Formation of Prismatic Dislocation Loop around a Spherical Inclusion Using Level Set Dislocation Dynamics

概要

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The whole process of a prismatic dislocation loop (PDL) formation around a misfitting spherical inclusion embedded in a homogeneous isotropic matrix is studied using level set dislocation dynamics. Two small half loops are first punched out around a spherical particle on a specific cylindrical surface along which the magnitude of the misfit shear stress reaches the maximum among all the homocentric cylinder surfaces. The edge dislocation segments glide away from the inclusion-matrix interface under the influence of the shear stress, while the screw components cross slip around the cylindrical surface. When two ends with opposite orientations of the top and bottom half dislocation loops intersect, the screw segments annihilate and a PDL is produced. Level set dislocation dynamics successfully presents such a topological evolution under elastic dislocationdislocation/ dislocation-inclusion interactions. During the process of PDL formation, the total elastic strain energy in the system first increases as the initial half loops expand on the cylindrical cross-slip plane and reaches the climax when two loops merge into a middle-bended loop, and then decreases since the middlebended loop becomes a PDL. Finally, it becomes saturated as this dislocation loop gradually glides away from the inclusion-matrix interface.