Abstract
Interfaces that exist in composites greatly influence their mechanical and conductive properties. There are usually three interface models to characterize the elastic and conductive properties of the interface in composites. For elastic problems, they are the interface stress model (ISM), linear spring model (LSM), and interphase model. For conductive problems, they are the high conducting (HC) interface model, low conducting (LC) interface model, and interphase model. For elastic problems with the interface effects, they can be divided into two types. The first kind of elastic problem concerns the solution of boundary value problems and aims to predict the effective properties of composites with interface effects. The second kind of elastic problem concerns the surface/interface stress effects on the elastic properties of nanostructured materials, which is usually characterized by the ISM. In this paper, three aspects in the elastic problems with interface effects are first reviewed, i.e., equivalent relations among the three interface models, Eshelby formalism, and micromechanical frameworks. Special emphasis is placed on the ISM to show how classical models can be extended to the nano-scale by supplementing the interface elasticity to the basic equations of the classical elastic problems. Then, the conductive problems of the composites with the interface effects are also reviewed, and the general frameworks for predicting the effective conductivity of the composites are given. Finally, scaling laws depicting the size-dependent elastic and conductive properties of the composites are discussed.
摘要
复合材料中存在界面, 这些界面极大地影响了复合材料的力学和传导性能. 复合材料中界面的弹性与传导特性通常通过三 种界面模型进行表征. 对于弹性问题, 这三种界面模型分别是界面应力模型(interface stress model, ISM)、线性弹簧模型(linear spring model, LSM)和界面相模型. 对于传导问题, 这三种界面模型分别是高传导(high conducting, HC)界面模型、低传导(low conducting, LC)界面模型和界面相模型. 具有界面效应的弹性问题又可以分为两类. 第一类弹性问题涉及边值问题的求解, 旨在预测具有界面效应 的复合材料等效性能; 第二种弹性问题涉及表面/界面应力对纳米结构材料弹性性能的影响, 通常以界面应力模型进行表征. 本文首先 回顾了具有界面效应的弹性问题的三个方面, 即三种界面模型之间的等价关系, Eshelby体系和细观力学框架. 本文着重以界面应力模 型为例, 展示了如何通过将界面弹性补充到经典弹性问题的基本方程中, 将经典理论框架扩展到纳米尺度. 然后, 还回顾了具有界面效 应的复合材料的传导问题, 并给出了预测复合材料等效传导性能的一般框架. 论文的最后还讨论了用于描述复合材料与尺寸相关的弹 性和传导性能的标度律.
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This work was supported by the National Natural Science Foundation of China (Grant Nos. 11988102, 11872004, and 91848201).
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Duan, H., Wang, J. & Huang, Z. Micromechanics of composites with interface effects. Acta Mech. Sin. 38, 222025 (2022). https://doi.org/10.1007/s10409-022-22025-x
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DOI: https://doi.org/10.1007/s10409-022-22025-x