QUANTITATIVE-ANALYSIS OF BRITTLE-FRACTURE SURFACES USING FRACTAL GEOMETRY
QUANTITATIVE-ANALYSIS OF BRITTLE-FRACTURE SURFACES USING FRACTAL GEOMETRY
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DOI：
10.1111/j.1151-2916.1989.tb05954.x
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发表时间：
1989-01-01
影响因子：
3.9
通讯作者：
FEINBERGRINGEL, KS
中科院分区：
文献类型：
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作者：
MECHOLSKY, JJ;PASSOJA, DE;FEINBERGRINGEL, KS
分形几何是一种非欧几里得几何，被开发用于分析不规则或分数形状。在本文中，陶瓷材料的断裂被分析为分形过程。这意味着断裂被视为一个自相似过程。我们检查了六种不同的氧化铝材料和五种具有不同微观结构的玻璃陶瓷的断裂表面，以测试分形行为。狭缝岛分析和傅里叶变换方法用于确定连续截面断裂表面的分形维数 D。我们发现增加分形维数的小数部分与增加韧性之间存在相关性。换句话说，随着韧性的增加，断裂表面的粗糙度也增加。然而，分形几何学对断裂的适用性不仅仅是粗糙度的测量，还意味着断裂表面的生成机制。这里给出的结果表明脆性断裂是一个分形过程；这意味着我们应该能够通过观察宏观尺度、找到分形过程中固有的生成器形状和生成方案来确定原子尺度上的过程。
Fractal geometry is a non‐Euclidean geometry which has been developed to analyze irregular or fractional shapes. In this paper, fracture in ceramic materials is analyzed as a fractal process. This means that fracture is viewed as a self‐similar process. We have examined the fracture surfaces of six different alumina materials and five glass‐ceramics, with different microstructures, to test for fractal behavior. Slit island analysis and Fourier transform methods were used to determine the fractal dimension,D, of successively sectioned fracture surfaces. We found a correlation between increasing the fractional part of the fractal dimension and increasing toughness. In other words, as the toughness increasing the fracture surface increases in roughness. However, more than just a measure of roughness, the applicability of fractal geometry to fracture implies a mechanism for generation of the fracture surface. The results presented here imply that brittle fracture is a fractal process; this means that we should be able to determine processes on the atomic scale by observing the macroscopic scale by finding the generator shape and the scheme for generation inherent in the fractal process.