On the Implementation of the Integral Method for Residual Stress Measurement by Integrated Digital Image Correlation

  • A. BaldiEmail author


The Integrated Digital Image Correlation method (iDIC) is a simple and effective approach for residual stress measurement. iDIC differs from Digital Image Correlation because it replaces the “generic” displacement functions used to describe the displacement field around the measurement point with problem-specific ones. By this simple modification, stress components become the unknowns of the problem, thus allowing a single-pass analysis. Advantages are significant in terms of accuracy, robustness and ease of implementation. However, the implementation of the Integral Method for estimation of depth-dependent residual stress components is difficult. This work suggests two alternative approaches to solve this problem; in the former, the direct solution of the triangular linear system is employed to incrementally identify the stress distribution. In the latter, a global spatio-temporal minimization involving all the acquired images is suggested.


Integrated digital image correlation Residual stress Integral method Reverse methods 



The author wishes to thank Mr. Gianluca Marongiu and Mr. Daniele Lai for their support during data acquisition.


  1. 1.
    ASTM E837-13a (2013) Standard test method for determining residual stresses by the hole-drilling strain-gage method. American Society for Testing and Materials International, West ConshohockenGoogle Scholar
  2. 2.
    Nelson DV, McCrickerd JT (1986) Residual-stress determination through combined use of holographic interferometry and blind hole drilling. Exp Mech 26:371–378. ISSN 0014-4851CrossRefGoogle Scholar
  3. 3.
    Nelson DV, Makino A, Fuchs EA (1997) The holographic-hole drilling method for residual stress determination. Opt Lasers Eng 27:3–23CrossRefGoogle Scholar
  4. 4.
    Lin ST, Hsieh C-T, Lee CK (1995) Full field phase-shifting holographic blind-hole techniques for in-plane residual stress detection. In: Honda T (ed) Int. conf. on applications of optical holography, volume 2577 of proceedings of SPIE, Bellingham, pp 226–237Google Scholar
  5. 5.
    Nicoletto G (1991) Moiré interferometry determination of residual stresses in presence of gradients. Exp Mech 31(3):252–256. ISSN 0014-4851CrossRefGoogle Scholar
  6. 6.
    Wu Z, Lu J, Han B (1998) Study of residual stress distribution by a combined method of moiré interferometry and incremental hole drilling, part i: theory. J Appl Mech 65(4):837–843CrossRefGoogle Scholar
  7. 7.
    Schwarz RC, Kutt LM, Papazian JM (2000) Measurement of residual stress using interferometric moiré: a new insight. Exp Mech 40(3):271–281. ISSN 0014-4851CrossRefGoogle Scholar
  8. 8.
    Steinzig M, Ponslet E (2003) Residual stress measurement using the hole drilling method and laser speckle interferometry: part i. Exper Techn 27(3):43–46. ISSN 1747-1567CrossRefGoogle Scholar
  9. 9.
    Ponslet E, Steinzig M (2003) Residual stress measurement using the hole drilling method and laser speckle interferometry part ii: analysis technique. Exper Techn 27(4):17–21. ISSN 1747-1567CrossRefGoogle Scholar
  10. 10.
    Ponslet E, Steinzig M (2003) Residual stress measurement using the hole drilling method and laser speckle interferometry part iii: analysis technique. Exper Techn 27(5):45–48. ISSN 1747-1567CrossRefGoogle Scholar
  11. 11.
    Baldi A (2005) A new analytical approach for hole drilling residual stress analysis by full field method. J Eng Mater Technol 127(2):165–169. ISSN 0094-4289CrossRefGoogle Scholar
  12. 12.
    Schajer GS, Steinzig M (2005) Full-field calculation of hole drilling residual stresses from electronic speckle pattern interferometry data. Exper Mech 45(6):526–532. ISSN 0014-4851CrossRefGoogle Scholar
  13. 13.
    Schajer GS (2010) Advances in hole-drilling residual stress measurements. Exp Mech 50(2):159–168. ISSN 0014-4851CrossRefGoogle Scholar
  14. 14.
    Schajer GS, Winiarski B, Withers PJ (2013) Hole-drilling residual stress measurement with artifact correction using full-field dic. Exper Mech 53(2):255–265. ISSN 0014-4851CrossRefGoogle Scholar
  15. 15.
    Réthoré J, Roux S, Hild F (2009) An extended and integrated digital image correlation technique applied to the analysis of fractured samples: the equilibrium gap method as a mechanical filter. Eur J Comput Mech/Revue Europé,enne de Mécanique Numérique 18(3-4):285–306zbMATHGoogle Scholar
  16. 16.
    Besnard G, Hild F, Roux S (2006) “finite-element” displacement fields analysis from digital images: application to portevin–le châtelier bands. Exp Mech 46(6):789–803CrossRefGoogle Scholar
  17. 17.
    Baldi A (2013) A new analytical approach for hole drilling residual stress analysis by full field method. Exper Mech 54(3):379–391. CrossRefGoogle Scholar
  18. 18.
    Baldi A (2014) Residual stress analysis of orthotropic materials using integrated digital image correlation. Exper Mech 54(7):1279–1292. ISSN 0014-4851CrossRefGoogle Scholar
  19. 19.
    Baldi A (2016) Sensitivity analysis of i-DIC approach for residual stress measurement in orthotropic materials. In: Bossuyt S, Schajer G, Carpinteri A (eds) Residual stress, thermomechanics & infrared imaging, hybrid techniques and inverse problems. ISBN 978-3-319-21764-2, vol 9. Springer, pp 355–362, DOI
  20. 20.
    Sutton MA, Orteu J-J, Schreier H (2009) Image correlation for shape, motion and deformation measurements: basic concepts, theory and applications. Springer, New York. ISBN 978-0-387-78746-6Google Scholar
  21. 21.
    Pan B, Xie H, Wang Z (2010) Equivalence of digital image correlation criteria for pattern matching. Appl Opt 49(28):5501–5509CrossRefGoogle Scholar
  22. 22.
    Lucas BD, Kanade T (1981) An iterative image registration technique with an application to stereo vision. In: Proceedings of imaging understanding workshop, vol 130, pp 121–130Google Scholar
  23. 23.
    Rupil J, Roux S, Hild F, Vincent L (2011) Fatigue microcrack detection with digital image correlation. J Strain Anal Eng Des 46(6):492–509CrossRefGoogle Scholar
  24. 24.
    Blaysat B, Hoefnagels JPM, Lubineau G, Alfano M, Geers MGD (2015) Interface debonding characterization by image correlation integrated with double cantilever beam kinematics. Int J Solids Struct 55:79–91CrossRefGoogle Scholar
  25. 25.
    Schajer GS (1988) Measurement of non-uniform residual stresses using the hole-drilling method. Part i—stress calculation procedures. J Eng Mater Technol 110(4):338–343CrossRefGoogle Scholar
  26. 26.
    Neggers J, Hoefnagels JPM, Geers MGD, Hild F, Roux S (2015) Time-resolved integrated digital image correlation. Int J Numer Methods Eng 103(3):157–182MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Besnard G, Leclerc H, Hild F, Roux S, Swiergiel N (2012) Analysis of image series through global digital image correlation. J Strain Anal Eng Des 47(4):214–228CrossRefGoogle Scholar
  28. 28.
    Press WH, Teukolsky SA, Vetterling WT, Flannery BP (2007) Numerical recipes. The art of scientific computing, 3rd edn. Cambridge University PressGoogle Scholar
  29. 29.
    Golub GH, Van Loan CF (2013) Matrix computations, 4th edn. John Hopkins University Press, Balrimore. ISBN 978-1-4214-0794-4zbMATHGoogle Scholar
  30. 30.
    Tikhonov AN, Goncharsky A, Stepanov VV, Yagola AG (1995) Numerical methods for the solution of ill-posed problems, volume 328 of mathematics and its applications. Springer, Netherlands. Originally published in Russian. CrossRefGoogle Scholar
  31. 31.
    Schajer GS, Prime MB (2006) Use of inverse solutions for residual stress measurements. J Eng Mater Technol 128:375–382. CrossRefGoogle Scholar
  32. 32.
    Schajer GS (2007) Hole-drilling residual stress profiling with automated smoothing. J Eng Mater Technol 129 (3):440–445. CrossRefGoogle Scholar
  33. 33.
    Schajer GS, Rickert TJ (2011) Incremental computation technique for residual stress calculations using the integral method. Exp Mech 51 (7):1217–1222. CrossRefGoogle Scholar
  34. 34.
    Orteu J-J, Garcia D, Robert L, Bugarin F (2006) A speckle texture image generator. In: Speckle06: speckles, from grains to flowers, vol 6341. International Society for Optics and Photonics, pp 63410HGoogle Scholar
  35. 35.
    Baldi A, Bertolino F (2015) Experimental analysis of the errors due to polynomial interpolation in digital image correlation. Strain 51(3):248–263. ISSN 1475-1305CrossRefGoogle Scholar
  36. 36.
    Baldi A, Bertolino F (2016) Assessment of h-refinement procedure for global digital image correlation. Meccanica 51(4):979–991MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Baldi A (2018) Digital image correlation and color cameras. Exp Mech 58(2):315–333. ISSN 0014–4851

Copyright information

© Society for Experimental Mechanics 2019

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria Meccanica, Chimica e dei MaterialiUniversità degli Studi di CagliariCagliariItaly

Personalised recommendations