Hall–Petch and dislocation strengthening in graded nanostructured steel Original Research Article

The structure and strength of low carbon steel samples have been analyzed after plastic deformation by shot-peening and cold-rolling. The fine scale surface microstructure caused by shot-peening extends to ∼50 μm below the surface. The structure is graded and subdivided by dislocation boundaries and high angle boundaries showing a clear resemblance to the lamellar structure, which evolves during conventional rolling of bulk metallic materials from medium to high strain. As the surface is approached, the boundary spacing decreases to ∼50 nm at the surface. In parallel, the misorientation angle across boundaries increases to ∼65% of high angle boundaries. The cold-rolled steel shows a low hardening rate at high strain and by assuming additive strength contributions from Hall–Petch and dislocation strengthening, the flow stress has been expressed by the relationship image, where Dav is the average spacing between the low and high angle boundaries which subdivide the microstructure, σ0 is the friction stress and k2 is a number which is expressed in terms of structural parameters which have been determined by electron backscattered diffraction. It is found that calculated k2 values are in accord with an experimental value of 310 MPa μm0.5. In the shot-peened steel the increase in Dav with increasing distance from the surface is transformed into a stress profile based on the σ - Dav relationship established for cold-rolled bulk samples. The calculated stress profile is validated by comparison with the experimental profile based on hardness measurements, and good agreement is found. This result points to a wider application of the suggested method to derive the local flow stress in a deformed microstructure based on a measurement of the local boundary spacing and the stress–structure relationship for the bulk material in the deformed state.