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)
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