| Perimeter-Area Relation and Fractal Dimension of Fracture Surfaces |
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| 摘 要： | We have theoretically analysed the perimeter-area relation and simulated its application to measuring the fractal dimension of fracture surfaces. It is proved that the fractal dimension Dobtained by slit island method (SIM) is related to the dependence of measured area A(δ) ofthe slit island on yardstick δ. So in some cases, the dimension D obtained by SIM is dependenton yardstick and in other cases independent on yardstick δ. But in all cases, when δ→0 thedimension D obtained by SIM approaches the real fractal dimension (similar dimension) of coastline' of the island. We analysed some experimental data and found some new and interestingcharacteristics of crack propagation in steels.
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| 收稿时间： | 1997-09-28 |
Perimeter-Area Relation and Fractal Dimension of Fracture Surfaces |
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| Authors: | Duanwen SHI Jian JIANG Enke TIAN and Chiwei LUNG |
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| Affiliation: | Duanwen SHI,Jian JIANG,Enke TIAN and Chiwei LUNG(International Centre for Materials Physics,Institute of Metal Research,Chinese Academy of Sciences,Shenyang,China) |
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| Abstract: | We have theoretically analysed the perimeter-area relation and simulated its application to measuring the fractal dimension of fracture surfaces. It is proved that the fractal dimension Dobtained by slit island method (SIM) is related to the dependence of measured area A(δ) ofthe slit island on yardstick δ. So in some cases, the dimension D obtained by SIM is dependenton yardstick and in other cases independent on yardstick δ. But in all cases, when δ→0 thedimension D obtained by SIM approaches the real fractal dimension (similar dimension) of coastline' of the island. We analysed some experimental data and found some new and interestingcharacteristics of crack propagation in steels. |
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