The Stress Field of a Rectangular Dislocation Loop in an Infinite Medium: Analytical Solution with Verification

The stress field of a rectangular dislocation loop in an isotropic solid, which is in an infinite medium, is obtained here for a Volterra-type dislocation which has three non-zero Burgers vector components. Explicitly, the stress field of the dislocation loop in an infinite isotropic material is developed by integrating the Peach-Koehler equation over a finite rectangular dislocation loop. In this work, analytical/numerical verification of the stress field is demonstrated. To be specific, the verification is carried out to ensure that both the Equilibrium Equations and the Strain Compatibility Equations are satisfied. Moreover, a comparison with the stress field of a rectangular loop summed as four dislocation segments, using the DeVincre formula, is performed. Due to analytical verification, no error was detected in the presented solution. Also, comparing with the DeVincre formula presented identical results, qualitatively and quantitatively.