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Los Alamos National Laboratory The Slitting Method for Residual Stress
Measurement          : bent beam application
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Residual stress measured in a known stress bent beam

This is a very nice validation of the slitting method and also an excellent way to make a known stress specimen.

Schajer, G. S., and Prime, M. B., 2006, "Use of Inverse Solutions for Residual Stress Measurements," Journal of Engineering Materials and Technology, 128(3), 375-382. preprint (pdf). (LA-UR-04-5890)  


Beam Specimen:

  • 21Cr-6Ni-9Mn austenitic stainless steel (Nitronic 40)
  • 30 mm height by 10 mm wide in gauge section
  • Bent in 4-point bending into plastic region and unloaded
  • Strains and loads measured during bending
  • Loading and unloading stress-strain curves calculated from strain and load data during bending
    • Mayville, R. A. and Finnie, I., “Uniaxial Stress-Strain Curves from a Bending Test,” Experimental Mechanics, 22, 197-201, 1982.
  • Loading and unloading curves superimposed to calculate residual stress
    • *** There was a Bauschinger Effect - so it is important to measured unloading curves

Cut slot using wire EDM:

  • Cut slot using 200 µm diameter Brass wire
  • 36 cut depths to a final depth of 29.26 mm (97.5% of beam thickness)
  • Submerged in de-ionized water during cutting
  • Strain at each depth was measured with strain gage on back surface (EDM machine turned off for measurement)
EDM slitting

Strain Data:

  • Strain measured on back face strain gage for all 36 depths of cut
  • Data is available in this text file.

Pulse Results :

  • Excellent agreement with known stress
  • These results use the "pulse" stress functions and regularization as described in
    • Schajer, G. S., and Prime, M. B., 2006, "Use of Inverse Solutions for Residual Stress Measurements," Journal of Engineering Materials and Technology, 128(3), 375-382. preprint (pdf). (LA-UR-04-5890)  
  • Compared here with stresses measured by neutron diffraction and surface x-rays as described in
    • M. B. Prime, P. Rangaswamy, M. R. Daymond, and T. G. Abeln, "Several Methods Applied to Measuring Residual Stress in a Known Specimen," Proc. SEM Spring Conf. on Experimental & Applied Mechanics, Houston, Texas, June 1-3, 1998, pp. 497-499. 101K pdf. (LA-UR-98-0904)

Series Expansion :

  • Slitting results using conventional series expansion as described in theory page
  • Used Legendre polynomials order 2 and up (order 0 and 1 do not satisfy equilibrium)
  • This is an 8 term series (orders 2-9). Order selected based on minimizing uncertainty
    • Prime, M. B., and Hill, M. R., 2006, "Uncertainty, Model Error, and Order Selection for Series-Expanded, Residual-Stress Inverse Solutions," Journal of Engineering Materials and Technology, 128(2), pp. 175-185. preprint (pdf). (LA-UR-05-2597)

Strain Fit:

  • This is how well the stress results above fit the measured strain data
  • Root-mean-square misfit is about 6 microstrain, and most of that is from the last data point
  • A higher order fit will the last data point, but is too unstable
  • You should always plot this strain fit to see how well your solution is performing

NOTE: The raw data from this test and any other data from published results can be made available for research purposes. Just email me.