Estimation of residual stresses in Zr-2.5%Nb PT material using hydride reorienation phenomenon and Gaussian process regression

The microstructure and texture of Zr-2.5%Nb alloy pressure tubes in Pressurized Heavy Water Reactors (PHWR) often lead to hydrides forming parallel to the transverse direction of the tube. However, applying a hoop stress above a threshold (σ_th) can cause hydrides to reorient perpendicular to the transverse direction, a phenomenon known as hydride reorientation. In this study, hydrided samples are heated to dissolve the hydrides and then cooled under varying circumferential stress fields in both the axial and radial directions of the tube, achieved through three-point bending. After testing, metallography is used to measure the hydride orientation with respect to the transverse direction. Additionally, the relationship between hydride orientation and applied stress at each location is examined to determine the minimum stress required for hydride reorientation. Interestingly, it’s observed that the minimum stress required for reorientation varies non-uniformly across the sample domain, despite the expected consistency due to the microstructure and texture of the tube. This variation is attributed to residual stress in the pressure tube, which alters the total stress (applied stress + residual stress). To predict the variation of threshold stress along the thickness, the observed data is trained using Gaussian process regression (GPR) with hydride length as the length scale parameter. The residual stress is then obtained from the predicted threshold stress variation along the thickness using an area compensation method. This approach allows determination of residual stress at high temperatures with a length scale as low as hydride length. Using this method, residual stress is determined at 573 K for different pressure tubes and plates made of Zr-2.5%Nb. The validity of the method is indirectly confirmed by comparing the predicted radial hydride boundary with observed radial hydride boundaries in internally pressurized tubes, showing good agreement.