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, 1, in accordance with the model-based relationship
for which c' is a numerical factor, s is the effective length of the local plastic zone associated with unstable crack growth, u,, 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 unde~tanding the fracture strength properties of engineering materials.