Application of micropolar theory to the description of the skin effect due to hydrogen saturation

Abstract

A model is proposed for the description of a highly inhomogeneous distribution of hydrogen within a saturated metal specimen (the so-called skin effect due to hydrogen saturation). The model is based on the micropolar continuum approach and results in a nonuniform stress–strain state of a cylindrical metal specimen due to distributed couples or microrotations. The dependence of the diffusion coefficient on the strain energy is considered in order to model stress-induced diffusion. Accumulation of hydrogen within a thin boundary layer results in a highly nonuniform distribution of hydrogen across the specimen. The mutual influence of the stress–strain state and hydrogen accumulation is taken into account. The estimated thickness of the surface layer containing hydrogen is comparable to the thickness observed in experiments. The predicted average concentration coincides with experimental data.

On modeling of stress‐induced diffusion within micropolar and classical approaches

“…The smaller these terms, the closer solution obtained within the micropolar problem to the solution obtained within the classical problem. In accordance with the approximate analytical solution of the microp-olar problem obtained in our previous paper [48], the axial displacement and microrotation around 𝐞 𝜑 are as follows:…”

“…The present paper models stress-induced diffusion and focuses on the application of the general micropolar theory to the description of the local increase of hydrogen in the vicinity of the border. In fact, this work continues and summarizes our previous theoretical investigation [46][47][48]. In Frolova et al [46], we considered continuum with constrained rotations when microrotations coincide with macrorotations determined by the displacement field.…”

“…Paper [47] dealt with the general micropolar continuum, an analytical solution was obtained with some restrictions. These restrictions were removed in Frolova et al [48]. An approximate analytical solution obtained under asymptotic assumptions was compared with a more accurate numerical one.…”

“…The two solutions were found to coincide. In our previous works [47,48], we followed Mikolaichuk and Knyazeva [39] and described the stress-induced diffusion through the dependence of the diffusion coefficient on the elastic strain energy. In the present paper, stress-induced diffusion is modeled in different ways.…”

“…In contrast to Refs. [47,48], we take into account that compassion of material decreases the diffusion coefficient and vice versa, its stretching increases diffusivity of impurity. Additionally, we compare the results based on the application of micropolar theory with the result based on classical theory.…”