MMC分维数测定与非线性动力过程分析

The Measurement for Fractal Dimension of Aluminium Matrix Composite and the Analysis of Nonlinear Dynamical Process

对ＭＭＣ微裂纹分布的ＳＥＭ照片连续地变换网格尺度，求得了ＭＭＣ微裂纹分布的自相似分形维数，Ｄ＝１．５６．对大塑性变形后ＭＭＣ分形重建后的σ（ｔ）时间序列进行了非线性动力学过程分析，找到了相空间吸引子积分关联函数，确定了该ＭＭＣ微裂纹演化存在吸引子，其分形关联维数值１．４８与实验测得自相似分形维数值１．５６接近．

By changing the grid scale of SEM photo of the micro-cracks configuration of MMC, its fractal dimension of self-similarity was obtained, D = 1.56. The nonlinear dynamical process of the fractal reconstructed σ (t) time series of MMC after large plastic deformation was analyzed. By using the G-P algorithm, it is found that there is a correlation function of the attractor and the dimensionality of the attractor is 1.48, which coincides with the experimental value 1.56 approximately.