材料断裂形貌分维的测量及计算机模拟

材料断裂形貌如断口表面、断裂裂等均被认为具有分形结构而被称为实际分形体，论述了这类实际分形体维数的实验测量、计算方法和分维测量、计算中出现的分维不性问题，指出生分维不确定性的原因，并且通过计算机模拟演示了一些实际测量因素对测量和计算实际分形体维数的影响。

MEASUREMENT AND CALCULATION OF FRACTAL DIMENSION OF FRACTURAL MORPHOLOGY AND COMPUTER SIMULATION

Fractural morphologies of materials, e.g. fractural surface and fractural crack featuring fractal structure, are called actual fractal, Measurement and calculation of fractal dimensions of these actual fractals are reviewed, and the uncertainty of fractal dimension is also discussed. We suggest that the finite-level structure of actual fractals is the reason why fractal dimensions of actual fractals have a uncertainty in actual measurement and calculation. Using computer simulation method, we studied the influence of kinds, levels of the actual fractals and measurement yardsticks on the measurement and calculation of the fractal dimension of the actual fractals, and found that the realistic fractal dimension can be easily obtained only when the numbers of the kinds and levels of the actual fractals are large enough. In addition, the selected range of the yardstick is suggested to be determined by the numbers of the levels of actual fractals.