Effects of Residual Interface Stress on Effective Thermal Expansion Coefficient of Particle-Filled Composite
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摘要: 根据黄筑平等人提出的基于“3个构形”的表/界面能理论,研究了热弹性纳米复合材料的有效性质,重点讨论了残余界面应力对纳米尺度夹杂填充的热弹性复合材料有效热膨胀系数的影响.首先,给出了由第一类Piola-Kirchhoff界面应力表示的热弹性界面本构关系和Lagrange描述下的Young-Laplace方程;其次,采用Hashin复合球作为代表性体积单元,推导了在参考构形下复合球内部由残余界面应力诱导的残余弹性场,并进一步计算了从参考构形到当前构形的变形场;最后,基于以上计算得到了热弹性复合材料有效体积模量和有效热膨胀系数的解析表达式.研究表明,残余表/界面应力对复合材料的热膨胀系数有重要影响.Abstract: The "three configurations" based surface/interface energy theory proposed by Huang et al was used to study the effective properties of thermal elastic nanocomposites.Particular emphasis was placed on the discussions of the influence of the residual interface stress on the thermal expansion coefficient of the said composites.First,the thermo-elastic interface constitutive relations expressed in terms of the first kind Piola-Kirchhoff interface stress and the Lagrangian description of the generalized Young-Laplace equation were presented.Second,the Hashin's composite sphere assemblage(CSA)was taken as the representative volume element(RVE),and the elastic deformations from the stress-free configuration to the reference configuration and from the reference configuration to the current configuration were calculated.Based on the above calculations,an analytical expression of the effective thermal expansion coefficient of thermo-elastic composite was derived.It is shown that the "residual" interface stress has a significant effect on the thermal expansion properties of the thermo-elastic nanocomposites.
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Key words:
- nanocomposites /
- effective thermal expansion /
- residual interface stress /
- size-dependent /
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[1] Mura T. Micromechanics of Defects in Solids[M]. Dordrecht: Martinus Nijhoff, 1987. [2] Nemat-Nasser S, Hori M. Micromechanics: Overall Properties of Heterogeneous Materials[M]. Amsterdam: Elsevier, 1993. [3] Milton G W. The Theory of Composites[M]. Cambridge: Cambridge University Press, 2002. [4] Torquato S. Random Heterogeneous Materials: Microstructure and Macroscopic Properties[M]. New York: Springer, 2002. [5] Buryachenko V A. Multiparticle effective field and related methods in micromechanics of composite materials[J]. Appl Mech Review, 2001, 54(1): 1-47. doi: 10.1115/1.3097287 [6] 胡更开, 郑泉水, 黄筑平. 复合材料有效弹性性质分析方法[J]. 力学进展, 2001, 31(3):361-393.(HU Geng-kai, ZHENG Quan-shui, HUANG Zhu-ping. Micromechanics methods for effective elastic properties of composite materials[J]. Advances in Mechanics, 2001, 31(3):361-393.(in Chinese)) [7] Levin V M. Thermal expansion coefficients of heterogeneous materials[J]. Mekhanika Tverdogo Tela,1967,2(1):88-94. [8] Ibach H. The role of surface stress in reconstruction, epitaxial growth and stabilization of mesoscopic structures[J]. Surface Sci Rep, 1997, 29(5/6): 193-263. [9] Steigmann D J, Ogden R W. Elastic surface-substrate interactions[J].Pro R Soc Lond A, 1999, 455(1982): 437-474. doi: 10.1098/rspa.1999.0320 [10] Haiss W. Surface stress of clean and adsorbate-covered solids[J]. Rep Prog Phys, 2001, 64(5):591-648. doi: 10.1088/0034-4885/64/5/201 [11] Müller P, Saúl A. Elastic effects on surface physics[J]. Surf Sci Rep, 2004, 54(5/8):157-258. doi: 10.1016/j.surfrep.2004.05.001 [12] Fried E, Gurtin M E. A unified treatment of evolving interfaces accounting for small deformations and atomic transport with emphasis on grain-boundaries and epitaxy[J]. Adv Appl Mech, 2004, 40:1-177. doi: 10.1016/S0065-2156(04)40001-5 [13] Murdoch A I. Some fundamental aspects of surface modeling[J]. J Elasticity, 2005, 80(1/3):33-52. doi: 10.1007/s10659-005-9024-2 [14] DUAN Hui-ling, WANG Jian-xiang, HUANG Zhu-ping, Karihaloo B L. Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress[J]. J Mech Phys Solids, 2005, 53(7):1574-1596. doi: 10.1016/j.jmps.2005.02.009 [15] Sharma P, Wheeler L T. Size-dependent elastic state of ellipsoidal nano-inclusions incorporating surface/interface tension[J]. J Appl Mech, 2007, 74(3): 447-454. doi: 10.1115/1.2338052 [16] Chen T Y, Dvorak G J, Yu C C. Solids containing spherical nano-inclusions with interface stresses: effective properties and thermal mechanical connections[J]. Int J Solids Struct, 2007, 44(3/4): 941-955. doi: 10.1016/j.ijsolstr.2006.05.030 [17] DUAN Hui-ling, Karihaloo B L. Thermo-elastic properties of heterogeneous materials with imperfect interfaces: generalized Levin’s formula and Hill’s connections [J]. J Mech Phys Solids, 2007, 55(5):1036-1052. doi: 10.1016/j.jmps.2006.10.006 [18] SUN Li, WU Yi-ming, HUANG Zhu-ping, WANG Jian-xiang. Interface effect on the effective bulk modulus of a particle-reinforced composite[J]. Acta Mech Sinica, 2004, 20(6): 676-679. doi: 10.1007/BF02485873 [19] HUANG Zhu-ping, WANG Jian-xiang. A theory of hyperelasticity of multi-phase media with surface/interface energy effect[J]. Acta Mech, 2006, 182(3/4):195-210. doi: 10.1007/s00707-005-0286-3 [20] HUANG Zhu-ping, SUN Li. Size-dependent effective properties of a heterogeneous material with interface energy effect: from finite deformation theory to infinitesimal strain analysis[J]. Acta Mech, 2007, 190(1/4):151-163. doi: 10.1007/s00707-006-0381-0 [21] HUANG Zhu-ping, WANG Zhi-qiao, ZHAO Ya-pu, WANG Jian-xiang. Influence of particle-size distribution on effective properties of nanocomposites[C]Advances in Heterogeneous Materials Mechanics (ICHMM-2008), Pennsylvania: Destech Publications, 2008: 925-932. [22] HUANG Zhu-ping. Erratum to: size-dependent effective properties of a heterogeneous material with interface energy effect: from finite deformation theory to infinitesimal strain analysis[J]. Acta Mech, 2010, 215(1/4):363-364. doi: 10.1007/s00707-010-0385-7 [23] HUANG Zhu-ping, WANG Jian-xiang. Erratum to: a theory of hyperelasticity of multi-phase media with surface/interface energy effect [J]. Acta Mech, 2010, 215(1/4): 365-366. doi: 10.1007/s00707-010-0384-8 [24] CHEN Huan, HU Geng-kai, HUANG Zhu-ping. Effective moduli for micropolar composite with interface effect[J]. Int J Solids Struct, 2007, 44(25/26): 8106-8118. doi: 10.1016/j.ijsolstr.2007.06.001 [25] WANG Zhi-qiao, ZHAO Ya-pu, HUANG Zhu-ping. The effects of surface tension on the elastic properties of nano structures[J]. Int J Eng Sci, 2010, 48(2): 140-150. doi: 10.1016/j.ijengsci.2009.07.007 [26] Park H S, Klein P A. Surface stress effects on the resonant properties of metal nanowires: the importance of finite deformation kinematics and the impact of the residual surface stress[J]. J Mech Phys Solids, 2008, 56(11): 3144-3166. doi: 10.1016/j.jmps.2008.08.003 [27] Park H S, Klein P A. Boundary condition and surface stress effects on the resonant properties of metal nanowires[C]Advances in Heterogeneous Materials Mechanics(ICHMM-2008), Pennsylvania: Destech Publications, 2008: 89-96. [28] 黄筑平. 连续介质力学基础[M]. 北京: 高等教育出版社, 2003. (HUANG Zhu-ping. Fundamentals of Continuum Mechanics[M]. Beijing: Higher Education Press, 2003.(in Chinese)) [29] Lu H M, Jiang Q. Surface tension and its temperature coefficient for liquid metals[J]. J Phys Chem B, 2005, 109(32):15463-15468. doi: 10.1021/jp0516341 [30] Zhao M, Zheng W T, Li J C, Wen Z, Gu M X, Sun C Q. Atomistic origin, temperature dependence, and responsibilities of surface energetics: an extended broken-bond rule[J]. Phys Rev B, 2007,75(8):085427. doi: 10.1103/PhysRevB.75.085427 [31] Mark J E. Polymer Data Handbook[M]. 2nd ed. New York: Oxford University Press, 2009. [32] 吴人洁. 高聚物的表面与界面[M]. 北京:科学出版社,1998. (WU Ren-jie. The Surface and Interface of Polymer[M]. Beijing: Science Press, 1998. (in Chinese))
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