Diffusion or imperfection modified long range interaction between a line dislocation and a spherical inclusion

Abstract

This paper addresses some aspects of the 3D elastic problem of a line dislocation interacting with a spherical inclusion particle. Specifically, the effects of imperfect interface bonding and diffusional relaxations on the long range dislocation-particle interaction are examined in some detail. It is known from the classical dislocation-particle analysis that a dislocation is repelled from a second phase particle if the shear modulus of the particle is higher than that of the matrix. However, when interface elastic boundary conditions are modified by imperfect interface bonding or diffusional relaxations, this interaction may be completely changed. Diffusion over length scales comparable to the width of the interface leads to a viscous-like relaxation of the shear tractions along the interface. Given enough time for diffusion to occur over distances of order of the inclusion radius, the normal traction gradient along the inclusion/matrix interface may also be completely relaxed. Particles or fibers with a flexible, thin layer of coating present another example of imperfect interface conditions. Closed form solutions are derived for the long range interaction between a line dislocation and a spherical inclusion with “imperfect” interface in the sense that the normal and shear tractions along the interface are taken to be proportional to the corresponding displacement discontinuities. A unique constant dependent on the properties of the interface and the elastic mismatch between the particle and the matrix is identified as the control parameter for the long range dislocation-particle interaction. The effects of diffusional relaxations are studied via solutions in the limit that both the shear traction and normal stress gradient along the interface have been completely eliminated. In that case, it is seen that screw dislocations and edge dislocations in glide orientation with respect to the particle are always attracted toward the particle while edge dislocations in climb orientation with respect to the particle are repelled from the particle.