Modelling of shear stress field in glide plane in substitutional solid solutions

The formation of stochastic shear stress field in the glide plane in the substitutional solid solution was investigated by computer simulation. If the atoms in the crystal lattice nodes of the substitutional solid solution are considered as a kind of point defects in the virtual solvent medium, the shear stress distribution in the glide plane can be calculated based on the interaction of edge dislocation and such defects. For concentrated solid solutions, the shear stress will be a normally distributed random value with zero mathematical expectation. The standard deviation of this distribution will be the greater the greater the effective distortion of crystalline lattice of the alloy. In the case of dilute solid solution, where one of the components has a predominant content, the simulation gives shear stress distribution in the glide plane, where large peaks are separated from each other by wide areas of near-zero stresses. Thus, there are separate discrete obstacles in the form of large stress peaks for the edge dislocation in the glide plane in dilute solid solution, and the space between the peaks is practically stress-free. The average distance between large peaks correlates with the average distance between the atoms of those components that are few in solution, if total atomic fraction of these components is considered. Thus, the proposed modeling gives a very realistic shear stress distribution in the glide plane for concentrated and dilute substitutional solid solutions with fcc and bcc structures. This can be useful in further modeling the yield strength in multicomponent alloys. Keywords: dislocation, distorsion, shear stresses.

Dislocations in an arbitrary angle wedge. Part I: The dislocation kernel

We consider the state of stress created by the presence of an edge dislocation at an arbitrary position, in a wedge of arbitrary internal angle. A method for determining the state of stress in the wedge is demonstrarted and verified against finite element method simulations. Furthermore, a Mellin transform is employed to ensure that the free surfaces of the wedge remain traction free along their length.