A Critical Discussion of the sin²ψ Stress Measurement Technique

Abstract:

The sin2ψ technique for near-surface and bulk stress evaluation is frequently considered to be the method of reference, largely due to the historical reason of being established early on in the development of experimental study of residual stress, and due to the widespread availability of laboratory X-ray facilities equipped with goniometers allowing ψ-tilting to be carried out. In recent years other diffraction-based techniques of residual strain and residual stress evaluation have been developed, some of them based at large facilities such as synchrotrons, neutron reactors or spallation sources, and others becoming available in the laboratory setting. It is therefore perhaps relevant and timely to review the strengths and shortcomings of the sin2ψ technique in today’s context. In the present study this task is addressed through the use of polycrystal elasto-plastic modelling that allows the determination of equivalent average elastic lattice strains following complex deformation history, and by post-processing of the model results in order to extract the parameters measurable in diffraction experiments. In particular, it is possible to extract the simulated strain values that would be measured at different tilt angles, and to build a family of sin2ψ plots for different reflections. It then becomes possible to assess the degree to which the hypotheses underpinning the principle of this method are enforced or violated; to select the most suitable reflections; and to discuss how the method could be improved or varied to provide more reliable residual stress measurement procedures.