Strain Field Development of a Rectangular Dislocation Loop in a Semi-Infinite Medium with Verification
Luo Li
Mechanical Engineering Department, University of New Mexico, Albuquerque, New Mexico, USA.
Tariq A. Khraishi *
Mechanical Engineering Department, University of New Mexico, Albuquerque, New Mexico, USA.
*Author to whom correspondence should be addressed.
Abstract
This paper considers a rectangular Volterra dislocation loop lying beneath and parallel to a free surface in a semi-infinite material. The paper utilizes the displacement field of an infinitesimal dislocation loop to obtain the strain field and then integrate over a finite rectangular area. For the loop, it can have three non-zero Burgers vector components. The stress field is also obtained from Hooke’s law for isotropic materials. Analytical and numerical verifications of the strain and stress fields are performed. In addition, the effect of the free surface on stresses is displayed versus depth from the surface. Verification includes satisfaction of the zero-traction boundary condition, the stress equilibrium equations and the strain compatibility equations.
Keywords: Rectangular dislocation loop, half medium, strain/stress field, numerical/analytical verification