Applications of Residual Stress Determination by the Spherical Harmonics Model

D. Balzar^1,2 and N. C. Popa^3,4

¹Department of Physics and Astronomy, University of Denver, Denver, CO 80208, USA.

²National Institute of Standards and Technology, Boulder, CO 80305, USA.

³Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia.

⁴National Institute for Materials Physics, P.O. Box MG-7, Bucharest, Romania.

The determination of residual strain/stress and texture through the spherical harmonics approach is becoming a route of choice for many researchers. The method can yield the full texture-weighted strain orientation distribution function for arbitrary crystal and sample symmetries. However, this approach requires the measurements of interplanar spacing of the several Bragg reflections at multiple sample orientations. Thus, energy-dispersive measurements and multiple detectors are very useful. We give an example of the neutron TOF measurements carried out at the LANSCE SMARTS station on the deformed uranium samples. We report the average macroscopic strain and stress tensors, as applied to the orthorhombic crystal symmetry and general triclinic sample symmetry of the sample. The strain tensor was determined by the least-squares refinement of interplanar spacings for 19 Bragg reflections, as determined from the neutron TOF. An annealed uranium plate was used as a reference sample, thus providing reference interplanar spacings for all 19 reflections. The resulting strain and stress tensors show strong shear components that could not be detected through the measurements customary carried out along a few principal directions in the sample.