Absorbed impact energy and mode of fracture: A statistical description of the micro-structural dispersion

A statistical model is proposed to account for the influence of the dispersion of the microstructure on the ductile-to-brittle transition in body centered cubic (bcc) metals and their alloys. In this model, the dispersion of the microstructure is expressed via a normal distribution of transition temperatures whereas a simple relation exists between the values of absorbed, lower and upper shelf energies, the ductile area fraction and the distribution parameters. It is shown that via an appropriate renormalization of energies and temperatures, experimental data for different materials and ageing conditions align all together on a master curve, guaranteeing thereby the effectiveness of the proposed statistical description.