On the relationship between critical tensile stress and fracture toughness in mild steel

An analysis is presented which relates the critical value of tensile stress (σ_f) for unstable cleavage fracture to the fracture toughness (K_Ic) for a high-nitrogen mild steel under plane strain conditions. The correlation is based on (i) the model for cleavage cracking developed by E. Smith and (ii) accurate plastic-elastic solutions for the stress distributions ahead of a sharp crack derived by J. R. Rice and co-workers. Unstable fracture is found to be consistent with the attainment of a stress intensification close to the tip such that the maximum principal stress σ_yy exceeds σ_f over a characteristic distance, determined as twice the grain size. The model is seen to predict the experimentally determined variation of K_Ic with temperature over the range -150 to -75°C from a knowledge of the yield stress and hardening properties. It is further shown that the onset of fibrous fracture ahead of the tip can be deduced from the position of the maximum achievable stress intensification. The relationship between the model for fracture ahead of a sharp crack, and that ahead of a rounded notch, is discussed in detail.