Stereological Modeling and Micromechanical Analysis of Fiber-Reinforced and Rubber-Modified Epoxy Composite Materials

树脂基复合材料的第一个断裂，例如碳纤维增强的环氧树脂，据说发生在纤维中。也就是说，这种复合材料中可能存在纤维端部裂纹。纤维断裂后，复合材料的韧性可能取决于基体的韧性。分散在材料中的橡胶粒子的裂纹桥联现象可以显着增韧某些脆性环氧树脂。将基于统计几何的体视学概念引入混杂复合材料的微观结构建模中，并考虑了橡胶颗粒与基体之间的界面现象，用广义等效夹杂法对纤维增强橡胶改性环氧混杂复合材料进行了细观力学分析。通过对细观力学模型的分析，可以计算出阻止扩展的基体裂纹的临界长度a_c，这意味着这种复合材料的断裂韧性。橡胶颗粒的体积分数和纤维的体积分数对韧性的影响可以评估。混杂复合材料的韧性随着颗粒体积分数和纤维体积分数的增加而增加。这些结果与常见的实验结果是一致的。

First fracture of the resin-based composite materials, such as carbon fiber-reinforced epoxies, is said to occur in fibers. Namely, the fiber-end cracks may exist in such composites. After the fiber fracture, the toughness of the composites may depend upon that of the matrix. Some brittle epoxies can be toughened significantly by the crack bridging phenomena of the rubber particles dispersed in the material. By using this effects, the tougher hybrid composites that the rubber particles are also dispersed in the matrix in addition to the fibers is examined experimentally.In the present research, by introducing the stereological concept based upon the statistical geometry to the microstructural modeling of the hybrid composites and considering the interfacia1 phenomena between a matrix and a rubber particle, the micromechanical analysis by means of the generalized equivalent inclusion method is made of the fiber-reinforced and rubber-modified epoxy hybrid composite having the crack bridging particles whose radii are various in size. By analyzing the micromechanical mode1, the critical length a_c of the matrix crack whose propagation will be arrested, that implies the fracture toughness of such a composite, can be calculated. The effects of the volume fraction of rubber particles and that of fibers on the toughness can be evaluated. The toughness of the hybrid composites increase in the increase of both the volume fraction of particles and that of fibers. These results are consistent with the common experimental findings.