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基于蒙特卡罗法,编写了随机分布颗粒增强复合材料的二维代表体积单元生成程序,建立了纳米颗粒增强树脂基复合材料的有限元模型,其中采用双线性内聚力模型描述复合材料弱界面的应力与位移关系。通过纳米TiO2颗粒增强环氧树脂基复合材料应力应变行为模拟结果与文献结果对比,证明了模型的有效性。讨论了弱界面情况下,TiO2颗粒质量分数与颗粒尺寸对复合材料宏观有效模量的影响,并对复合材料弱界面渐进损伤过程进行了非线性分析。结果表明:随着纳米TiO2颗粒质量分数增加,复合材料杨氏模量和断裂延伸率均有所增强,但材料屈服强度有所降低;相同颗粒质量分数情况下,随着颗粒尺寸的增大,颗粒与基体材料之间界面单元总长度减小,复合材料断裂延伸率有所下降。
Based on the Monte Carlo method, a two-dimensional representative volume element generating program of randomly distributed particle-reinforced composites was prepared and a finite element model of nano-particle reinforced resin matrix composites was established. The bilinear cohesion model was used to describe the weak interface Relationship between stress and displacement. The simulation results of the stress-strain behavior of epoxy resin-based composites reinforced by nano-TiO2 particles are compared with those of the literature. The results show that the model is effective. The effects of the mass fraction of TiO2 particles and the particle size on the macroscopic effective modulus of the composites under weak interface were discussed. The progressive damage process of the weak interface of the composites was analyzed nonlinearly. The results show that the Young’s modulus and elongation at break of the composites increase with the increase of the mass fraction of nano-TiO2, but the yield strength of the composites decreases. With the increase of particle size, The total length of the interfacial unit between the particles and the matrix material decreases, and the elongation at break of the composite material decreases.