Engineering science aspects of the Hall-Petch relation

Hall and Petch had established in the early 1950s a linear inverse square root of grain diameter dependence for yielding and cleavage of polycrystalline iron and steel materials, with ordinate intercept stress, sigma (0), and slope value, k. Petch and colleagues extended the relationship in 1962 to the full stress-strain behavior of a diverse number of metals and alloys. Connection with other mechanical properties such as the hardness, fatigue and strain rate sensitivity properties was demonstrated in 1970. In 1983, Weng incorporated the dependence into a micromechanical analysis of material strength by building onto earlier Taylor-initiated work on multiply-coupled grain deformations. More recently, Armstrong, Weng and colleagues have applied dislocation and continuum mechanics models of the H-P relationship to predict order-of-magnitude increases in strength properties of nanopolycrystalline materials, especially including description of the strain rate sensitivity dependence on average grain diameter. These topics are assessed from a dislocation mechanics viewpoint in the present report that provides H-P connection with the Taylor dislocation density-based theory of strength properties, in sigma (0 E >) , and with the Griffith brittle fracture theory by way of pointing to the H-P slope value, k (E >) , being a microstructural stress intensity analogous to the fracture mechanics parameter, K.