Abstract: The following aspects are studied in the present paper:①Conven-tional methods and their some disadvantages on the fractal dimension measure of fracture surfaces②A type of bifurcation and chaos, which is found to exist in the evolution of microcrack density in active growth areas when constant ampli-tude loading spectrum is applied,and a mathematical model for describing this phenomenon. ③The reasonable definition and cumulative rule.of fatigue damage as an indirect result of bifurcation and chaos.