A coherent polycrystal model for the inverse Hall-Petch relation in nanocrystalline materials

Triple junction diffusion and plastic flow in fine-grained materials

“…The dependences rðd À1=2 Þ taking into account respectively the only grain boundary diffusional creep (dashed curve) and both the grain boundary and triple junction Fig. 1) at small values of grain size d. Similar deviations are inherent to dependence observed experimentally [4][5][6]15,[36][37][38][39]) for mechanical characteristics (yield stress, microhardness) of real fine-grained copper materials (see Fig. 1).…”

“…[1][2][3][4][5][6]. Of the special interest for numerous applications are the outstanding mechanical properties (high strength, good fatigue resistance, ductility) of nanocrystalline materials, which are essentially different from those of conventional coarse-grained polycrystals (for a review, see [4][5][6]). One of the specific features of deformation processes in nanocrystalline materials manifests itself in deviations from the known grain size scaling relations.…”

“…The three types of behavior have been experimentally documented for nanocrystalline materials: a constant positive Hall-Petch gradient as with coarse-grained polycrystals, a decreasing positive gradient at some critical grain size and a Scripta Materialia 47 (2002) 51-55 www.actamat-journals.com negative gradient below some critical grain size [4][5][6]. At present, the nature of the deviations from the conventional Hall-Petch grain size scaling relation in nanocrystalline materials is the subject of controversy; see e.g., [6,[9][10][11][12][13][14][15][16][17][18][19][20][21]. The generic idea of the most models of the abnormal Hall-Petch relationship is that the grain boundary phase provides the effective action of deformation mechanism(s) in nanocrystalline materials, which is (are) different from the conventional lattice dislocation slip realized in coarse-grained polycrystals.…”

Deformation twinning in nanocrystalline materials

“…For example, the strength of nc materials have been observed to deviate from the Hall-Petch relationship, and even exhibit an inverse Hall-Petch relationship in some cases. Numerous analytical models and computational simulations have been carried out to describe and investigate this phenomenon [336][337][338][339][340][341][342][343][344][345][346][347][348][349][350][351][352][353][354][355]. The analytical Hall-Petch models are based on various assumptions and all of them can qualitatively describe the inverse grain size effect on strength.…”

Local atomic arrangement in mechanosynthesized Co x Fe1−x−y Ni y alloys studied by Mössbauer spectroscopy

“…These are the most finegrained samples with the average grain size, D, of 15 and 10 nm, respectively. Using the coherent polycrystal model [31] and assuming that the average grain boundary thickness is about 1 nm [30], it can be estimated that for the samples mentioned above, about 20-30 % of atoms is Fig. 1 …”