Refining a metal's grain size can result in dramatic increases in strength, and the magnitude of this strengthening increment can be estimated using the Hall-Petch equation. Since the Hall-Petch equation was proposed, there have been many experimental studies supporting its applicability to pure metals, intermetallics, and multi-phase alloys. In this article, we gather the grain size strengthening data from the Hall-Petch studies on pure metals and use this aggregated data to calculate best estimates of these metals'Hall-Petch parameters. We also use this aggregated data to re-evaluate the various models developed to physically support the Hall-Petch scaling.

a b s t r a c tElectrons injected into the build envelope during powder bed electron-beam additive manufacturing can accumulate on the irradiated particles and cause them to repel each other. Under certain conditions, these electrostatic forces can grow so large that they drive the particles out of the build envelope in a process known as "smoking". In the present work, we investigate the causes of powder bed charging and smoking during electron-beam additive manufacturing. In the first part of the paper, we characterize the surface chemistry of a common feedstock materialdgas-atomized Ti-6Al-4V powderdand find that a thick, electrically insulating oxide overlayer encapsulates the particles. Based on these experimental results, we then formulate an analytical model of powder bed charging in which each particle is approximated as a capacitor, where the particle and its substrate are the electrodes and the oxide overlayer is the dielectric. Using this model, we estimate the charge distribution in the powder bed, the electrostatic forces acting on the particles, and the conditions under which the powder bed will smoke. It is found that the electrical resistivity of the oxide overlayer strongly influences the charging behavior of the powder bed and that a high resistivity promotes charge accumulation and consequent smoking. This analysis suggests new quality control and process design measures that can help suppress smoking.

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