Statistical Characters Of Effective Properties Of Random Composite Materials

Properties of Composite material depend on its microstructures. For example, the mechanical properties of particle reinforced composites mainly depend on the representative parameters of microstructures: the modulus of particles and matrix, bond strength, and the volume contents and distribution of particles etc. However, uncertainties of microstructure induce uncertainties of effective properties. Therefore statistical analysis of elastic performance distribution of composite material is necessary. On the other hand, microstructure mechanical methods, such as homogenization and self-consistent method, which are all based on the assumption that microstructure size is negligible, are generally used to determine macro average properties of composites. While on which level of the relative small size can we get the forecast accuracy of material properties though homogenization method is a problem that worth studying. At present, the effect of the randomness of composites micro parameters to its macro average properties statistic character, and that of microstructure size to material properties have seldom been studied.Homogenization method which is base on FE technology is used of to research the effect on elastic constant of macrostructure due to uncertainties of microstructure characters and analyze their distributing rule with mathematical statistics methods. In addition, the study of the scale effect of the material microstructure is carried out, the effect of microstructure scale relative representative volume element (RVE) scale to determined material effective properties is analyzed, and the least relative scale which describes material effective properties accurately and represents the relative microstructure scale of volume elements is the objective of the work. The concrete work is as follows:1. Base on correlated references, the state of the study of composite material performance forecast was summarized and remarked, microstructure mechanical method of composite materials was mainly introduced, the fundamental idea and implement process of homogenization by which forecast effective properties of composite materials and the theory and method of statistic and analysis with which analysis statistical characters of uncertain problems were introduced in detail.2. Studied microstructure model of particle reinforced composite material, shown establishing process of microstructure model with uncertainties considering particle shape, size and distribution. Took rounded and oval-shaped particle reinforced composite materials as examples, Established random distributing models in which volume contentwas given and particle position distributed uniformly in the reference domain and created finite element discrete models.3. With homogenization method, studied the effect of uncertainties of micro structure parameters (such as size, shape and distribution style.) of rounded and oval-shaped particle reinforced composite to equivalent elastic constant, studied statistical characters of composites equivalent properties.4. The scale effect of microstructure is discussed in this research. The effect of the ratio of RVE scale to microstructure scale to certain material effective properties is analyzed with numerical results. And the least relative scale of REV which describes material properties correctly is found out.This research is supported by National Nature Science Foundation of China (No. 10332010), the Innovative Research Team Program (10421202), National Basic Research Program (No. 2006CB601205), and by the Program for New Century Excellent Talents in University of China.