摘要
本文分析与研究了 Slit Island Method(SIM)测量断口磨面“小岛”周长-面积关系,指出由这种方法所测得的分形维数 Dm 不是金属断裂表面的真正分形维数 D_o,D_m 取决于测量“小岛”时的码尺长度并与 D_o 有定量关系。只有当测量码尺足够小时,D_m 才接近真正的分形维数 D_o。同时指出,许多作者所得到的 D_m 与韧性之间相反变化的原因是由于测量码尺太大造成的,当测量码尺的绝对长度小于临界长度,即“小岛”周长 Koch 曲线始图的边长时,D_m 与韧性之间才会呈现正变化的关系。
This paper shows that the fractal dimension D_m,as determi-ned by the perimeter-area relation is not the intrinsic fractal dimension,D。of a fractured metal surface.The measured value of D_m depends on thelength of yardstick used to measure the perimeter and has a quantitative relationwith D。.When the yardstick is small enough,D_m approaches D。.It is alsoshown that the origin of the negative correlation between D_m and toughness ofmaterials is that the yardstick used by many authors for measuring D_m is toolarge.As was expected,a positive correlation was obtained when the lengthof the yardstick becomes smaller than a critical length of the side of theKoch generation.It seems hopeful to use fractal to characterize fracturedsurfaces with which material parameters can be correlated.
关键词
分形维数
测量
金属材料
韧性
fractal dimension
yardstick
slit island method(SIM)
fracture toughness
fracture surface
