| In this paper, based on facts that damage of materials are characteristic of fractal and aimed at the fatigue behaviors of electronic beam welded joint of TC11 titanium-alloy, the damage mechanics theory and fractal theory are combined to analyze the low-cycle fatigue damage and to study the life prediction method of welded joints.A new fractal damage model in fractional dimensional space is proposed and a new fractal damage variable is educed in which both micro and macro damages of welded joint are considered. The reasons that fractal dimension of line in the past is disadvantageous are given and fractal dimension of area in the three-dimensional space is pointed out. A fractal expression is given to describe the fatigue damage evolution of TC11 welded joint, and fractal damage evolution equations (FDEE) are built up.The ways of measuring fractal dimension are studied and two methods of estimation of fractal dimension of area are given. With scan electron microscope and digital image analysis technology and with VC++, a program for measuring fractal dimension is developed. The best ruler length of measuring fractal dimension used in studying the fracture surface of TC11 welded joint is determined. The relationships between fractal dimensions of fracture surface and strain as well as fatigue life are established. Additionally, macrostructure and microstructure on fracture feature of TC11 Alloy also is studied.Parameters in FDEE are obtained on the experimental data, which reveal that both original fractal damage and critical fractal damage are dependent on load. Based on this, the relationship between strain and FDEE is studied and a unified equation for low-cycle fatigue fractal damage evolution depended on strain is established, a life prediction method for TC11 welded joint is obtained.
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