Mesoscale modeling of coherent zirconium hydride precipitation under an applied stress

Numerous experimental studies reveal hydride dissolution, re-precipitation and re-orientation when thermomechanical cycles are applied to zirconium alloys containing hydrogen. These phenomena, that may strongly influence the mechanical properties of structural materials used in nuclear power plants, rest in subtle precipitation-stress interactions that have not been fully investigated until now, especially in the framework of inhomogeneous elasticity. In this work, we propose a combined study based on a micromechanical phase-field model and a previously developed mean-field approach to analyze the influence of an applied stress on the precipitation of coherent hydrides in zirconium. The mean-field criterion has to be modified in the low precipitate volume fraction limit to correctly predict hydride orientation and be in good agreement with phase-field modeling. The results also indicate that hydride variants the normal of which is the closest to the direction of the uniaxial applied stress are stabilized while the other variants shrink. This study provides new insights to explain on physical grounds the macroscopically observed stress-induced re-orientation of hydrides.

► We model ζ hydride precipitation in α-Zr matrix by a phase-field method. ► Elastic inhomogeneities are essential to explain variant selection under load. ► We propose an original mean-field criterion to predict hydride orientation under load. ► This new mean-field criterion is validated by comparison with the phase-field results.