A model of evolving damage bands in materials

This paper develops a model that incorporates damage band evolution at three levels: (i) at the mechanism level, the damage mechanisms, such as diffusive void growth and fatigue cracks, determine the damage growth rate ; (ii) at an intermediate level, the damage band is modeled as springs connecting undamaged materials, and the spring constants change as damage develops; (iii) at the continuum level, the damage band is modeled as an array of dislocations to satisfy equilibrium. We demonstrate this model with an example of a band of microcracks subject to remote tensile cyclic stress. It is observed that damage rapidly grows at the weakest regions in the band, and a macroscopic crack nucleates while the overall damage level is still very low. The model shows that there exists a critical number of cycles for macroscopic crack nucleation, N_nucleation, which depends on materials as well as the amplitude of applied cyclic stress. This critical number of cycles is insensitive to the size of damage cluster, but decreases rapidly as the local excess of damage increases.