Fractal based correlations for Nb microalloyed steel undergoing static recrystallization

• Fractal analysis of microstructural images of Nb-microalloyed-steel was performed.
• A correlation between deformation temperature and fractal dimension was obtained.
• A new elliptical function for predicting the area fraction of sub-grains is proposed.
• These fractal based models improve the prediction of final grain size distribution.

A new elliptical function for predicting the area fraction of the nucleated sub-grains during static recrystallization has been proposed which considers the fractal based correlation between the sub-grain size and the prior austenite grain size for Nb microalloyed steel. To derive the correlation, fractal analysis of microstructural images of Nb microalloyed steel was performed. The proposed elliptical model in conjunction with the fractal based grain size model improves the prediction of the final grain size distribution for the Nb microalloyed steel and gives excellent correlation with experimental results.