Investigation effect of external stress on hydrogen solvus in a zircaloy-4 fuel cladding alloy: application of in situ diffraction technique and mesoscale phase-field simulation

Zircaloy-4 is widely used as a nuclear fuel cladding material in light water reactors (LWRs). However, the formation of the zirconium hydride phase in the cladding significantly degrades its mechanical properties by reducing the local ductility and initiating crack propagation. Therefore, one of the current fuel performance modeling efforts is to simulate the degradation of the cladding properties caused by the hydride phase. Distribution of the hydride phase in the cladding is mainly controlled by the temperature and the stress value. The temperature effect can be modeled using the hydrogen solvus and the temperature-driven hydrogen diffusion (Soret effect). However, while correlating the effect of stress on hydride formation, a disagreement arises between the experimental data and the theoretical model. The theory predicts that the effect of stress is negligible while experiments observe that hydrides preferentially accumulates in regions with high tensile stress. This contradiction hinders accurately incorporating the stress effect into the fuel performance code. The purpose of this doctoral research is to resolve this disagreement by performing a systematic experimental and modeling study; also to provide valuable information to model the effect of stress on hydride formation in zirconium-based alloys. For the experimental study, we utilized an in situ diffraction technique to investigate the evolution of hydride phase in a Zircaloy-4 material under different thermo-mechanical conditions. Zircaloy-4 tensile specimens with hydrogen concentrations ranging from 0 to 977 wppm were tested under isothermal, slow cooling and thermal cycling conditions. A uniaxial tensile stress was applied to the specimens throughout the thermal processes. The test temperature ranged from 25 to 420◦C and the applied stress ranged from 78 to 218 MPa. Diffraction spectra were recorded during the thermo-mechanical processes as a function of temperature and stress value; phase information was obtained from the spectra. The analysis focused on the effect of stress on precipitation and dissolution of the hydride phase. Experimental results showed the hydride phase was stable under the isothermal condition if the applied stress was less than the yield stress of the zirconium matrix. However, the stress significantly affected the hydride precipitation and dissolution behavior under slow-cooling and thermal-cycling conditions. This stress effect depended on the Zr crystalline orientation. The stress increased the amount of hydrogen in solution for Zr crystals which had their basal plane normal (c-axis) inclined toward the tensile stress direction. This also implies the stress delayed hydride precipitation or promoted hydride dissolution in these crystals. If we described the evolution of the hydrogen concentration in solution of these crystals by an Arrhenius type equation, we find that stress significantly decreased the energy term Q in the Arrhenius behavior. The average Q reduction was 97 J/molH per MPa of tensile stress. This is a significant effect compared to the current theory (∼ 0.086 J/molH per MPa of tensile stress). Thus, our experimental result is inconsistent with the theory. We performed the phase-field modeling to understand this disagreement. The CALPHAD- based phase-field code Hyrax was used to quantitatively model the hydrogen solvus in a zirconium solution. Hyrax was built on the finite element framework MOOSE and was specifically developed for the binary zirconium-hydrogen system. We first modeled the hydrogen solvus in an external-stress free, single zirconium crystal system. The output of this modeling was successfully validated by comparing with experimental data. The external stress effect was then incorporated. Tensile stress was applied to a single zirconium crystal and a bi-crystal system. For the single crystal system, the hydrogen solvus was not affected by the stress, regardless of the loading direction. For the bi-crystals system, the stress redistributed the hydride between the two crystals. The hydride phase preferentially accumulated in the crystal which had the c-axis parallel to the stress. However, the equilibrium hydrogen solvus in the bi-crystal system was not affected by the stress. These results indicate the stress does not affect the hydrogen solvus but re-distributes the hydride between zirconium crystals. This is because the stress yields different strain energy in crystals with different crystalline orientations and creates an energy gradient that drives the hydrogen diffusion. The hydride preferentially precipitates in low strain energy region which creates more lattice misfit strain to compensate the gradient. This explains why stress would affect hydride dissolution and precipitation differently in different Zr crystals as observed by the diffraction experiments. The modeling result also supports the theoretical prediction that the external stress does not affect hydrogen solvus. An important conclusion is that the external stress does not affect hydrogen solvus in zirconium solution but facilitates hydride re-distribution in a system. The hydride phase distribution does not depend on the stress value but depend on the strain energy gradient. Hydrides re-distribute and accumulate in regions which have relatively low strain energy