【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。更多还原

【Abstract】 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.更多还原