FRACTAL DIMENSION MEASURED WITH PERIMETER-AREA RELATION AND TOUGHNESS OF MATERIALS
FRACTAL DIMENSION MEASURED WITH PERIMETER-AREA RELATION AND TOUGHNESS OF MATERIALS
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DOI：
10.1103/physrevb.38.11781
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发表时间：
1988-12-01
影响因子：
3.7
通讯作者：
MU, ZQ
中科院分区：
文献类型：
--
作者：
LUNG, CW;MU, ZQ
本文证明了由周长-面积关系确定的分形维数Dm不是金属断裂表面的本征分形维数D 0。D m的测量值取决于用于测量周长的标尺的长度，并且与D 0有定量关系。当尺度足够小时，Dm接近D 0.本文还指出，Dm与材料韧性呈负相关关系的根源是许多作者所用的Dm度量尺度过大。正如我们所预料的，当尺度的长度小于Koch代边的临界长度时，得到了正相关。用分形来表征断裂面，并与材料参数相关联，似乎是有希望的。
This paper shows that the fractal dimension D m as determined by the perimeter-area relation is not the intrinsic fractal dimension D 0 of a fractured metal surface. The measured value of D m depends on the length of the yardstick used to measure the perimeter and has a quantitative relation with D 0. When the yardstick is small enough, D m approaches D 0. It is also shown that the origin of the negative correlation between D m and toughness of materials is that the yardstick used by many authors for measuring D m is too large. As we expected, a positive correlation is obtained when the length of the yardstick becomes smaller than a critical length of the side of the Koch generation. It seems hopeful to use fractals to characterize fractured surfaces with which material parameters can be correlated.