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Contour Method: Calculating Stress Using Finite Elements

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   - make cut
   - measure surface
>    - calculate stress
   - bent beam
   - weld plate
   - quenched steel
   - impacted plate
   - alum. forging
   - friction stir weld
   - Ti FSW
   - Railroad rails
More info
Residual Stress
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this page:calculate stress
Calculate Stress

For help with calculations: Download pdf (26 MB) Johnson, G, 2008, "Residual stress measurements using the contour method," Ph.D. Dissertation, University of Manchester, School of Materials. A very thorough thesis with lots of practical and helpful information on the contour method and then some very good applications including several advances.The Matlab files described in the dissertation and some examples are available here: GJohnsonFiles.zip (3.6Mb). Use of the spline program requires the curve fitting toolbox. (Posted with permission of author)

Build finite element model of cut part
  • No need to model actual deformed shape - displacements are small
  • Shown here in 2-D, build 3-D model to get full cross-sectional stress map
undeformed finite element mesh
Take opposite of measured contour
  • Because we need to force deformed shape back to flat
Apply to finite element model
  • Apply to edge of model as displacement boundary conditions
  • Apply in normal direction only, leave other directions unconstrained
apply displacments to mesh
Extract results
  • Post-process finite element results to get stress along edge where boundary conditions were applied
stress map


Now we have the residual stresses that originally existed normal to the plane of the cut! Illustrated here for just a 1-D stress profile, but see Applications for examples of getting a full 2-D stress map.



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contact: Mike Prime at prime@lanl.gov | Copyright & Disclaimer
U.S. patent 6,470,756 | Last Modified: January 23, 2014

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