求解具有弱界面的复合材料有效性能的近似模型与边界元法  

Application of approximation model and boundary element method in solving effective properties of composites with imperfect interface

作　　者：陈龙[1] 朱兴一[2] 

机构地区：[1]浙江大学建筑设计研究院,杭州310012 [2]上海大学上海市应用数学和力学研究所,上海200072

出　　处：《复合材料学报》2013年第2期137-143,共7页Acta Materiae Compositae Sinica

基　　金：国家自然科学基金(11102104)

摘　　要：基于中间层模型,建立了用于描述具有弱界面的多夹杂复合材料的三层嵌入式模型。首先,给出了计算多夹杂复合材料有效性能的公式,随后将三层嵌入式模型分成两种体系得到了相应的细观力学近似方法。此外,针对中间层模型进一步给出了快速多极边界元的基本列式。最后,通过算例验证所提出的两种方法的正确性及有效性,并进一步考察了界面性能对复合材料整体宏观性能的影响。比较结果发现,细观力学近似模型形式简单,易于编程计算,适用于快速预测具有弱界面的复合材料有效弹性性能。而数值算法能够快速有效直观的考察复合材料内部受弱界面影响后的应力分布。算例分析结果表明,当中间层厚度较大而弹性模量较低时,会使得夹杂不再具有增强效果。并且,随着中间层厚度的增加,基体内承担的最大应力也随之增加,从而容易导致复合材料在界面处产生破坏。Based on the interphase model,the three-layer built-in model was established to describe the multi-inclusion composites with imperfect interface.Firstly,the formulations for predicting effective elastic properties of multi-inclusion composites were presented.Then,by separating the three-layer built-in model into two solving systems,the micromechanical approximation model was obtained.Secondly,the basic formulations of fast multipole boundary element method were developed according to the interphase model.Finally,these two methods were compared with each other to verify the correctness and effectiveness,and the effect of imperfect interface on the macromechanical behavior of composites was further investigated.It has been shown that the micromechanical approximation method is quite easy to perform and suitable to fast predict the effective elastic properties of composites with imperfect interface,while the numerical algorithm is able to fast and directly observe the stress distribution in the composites under the influence of the interface imperfection.Based on the analysis,it can be also observed that a stiff inclusion surrounded by a weak interphase（with thicker thickness and lower elastic modulus） behaves as a soft inclusion,and the matrix will take on more stress with the increase of the thickness of interphase,which will easily result in the failure occurred at the interphase.

关 键 词：复合材料 弱界面 细观力学 快速多极边界元 有效弹性性能 

分 类 号：TB330.1[一般工业技术—材料科学与工程]