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Homogenization-based Method for Simulating Macro and Micro Mechanical Properties of 3D Braided Composites

Author: DongJiWei
Tutor: SunLiangXin
School: Nanjing University of Aeronautics and Astronautics
Course: Mechanical Design and Theory
Keywords: 3D braided composite unit cell homogenization theory effective modulus micro-stress failure pattern strength criterion
Type: PhD thesis
Year: 2007
Downloads: 786
Quote: 8
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In this thesis, the spatial location of yarns was analyzed first according to the 3D braided technique—four-step procedure and then proper curves were used to simulate the routes of yarns so that macrostructure of the fabric was precisely formed. By using a proper method to divide the fabric into unit cells, the completed macrostructure was divided and three kinds of micro unit cell—body cell、face cell and corner cell were simulated precisely. By analyzing the microstructure, some important laws about the microstructure of 3D 4 directional braided composites were found and some general geometric and technical parameters were easily calculated.In order to analyze the stiffness of 3D 4 directional braided composites, the homogenization theory based on the multi-scale perturbation theory was used as the basic theory. The virtual displacement principle was used to educe the homogenization formulation of effective elastic modulus and the schemes to solve the problem using finite element method. The effective elastic modulus of 3D braided composites were predicted by this method and the calculation results agree quite well with experiment results. At the same time, the influences of some technical parameters such as braid angle and fiber volume fraction on effective modulus were discussed in detail, and lots of valuable conclusions are obtained.Then micro-stress of 3D braided composites under the loading of uniaxial tension and three point bending was simulated by the method of the homogenization theory combined with finite element analysis. At the beginning of micro-stress simulation, the problem of periodic boundary conditions which were applied for three kinds of unit cells was discussed in detail first, then the section analysis method was used to simulate the fluctuate of micro-stress on a random section within a certain unit cell. Some simulation results show that braid angle has a great influence on the distribution status of micro-stress. Conclusions obtained by micro-stress analysis agree quite well with experiment conclusions.In order to study tensile strength of 3D braided composites from microcosmic angle, nonlinear damage under many tensile load steps was analyzed, proper criteria of strength were used to judge damage condition and damage pattern of each element in unit cells, and then stiffness degradation method was used to deal with damaged elements. The results of damage analysis indicate that composites with different braid angle have different micro failure pattern. According to this conclusion, an important parameter which reflect the transform of failure mechanism of 3D braided composites—critical braid angle was defined and then different tensile criterion was established for small angle braided composites and large angle braided composites. These criteria were used to predict the tensile strength of 3D braided composites. The calculated results of the strength agree quite well with the experimental results.Moreover, in this thesis, a relatively completed software for analyzing the mechanical properties of 3D 4 directional braided composites was designed. This software provides a user interactive interface so that the research、design and development on the kind of new material can be easily realized.In a word, in this thesis, a popular method—homogenization theory which was often applied in composites with periodic structure was effectively used to solve the problem of stress and strength from microcosmic angle of 3D braided composites. The research achievements of micro-stress simulation、micro failure pattern analysis and micro strength criteria establishment are all not mentioned in previous research work of others so that the blank field in micro strength analysis of 3D braided composites has been effectively made up.

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