The Hall–Petch effect as a manifestation of the general size effect

Abstract

The experimental evidence for the Hall-Petch dependence of strength on the inverse square-root of grain size is reviewed critically. Both the classic data and more recent results are considered. While the data are traditionally fitted to the inverse squareroot dependence, they also fit well to many other functions, both power law and non-power law. There have been difficulties, recognized for half-a-century, in the inverse square-root expression. It is now explained as an artefact of faulty data analysis. A Bayesian meta-analysis shows that the data strongly support the simple inverse or lnd/d expressions. Since these expressions derive from underlying theory, they are also more readily explicable. It is concluded that the Hall-Petch effect is not to be explained by the variety of theories found in the literature, but is a manifestation of, or to be underlain by the general size effect observed throughout micromechanics, owing to the inverse relationship between the stress required and the space available for dislocation sources to operate.

Effects of the grain size and shape on the flow stress: A dislocation dynamics study

“…The good alignment with 1/Öd is evidenced, in Figure 5 and Figure 6 for the one-grain simulations and in Figure 7 for the four-grain simulations. This choice is consistent with the initial HP relation (Hall, 1951) and many experimental investigations (Armstrong et al, 1962;Cordero et al, 2016;Li et al, 2016). Since dislocation storage strongly increases when grain size decreases, it is interesting to check whether the obtained size effects can be explained by an isotropic hardening resulting from the increase in dislocation density.…”

“…Intensive research has been dedicated to the effect of grain size on the mechanical properties of metals and alloys Cordero et al, 2016;Lasalmonie and Strudel, 1986;Li et al, 2016). At the beginning of 1950, Hall (Hall, 1951) used the dislocation pileup model proposed by Cottrell (Cottrell, 1953) to explain the relation observed experimentally between the lower yield stress of mild steels and the grain size, d. This relation is recognized today as the Hall-Petch (HP) law:…”

Low‐Temperature Plasticity in Olivine: Grain Size, Strain Hardening, and the Strength of the Lithosphere

“…General consistency exists among these data sets demonstrating that smaller characteristic length scales lead to higher yield stresses. This agreement also suggests that similar mechanisms lead to the dependence of strength on grain size and to the dependence of strength on contact radius, consistent with compilations of existing metallurgical literature (Dunstan & Bushby, ; Li et al, ).…”

Knowledge of process-structure-property relationships to engineer better heat treatments for laser powder bed fusion additive manufactured Inconel 718

“…To fully "reset" the microstructures of AM-IN718, recrystallization at temperatures above 1100 ºC is necessary. However, grain growth, in addition to oxide and carbide particle growth at GBs also occur during recrystallization [12,13], which are well known to diminish mechanical performances [18,19].…”