界面あるいは表面不均質変形のフラクタル特性

抄録

Fractal concepts have recently been introduced to the field of fractography in order to characterize the fractured surface quantitatively. This paper puts great emphasis on the self-similarity of inhomogeneous deformation which results from the finite geometric changes of microstructure with strain. Fractal dimensions are obtained by using the familiar Richardson's structured walk method. Correspondence of the fractal property to the formation of crystallographic microstructure is discussed. We also perform fractal analyses for the pseudo-roughening profiles generated by computer simulations to interpret qualitatively the results obtained from the profiles of roughening in aluminum foils subjected to biaxial tension. Two kinds of roughening profiles are given by pure aluminum and aluminum alloy foils subjected to biaxial tension. The paper submitted formerly reported that the inhomogeneous deformation formed by the superposition of two kinds of microstructural changes was observed on pure aluminum.
Fractal analyses to such profiles gave the following conclusions. The fractal dimension for pure aluminum increases a little with strain. On the other hand, as for the aluminum alloy it holds almost constant. The difference between them may be dependent on the mechanism of the formation of these roughening. This tendency also has good qualitative agreement with the results from the computer simulations by using the Gaussian distribution. Roughening formed by two kinds of the microstructural changes gives two different fractal dimensions, corresponding to the characteristic length of them.