中文摘要：

复合材料失效大多数情况都起始于微观水平的破坏，比如微裂纹的萌生、扩展，直到最后的失稳断裂，而微裂纹的扩展只受附近几个晶粒影响，所以不仅要考虑这几个晶粒的取向，还要考虑边界形貌，所谓考虑边界形貌就是要引进3个位置变量．对于位置一取向空间的引出和分析搭建一个数学模型并提供解决问题的思路，基于Voronio增量算法，利用C语言编程获得复合材料微观组织几何数据信患，通过OpenGL进行可视化，模拟结果再现复合材料的真实结构，为采用数值化技术对多晶体集合进行定量分析创造条件．

英文摘要：

In most cases, composite failure begin at the moment of material damage at microscopic levels such as initiation, propagation of micro-cracks, and final its unstable fracture. Micro-crack growth was af- fected by its several vicinal grains only, so their orientation as well as the boundary morphology should be taken into consideration. The so called consideration of boundary morphology means to introduce three po- sition variables. A mathematical model was set up for derivation and analysis of position orientation space, and a way of problem solving was provided thereby. Based on Voronio increment algorithm, the geometric information of composite microstructure was obtained by means of programming with C-language and its visualization was realized through program interface OpenGL. The simulation result reproduced composite real structure, laying down a basis for quantitative analysis of multi-crystalline set with numerical technique.