Optimum shape and orientation of δ-hydride precipitate in α-zirconium matrix for different temperatures

Highlights: • Obtained optimal shape and orientation of δ-hydrides in α-Zr by energy minimization. • It was found at different precipitation temperatures viz. 25, 100, 200, 300 & 400 °C. • Flat cross section was observed to be the optimum shape of δ-hydride precipitates. • Optimum orientation (habit plane) was observed to be parallel to basal plane of α-Zr. • Compared the results with the experimental observations from the literature. Precipitation of δ-hydride in α-Zr matrix deleteriously affects the matrix toughness. Hence, the formation of these hydrides and their equilibrium shape and orientation is studied. The precipitation of hydrides is associated with a volume change and associated chemical free energy. Hence, a multi-physics finite element model is developed to determine the optimal shape and orientation of the hydrides by minimizing accommodation free energy. The model is applied at various temperatures viz., 25, 100, 200, 300 and 400 °C. Three cases of fully elastic, elastic perfectly-plastic and elastic work-hardening plastic systems are studied and compared. The model takes into account the temperature variation of stiffness tensor, yield strength, hardening coefficients, volumetric change in the precipitation process and volume change in matrix due to hydrogen depletion. It is found that a flat hydride with its geometric orientation such that its major axis coincide the basal plane of the parent matrix is the most optimal shape and orientation. This is irrespective of whether the system is modeled as fully elastic, elastic perfectly-plastic or elastic work-hardening plastic. The results are discussed based on microscopic experiments and from experimental observations from the literature.