Size Effect of Microdamage Growth and Its Relation to Macro Fatigue Life

摘要

In its initial evolution stage, fatigue damage consists of many microdamage sites, having random sizes and locations. The way in which these sites grow and coalesce has a crucial effect on the macro fatigue life. A statistical micromechanic fatigue model has been developed, in which the material is composed of microelements of random strength with a certain probabilistic dispersion parameter (β). In addition, the model takes into account local interactions between damaged microelements and their first neighbors by considering a failure sensitivity factor (c), which is the probability that the neighbor will survive the local (micro) stress concentration. It was shown analytically in previous studies that β is proportional to the S-N power intensity, and ln (1-c) is proportional to the macro endurance limit. In this study, the analysis is generalized to the case where the growth of each micro-damage is size dependent, i.e., each damage site grows at a rate which depends on its current size. The strength of this rate-size relation controls the order of the governing differential equation. It was found that certain "microdamage growth laws" still preserve the macro power law, so that the power on the S-N diagram can be directly related to the local microdamage evolution. While the analytical micro-macro relation is still under current study, a numerical simulation of fatigue damage evolution has been obtained and revealed that the macro S-N power law prevails in spite of the noticeable complexity.