Hall-Petch effect

Carlton C. E., Ferreira P. J. What is behind the inverse Hall-Petch effect in nanocrystalline materials Acta Materialia. 2007. V. 55. P. 3749-3756. 

Dense nanostructured monoliths are of interest for a range of applications where materials experience extreme conditions of pressure and temperature. In this case, hardness must be pursued and grain boundaries can enhance such properties, for instance, by the Hall-Petch effect. The management of thermal and electrical behaviors at the same time is also of prime importance in thermoelectricity, for which devices often rely on monolith-shaped materials. In this case, incorporation of grain boundaries may be a mean to fine-tune thermal conductivity independent of electrical conductivity. In both cases, the design of nanostructured monoliths may represent a significant advance in the respective fields. 

S. Lefebvre, B. Devincre, T. Hoc, Simulation of the Hall-Petch effect in ultra-fine grained copper. Mater. Sci. Eng. 400, 150-153 (2005). Structural Materials Properties Microstructure and Processing... 

From the Hall-Petch relationship, we know that (1/V[Pg.124]

The Hall-Petch relation (Eq. 14.8) indicates the effect of grain size, d, on the stress required to make the dislocation move in a polycrystalline sample. The origin of the relation is that the stress to operate a Frank-Read source increases as the size of the source decreases. If the grain size decreases, then the maximum size of the Frank-Read source also decreases. The result is the famous d relationship. 

Many measurements in polycrystalline Cu, Au and Al wires have shown that the yield stress Oy varies as shown in Fig. 21 with the reciprocal square root of the grain size. This relation between yield stress and grain size d, usually referred to as the Hall-Petch relationship, expresses the strengthening effect of the grain boundaries. 

Various strength properties of materials (especially metals) are related to the grain size effect. The well-known, empirical Hall-Petch (henceforth H-P) relation addresses the grain size effect of these properties [7], expressed as ... 

It is known from previously conducted studies [30, 31] and the effect of the Hall-Petch, the effective bulk modulus and effective shear modulus of nano-objects is not a linear function of their size. Generalized dependence of these quantities can be written in the form of expressions. 

N. Ono, R. Nowak, S. Miura, Effect of deformation temperature on Hall-Petch relationship registered for polycrystalline magnesium. Mater. Lett. 58(1-2), 39-43 (2004)... 

C.S. Pande, B.B. Rath, M.A. Imam, Effect of annealing twins on Hall-Petch relation in polycrystalline materials. Mater. Sci. Eng. A-Struct Mater. Prop. MicrostrucL Process. 367(1-2), 171-175 (2004)... 

Li] Li, X., Baker, L, The Effect of Boron on the Hall-Petch Behavior of Fe-45A1 , Scr. Mater, 34(8), 1219-1223 (1996) (Experimental Meehan. Prop., 47)... 

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