Three dimensional structures of the geometrically necessary dislocations in matrix-inclusion systems under uniaxial tensile loading

Plastic slip deformation in matrix-inclusion systems, in which a cuboidal or spherical shaped inclusion is embedded in a softer matrix, are numerically analyzed by a finite element technique. Edge and screw components of the geometrically necessary dislocations on slip systems are evaluated for each finite element from the spatial gradient of plastic shear strain. The character of the dislocation segments in each element is deduced from the data for edge and screw components and the directions of dislocation segments are determined. The aggregate of the dislocation segments in the whole specimen shows typical structures of dislocations, such as the Orowan loops around the inclusion and tilt boundaries that develop perpendicular to the primary slip plane. Stress state and shape of dislocations in deformable inclusions are discussed.