A STOCHASTIC MODEL FOR EVOLUTION OF COLLECTIVE SHORT-FATIGUE-CRACKS BASED ON LOCAL FIELD ANALYSIS 1)
基于局域分析的疲劳短裂纹群体演化随机模型

It has been observed that, the evolution process of short fatigue cracks in some metallic materials presents collective damage characteristics The cumulation of the damage is produced by a number of short fatigue cracks The extent of damage is not dependent on a single crack, but on the whole response of total short cracks For this situation, we adopted the method of the balance of crack number density to describe such an evolutionary process The basic consideration of the model is that, at a certain time duration, the number of cracks with a given length is due to two aspects: (a) crack nucleation, and (b) crack growth In the previous study, the evolution of short cracks is considered uniform throughout the gauge area of a specimen However, during a fatigue damage process, the initiation and the growth of short cracks are always randomly distributed In some local areas, short cracks may densely appear; simultaneously, there may exist some other areas even without any short crack damage In this paper, the development of collective damage for short fatigue cracks in different local fields of metallic materials is described by local crack numerical density By considering the influence of the local damage and the stochastic fluctuation of local material properties on the evolution of total extent of damage, the evolution equation of local crack numerical density is established The process of short crack fatigue damage is simulated by solving the evolution equation numerically The results demonstrate the stochastic distribution of short crack growth, which imply that fast damage development area in the beginning stage may not be the location of a main crack, whereas the local area with slow speed of damage development at the beginning may form a main crack leading to final fracture In addition, with the progression of fatigue process, the difference between the mean-field theory and the stochastic analysis becomes evident, showing the value of the maximum crack length in the whole field obtained by the mean-field theory being larger than that obtained by the stochastic analysis The characteristics of statistical development for the maximum crack length and the total number of cracks are further discussed