Computer simulation of morphological evolution of hydride in zirconium under applied stress

For hydride forming metals and alloys, an important mechanism for hydrogen related failure is due to the stress-induced formation and subsequent fracture of hydrides at stress concentrators. It is believed that critical conditions for the fracture initiation at hydrides are controlled by the morphology of hydride precipitates. This work will make use of the phase-field kinetic model to simulate and to predict a realistic morphological evolution of γ-hydride precipitation in zirconium. A conserved parameter c( r,t) is used to describe hydrogen concentration; and a set of non-conserved parameters ŋ(r, t), the long-range order parameters, are used to describe the structural change during the phase transformation. The governing equations for these parameters are Cahn-Hilliard equation and time-depended Ginzberg-Landau (TDLG) equation. The free energy of the system, including bulk chemical free energy, interfacial energy between hydride and zirconium matrix, linear elastic energy due to hydride expansion, interaction energy between hydrides and between hydride and external load, and grain boundary energy etc., is considered in this study.; Four aspects of γ-hydride precipitation in zirconium have been simulated: (1) γ-hydride precipitation in a single crystalline zirconium material, (2) γ-hydride precipitation in a bi-crystalline zirconium material, (3) hydrogen diffusion under a blunt notch stress field in fine-grain polycrystalline zirconium material and (4) γ-hydride precipitation near a blunt notch in a fine-grain polycrystalline zirconium material.; In (1) our result shows that hydrides precipitate along three equivalent crystallographic directions. The effects of uniform applied stress on the precipitation direction of the hydrides and on the different precipitation stages have been discussed. In (2) we have set up a model that can reflect both the orientation effect and grain boundary effect. In (3) the Cahn-Hilliard equation is used to solve the hydrogen diffusion under a non-uniform applied stress field near a blunt notch. Quantitative results have been obtained. In (4) A multi-variant model that can be used for the simulation of the hydrides precipitation in a continuum media under non-uniform applied stress condition has been built up. These simulation results are consistent with experimental observations.