The interplay between thermomigration and stress-driven hydrogen transport in metals

Abstract

Thermomigration is the driving force for hydrogen transport due to a temperature gradient. It can compete with hydrogen transport induced by stress gradients. While stress-driven hydrogen migration is well established, thermomigration remains comparatively underexplored, largely due to limited mechanistic understanding and a scarcity of experimental data. In this work, we develop a thermodynamically consistent framework for hydrogen transport, incorporating a mechanistic model for thermomigration. This is implemented within a finite element framework using an effective chemical potential. Using case studies of iron and nickel heat exchangers and zirconium alloy nuclear fuel cladding, we quantify the competing and synergistic effects of thermomigration and stress-driven transport. We show that thermomigration often dominates hydrogen redistribution in heat-carrying components, even in the presence of significant thermal incompatibility stresses. However, stress-driven transport is shown to become decisive near sharp stress concentrators. A graphical method is introduced to rapidly identify the dominant transport mechanism without requiring fully coupled simulations. The results provide practical guidance for assessing hydrogen redistribution and embrittlement risk in heat-carrying structural components.

Figures (7)

• Figure 1: Comparison of mechanistic model for the heat of transport with experimental data, $Q^*_{\mathrm{exp}}$, from Gonzalez and Oriani GONZALEZ1965 for (a) iron and (b) nickel. Dashed lines represent individual contributions (intrinsic, electrostatic, and electron-wind) to the total heat of transport.
• Figure 2: Overview of heat exchanger finite element model. (a) The chosen counterflow heat exchanger geometry and unit cell. Horizontal black lines correspond to boundaries between plates (diffusion bonding lines). (b) 3D unit cell geometry and mesh. A single element is used in the through thickness direction as generalised plane strain conditions are enforced. (c) Thermal model boundary conditions. Convective heat transfer is applied to internal wall surfaces. Periodic temperature boundary conditions are enforced between top and bottom surfaces. There is no heat transfer through any other surface due to symmetry. (d) Displacement boundary conditions in H transport model. Left and rear surfaces fixed in normal directions. Generalised plane strain enforced by symmetry on right and front surfaces. Normal displacements mapped between top and bottom surfaces. Superscripts B, F, R, and T represent bottom, front, right, and top surfaces, respectively.
• Figure 3: Distributions of (a) stress at steady state and (b) - (f) lattice occupancy in iron at $t=0$, $25$, $50$, $75$, and $100$ s, respectively. The steady state temperature profiles in iron and nickel are near equivalent and are shown in (g). Lattice occupancy distributions in nickel are shown in (h) - (i) at $t=0$, $7.5\times10^5$, $1.5\times10^6$, $2.25\times10^6$, and $3\times10^6$ s, respectively.
• Figure 4: Graphical analysis of contributions from stress and temperature gradients to H transport in (a) iron and (b) nickel. The black dashed line represents the hydrostatic stress to temperature gradient ratio at which the contributions to H transport are equal in magnitude (based on Equation (\ref{['Q*1']}) for $Q^*$). Individual markers represent the same metric, but use real $Q^*$ measurements GONZALEZ1965 directly. The shaded region represents the domain in which either stress or temperature dominates by up to one order of magnitude. Histograms along horizontal and vertical axes represent the predicted steady state distributions of temperature and hydrostatic stress to temperature gradient ratio from the analyses in Section \ref{['Fe_Ni_contours']}. The intersections of these distributions are indicative of the H transport regime (e.g. temperature-dominated, stress-dominated, or multimodal).
• Figure 5: Published experimental measurements SAWATZKY1960KAMMENZIND1996KANG2023 of $Q^*$ in zirconium fuel cladding alloys (Zircaloy-2 and Zircaloy-4) at different temperatures. The temperature range (as per the temperature gradient) for each measurement is shown using horizontal error bars.