利用计算机模拟了不同分维的断口形貌 ,并对各种分维测量方法在纳米度域的适用性和可靠性从理论和实验两方面进行了研究 .对于金属断口 ,在进入纳米度域后 ,由于小岛截面数的限制或数据量的有限性 ,面积 周长法和基于Fourier变换的功率谱方法遇到了困难 .模拟计算表明 ,盒子计数分维测量方法可以作为纳米度域分维的测量方法 .用扫描隧道显微镜 (STM)采用立方体元方法在纳米尺度测定了5Cr2 1Mn9Ni4N汽阀钢断口的分形维数 .结果表明分形维数在纳米度域具有方向性 ,对于理论分形曲面 ,这种分形维数的方向性是由数据点数的有限性所造成的 ,即是一种边界效应 ;然而 ,对于实际断口 ,这种方向性除了边界效应外 ,还是材料的内禀特性的反映 .宏观度域的分形维数与材料性能的关系在纳米度域仍然存在 . The fractographs of different fractal dimensions were simulated by computer, and the applicability and reliability of various fractal dimension methods in nanometer range were studied both theoretically and experimentally. For metal fracture, Due to the limitation of the number of islets or the limited data, the area perimeter method and power spectrum method based on Fourier transform have encountered difficulties. Simulation results show that the box counting fractal dimension method can be used as a measure method for the fractal dimension of nanoscale fields. The fractal dimension of fracture surface of 5Cr2 1Mn9Ni4N steam valve steel was measured by scanning tunneling microscope (STM) using cubic element method at the nanoscale. The results show that the fractal dimension has directivity in the nanometer range. For the fractal theory, the fractal dimension The directionality is caused by the finite number of data points, ie, a boundary effect; however, for the actual fracture, in addition to the boundary effect, this orientation is a reflection of the intrinsic properties of the material. The relationship between dimensionality and material properties still exists in the nanometer range.