The (cleavage) strength of pre-cracked polycrystals

Abstract The fracture mechanics stress intensity, K, measured for the cleavage strength of carbon steel by Professor Yokobori and colleagues, at Tohoku University and elsewhere, is shown to follow a Hall-Petch dependence on average grain diameter, l, in accordance with the model-based relationship K = c's 1 2 [σ 0 +kl −1 2 ]; for which c' is a numerical factor, 5 is the effective length of the local plastic zone associated with unstable crack growth, σ0 is a friction stress for appropriate dislocation movement within the polycrystal grains and k is a microstructural stress intensity intermediate between that for the plastic flow or fracture of crack-free material. The separated terms in the K relationship are matched with corresponding Hall-Petch friction stress and microstructural stress intensity measurements for yielding and fracture. In this way, the K relationship is proposed to provide a bridge for the goal set some time ago by Professor Yokobori of combining the microscopic and macroscopic (continuum) viewpoints for understanding the fracture strength properties of engineering materials.