Stress-induced diffusion of hydrogen in metallic membranes: cylindrical vs. planar formulation. II

Effects of self-stress on hydrogen diffusion in Pd membranes in the coexistence of α and β phases

“…(13) and (14), respectively, by u σ = 0 (see Fig. 7B (dots) for a plot of ξ ss s versus n R , at u σ = 0 for n H0 = 0.001).…”

“…(5) and (6) that both in the ␣ and ␤ phases the hydrogen flux is proportional to the concentration gradient. Therefore, in cylindrical geometry, even in the presence of stress-induced diffusion, the flux expression is strictly Fickian, whereas in the planar case, a non-local integral contribution to hydrogen flux is also present [10][11][12][13][14]. Consequently, the role of self-stresses in tubular membranes is solely that of increasing the effective (concentration dependent) diffusion coefficient both in the ␣ and in the ␤ phases.…”

“…In previous papers, Adrover et al [12][13][14] and Zhang et al [10,11] have made use of the SJD model to analyze the occurrence of the uphill-diffusion in planar and tubular Pd membranes, for hydrogen contents falling within the ␣ phase composition range. These authors have shown that: (i) the SID model does not display any non-local contribution to the flux in a cylindrical membrane; but (ii) the uphill effect occurs as a direct consequence of the non-linear, non-local, time-dependent boundary conditions, corresponding to a permeation experiment.…”

“…More recently, Zhang et al [10,11] and Adrover et al [12][13][14] have provided analytical and numerical evidence that hydrogen transport exhibits different macroscopic features in thin cylindrical and planar membranes, as a consequence of the different propagation mechanisms of the stress field in each of these geometries.…”

Stress diffusion interactions in an elastoplastic medium in the presence of geometric discontinuity

“…The presence of diffusion species, either as an external gas or resulting from electrochemical reactions leads to the severe degradation in the material properties and failure of the material [6,7,8,9]. Frailure due to these multi-physical phenomenon (stress-diffusion interactions [10]) shares a major portion of material failures, viz., chloride diffusion in civil structures [3,11,12], hydrogen diffusion in steels [1,13,14,15,16,17,18,19], aluminum [20] and NiTi alloys [21,22,23], bacteria diffusion in biofilms [24,25,26], Li diffusion in LIBs [9,8,27,28].…”