Skip to main content

Advertisement

SpringerLink
Log in

Precision of Hole-Drilling Residual Stress Depth Profile Measurements and an Updated Uncertainty Estimator

  • Research paper
  • Published:
Experimental Mechanics Aims and scope Submit manuscript

Abstract

Background

Measurement precision and uncertainty estimation are important factors for all residual stress measurement techniques. The values of these quantities can help to determine whether a particular measurement technique would be viable option.

Objective

This paper determines the precision of hole-drilling residual stress measurement using repeatability studies and develops an updated uncertainty estimator.

Methods

Two repeatability studies were performed on test specimens extracted from aluminum and titanium shot peened plates. Each repeatability study included 12 hole-drilling measurements performed using a bespoke automated milling machine. Repeatability standard deviations were determined for each population. The repeatability studies were replicated using a commercially available manual hole-drilling milling machine (RS-200, Micro-Measurements). An updated uncertainty estimator was developed and was assessed using an acceptance criterion. The acceptance criterion compared an expected percentage of points (68%) to the fraction of points in the stress versus depth profile where the measured stresses ± its total uncertainty contained the mean stress of the repeatability studies.

Results

Both repeatability studies showed larger repeatability standard deviations at the surface that decay quickly (over about 0.3 mm). The repeatability standard deviation was significantly smaller in the aluminum plate (max ≈ 15 MPa, RMS ≈ 6.4 MPa) than in the titanium plate (max ≈ 60 MPa, RMS ≈ 21.0 MPa). The repeatability standard deviations were significantly larger when using the manual milling machine in the aluminum plate (RMS ≈ 21.7 MPa), and for the titanium plate (RMS ≈ 18.9 MPa).

Conclusions

The single measurement uncertainty estimate met a defined acceptance criterion based on the confidence interval of the uncertainty estimate.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

Abbreviations

:

Numerical calibration coefficient matrices

p, q, t :

Strain invariant vectors

P, Q, T :

Stress invariant vectors

N :

Number of rows in the invariant vectors

ν :

Poisson’s ratio

E :

Elastic modulus

ε :

Measured strain

\( \overline{z} \) :

Average cut depth

h :

Cut depth

σ :

Normal stress

τ :

Shear stress

β:

Regulation parameter

C :

penalization matrix

α:

Regulation parameter

\( \hat{\boldsymbol{p}},\hat{\boldsymbol{q}} \), and \( \hat{\boldsymbol{t}} \) :

Fitted strain invariants

U σ,ε :

Stress uncertainty from strain uncertainty

U ε :

Strain uncertainty

e :

Lower limit of strain uncertainty

U σ, reg :

Stress uncertainty from regularization uncertainty

U σ, tot :

Total stress uncertainty

p std, q std, t std :

“Standard errors” in the strain invariants

p rms, q rms, t rms :

Mean squares of the misfit strain vectors

References

  1. ASTM (2020) Standard E177–20, Practice for Use of the Terms Precision and Bias in ASTM Test Methods, ASTM International, West Conshohocken, PA

  2. Lestari S (2004) “Residual stress measurements of Unblasted and sandblasted mild steel specimens using X-ray diffraction, strain-gage hole drilling, and electronic speckle pattern interferometry (ESPI) hole drilling Methods,” University of New Orleans, New Orleans, LA

  3. Olson MD, Robinson JS, Wimpory RC, Hill MR (2016) Characterisation of residual stresses in heat treated, high strength aluminium alloy extrusions. Mater Sci Technol 32(14):1427–1438

    Article  Google Scholar 

  4. Fitzpatrick ME, Lodini A (2003) Analysis of residual stress by diffraction using neutron and synchrotron radiation. CRC Press, London

    Book  Google Scholar 

  5. Prime MB, Gnäupel-Herold T, Baumann JA, Lederich RJ, Bowden DM, Sebring RJ (2006) Residual stress measurements in a thick, dissimilar aluminum alloy friction stir weld. Acta Mater 54(15):4013–4021

    Article  Google Scholar 

  6. Upshaw D, Steinzig M, Rasty J (2014) Influence of Drilling Parameters on the Accuracy of Hole-drilling Residual Stress Measurements. Experimental Mechanics 54(9):1537–1543

  7. Steinzig M, Takahashi T (2003) Residual stress measurement using the hole drilling method and laser speckle interferometry part IV: measurement accuracy. Exp Tech 27(6):59–63

    Article  Google Scholar 

  8. ASTM (2013) Standard E837-13, Standard Test Method for Determining Residual Stresses by the Hole-Drilling Strain-Gage Method, ASTM international, West Conshohocken, PA

  9. Lord JD, Fry AT, Grant PV (2002) A UK residual stress Intercomparison exercise - an examination of the XRD and hole drilling techniques, National Physical Laboratory, Report MATC(a)98, Teddington, UK

  10. Micro-Measurements. Milling Guide for Residual Stress Measurements (Document No.: 11304), Vishay Precision Group; 17-May-2011. Available: http://www.vishaypg.com/docs/11304/rs200.pdf. Accessed Jan 2020

  11. Schajer GS, Whitehead PS (2013) Hole Drilling and Ring Coring. In: Schajer GS (ed) Practical Residual Stress Measurement Methods. Wiley, West Sussex, pp 29–64. https://doi.org/10.1002/9781118402832.ch2

    Chapter  Google Scholar 

  12. Schajer GS (1988) Measurement of non-uniform residual stresses using the hole-drilling method. Part I - stress calculation Proceedures. J Eng Mater Technol 110:338–343

    Article  Google Scholar 

  13. Schajer GS (1988) Measurement of non-uniform residual stresses using the hole-drilling method. Part II - practical application of the integral method. J Eng Mater Technol 110:344–349

    Article  Google Scholar 

  14. Schajer GS (2007) Hole-drilling residual stress profiling with automated smoothing. J Eng Mater Technol Trans ASME 129(3):440–445. https://doi.org/10.1115/1.2744416

    Article  Google Scholar 

  15. Prime MB, Hill MR (2006) Uncertainty, model error, and order selection for series-expanded, residual-stress inverse solutions. J Eng Mater Technol 128(2):175–185

    Article  Google Scholar 

  16. Olson MD, DeWald AT, Hill MR (2020) An uncertainty estimator for slitting method residual stress measurements including the influence of regularization. Experimental Mechanics 60(1):65–79

  17. Girinon M, Robin V, Jourden E, Vakiorgue F, Rech J, Feulvarch E (2016) A Method to Characterize Residual Stresses Induced by Machining. Proceedings of the ASME 2016 Pressure Vessels and Piping Conference, Vol. 50435, p. V06BT06A001, American Society of Mechanical Engineers, New York, NY, USA

  18. Madariaga A, Perez I, Arrazola PJ, Sanchez R, Ruiz JJ, Rubio FJ (2018) Reduction of distortions in large aluminium parts by controlling machining-induced residual stresses. Int J Adv Manuf Technol 97:967–978. https://doi.org/10.1007/s00170-018-1965-2

    Article  Google Scholar 

  19. Olson MD, DeWald AT, Hill MR, Prime MB (2014) Estimation of uncertainty for contour method residual stress measurements. Exp Mech 55:577–585

    Article  Google Scholar 

  20. Olson MD, DeWald AT, Hill MR (2018) Validation of a contour method single-measurement uncertainty estimator. Exp Mech 58:767–781. https://doi.org/10.1007/s11340-018-0385-4

    Article  Google Scholar 

  21. Upshaw D, Steinzig M, Rasty J (2011) Influence of drilling parameters on the accuracy of hole-drilling residual stress measurements. Eng Appl Residual Stress 8:95–109

    Google Scholar 

  22. Olson MD, DeWald AT, Hill MR (2018) Repeatability of contour method residual stress measurements for a range of materials, processes, and geometries. Mater Perform Charact 7(4):427–445

    Google Scholar 

  23. Schajer GS, Altus E (1996) Stress calculation error analysis for incremental hole-drilling residual stress measurements. J Eng Mater Technol Am Soc Mech Eng 118:120–126. https://doi.org/10.1115/1.2805924

    Article  Google Scholar 

  24. Ajovalasit A (1979) Measurement of residual stresses by the hole-drilling method: influence of hole eccentricity. J Strain Anal Eng Des IMECHE 14:171–178. https://doi.org/10.1243/03093247V144171

    Article  Google Scholar 

  25. Barsanescu P, Carlescu P (2009) Correction of errors introduced by hole eccentricity in residual stress measurement by the hole-drilling strain-gage method. Measurement Elsevier 42:474–477. https://doi.org/10.1016/j.measurement.2008.09.002

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Hill Engineering, LLC, 3083 Gold Canal Drive, Rancho Cordova, CA, USA

    M. D. Olson & A. T. DeWald

  2. Department of Mechanical and Aerospace Engineering, University of California, One Shields Avenue, Davis, CA, USA

    M. R. Hill

Authors
  1. M. D. Olson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. T. DeWald
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. R. Hill
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. D. Olson.

Ethics declarations

Conflict of Interest

The authors have no conflicts of interest to disclose and did not involve human or animal participants nor was informed consent applicable.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Olson, M.D., DeWald, A.T. & Hill, M.R. Precision of Hole-Drilling Residual Stress Depth Profile Measurements and an Updated Uncertainty Estimator. Exp Mech 61, 549–564 (2021). https://doi.org/10.1007/s11340-020-00679-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11340-020-00679-1

Keywords

Search

Navigation