Numerical modeling of braided composites using energy method

Based on the braiding process and force analysis of yarn, a mesoscopic numerical modeling approach was established, which divided the modeling process as follows: establishing the control points according to the braiding process, establishing the fixed points during jamming, adjusting the control points after jamming, changing the position of fiber bundle due to the fiber bundle intertwined each other and establishing the fiber bundle trajectory according to the minimum strain energy. In the process of adjusting the intertwined fiber bundle trajectories, the fiber bundle trajectory was scattered. Using extrapolation adjustment method, discrete points of fiber bundle trajectory intertwined were adjusted in turn from the control points to the fixed points. Adjusted discrete points were equivalent at the corresponding location points of the corresponding trajectory, and at the same time, there was noninterference between the fiber bundle trajectories. Using this method, fiber bundle trajectory and cross section of the models of 2-D woven and 3-D four-directional braided composite materials were established, compared with the experiment result, which were consistent with the electronic microscope scan images and calculated woven structure size was in agreement with the measured data. The maximum relative calculation error of braiding bitch of 3-D four-directional braided structure was about 5%, especially braiding angle was 21°or so, the relative calculation error was below 2%. The maximum relative calculation error of surface braiding angle of 3-D four-directional braided structure was about 4%, especially braiding angle was 21°or so, the relative calculation error was below 2.4%. This modeling approach was fundamental for further analysis of the micromechanical strength and life of braided composites, which was applied to aero-engine hot section.