Dispersed barrier hardening modeling on depth-distributed helium bubbles in iron-based alloys

Abstract

The present study investigates the irradiation hardening in pure Fe and Fe-0.3 wt.% Si alloys after He⁺ ion implantation tests in order to obtain a representative value for the barrier strength (α-value) of helium bubbles in model ferritic alloys. 160 keV He⁺ ion implantation was performed at 400 ± 2 °C with a fluence up to 3.6 × 10¹⁶ cm^-2 at a flux of 4.0 × 10¹³ cm^-2∙s^-1. Hardness was measured using the nanoindentation technique at different indentation depths, and the depth-distributed helium bubbles were observed by transmission electron microscopy (TEM). The results of the hardness measurement demonstrated a significant damage gradient effect in both He⁺ implanted specimens. This could be attributed to the presence of depth-distributed helium bubbles. Additionally, a significant dose dependence on swelling was observed in both alloys, suggesting that the primary parameter governing the evolution of helium bubbles is the dose. While the traditional dispersed barrier hardening (DBH) model could be employed to evaluate the α-value based on helium bubble-induced hardening, the distribution of dispersed barriers should be uniform. Consequently, we proposed a more efficacious application of the dispersed barrier hardening model to describe the depth-distributed helium bubble-induced hardening in iron-based materials by integrating the nanoindentation technique with TEM. The α-value for helium bubbles of approximately 2∼3 nm in diameter in model ferritic alloys is estimated to be approximately 0.15 to 0.16 based on the revised DBH model, which is consistent with the value observed in annealed F82H of neutron irradiation. Furthermore, this study suggested that the much greater hardness increase and swelling rate of implanted Fe-0.3Si than that of pure iron is due to the additive silicon, which has a strong ability to inhibit vacancy diffusion in the evolution of helium bubbles.