以分维几何学为基础，建立了断口二次电子像的分维Ｂｒｏｗｎｉａｎ模型，提出了以图像处理系统为手段的断口形貌的分维测量方法。研究了Ｎｉ粘结的Ｔｉ（Ｃ，Ｎ）金属陶瓷在三点弯曲条件下，断裂表面的分形维数与横向断裂强度及显微组织之间的关系，建立了金属陶瓷的微观断裂的Ｆｒａｃｔａｌ模型，给出断口分形维数的计算表达式。实验结果表明，横向断裂强度的对数值ｌｇσ＿（ｂｂ）随分形维数Ｄ＿Ｆ增加呈单调上升的直线关系；显微组织的变化对分形维数有重要影响；断口的分形维数依赖于测量码尺的选择，且存在上临界点ε＿ｋ′。
The relationships among the fractal dimension of fracture surfaces, transverse rupture strength and microstructure of Ti(C, N) based cermets have been studied. The microfracture fractal model of cermets and the estimated fractal dimension formula of fracture surfaces have been proposed. The experimental results have shown that the logarithm value of transverse rupture strength, lgσbb , increases with the increase of fractal dimension DF, and has a linear equation relationship. The change of microstructure has a considerable effect on the fractal dimension. The measured fractal dimension depends on the choice of measuring unit. There is an upper critical measuring unit εK′to the Ti(C, N) based ceimets.
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