IFS FRACTAL RECONSTRUCTION FOR THE CONSTITUTIVE RELATION OF METAL MATRIX COMPOSITE AND THE TIME SERIES ANALYSIS

When the compressive specimens of Al2014+15 vol% SiCp MMC were loaded approximately to 40 % in strain, the irregular oscillations in their stressstrain curves were observed for the first time. These oscillations are considered to be the macro manifestations of the fractal processes corresponding to the microcracks evolution in the specimens. The data of oscillations werefractal interpolated. An iterative function system (IFS) corresponding to a contractions affine transform can be obtained. A random iterative algorithm was used for this IFS and the constitutive relations with the fractal microcracks evolution were reconstructed satisfactorily. The power spectrums for the original oscillation curves and the reconstructed curves were analyzed. Their agreement is reasonably good. By using the GP algorithm, it is found that there is a correlation function of the attractor and the dimensionality of the attractor is 1.48. The minimum number of variables necessary to model the microcracks evolution is dete