Investigation of effect of specimen size on the hall-petch relationship for CuZn30 brass

It is well known that as grain size decreases, the strength of the material increases. Hall-Petch relationship gives the relationship between grain size and the yield strength of a material. If the Hall-Petch constants of the material are known, the yield strength of the material can be calculated. The Hall-Petch relationship was generalized to include flow stress regions as well. The aim of this study is to investigate the effect of specimen size on the Hall-Petch relationship in CuZn30 brass. To do this, the experimental results of another study are used. At that study, different sizes of compression specimens were machined from as received cold-rolled CuZn30 sheets, which were then annealed at three different temperatures to produce different grain sizes. Via compression tests, true stress-true strain curves for different specimen, and grain sizes were obtained. In this study, by utilizing these true stress-true strain values, Hall-Petch constants for different specimen sizes were determined at various strains for CuZn30. A variation was found in the determined values of the Hall-Petch constants with respect to specimen size. As specimen size has decreased, an increase in the determined k(ε) values, and a decrease in the σ0(ε) values was observed. This result can be explained by the surface layer model, which was proposed to explain the decrease in the flow stress of material when specimen size is decreased. As specimen size decreases, the ratio of the surface layer (grains) in the cross-section area increases, and consequently, the flow stress of the material decreases. Besides, the decrease in the flow stress is more significant for coarse grain size when compared to fine grain size cause of the increase in the surface layer ratio is more significant for coarse grain-sized specimens when specimen size is decreased. As a result, the determined Hall-Petch constants are depended on the specimen size when 2 mm or 1 mm thick specimens were used in the experiments. To determine specimen size independent Hall-Petch constants, the experiments were performed with specimens that are thick enough in which the surface layer ratio can be neglected. The theoretical calculations made for a hypothetical material indicate that to find a specimen size-independent, Hall-Petch constant specimens with a thickness of at least 8 mm should be used to determine a specimen size-independent Hall-Petch constants.