Abstract
In this paper, the modified Young’s moduli in both directions are obtained for the two-dimensional single crystal body with a square lattice by using the continuum approach of continuum mechanics and taking into account only the interaction of neighboring atoms. Separately, an expression is obtained taking into account the linear defects such as vacancies. The values of effective Young’s moduli compared with the same values for an infinite crystal lattice. Analyses show that the influences of scale effects and vacancies on the Young’s moduli are considerable. In addition, it is shown that the effective Young’s moduli have three components: the macroscopic value; factors determining the scale effect; factors determining the vacancy. The last component is analogous to the parameter of the damage of the theory of fracture.
Similar content being viewed by others
References
Gleiter H (1989) Nanocrystalline materials. Prog Mater Sci 33:223–315
Podgaets AR, Sokolin UV (2004) Modern problems of nano-mechanics all-Russia scientific-technical conference “Aerospace and high technology”-2004, State University of Perm, Russia, p 106 (in Russian)
Krivtsov AM, Morozov NF (2002) On the mechanical characteristics of nano-scale objects. Phys Solid Body 44:2158–2163 (in Russian)
Ravindran P, Fast L, Korzhavyi PA, Johansson B, Wills J, Eriksson O (1998) Density functional theory for calculation of elastic properties of orthorhombic crystals: Application to TiSi2. Appl Phys 84:4891
Moon WH, Hwang HJ (2005) Theoretical study of defects of BN nanotubes: A molecular-mechanics study. Physica E 28:419–422
Wang T, Dai YB, Ouyang SK, Shen HS, Wang QK, Wu JS (2005) Investigation of vacancy in C54 TiSi2 using ab initio method. Mater Lett 59:885–888
Song YS, Youn JR (2006) Modeling of effective elastic properties for polymer based carbon nanotube composites. Polymer 47:1741–1748
Beckman SP, Chelikowsky JR (2007) The structure and properties of vacancies in Si nano-crystals calculated by real space pseudo potential methods Physica B 401–402:537–540
Karimzadeh F, Ziaei-rad S, Adibi S (2007) Modeling consideration and material properties evaluation in analysis of carbon nano-tube composite. Metall Mater Trans B 38:695–705
Zhou J, Li Y, Zhu R, Zhang Z (2007) The grain size and porosity dependent elastic moduli and yield strength of nanocrystalline ceramics. Mater Sci Eng A 445–446:717–724
Zhou J, Zhu R, Zhang Z (2008) A constitutive model for the mechanical behaviors of bcc and fcc nanocrystalline metals over a wide strain rate range. Mater Sci Eng A 480:419–427
Li PG, Lei M, Wang X, Tang WH (2009) Large-scale SnO2 nanowires synthesized by direct sublimation method and their enhanced dielectric responses. Mater Lett 63:357–359
Kadkhodapour J, Ziaei-Rad S, Karimzadeh F (2009) Finite-element modeling of rate dependent mechanical properties in nano-crystalline materials. Comput Mater Sci 45:1113–1124
Oh ES (2010) Elastic properties of boron-nitride nanotubes through the continuum lattice approach. Mater Lett 64:859–862
Wan H, Delale F (2010) A structural mechanics approach for predicting the mechanical properties of carbon nanotubes. Meccanica 45:43–51
Rabotnov, YN (1988) Mechanics of deformable solids. Nauka, Moscow, 712 p
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Alizada, A.N., Sofiyev, A.H. Modified Young’s moduli of nano-materials taking into account the scale effects and vacancies. Meccanica 46, 915–920 (2011). https://doi.org/10.1007/s11012-010-9349-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11012-010-9349-1