A Fractal Study On Collective Damage Evolution Of Low Cycle Short Fatigue Cracks At High Temperature

In the modern industries of energy, chemical, aerospace and power machinery, most engineering structures involve parts subjected to high temperature and alternating loads and, according to Stat., the majority of all structural failures occur due to a fatigue mechanism. The fatigue behavior in modern engineering realm is considered to be a very important factor in recent structural security and economy analysis procedures. Fatigue failures, ultimately, result of cracks in the material either overtly or covertly. With the development of modern smelting and manufacturing technology, the emergence of long cracks in the material and structures becomes less and less, whereas short cracks are mostly observed. Research shows that most of the fatigue life is occupied by short crack stage. Traditional methods have limitations in the research on the collective damage evolution of short fatigue cracks for the uncertainty and random statistical complexity during the fatigue damage process. In order to revealing the physical mechanisms of the material damage, a new method is essentially to be adopted for the further study of damage evolution law of short fatigue cracks, and then provide the theory basis for safety and reliability evaluation of structures. The introduction of fractal theory provides a new idea for the study of short fatigue cracks.The collective damage evolution of short fatigue cracks under complex stress conditions was experimentally studied in cylindrical specimens with a shallow annular notch, and the high temperature low cycle tests on20#steel were carried out under various constant nominal strain ranges and different temperatures. Characteristics of the initiation, propagation, coalition and interference of short fatigue cracks were obtained, and collective damage laws of short fatigue cracks were studied by using the fractal method. The main contents can be given as follows:1. The back ground and meaning of research on low cycle short fatigue cracks at high temperature are discussed. A summary is made on the leading models and methods in the modern fatigue fracture mechanics. The generation of fractal theory and its domestic and overseas present status and tends are reviewed, too.2. Interrupted fatigue tests were carried out using a closed loop servo-hydraulic testing system. Different nominal strain levels were imposed at a constant R ratio of-1and a frequency of0.5Hz with a triangular command signal. Micrographic together with the image processing technique was applied for the short fatigue crack observation as well as for the extraction of short crack information. Statistic analysis on the numerical density of short fatigue cracks was done, too. Test results show that:short fatigue cracks display a good collective behavior. Most of the short fatigue cracks initiate from the grain boundary at high temperature and present objective statistical laws of the randomicity. Some individual short cracks expand to the dominant crack resulting in collapse, but most ultimately become non-propagating cracks. The numerical density of short fatigue cracks increases at first, but decreased later, the larger the strain amplitudes and the higher the temperature, the more rapidly it increases.3. The definition and properties of fractal dimension are detailed, and box dimension is used for a quantitative analysis of collective damage evolution of short fatigue cracks. A valid method, Otsu method, based on the maximum between-class variance to adaptively decide the number of image regions is introduced. A gradient trial algorithm based on fractal scale effect is presented and it has been proven to improving the computing accuracy greatly. A fractal analysis on the test results under various strain ranges and different temperatures is applied, and the results show that the fractal dimension is a good parameter to indicate the damage evolution law of short fatigue cracks. The test images show a good fractal behavior in the the scaling region defined by the gradient trial algorithm. And the fractal dimension of test images varies obviously and consistently under the different nominal strain ranges and temperatures.