摘要：利用分形理论盒维数法对复合材料第二相颗粒分布均匀性进行定量评价,通过MATLAB建模实现图像的数字化处理,对盒维数MATLAB模型的准确性进行实验验证,并分析视场边界颗粒对盒维数的影响;对3个不同颗粒分布的图像进行颗粒分布均匀性的评价,并将实验结果与锐角比率法的评价结果进行比较。结果表明:除去与不除边界颗粒二次分形计算的盒维数呈线性关系;对颗粒均匀分布图像进行分形计算得盒维数为1.998,与理论值为2的误差为0.077%;盒维数评价法有效可行,且区分度明显。

关键词：分形理论；盒维数；第二相颗粒；分布均匀性

Abstract: The quantitative evaluation of the fractal theory box dimension method was adopted to evaluate the distribution uniformity of the second phase particles in composites. The digital processing of images was realized by MATLAB modeling. The accuracy of MATLAB model was verified by the experiment. The effect of boundary particles on box dimensions was analyzed. Three images of different distribution of particles were evaluated on particles distribution uniformity. Experimental results were compared with results of the acute angle ratio method. The results show that box dimension values retaining and except boundary particles by twice fractal calculation have a linear relationship. The box dimension value by fractal calculation on images particles uniformly distributed is 1.998， which has the error of 0.077% with the theory value of 2. The box dimension method is accurate and feasible， and its discrimination is apparent. 

Keywords: fractal theory； box dimension； second phase particle； distribution uniformity