Analytical solutions for determining residual stresses in two-dimensional domains using the contour method

Area of Science:

• Materials Science
• Mechanical Engineering
• Non-Destructive Testing

Background:

• The contour method is a prevalent destructive technique for residual stress measurement.
• Current applications rely on the finite-element (FE) method to interpret experimental data.
• This approach can be computationally intensive and introduce potential inaccuracies.

Purpose of the Study:

• To develop and present analytical solutions for the contour method.
• To enable direct calculation of residual stresses from measured data.
• To eliminate the necessity of finite-element analysis in residual stress determination.

Main Methods:

• Derivation of analytical solutions for semi-infinite strips and finite rectangles.
• Application of the derived solutions to experimental measurements.
• Validation against independent measurement techniques.

Main Results:

• Analytical solutions were successfully obtained for both semi-infinite strip and finite rectangle geometries.
• The developed technique allows for direct calculation of residual stresses, bypassing FE analysis.
• Residual stress measurements in a plasma-arc welded plate showed good agreement with neutron diffraction data.

Conclusions:

• The presented analytical solutions provide a more efficient and direct approach to residual stress measurement using the contour method.
• This method eliminates the dependency on finite-element analysis, simplifying the process.
• The findings are validated by experimental results, confirming the accuracy and applicability of the technique.