Experimental Mechanics

, Volume 50, Issue 2, pp 187–194 | Cite as

Measuring Multiple Residual-Stress Components using the Contour Method and Multiple Cuts

  • P. Pagliaro
  • M. B. PrimeEmail author
  • H. Swenson
  • B. Zuccarello


The conventional contour method determines one component of residual stress over the cross section of a part. The part is cut into two, the contour (topographic shape) of the exposed surface is measured, and Bueckner’s superposition principle is analytically applied to calculate stresses. In this paper, the contour method is extended to the measurement of multiple residual-stress components by making multiple cuts with subsequent applications of superposition. The theory and limitations are described. The theory is experimentally tested on a 316L stainless steel disk with residual stresses induced by plastically indenting the central portion of the disk. The multiple-cut contour method results agree very well with independent measurements using neutron diffraction and with a computational, finite-element model of the indentation process.


Residual stress measurement Contour method Multiaxial stress Neutron diffraction Bueckner’s principle Finite element method 



This work was performed at Los Alamos National Laboratory, operated by the Los Alamos National Security, LLC for the National Nuclear Security Administration of the U.S. Department of Energy under contract DE-AC52-06NA25396. Mr. Pagliaro's work was sponsored by a fellowship from the Università degli Studi di Palermo.


  1. 1.
    Withers PJ, Turski M, Edwards L, Bouchard PJ, Buttle DJ (2008) Recent Advances in Residual Stress Measurement. The International Journal of Pressure Vessels and Piping 85:118–127Google Scholar
  2. 2.
    DeWald AT, Rankin JE, Hill MR, Lee MJ, Chen HL (2004) Assessment of Tensile Residual Stress Mitigation in Alloy 22 Welds Due to Laser Peening. Journal of Engineering Materials and Technology 126:465–473CrossRefGoogle Scholar
  3. 3.
    Hatamleh O, Lyons J, Forman R (2007) Laser Peening and Shot Peening Effects on Fatigue Life and Surface Roughness of Friction Stir Welded 7075–T7351 Aluminum. Fatigue and Fracture of Engineering Material and Structures 30:115–130CrossRefGoogle Scholar
  4. 4.
    Hatamleh O (2008) Effects of Peening on Mechanical Properties in Friction Stir Welded 2195 Aluminum Alloy Joints. Materials Science and Engineering: A 492:168–176CrossRefGoogle Scholar
  5. 5.
    DeWald AT, Hill MR (2009) Eigenstrain Based Model for Prediction of Laser Peening Residual Stresses in Arbitrary 3D Bodies. Part 2: Model Verification. Journal of Strain Analysis for Engineering Design 44:13–27CrossRefGoogle Scholar
  6. 6.
    Woo W, Choo H, Prime MB, Feng Z, Clausen B (2008) Microstructure, Texture and Residual Stress in a Friction-Stir-Processed AZ31B Magnesium Alloy. Acta Mat. 56:1701–1711CrossRefGoogle Scholar
  7. 7.
    Zhang Y, Pratihar S, Fitzpatrick ME, Edwards L (2005) Residual Stress Mapping in Welds Using the Contour Method. Materials Science Forum 490:294–299CrossRefGoogle Scholar
  8. 8.
    Edwards L, Smith M, Turski M, Fitzpatrick M, Bouchard P (2008) Advances in Residual Stress Modeling and Measurement for the Structural Integrity Assessment of Welded Thermal Power Plant. Advanced Materials Research 41–42:391–400CrossRefGoogle Scholar
  9. 9.
    Kartal M, Turski M, Johnson G, Fitzpatrick ME, Gungor S, Withers PJ, Edwards L (2006) Residual Stress Measurements in Single and Multi-Pass Groove Weld Specimens Using Neutron Diffraction and the Contour Method. Materials Science Forum 524:671–676CrossRefGoogle Scholar
  10. 10.
    Zhang Y, Ganguly S, Edwards L, Fitzpatrick ME (2004) Cross-Sectional Mapping of Residual Stresses in a VPPA Weld Using the Contour Method. Acta Mat. 52:5225–5232CrossRefGoogle Scholar
  11. 11.
    Thibault D, Bocher P, Thomas M (2009) Residual Stress and Microstructure in Welds of 13%Cr-4%Ni Martensitic Stainless Steel. Journal of Materials Processing Technology 209:2195–2202CrossRefGoogle Scholar
  12. 12.
    Kelleher J, Prime MB, Buttle D, Mummery PM, Webster PJ, Shackleton J, Withers PJ (2003) The Measurement of Residual Stress in Railway Rails by Diffraction and Other Methods. Journal of Neutron Research 11:187–193CrossRefGoogle Scholar
  13. 13.
    Evans A, Johnson G, King A, Withers PJ (2007) Characterization of Laser Peening Residual Stresses in Al 7075 by Synchrotron Diffraction and the Contour Method. Journal of Neutron Research 15:147–154CrossRefGoogle Scholar
  14. 14.
    Martineau RL, Prime MB, Duffey T (2004) Penetration of HSLA-100 Steel with Tungsten Carbide Spheres at Striking Velocities between 0.8 and 2.5 km/s. International Journal of Impact Engineering 30:505–520CrossRefGoogle Scholar
  15. 15.
    Schajer GS (2001) "Residual Stresses: Measurement by Destructive Testing." Encyclopedia of Materials: Science and Technology, Elsevier, 8152–8158.Google Scholar
  16. 16.
    Ueda Y, Fukuda K (1989) New Measuring Method of Three-Dimensional Residual Stresses in Long Welded Joints Using Inherent Strains as Parameters-Lz Method. Journal of Engineering Materials and Technology 111:1–8CrossRefGoogle Scholar
  17. 17.
    Hutchings MT, Withers PJ, Holden TM, Lorentzen T (2005) Introduction to the Characterization of Residual Stress by Neutron Diffraction. Routledge, USAGoogle Scholar
  18. 18.
    Smith DJ, Bouchard PJ, George D (2000) Measurement and Prediction of Residual Stresses in Thick-Section Steel Welds. Journal of Strain Analysis for Engineering Design 35:287–305CrossRefGoogle Scholar
  19. 19.
    Korsunsky AM, Hills DA (2009) Residual Strain Analysis. The Journal of Strain Analysis for Engineering Design 44:i-iv.Google Scholar
  20. 20.
    DeWald AT, Hill MR (2009) Eigenstrain Based Model for Prediction of Laser Peening Residual Stresses in Arbitrary 3D Bodies. Part 1: Model Description. Journal of Strain Analysis for Engineering Design 44:1–11CrossRefGoogle Scholar
  21. 21.
    Korsunsky AM, Regino GM, Nowell D (2007) Variational Eigenstrain Analysis of Residual Stresses in a Welded Plate. International Journal of Solids and Structures 44:4574–4591zbMATHCrossRefGoogle Scholar
  22. 22.
    Cheng W (2000) Measurement of the Axial Residual Stresses Using the Initial Strain Approach. Journal of Engineering Materials and Technology 122:135–140CrossRefGoogle Scholar
  23. 23.
    Smith DJ, Farrahi GH, Zhu WX, McMahon CA (2001) Obtaining Multiaxial Residual Stress Distributions from Limited Measurements. Materials Science & Engineering A A303:281–291CrossRefGoogle Scholar
  24. 24.
    Beghini M, Bertini L (2004) Residual Stress Measurement and Modeling by the Initial Strain Distribution Method: Part I - Theory. Journal of Testing and Evaluation 32:167–176Google Scholar
  25. 25.
    Prime MB, Newborn MA, Balog JA (2003) Quenching and Cold-Work Residual Stresses in Aluminum Hand Forgings: Contour Method Measurement and FEM Prediction. Materials Science Forum 426–432:435–440CrossRefGoogle Scholar
  26. 26.
    DeWald AT, Hill MR (2006) Multi-Axial Contour Method for Mapping Residual Stresses in Continuously Processed Bodies. Experimental Mechanics 46:473–490CrossRefGoogle Scholar
  27. 27.
    Kartal ME, Liljedahl CDM, Gungor S, Edwards L, Fitzpatrick ME (2008) Determination of the Profile of the Complete Residual Stress Tensor in a VPPA Weld Using the Multi-Axial Contour Method. Acta Mat. 56:4417–4428CrossRefGoogle Scholar
  28. 28.
    Pagliaro P, 2008, "Mapping Multiple Residual Stress Components Using the Contour Method and Superposition," Ph.D. Dissertation, Universitá degli Studi di Palermo, Palermo.Google Scholar
  29. 29.
    Prime MB (2001) Cross-Sectional Mapping of Residual Stresses by Measuring the Surface Contour after a Cut. Journal of Engineering Materials and Technology 123:162–168CrossRefGoogle Scholar
  30. 30.
    Bueckner HF (1973) "Field Singularities and Related Integral Representations." Mechanics of Fracture G. C. Sih, ed., 239-314.Google Scholar
  31. 31.
    Pagliaro P, Prime MB, Zuccarello B (2007) Inverting Multiple Residual Stress Components from Multiple Cuts with the Contour Method. Proceedings of the SEM Annual Conference and Exposition on Experimental and Applied Mechanics 2007:1993–2005Google Scholar
  32. 32.
    Mahmoudi AH, Stefanescu D, Hossain S, Truman CE, Smith DJ, Withers PJ (2006) Measurement and Prediction of the Residual Stress Field Generated by Side-Punching. Journal of Engineering Materials and Technology 128:451–459CrossRefGoogle Scholar
  33. 33.
    Pagliaro P, Prime MB, Clausen B, Lovato ML, Zuccarello B (2009) Known Residual Stress Specimens Using Opposed Indentation. Journal of Engineering Materials and Technology 131:031002CrossRefGoogle Scholar
  34. 34.
    Prime MB, Sebring RJ, Edwards JM, Hughes DJ, Webster PJ (2004) Laser Surface-Contouring and Spline Data-Smoothing for Residual Stress Measurement. Experimental Mechanics 44:176–184CrossRefGoogle Scholar
  35. 35.
    Johnson G, 2008, "Residual Stress Measurements Using the Contour Method," Ph.D. Dissertation, University of Manchester.Google Scholar
  36. 36.
    Abaqus 6.4, ABAQUS, inc., Pawtucket, RI, USA, 2003.Google Scholar
  37. 37.
    Brand PC, Prask HJ, Gnaeupel-Herold T, 1997, "Residual Stress Measurements at the NIST Reactor." Physica B, Elsevier, Netherlands, 1244-1245.Google Scholar
  38. 38.
    Pearce SV, Linton VM, Oliver EC (2008) Residual Stress in a Thick Section High Strength T-Butt Weld. Materials Science & Engineering: A 480:411–418CrossRefGoogle Scholar
  39. 39.
    Sasaki T, Takahashi S, Kanematsu Y, Satoh Y, Iwafuchi K, Ishida M, Morii Y (2008) Measurement of Residual Stresses in Rails by Neutron Diffraction. Wear 265:1402–1407CrossRefGoogle Scholar
  40. 40.
    Stacey A, MacGillivary HJ, Webster GA, Webster PJ, Ziebeck KRA (1985) Measurement of Residual Stresses by Neutron Diffraction. Journal of Strain Analysis for Engineering Design 20:93–100CrossRefGoogle Scholar
  41. 41.
    Stefanescu D, Browne P, Truman CE, Smith DJ (2003) Residual Stress Measurement within a European UIC60 Rail Using Integrated Drilling Techniques. Materials Science Forum 440–441:85–92CrossRefGoogle Scholar
  42. 42.
    Tawfik D, Kirstein O, Mutton PJ, Wing Kong C (2006) Verification of Residual Stresses in Flash-Butt-Weld Rails Using Neutron Diffraction. Physica B 385–386:894–896CrossRefGoogle Scholar
  43. 43.
    Buttle DJ, Culham Science Centre A, Collett N, Webster PJ, Hughes DJ, Mills G (2002) A Comparison of Maps and Synchrotron X-Ray Methods: Stresses Measured in Railway Rail Sections. Materials Science Forum 881-886.Google Scholar
  44. 44.
    de Oliveira U, Ocelik V, De Hosson JTM (2006) Residual Stress Analysis in Co-Based Laser Clad Layers by Laboratory X-Rays and Synchrotron Diffraction Techniques. Surface and Coatings Technology 201:533–542CrossRefGoogle Scholar
  45. 45.
    Djapic Oosterkamp L, Webster PJ, Browne PA, Vaughan GBM, Withers PJ (2000) Residual Stress Field in a Friction Stir Welded Aluminium Extrusion. Materials Science Forum 678-683.Google Scholar
  46. 46.
    Webster PJ, Hughes DJ, Mills G, Vaughan GBM (2002) Synchrotron X-Ray Measurements of Residual Stress in a Worn Railway Rail. Materials Science Forum 767-772.Google Scholar
  47. 47.
    McDonald EJ, Hallam KR, Bell W, Flewitt PEJ (2002) Residual Stresses in a Multi-Pass CrMoV Low Alloy Ferritic Steel Repair Weld. Materials Science and Engineering A 325:454–464CrossRefGoogle Scholar

Copyright information

© Society for Experimental Mechanics 2009

Authors and Affiliations

  • P. Pagliaro
    • 1
    • 2
  • M. B. Prime
    • 2
    Email author
  • H. Swenson
    • 2
  • B. Zuccarello
    • 1
  1. 1.Dipartimento di MeccanicaUniversità degli Studi di PalermoPalermoItaly
  2. 2.Los Alamos National LaboratoryLos AlamosUSA

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