Cyclic deformation behavior and dislocation substructures of hexagonal Zircaloy-4 under out-of-phase loading

Macroscopic response and microscopic dislocation structures of Zr-4 subjected to biaxial fatigue under different phase angles of 30 degree, 60 degree, 90 degree, and different equivalent strain ranges of 0.8%, 0.6%, 0.4% were studied. The testing results show that the delay angle between the stress deviators and strain increment tensors is strongly dependent on phase angle and the equivalent strain range. When phase angle equals 60degree, the delay angle has the minimum variation range for all specimens. The mean value of the delay angle decreases with increasing phase angle or the equivalent strain range. The variation range and average value of the Mises equivalent stress have the maximum in S3 with the phase angle of 90degree. They decrease as the equivalent strain range decreases. Zr-4 displays a pronounced initial hardening followed by a continuous softening for all specimens during out-of-phase cycling. The stabilized saturation stresses of Zr-4 under out-of-phase cycling are much higher than that under uniaxial cycling. It indicates that Zr-4 displays an obvious additional hardening. As the phase angle increases, the typical dislocation structure changes from dislocation cells to tangles. The dislocation-dislocation interactions increase resulting in an additional hardening. In essence, the degree of additional hardening depends, among other factors, on the maximum shear stress ratio of resolved shear stresses and critical resolved shear stresses (RSS/CRSS)