Fractal Dimension of Ductile-Fractured Surface of Copper-Brazed Steel Calculated from Its Dimple Size Distribution

抄録

The fractal dimension is related to dimple size distribution for the fractured surface of the copper-brazed steel joint, which has a macroscopically flat and microscopically dimple-covered texture. Under the assumption that the distribution density function of dimple size is the power function of the dimple size, and that a dimple's shape is in the cosine curve, the fractal dimension D of the modeled surface is deduced to be D=(α-1)/2, where α is the exponent of the power function of the dimple size distribution. For the experimentally fractured surface of a copper-brazed steel joint, the fractal dimensions calculated using the conventional height-height correlation method and the deduced formula show agreement in the tendencies to the brazing filler thickness, and the obtained relationship is confirmed. Considering the geometrical similarity between the fractured surface of the copper-brazed steel joint and the cup-and-corn type ductile-fractured surface, the obtained formula could be adapted to the more general ductile-fractured surfaces.