Simulation of macroscopic systems with non-vanishing elastic dipole components

Abstract

To simulate a macroscopic system from a simulation cell, a direct summation of the elastic fields produced by periodic images can be used. If the cell contains a non-zero elastic dipole component, the sum is known to be conditionally convergent. In analogy with systems containing electric or magnetic dipoles, we show that the sum introduces a component which only depends on the shape of the summation domain and on the dipole density. A correction to the direct summation is proposed for the strain and stress fields in the simulation cell, which ensures that zero tractions are imposed on the boundary of the macroscopic system. The elastic fields then do not depend anymore on the shape of the domain. The effect of this correction is emphasized on the kinetics of dislocation loop growth by absorption of point defects. It is shown that correcting elastic fields has an influence on the kinetics if defects have different properties at stable and saddle points.

Enforcing local equilibrium of point defects near sinks in object kinetic Monte Carlo simulations

“…Such energy changes are too small to have an appreciable influence on the point defect kinetics. This is in line with a previous study, where stresses of several hundreds of MPa have been shown to be necessary to modify the defect kinetics in Al at 300 K [48]. Since stress effects on diffusion decrease as temperature increases, this validates the approximation of infinite medium for the elastic solution in the present conditions.…”

Perspectives on multiscale modelling and experiments to accelerate materials development for fusion

“…The elastic interaction between defects can produce spatial ordering [47] and elastic self-pinning of loops [48] , matching experimental TEM observations. But traction-free boundary conditions have also been shown to affect the kinetics of defect coalescence [49] , and the efficiency of defect sinks [50][51][52] . These observations imply the evolution of the nanoscale stress state observed due to defects [53] , and hence the evolution of defect microstructure, must both drive and be driven by component level elastic relaxation [45,54] .…”

Object kinetic Monte Carlo modelling of irradiation microstructures with elastic interactions

“…Recently it has been shown that for a box containing an elastic dipole component but no monopole term, the field ε 0 can be written in the following explicit form [48]:…”

“…The field ε 0 is calculated at the centre of the simulation box. In isotropic elasticity, it is convenient to use the analytical form given in [48] and recalled in appendix F. Removing ε 0 amounts to simulating a finite macroscopic system under loading given by σ = −p [48]. This means that to simulate a physical system with free surfaces, this loading should be removed.…”

“…The field which must be subtracted from the discrete sum of the dipolar field over neighbour boxes, in order to get a periodic solution, has an analytical form if the sum is performed over a cuboid domain centred on the simulation box [48]. We recall here its expression for the sake of completeness.…”