Volume 43 Issue 8
Aug.  2022
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CUI Chunli, XU Yaoling. The Interface Model and the Interphase Model for Predicting the Effective Elastic Properties of Nano-Fiber Composites[J]. Applied Mathematics and Mechanics, 2022, 43(8): 877-887. doi: 10.21656/1000-0887.420231
Citation: CUI Chunli, XU Yaoling. The Interface Model and the Interphase Model for Predicting the Effective Elastic Properties of Nano-Fiber Composites[J]. Applied Mathematics and Mechanics, 2022, 43(8): 877-887. doi: 10.21656/1000-0887.420231

The Interface Model and the Interphase Model for Predicting the Effective Elastic Properties of Nano-Fiber Composites

doi: 10.21656/1000-0887.420231
  • Received Date: 2021-08-05
  • Rev Recd Date: 2021-11-24
  • Available Online: 2022-07-01
  • Publish Date: 2022-08-01
  • The effective bulk modulus and the effective in-plane shear modulus of nano-fiber composites were investigated with the interface model and the interphase model based on the generalized self-consistent method, and the closed-form analytical solutions of the effective bulk modulus and all equations for numerically predicting effective in-plane shear modulus based on the 2 models, were presented. With the interface model, interface effects of the effective bulk modulus and the effective in-plane shear modulus were discussed through numerical examples. Furthermore, the solutions of the interface model were proved to be degenerated ones of those of the interphase model, where the effective bulk modulus can be obtained through analytical degeneration and the numerical results of the effective in-plane shear modulus through numerical degeneration. An example of aluminium containing nano voids shows that, the effective bulk modulus and the effective in-plane shear modulus predicted with the interface model have large deviations from those with the interphase model for small void radii, however, small deviations for larger void radii.

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  • [1]
    刘旭, 姚林泉. 热环境中旋转功能梯度纳米环板的振动分析[J]. 应用数学和力学, 2020, 41(11): 1224-1236

    LIU Xu, YAO Linquan. Vibration analysis of rotating functionally gradient nano annular plates in thermal environment[J]. Applied Mathematics and Mechanics, 2020, 41(11): 1224-1236.(in Chinese)
    [2]
    SHUKLA P, SAXENA P. Polymer nanocomposites in sensor applications: a review on present trends and future scope[J]. Chinese Journal of Polymer Science, 2021, 39(6): 665-691. doi: 10.1007/s10118-021-2553-8
    [3]
    CAMMARATA R C. Surface and interface stress effects on interfacial and nanostructured materials[J]. Materials Science and Engineering: A, 1997, 237(2): 180-184. doi: 10.1016/S0921-5093(97)00128-7
    [4]
    周强, 张志纯, 龙志林, 等. 考虑表面效应的压电纳米梁的振动研究[J]. 应用数学和力学, 2020, 41(8): 853-865

    ZHOU Qiang, ZHANG Zhichun, LONG Zhilin, et al. Vibration of piezoelectric nanobeams with surface effects[J]. Applied Mathematics and Mechanics, 2020, 41(8): 853-865.(in Chinese)
    [5]
    GURTIN M E, MURDOCH A I. A continuum theory of elastic material surfaces[J]. Archive for Rational Mechanics and Analysis, 1975, 57(4): 291-323. doi: 10.1007/BF00261375
    [6]
    GURTIN M E, MURDOCH A I. Surface stress in solids[J]. International Journal of Solids and Structures, 1978, 14(6): 431-440. doi: 10.1016/0020-7683(78)90008-2
    [7]
    ODEGARD G M, CLANCY T C, GATES T S. Modeling of the mechanical properties of nanoparticle/polymer composites[J]. Polymer, 2005, 46(2): 553-562. doi: 10.1016/j.polymer.2004.11.022
    [8]
    PALIWAL B, CHERKAOUI M. Estimation of anisotropic elastic properties of nanocomposites using atomistic-continuum interphase model[J]. International Journal of Solids and Structures, 2012, 49(18): 2424-2438. doi: 10.1016/j.ijsolstr.2012.05.004
    [9]
    LUO J, WANG X. On the anti-plane shear of an elliptic nano inhomogeneity[J]. European Journal of Mechanics A: Solids, 2009, 28(5): 926-934. doi: 10.1016/j.euromechsol.2009.04.001
    [10]
    TIAN L, RAJAPAKSE R K N D. Analytical solution for size-dependent elastic field of a nanoscale circular inhomogeneity[J]. Journal of Applied Mechanics, 2007, 74(3): 568-574. doi: 10.1115/1.2424242
    [11]
    TIAN L, RAJAPAKSE R K N D. Elastic field of an isotropic matrix with a nanoscale elliptical inhomogeneity[J]. International Journal of Solids and Structures, 2007, 44(24): 7988-8005. doi: 10.1016/j.ijsolstr.2007.05.019
    [12]
    DONG C Y, PAN E. Boundary element analysis of nano-inhomogeneities of arbitrary shapes with surface and interface effects[J]. Engineering Analysis With Boundary Elements, 2011, 35(8): 996-1002. doi: 10.1016/j.enganabound.2011.03.004
    [13]
    MOGILEVSKAYA S G, CROUCH S L, STOLARSKI H K. Multiple interacting circular nano-inhomogeneities with surface/interface effects[J]. Journal of the Mechanics and Physics of Solids, 2008, 56(6): 2298-2327. doi: 10.1016/j.jmps.2008.01.001
    [14]
    DUAN H L, WANG J, HUANG Z P. Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress[J]. Journal of the Mechanics and Physics of Solids, 2005, 53(7): 1574-1596. doi: 10.1016/j.jmps.2005.02.009
    [15]
    CHEN T Y, DVORAK G J, YU C C. Solids containing spherical nano-inclusions with interface stresses: effective properties an thermal-mechanical connections[J]. International Journal of Solids and Structures, 2007, 44(3/4): 941-955.
    [16]
    肖俊华, 徐耀玲, 王美芬, 等. 考虑界面应力时纳米涂层纤维增强复合材料的有效力学性能[J]. 固体力学学报, 2013, 34(4): 374-379 doi: 10.3969/j.issn.0254-7805.2013.04.007

    XIAO Junhua, XU Yaoling, WANG Meifen, et al. Effective mechanical property of nano coated fiber reinforced composites due to interface stress[J]. Chinese Journal of Solid Mechanics, 2013, 34(4): 374-379.(in Chinese) doi: 10.3969/j.issn.0254-7805.2013.04.007
    [17]
    LI Y, WAAS A M, ARRUDA A E. A closed-form, hierarchical, multi-interphase model for composites-derivation, verification and application to nanocomposites[J]. Journal of the Mechanics and Physics of Solids, 2011, 59(1): 43-63. doi: 10.1016/j.jmps.2010.09.015
    [18]
    PALIWAL B, CHERKAOUI M. Atomistic-continuum interphase model for effective properties of composite materials containing nano-inhomogeneities[J]. Philosophical Magazine, 2011, 91(30): 3905-3930. doi: 10.1080/14786435.2011.597361
    [19]
    WANG Z, OELKERS R J, LEE K C, et al. Annular coated inclusion model and applications for polymer nanocomposites, part Ⅰ: spherical inclusions[J]. Mechanics of Materials, 2016, 101: 170-184. doi: 10.1016/j.mechmat.2016.07.004
    [20]
    WANG Z, OELKERS R J, LEE K C, et al. Annular coated inclusion model and applications for polymer nanocomposites, part Ⅱ: cylindrical inclusions[J]. Mechanics of Materials, 2016, 101: 50-60. doi: 10.1016/j.mechmat.2016.07.005
    [21]
    BENVENISTE Y, MILOH T. Imperfect soft and stiff interfaces in two-dimensional elasticity[J]. Mechanics of Materials, 2001, 33(6): 309-323. doi: 10.1016/S0167-6636(01)00055-2
    [22]
    WANG J, DUAN H L, ZHANG Z. An anti-interpenetration model and connections between interphase and interface models in particle-reinforced composites[J]. International Journal of Mechanical Sciences, 2005, 47(4/5): 701-718.
    [23]
    MUSKHELISHIVILI N I. Some Basic Problem of the Mathematical Theory of Elasticity[M]. Leyden: Noordhoff International Publishing, 1977.
    [24]
    PARVANOVA S L, VASILEV G P, DINEVA P S, et al. Dynamic analysis of nano-heterogeneities in a finite-size solid by boundary and finite element methods[J]. International Journal of Solids and Structures, 2016, 80(1): 1-18.
    [25]
    WANG W F, ZENG X W, DING J P. Finite element modeling of two-dimensional nanoscale structures with surface effects[J]. World Academy of Science, Engineering and Technology, 2010, 48: 865-870.
    [26]
    TIAN L, RAJAPAKSE R K N D. Finite element modelling of nanoscale inhomogeneities in an elastic matrix[J]. Computational Materials Science, 2004, 41(1): 44-53.
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