Grain-size dependence of the flow stress of Cu from millimeters to nanometers

Abstract

Data in the literature on the effect of grain size (d) from millimeters to nanometers on the flow stress of Cu are evaluated. Three grain-size regimes are identified: regime I, d Ͼ ϳ10 Ϫ6 m; regime II, d Ϸ 10 Ϫ8 to 10 Ϫ6 m; and regime III, d Ͻ ϳ10 Ϫ8 m. Grain-size hardening occurs in regimes I and II; grain-size softening occurs in regime III. The deformation structure in regime I consists of dislocation cells; in regime II, the dislocations are mostly restricted to their slip planes; in regime III, computer simulations indicate that dislocations are absent and that deformation occurs by the shearing of grain-boundary atoms. The transition from regime I to II occurs when the dislocation cell size becomes larger than the grain size, and the transition from regime II to III occurs when the dislocation spacing due to elastic interactions becomes larger than the grain size. The rate-controlling mechanism in regime I is concluded to be the intersection of dislocations; in regime II, it is proposed to be grain-boundary shear promoted by the pileup of dislocations; in regime III, it appears to be grain-boundary shear by the applied stress alone.

Low-Cycle Fatigue of Ultra-Fine-Grained Cryomilled 5083 Aluminum Alloy

“…[1] Research has shown that various UFG materials exhibit different hardening and deformation mechanisms when subjected to monotonic loading. [2,3] However, the application of UFG materials in mechanical or structural designs is not only dependent on strength but also on properties such as corrosion resistance, ductility, fatigue resistance, formability, machinability, and welding characteristics. Fatigue resistance is a measure of a material's ability to resist damage accumulation and crack initiation under cyclic loading.…”

Modeling the dependence of strength on grain sizes in nanocrystalline materials

“…Recent molecular dynamics (MD) simulations have improved our understanding of the deformation of nanocrystalline materials [13]. The MD simulations in nanocrystalline copper [20][21][22][23], aluminum [11,24], nickel [22,23] and cobalt [25], where an inverse Hall-Petch effect was observed [11,17,20,21,[24][25][26], revealed the difference between the grain interior and the grain boundary regions where most of the deformation occurred due to the inter-grain deformation (sliding) mechanism [20,22,23,27,28]. It was further observed that the volume fraction of the total grain boundaries, which increases with decreasing grain size [29], increases under straining conditions, indicating an expansion of the grain boundary regions during straining [11].…”

Hall–Petch Relationship and Dislocation Model for Deformation of Ultrafine-Grained and Nanocrystalline Metals

“…Relating to the above anomalous temperature dependence of activation volume, Conrad 14,45) and Conrad and Yang 68) have shown for their regime II of the grain size (d µ 101000 nm) that the activation volume v à becomes an increasing function of the applied stress. According to them, this anomalous stress dependence of v à is also consistent with their proposed rate-controlling process for fcc UFG materials in regime II, i.e., GB shear promoted by the pile-up of dislocations.…”

“…For this purpose, numerical values for Ni will be chosen as in the previous study: is an increasing function or v * d is a decreasing function of temperature. This unique and anomalous behavior, different from that for coarse-grained polycrystals, has been noted 14,45,56) and some researchers discussed it using Kato's model.…”

“…14) They have concluded that deformation kinetics of UFG metals with d between 10 and 100 nm (Regime II in their studies) is controlled by GB shear promoted by the dislocation pile-up.…”