Experimental Mechanics

, Volume 52, Issue 4, pp 417–428 | Cite as

Micron-Scale Residual Stress Measurement by Micro-Hole Drilling and Digital Image Correlation



This paper reports a new technique, namely the incremental micro-hole-drilling method (IμHD) for mapping in-plane residual or applied stresses incrementally as a function of depth at the micron-scale laterally and the sub-micron scale depth-wise. Analogous to its macroscale counterpart, it is applicable either to crystalline or amorphous materials, but at the sub-micron scale. Our method involves micro-hole milling using the focused ion beam (FIB) of a dual beam FEGSEM/FIB microscope. The resulting surface displacements are recorded by digital image correlation of SEM images recorded during milling. The displacement fields recorded around the hole are used to reconstruct the stress profile as a function of depth. In this way residual stresses have been characterized around a drilled hole of 1.8microns. diameter, enabling the profiling of the stress variation at the sub-micron scale to a depth of 1.8 microns. The new method is used to determine the near surface stresses in a (peened) surface-severe-plastically-deformed (S2PD) Zr50Cu40Al10 (in atomic percent, at.%) bulk metallic glass bar. In plane principal stresses of -800 MPa ± 90 MPa and −600 MPa ± 90 MPa were measured, the maximum compressive stress being oriented 15° to the axis of the bar.


Scanning electron microscopy (SEM) Residual stress 2D digital image correlation Surface decoration methods Incremental centre hole drilling 


  1. 1.
    Withers PJ (2007) Residual stress and its role in failure. Rep Prog Phys 70(12):2211–2264. doi:10.1088/0034-4885/70/12/R04 CrossRefGoogle Scholar
  2. 2.
    Schajer GS, Prime MB (2007) Residual stress solution extrapolation for the slitting method using equilibrium constraints. ASME J Eng Mater Technol 129(2):227–232. doi:10.1115/1.2400281 CrossRefGoogle Scholar
  3. 3.
    Schajer GS, An Y (2010) Residual stress determination using cross-slitting and dual-Axis ESPI. Exp Mech 50:169–177. doi:10.1007/s11340-009-9317-7 CrossRefGoogle Scholar
  4. 4.
    Schajer GS (1988) Measurement of non-uniform residual-stresses using the hole-drilling method. 1. Stress calculation procedures. ASME J Eng Mater Technol 110(4):338–343CrossRefGoogle Scholar
  5. 5.
    Schajer GS (1988) Measurement of non-uniform residual-stresses using the hole-drilling method. 2. Practical application of the integral method. ASME J Eng Mater Technol 110(4):344–349CrossRefGoogle Scholar
  6. 6.
    McGinnis MJ, Pessiki S, Turker H (2005) Application of three-dimensional digital image correlation to the core-drilling method. Exp Mech 45(4):359–367. doi:10.1177/0014485105055435 CrossRefGoogle Scholar
  7. 7.
    Cárdenas-García JF, Preidikman S (2006) Solution of the moire´ hole drilling method using a finite-element-method-based approach. Int J Solids Struct 46:6751–6766. doi:10.1016/j.ijsolstr.2006.02.010 CrossRefGoogle Scholar
  8. 8.
    Beghini M, Bertini L, Mori LF, Rosellini W (2009) Genetic algorithm optimization of the hole-drilling method for non-uniform residual stress fields. J Strain Anal 44:105–115. doi:10.1243/03093247JSA457 CrossRefGoogle Scholar
  9. 9.
    Schajer GS, Stainzig M (2010) Dual-axis hole-drilling ESPI residual stress measurements. ASME J Eng Mater Technol 132:011007_1-5. doi:10.1115/1.3184035.Google Scholar
  10. 10.
    Flaman MT, Herring JA (1982) Comparison of four hole-producing techniques for the center-hole residual-stress measurement method. Exp Tech 9(8):30–32CrossRefGoogle Scholar
  11. 11.
    Vangi D (1994) Data managements for the evaluation of residual-stresses by the incremental hole-drilling method. ASME J Eng Mater Technol 116(4):561–566CrossRefGoogle Scholar
  12. 12.
    Klein CA (2000) How accurate are Stoney’s equation and recent modifications. J Appl Phys 88(9):5487–5489CrossRefGoogle Scholar
  13. 13.
    Sabate N, Vogel D, Gollhardt A, Keller J, Cane C, Gracia I, Morante JR, Michel B (2006) Measurement of residual stress by slot milling with focused ion-beam equipment. J Micromechanics Microengineering 16(2):254–259. doi:10.1088/0960-1317/16/2/009 CrossRefGoogle Scholar
  14. 14.
    Kang KJ, Yao N, He MY, Evans AG (2003) A method for in situ measurement of the residual stress in thin films by using the focused ion beam. Thin Solid Films 443:71–77. doi:10.1016/S0040-6090(03)00946-5 CrossRefGoogle Scholar
  15. 15.
    McCarthy J, Pei Z, Becker M, Atteridge D (2000) FIB micromachined submicron thickness cantilevers for the study of thin film properties. Thin Solid Films 358(1–2):146–151CrossRefGoogle Scholar
  16. 16.
    Massl S, Keckes J, Pippan R (2008) A new cantilever technique reveals spatial distributions of residual stresses in near-surface structures. Scr Mater 59(5):503–506. doi:10.1016/j.scriptamat.2008.04.037 CrossRefGoogle Scholar
  17. 17.
    Vogel D, Sabate N, Gollhardt A, Keller J, Auersperg J, Michel, B (2006) FIB based measurement of local residual stresses on microsystems. in Proceedings of SPIE - The International Society for Optical Engineering San Diego, CA. 2006. 6175: 617505. doi:10.1117/12.658298
  18. 18.
    Korsunsky AM, Sebastiani M, Bemporad E (2010) Residual stress evaluation at the micrometer scale: analysis of thin coatings by FIB milling and digital image correlation. Surf Coat Technol 205:2393–2403. doi:10.1016/j.surfcoat.2010.09.033 CrossRefGoogle Scholar
  19. 19.
    Cho S, Cárdenas-García JF, Chasiotis I (2005) Measurement of nanodisplacements and elastic properties of MEMS via the microscopic hole method. Sens and Actuators A 120:163–171. doi:10.1016/j.sna.2004.11.028 CrossRefGoogle Scholar
  20. 20.
    Winiarski B, Langford LR, Tian J, Yokoyama Y, Liaw PK, Withers PJ (2010) Mapping residual-stress distributions at the micron scale in amorphous materials. Metall Mater Trans A 41A:1743–1751. doi:10.1007/s11661-009-0127-4 CrossRefGoogle Scholar
  21. 21.
    Winiarski B, Withers PJ (2010) Mapping residual stress profiles at the micron scale using FIB micro-hole drilling. Appl Mech Mater 24–25:267–272. doi:10.4028/www.scientific.net/AMM.24-25.267 CrossRefGoogle Scholar
  22. 22.
    Winiarski B, Wang G, Xie X, Cao Y, Shin Y, Liaw PK and Withers PJ (2011) Mapping Residual-Stress Distributions in a Laser-Peened Vit-105 Bulk-Metallic Glass Using the Focused-Ion-Beam Micro-Slotting Method, Proceedings of MRS Fall Meeting, 29 November - 3 December 2010, Boston, MA, U.S.A.Google Scholar
  23. 23.
    Liaw PK, Xie X, Cao Y, Winiarski B, Wang G, Withers PJ, Shin Y (2011) Surface Modification of Bulk-Metallic Glasses by Laser-Peening Process Proceedings of 2011 NSF Engineering Research and Innovation Conference, January 4–7 2011,Atlanta, GA, U.S.A.Google Scholar
  24. 24.
    Cao Y, Xie X, Winiarski B, Wang G, Shin YC, Withers PJ, Liaw PK (2011) Residual Stresses Induced by Laser Shock Peening on Zr-based Bulk Metallic Glass and Its Effect on Plasticity, Proceedings of TMS2011Annual Meeting and Exhibition, Bulk Metallic Glasses VIII, Feb. 27 – Mar. 3, 2011 San Diego, California, U.S.A.Google Scholar
  25. 25.
    Massl S, Keckes J, Pippan R (2007) A direct method of determining complex depth profiles of residual stresses in thin films on a nanoscale. Acta Mater 55(14):4835–4844. doi:10.1016/j.actamat.2007.05.002 CrossRefGoogle Scholar
  26. 26.
    Quinta De Fonseca J, Mummery PM, Withers PJ (2004) Full-field strain mapping by optical correlation of micrographs acquired during deformation. J Microsc 218:9–21. doi:10.1111/j.1365-2818.2005.01461 CrossRefGoogle Scholar
  27. 27.
    Peters WH, Ranson WF (1982) Digital imaging techniques in experimental stress-analysis. Opt Eng 21(3):427–431Google Scholar
  28. 28.
    Lecompte D, Smits A, Sven B, Sol H, Vantomme J, Van Hemelrijck D, Habraken AM (2006) Quality assessment of speckle patterns for digital image correlation. Opt Lasers Eng 44(11):1132–1145. doi:10.1016/j.optlaseng.2005.10.004 CrossRefGoogle Scholar
  29. 29.
    van Kouwen L, Botman A, Hagen CW (2009) Focused electron-beam-induced deposition of 3 nm dots in a scanning electron microscope. Nano Lett 9(5):2149–2152. doi:10.1021/nl900717r CrossRefGoogle Scholar
  30. 30.
    Winiarski B, Schajer GS, Withers PJ, Surface decoration for improving the accuracy of displacement measurements by Digital Image Correlation in Scanning Electron Microscopy. In Peer-review - Experimental Mechanics.Google Scholar
  31. 31.
    Vogel D, Lieske D, Gollhardt A, Keller J, Sabate N, Morante JR, Michel B (2005) FIB based measurements for material characterization on MEMS structures. in Proceedings of SPIE - The International Society for Optical Engineering, San Diego, CA, 2005. doi:10.1117/12.599891.
  32. 32.
    Tikhonov AN, Arsenin VY (1977) Solution of Ill-posed problems. John Wiley & Sons, New YorkGoogle Scholar
  33. 33.
    Tjhung T, Li KY (2003) Measurement of in-plane residual stresses varying with depth by the Interferometric Strain/Slope Rosette and incremental hole-drilling. ASME J Eng Mater Technol 125(2):153–162. doi:10.1115/1.1555654 CrossRefGoogle Scholar
  34. 34.
    Tian JW, Shaw LL, Wang YD, Yokoyama Y, Liaw PK (2009) A study of the surface severe plastic deformation behaviour of a Zr-based bulk metallic glass (BMG). Intermetallics 17(11):951–957. doi:10.1016/j.intermet.2009.04.010 CrossRefGoogle Scholar
  35. 35.
    Yaofeng S, Pang JHL (2007) Study of optimal subset size in digital image correlation of speckle pattern images. Opt Lasers Eng 45(9):967–974. doi:10.1016/j.optlaseng.2007.01.012 CrossRefGoogle Scholar
  36. 36.
    Jin H, Lu WY, Korellis J (2008) Micro-scale deformation measurement using the digital image correlation technique and scanning electron microscope imaging. J Strain Anal Eng Des 43(8):719–728. doi:10.1243/03093247JSA412 CrossRefGoogle Scholar
  37. 37.
    Sutton MA, Li N, Joy DC, Reynolds AP, Li X (2007) Scanning electron microscopy for quantitative small and large deformation measurements Part I: SEM imaging at magnifications from 200 to 10,000. Exp Mech 47(6):775–787. doi:10.1007/s11340-007-9042-z CrossRefGoogle Scholar
  38. 38.
    Muskhetishvili NL (1977) Some Basic Problems of the Mathematical Theory of Elasticity, Leyden, the Netherlands: Noordhoff GroningenGoogle Scholar
  39. 39.
    Pelletier JM, Yokoyama Y, Inoue A (2007) Dynamic mechanical properties in a Zr50Cu40Al10 bulk metallic glass. Mater Trans 47:1359–1362. doi:10.2320/matertrans.MF200626 CrossRefGoogle Scholar
  40. 40.
    Schajer GS, Altus E (1996) Stress calculation error analysis for incremental hole-drilling residual stress measurements. ASME J Eng Mater Technol 118(1):120–126CrossRefGoogle Scholar
  41. 41.
    Zucarrello B (1999) Optimal calculation steps for the evaluation of residual stress by the incremental hole-drilling method. Exp Mech 39(2):117–124. doi:10.1007/BF02331114 CrossRefGoogle Scholar
  42. 42.
    Schajer GS, Prime MB (2006) Use of inverse solutions for residual stress measurements. J Eng Mater Technol-Transactions of the ASME 128(3):375–382. doi:10.1115/1.2204952 CrossRefGoogle Scholar
  43. 43.
    Neubauer A (1997) On converse and saturation results for Tikhonov regularization of linear ill-posed problems. SIAM J Numer Anal 34(2):517–527MathSciNetMATHCrossRefGoogle Scholar
  44. 44.
    Lamm PK, Elden L (1997) Numerical solution of first-kind Volterra equations by sequential Tikhonov regularization. SIAM J Numer Anal 34(4):1432–1450MathSciNetMATHCrossRefGoogle Scholar
  45. 45.
    Beck JV, Blackwell B, St.Clair CR Jr (1985) Inverse heat conduction - Ill-posed problems. Wiley-Interscience, New YorkMATHGoogle Scholar
  46. 46.
    Prime MB, Hill MR (2006) Uncertainty, model error, and order selection for series-expanded, residual-stress inverse solutions. ASME J Eng Mater Technol 128(2):175–185. doi:10.1115/1.2172278 CrossRefGoogle Scholar

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© Society for Experimental Mechanics 2011

Authors and Affiliations

  1. 1.School of Materials, Materials Science CentreThe University of ManchesterManchesterUK

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