GUO Hui, GUO Xing-ming. Scale Effect and the Geometric Shapes of Grains[J]. Applied Mathematics and Mechanics, 2007, 28(2): 127-134.
Citation: GUO Hui, GUO Xing-ming. Scale Effect and the Geometric Shapes of Grains[J]. Applied Mathematics and Mechanics, 2007, 28(2): 127-134.

Scale Effect and the Geometric Shapes of Grains

  • Received Date: 2006-07-10
  • Rev Recd Date: 2006-12-07
  • Publish Date: 2007-02-15
  • The "rule-of-mixture" approach has become one of the widely spread ways to investigate the mechanical properties of nano-materials and nano-structures,and it is very important for the simulation results to exactly compute phase volume fractions.The nanocrystalline(NC) materials were treated as three-phase composites consisting of grain core phase,grain boundary (GB) phase and triple junction phase,and a two-dimensional three-phase mixture regular polygon model was established to investigate the scale effect of NC materials mechanical properties due to the geometrical polyhedron characteristics of crystal grain.For different multi-sides geometrical shapes of grains,the corresponding multi-sides regular polygon model was adopted to obtain more precise phase volume fractions and exactly predict the mechanical properties of NC materials.
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  • [1]
    Hall E O.The deformation and aging of mild steel:Ⅲ discussion of results[J].Proc Phys Soc B,1951,64(1):747-753. doi: 10.1088/0370-1301/64/9/303
    Petch N J. The cleavage strength of polycrystals[J].J Iron Steel Inst,1953,174(5):25-28.
    Gleiter H. Nanocrystalline materials[J].Prog Mater Sci,1989,33(4):223-315. doi: 10.1016/0079-6425(89)90001-7
    Nieman G W, Weertman J R, Siegel R W. Microhardness of nanocrystalline palladium and copper produced by inert-gas condensation[J].Scripta Metall,1989,23(13):2013-2018. doi: 10.1016/0036-9748(89)90223-8
    Palumbo G, Erb U, Aust K T. Triple line disclination effects on the mechanical behaviour of materials[J].Scripta Metall Mater,1990,24(12):2347-2350. doi: 10.1016/0956-716X(90)90091-T
    Lu K.Nanocrystalline metals crystallized from amorphous solids: nanocrystallization, structure, and properties[J].Mater Sci Eng R,1996,16:161-221. doi: 10.1016/0927-796X(95)00187-5
    Mallow T R, Koch C C. Grain growth in nanocrystalline iron prepared by mechanical attrition[J].Acta Mater,1997,45(5):2177-2186. doi: 10.1016/S1359-6454(96)00300-X
    Sanders P G, Eastman J A, Weertman J R. Elastic and tensile behavior of nanocrystalline copper and palladium[J].Acta Mater,1997,45(10):4019-4025. doi: 10.1016/S1359-6454(97)00092-X
    Masumura R A, Hazzledine P M, Pande C S. Yield stress of fine grained materials[J].Acta Mater,1998,46(13):4527-4534. doi: 10.1016/S1359-6454(98)00150-5
    Yamakov V, Wolf D, Phillpot S R,et al.Grain-boundary diffusion creep in nanocrystalline palladium by molecular-dynamics simulation[J].Acta Mater,2002,50(1):61-73. doi: 10.1016/S1359-6454(01)00329-9
    Seattergood R O, Koch C C. A modified model for hall-petch behavior in nanocrystalline materials[J].Scripta Mater,1992,27(9):1195-1200. doi: 10.1016/0956-716X(92)90598-9
    Hahn H, Padmanabhan K A. A model for the deformation of nanocrystalline materials[J].Philosophical Magazine B,1997,76(44):559-571. doi: 10.1080/01418639708241122
    Fedorov A A, Gutkin M Yu, Ovid'ko I A. Transformations of grain boundary dislocation pile-ups in nano- and polycrystalline materials[J].Acta Mater,2003,51(4):887-898. doi: 10.1016/S1359-6454(02)00433-0
    Fedorov A A, Gutkin M Yu,Ovid'ko I A. Triple junction diffusion and plastic flow in fine-grained materials[J].Scripta Mater,2002,47(1):51-55. doi: 10.1016/S1359-6462(02)00096-9
    Gutkin M Yu, Kolesnikova A L, Ovid'ko I A,et al.Disclinations and rotational deformation in fine-grained materials [J].Phil Mag Lett,2002,82(12):651-657. doi: 10.1080/0950083021000036742
    Ovid'ko I A.Materials science: deformation of nanostructures[J].Science,2002,295(2395):2386-2386. doi: 10.1126/science.1071064
    Gutkin M Yu, Ovid'ko I A. Yield stress of nanocrystalline materials: role of grain grainboundary dislocations, triple junctions and coble creep[J].Philosophical Magazine,2004,84(9):847-863. doi: 10.1080/14786430310001616063
    Kocks U F. Relation between polycrystal deformation and single-crystal deformation[J].Metal Trans,1970,1(55):1121-1143.
    Carsley J E, Ning J, Milligan W W,et al.A simple, mixtures-based model for the grain size dependence of strength in nanophase metals[J].Nanostruct Mater,1995,5(4):441-448. doi: 10.1016/0965-9773(95)00257-F
    Konstantinidis D A, Aifantis E C. On the “anomalous” hardness of nanocrystalline materials[J].Nanostruct Mater,1998,10(7):1111-1118. doi: 10.1016/S0965-9773(98)00145-7
    Benson David J,FU Hsueh-hung, Meyers Marc Andre′. On the effect of grain size on yield stress: extension into nanocrystalline domain[J].Mat Sci Eng A,2001,319/321:854-861. doi: 10.1016/S0921-5093(00)02029-3
    Song H W, Guo S R, Hu Z Q. A coherent polycrystal model for the inverse Hall-Petch relation in nanocrystalline materials[J].Nanostruct Mater,1999,11(2):203-210. doi: 10.1016/S0965-9773(99)00033-1
    XIANG Qing,GUO Xing-ming. The scale effect on the yield strength of nanocrystalline materials[J].Internat J Solids and Structures,2006,43(9):7793-7799. doi: 10.1016/j.ijsolstr.2006.04.015
    Wang N, Wang Z,Aust K T,et al.Effect of grain size on mechanical properties of nanocrystalline materials[J].Acta Metal Mater,1995,43(2):519-528. doi: 10.1016/0956-7151(94)00253-E
    Kim H S. A composite model for mechanical properties of nanocrystalline materials[J].Scripta Mater,1998,39(8):1057-1061. doi: 10.1016/S1359-6462(98)00257-7
    Kim H S, Bush M B.The effects of grain size and porosity on the elastic modulus of nanocrystalline materials[J].Nanostruct Mater,1999,11(3):361-367. doi: 10.1016/S0965-9773(99)00052-5
    Kim H S, Estrin Y,Bush M B. Plastic deformation behaviour of fine-grained materials[J].Acta Mater,2000,48(2):493-504. doi: 10.1016/S1359-6454(99)00353-5
    Kim H S, Estrin Y. Phase mixture modeling of the strain rate dependent mechanical behavior of nanostructured materials[J].Acta Mater,2005,53(3):765-772. doi: 10.1016/j.actamat.2004.10.028
    Gutkin M Yu, Ovid'ko I A, Pande C S. Theoretical models of plastic deformation process in nanocrystalline materials[J].Rev Adv Mater Sci,2001,2(1):80-102.
    Tjong S C, Chen Haydn. Nanocrystalline materials and coating[J].Math Sci Engrg R,2004,45(1):1-88. doi: 10.1016/j.mser.2004.07.001
    Zhou Y, Erb U, Aust K T,et al.The effects of triple junctions and grain boundaries on hardness and Young's modulus in nanostructured Ni-P[J].Scripta Mater,2003,48(6):825-830. doi: 10.1016/S1359-6462(02)00511-0
    Zhao M, Li J C,Jiang Q,et al.Hall-Petch relationship in nanometer size range[J].J Alloy Compd,2003,361(1/2):160-164. doi: 10.1016/S0925-8388(03)00415-8
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