Influence of elasticity on the morphology of fcc-Cu precipitates in Fe-Cu alloys. A phase-field study

Abstract

Cu-rich precipitation ensures high strength and satisfactory ductility of steels at low carbon content. Although in an over-aged state, it leads to the degradation of mechanical properties. It is of prime importance for nuclear reactor vessel steels, which are exposed to extreme conditions at elevated temperature for a long time. The precipitates at this state have an fcc structure and possess a characteristic elongated morphology. The invariant-line model was mostly used to explain the morphology of fcc-Cu precipitates in the bcc-Fe matrix, although it has several limitations. It idealizes morphology and does not consider the elastic properties of both precipitate and matrix. Also, this method does not reveal the influence of the eigenstrains on kinetics and the formation of the nanostructure. Besides, the influence of the applied stress on the precipitation process can’t be revealed with this method.With this in mind, we developed a phase-field model to investigate the formation of the elongated morphology of fcc-Cu precipitates in the bcc-Fe matrix. The effect of diffuse interface and discretization on the behavior of solution was verified with a sharp-interface model and invariant-line prediction. It was found that simulated precipitates agree qualitatively with available experimental data. The role of a minimal mismatch line on the morphology formation was verified. Also, it was shown that the anisotropy of elastic properties has a minor effect on morphology formation. The applied stress with different magnitudes and directions has a minor effect on the morphology of precipitates. Nevertheless, it results in variant selection due to the difference in interaction energy. The bifurcation diagram of interaction of two precipitates was constructed. The equilibrium configurations reveal that elasticity enhances the kinetics of the reaction and that there is a twin-like configuration, which enhances the accommodation of shear-like eigenstrain and reduces the elastic interaction energy.