1999
DOI: 10.1016/s0965-9773(99)00033-1
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A coherent polycrystal model for the inverse Hall-Petch relation in nanocrystalline materials

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Cited by 107 publications
(67 citation statements)
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“…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).…”
Section: Resultssupporting
confidence: 68%
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“…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).…”
Section: Resultssupporting
confidence: 68%
“…[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.…”
Section: Introductionmentioning
confidence: 99%
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“…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.…”
Section: Implications Of Deformation Twinning Within Materials Sciencementioning
confidence: 99%
“…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 …”
Section: Resultsmentioning
confidence: 99%