测量断口分维的一种变分辨率码尺方法

A new yard-stick method for fractal dimension determination by varying instrumental resolution

本文提出了测量断口分维的一种变分辨率码尺方法，并利用ＷｅｉｅｒｓｔｒａｓＭａｎｄｅｌｂｒｏｔ理论分形曲线对变分辨率码尺方法与传统的变码尺方法进行了对比。结果表明，变分辨率码尺方法优于传统的变码尺方法。用扫描隧道显微镜（ＳＴＭ）利用变分辨率码尺方法在纳米尺度测定了Ｔｉ３ＡｌＴｉ２４Ａｌ１１Ｎｂ合金断口的分形维数。发现断裂表面在纳米尺度上存在分形结构。

A new -stick method by varying instrumental resolution for determining the fractal dimension was proposed. Weierstrass-Mandelbrot fractal curves was used to verify the accuracy and reliability. Computer simulation showed that the fractal dimension obtained with yard stick method by varying instrumental resolution generally out runs the traditional yard-stick method.The new method has been applied to fractal dimension determination of the fractures of alloys Ti3Al and Ti 24Al 11Nb with STM at nanometer scale. Results showed that the fractal dimensions of Ti 24Al 11Nb alloy are higher than those of Ti3Al,and the rfactal dimensions vary with the directions as to crack orientation.