New physical interpretation of incompatibility and application to dislocation substructure evolution

Physical interpretations of the incompatibility tensor are extensively discussed and applied to model several practically-important dislocation substructures in metallic materials. This paper firstly performs a tangible decomposition of the incompatibility tensor into the two types of defects by introducing Nye's contortion tensor, and also clarifies the interrelationship with expressions given based on differential geometry. The effects on the evolutions of intra-granular substructures like cells and geometrically- necessary type bands are examined based on finite element simulations on multi-grain models under tension and simple shear with several representative orientations.