非椭球TiB2颗粒对复合材料有效性能的影响分析

Micromechanical Analysis of the Influence of Non-ellipsoidal TiB2 Particles on the Equivalent Elastic Property of the Composite Ceramics

摘要:

非椭球颗粒Eshelby张量不为常数，没有解析解，理论计算中通常将非椭球颗粒简化为椭球形进行分析。实际材料中颗粒并非都为规则的椭球形，因此这种简化的合理性是有待讨论的。本文通过数值方法计算了几种特殊的非椭球颗粒的Eshelby张量和平均Eshelby张量，与有限元结果对比验证了数值结果的准确性。在此基础上，根据相互作用直推估计法分析了非椭球颗粒形状对有效性能的影响，并分析了用椭球颗粒代替异形颗粒的可行性。结果显示，数值方法计算的Eshelby精度较高，将对称性较高的非椭球颗粒等效为椭球颗粒是可行的，片状TiB2颗粒对材料刚度影响更大，将其简化为近似的片状椭球进行计算也将带来更大的误差。

Abstract:

Eshelby tensor is not a constant parameter and there is no analytical expression for a non-ellipsoidal particle. To simplify the calculation, non-ellipsoidal particle usually was treated as ellipsoidal in most analysis, while the simplification is need to be verificated for particles in composite are not always ellipsoid actually. To study the error of the simplification, the Eshelby tensor and the average Eshelby tensor of several non-ellipsoidal particles were calculated numerically, and the numerical result is verified by comparing to the finite element method result. Base on the numerical result, the influence of the non-ellipsoidal to equivalent elastic property of the composite is analyzed, and the condition of the simplificating the non-ellipsoidal particle to ellipsoidal particle was obtained. The result indicated that using the numerical method in Eshelby tensor calculation is highly precise. It is acceptable to simplify the non-ellipsoidal particle to ellipsoidal particle when the non-ellipsoidal particle is highly symmetrical. The oblate particle has more important influence on the equivalent elastic property of the composite than other shapes, and hence it cause larger error for simplifying the non-ellipsoidal to ellipsoidal particle than other shapes.