On the diffusion process of point defects in the stress field of edge dislocations

Abstract

An analytic solution of the time‐dependent diffusion equation for point defects in the stress field of a straight edge dislocation is given taking into account the elastic interaction due to the first‐order size‐effect. Modified Bessel functions determine the steady‐state contribution to the defect concentration whereas the time‐dependent part is governed by modified Mathieu functions. The results are applied to the calculation of the dislocation bias for interstitial absorption playing an important role with regard to void swelling and irradiation‐induced creep in metals. This reveals that the definition of a constant bias as conveniently used in steady‐state theories has to be extended to a bias function depending on radius and time.

Numerical evaluation of dislocation loop sink strengths: A phase-field approach

“…In the case of pure straight dislocations, it has been shown [9] that, without elasticity, the present model gives results in good agreement with the Wiedersich solution. Further comparison showed that, when taking into account elasticity, the Rauh and Simon solution [5] underestimates the sink strength and the elastic bias at dislocation densities which can be encountered in real irradiated materials. This previous validation work allows to apply the model to dislocation loops.…”

“…In the models described by Nichols [1], the effect of the dislocation stress field on PD diffusion was neglected. As the elastic drift is thought to be one of the driving forces for swelling in irradiated fcc crystals [2,3], the elastic interaction between the dislocation line and PDs has been first taken into account assuming that the crystal properties were isotropic with PDs modelled as dilatation centres [4][5][6][7][8][9]. More recent works considered the influence of the anisotropy of the crystal and of the PD shape in its equilibrium [10] and saddle point configuration [11][12][13][14][15][16] on sink strength.…”

A fully coupled diffusional-mechanical formulation: numerical implementation, analytical validation, and effects of plasticity on equilibrium

“…For instance, the diffusion of vacancies within the heterogeneous stress field around an edge dislocation core has been treated in [19] using Bessel functions. In contrast, boundary value problems involving coupled diffusion-stress phenomena have been solved analytically using Cosserat spectrum theory in [15].…”

Numerical evaluation of the dislocation loop bias

“…Rauch and Simon [3] have found an analytical solution of Eq. (8) subject to the exact boundary condition (10), which yields the following expression for the PD current into a dislocation:…”

“…In this regard, the point defect diffusion into a straight dislocation and a dislocation loop with account of its stress field has been a subject of numerous investigations [1][2][3][4][5][6][7][8][9]. Most of the work is based on the analysis of the size effect, which is the principle elastic interaction between point defects and dislocations in most metals [1][2][3][4][5][6][7].…”