Curvature-dependent interfacial energy and its effects on the elastic properties of nanomaterials
Curvature-dependent interfacial energy and its effects on the elastic properties of nanomaterials
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DOI：
10.1016/j.ijsolstr.2017.01.021
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发表时间：
2017-05
影响因子：
3.6
通讯作者：
Xiang Gao;Zhuping Huang;D. Fang
中科院分区：
文献类型：
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作者：
Xiang Gao;Zhuping Huang;D. Fang
材料界面可以被看作是二维曲面，因为它们的厚度与它们的平面尺寸相比小得可以忽略。实验和材料模拟表明，界面的弹性能不仅与界面应变有关，而且与界面曲率有关。本文首先研究了界面能与曲率的关系，并给出了形式简单、物理意义明确的界面能公式。其次，建立了线性小变形界面应力模型。考虑了曲率对界面能的影响，提出采用基于拉格朗日方程的界面基本方程来研究界面问题，特别是残余界面应力的影响是方便和有利的。在此基础上，提出了一个同时考虑界面效应和颗粒尺寸分布的细观力学框架来预测纳米复合材料的整体弹性性能。最后，将所建立的界面模型和细观力学方法应用于纳米颗粒增强复合材料的有效模量研究。结果表明，曲率效应使有效模量具有更强的尺寸依赖性，当颗粒半径的离散度较大时，颗粒尺寸分布对有效模量的影响更为明显。
Material interfaces can be regarded as two dimensional curved surfaces since their thickness is negligibly small in comparison with their planar dimensions. Experiments and materials simulation have demonstrated that the elastic energy of interface depends not only on its strain but also on its curvature. In this paper, first, the curvature-dependence of interfacial energy is studied and an interfacial energy formula is formulated, which has simple form and clear physical meanings. Next, a linear small deformation interface stress model is developed. It considers the curvature effect on interfacial energy and suggests that it would be convenient and advantageous to employ the Lagrangian description-based fundamental equations of the interface to study interface problems, especially the effect of residual interface stress. Then, a micromechanics framework considering both the interface effect and particle size distribution is proposed to predict the overall elastic properties of nanocomposites. Finally, the developed interface model and micromechanics approach are applied to study the effective modulus of nanoparticle reinforced composites. The results show that the curvature effect causes a much stronger size dependence of the effective modulus and the influence of particle size distribution becomes obvious when the dispersion of the particle radius is large.