no. 2015-0891. AIAA, RestonGoogle Scholar
  29. 29.
    Maxwell D, Nicholas T (1998) A rapid method for generation of a haigh diagram for high cycle fatigue. Journal of Fatigue and Fracture Mechanics 29:626–641Google Scholar
  30. 30.
    Knapp K, Scott-Emuakpor O, George T, Holycross C, Palazotto A (2016) Improved Pre-Strain method for generating goodman data with Vibration-Based fatigue testing. In: 57Th AIAA/ASCE/AHS/ASC structures, structural dynamics, and materials conference, AIAA scitech forum, San Diego, California, 4-8 january 2016, paper no. 2016-0925. AIAA, RestonGoogle Scholar
  31. 31.
    Scott-Emuakpor O (2004) Development of an improved Energy-Based criterion for fatigue life assessment MS thesis, The Ohio State University, OHGoogle Scholar
  32. 32.
    George T (2002) Development of Methodologies for Ensuring Structural Safety of Gas Turbines and Launch Vehicles PhD Thesis, The Ohio State University, OHGoogle Scholar
  33. 33.
    (2009) American Society for Testing and Materials, 8M-09: Standard test methods for tension testing of metallic material. ASTM book of standards. ASTM International, West Conshohocken, PAGoogle Scholar
  34. 34.
    Seymen Y, Güler B, Efe M (2016) Large strain and Small-Scale biaxial testing of sheet metals. Journal of Experimental Mechanics 56:1519–1530CrossRefGoogle Scholar
  35. 35.
    Simons D, Leissa A (1971) Vibrations of rectangular cantilever plates to In-Plane acceleration loads. J Sound Vib 17(3):407–422CrossRefzbMATHGoogle Scholar
  36. 36.
    Mierovich L (1997) Principles and techniques of vibrations. Prentice Hall, New JerseyGoogle Scholar
  37. 37.
    Wagle S, Kato H (2011) Size estimation of fatigue crack appearing at bolt joints of aluminum alloy plates by synchronized SAW measurement large strain and Small-Scale biaxial testing of sheet metals. Journal of Experimental Mechanics 51:869–878CrossRefGoogle Scholar
  38. 38.
    Bruns J (2014) Fatigue Crack growth behavior of structures subject to vibratory stresses. In: Society of experimental mechanics annual conference, pp 2–6Google Scholar
  39. 39.
    Cook R, Malkus D, Plesha M, Witt R (2002) Concepts and applications of finite element analysis, 4th edn. Wiley, New YorkGoogle Scholar

Copyright information

© This is a U.S. government work and its text is not subject to copyright protection in the United States; however, its text may be subject to foreign copyright protection 2019

Authors and Affiliations

  • K. Knapp
    • 1
    Email author
  • A. Palazotto
    • 2
  • O. Scott-Emuakpor
    • 3
  • C. Holycross
    • 3
  1. 1.Department of Engineering MechanicsUnited States Air Force AcademyColorado SpringsUSA
  2. 2.Department of Aeronautics & AstronauticsAir Force Institute of Technology, Wright-Patterson AFBDaytonUSA
  3. 3.Air Force Research LaboratoryWright-Patterson AFBDaytonUSA

Personalised recommendations