Geometrically necessary boundaries accommodate the residual elastic strain in cold-rolled Fe-3%Si

Abstract

The relationship between plastic deformation accommodation structures and residual elastic strain fields in deformed metals is poorly understood at the intragranular scale, largely because no experimental technique has provided simultaneous, three-dimensional, bulk-sensitive access to both fields at the length scale of dislocation boundaries. Here we use dark-field X-ray microscopy (DFXM) to map intragranular misorientation and residual elastic strain simultaneously in three dimensions within a grain of 50% cold-rolled Fe 3%Si alloy. We resolve geometrically necessary boundaries (GNBs) and incidental dislocation boundary (IDB) cell structures in the bulk non-destructively. Correlating the elastic strain field with the segmented plastically deformed substructure reveals that GNBs act as the primary carriers and distributors of long range residual elastic strain. GNBs separate subdomains of distinct mean d-spacing, across the grain volume. The plastic misorientation associated with IDBs and dislocation cells develops within GNB-delimited subdomains that carry comparatively similar values of elastic strain. This supports a mechanistic picture in which GNBs accommodate nearly all the long-range residual elastic strain in the deformed state, while plastic slip propagates into GNB interiors to organize into IDB cells with similar strain levels. The three-dimensional misorientation and strain gradients quantified here provide direct experimental input for recovery and recrystallization modelling in ferritic steels, such as electrical steels.