Engineering Science Aspects of the Hall-Petch Relation
Ronald Armstrong (University of Maryland)
Prager Medal Symposium in honor of George Weng: Micromechanics, Composites and Multifunctional Materials
Mon 2:40 - 4:00
MacMillan 117
There is a substantial history both before and after 1962 when the Hall-Petch relation describing an inverse square root of grain diameter dependence for yielding and cleavage of polycrystalline iron and steel materials was extended to the full stress – strain behavior of bcc, hcp and fcc metals and alloys. Hall and Petch had established the relationship in the early 1950’s. In 1983, George Weng incorporated the dependence into a micromechanical description of material strength by building onto his earlier work on individual grain deformations. And more recently, Weng and colleagues and students have applied a composite model description to predicting the strength properties of nanopolycrystalline materials, especially including analyses both for a limiting smallest grain size reversal of the H-P dependence and for a strain rate sensitivity dependence on average grain diameter. These topics are assessed from a dislocation mechanics viewpoint in the present report that provides an evaluation of the H-P microstructural stress intensity (slope value) in terms of the local concentrated stress requirement for cross-slip at fcc grain boundaries. An analogous H-P-type dependence is demonstrated for inverse activation volume, (1/v*), measurements reported for both hcp and fcc metal structures. The local stress for interstitial-locked dislocations at bcc grain boundaries is too high for thermal activation. Thus, the parameter, v*, provides an important interpretation of strain rate sensitivity measurements in terms of the specific dislocation mechanisms which are operative separately in grain volumes and at grain boundaries.