残余界面应力对粒子填充热弹性纳米复合材料有效热膨胀系数的影响

Effects of Residual Interface Stress on Effective Thermal Expansion Coefficient of Particle-Filled Composite

根据黄筑平等人提出的基于"三个构形"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.

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.