Modification of the Hall-Petch equation for friction-stir-processing microstructures of high-nitrogen steel

The classic Hall-Petch (H-P) equation is unsuitable for linear fitting of the hardness and grain size relationship of friction stir processing (FSP) microstructures of high-nitrogen steel. The concept of effective grain size was defined in this study by considering low angle boundaries (LABs) in the interiors of grains using grain orientation spread. The H-P equation was modified for FSP microstructures by regression to obtain a linear relationship based on effective grain size. The mechanism of boundary strengthening of LABs was also discussed.