Hybrid discrete dislocation models for fatigue crack growth

A framework for accurately modeling fatigue crack growth in ductile crystalline solids is necessarily multiscale. The creation of new free surface occurs at the atomistic scale, where the material’s cohesive strength is controlled by the local chemistry. On the other hand, significant dissipation during fatigue crack growth takes place at a size scale that can be modeled appropriately by conventional continuum mechanics. The intermediate size scale where the discreteness of dislocations comes into play is the main origin of the hysteresis needed for fatigue and of the high stresses required for atomistic separation to take place. We focus on recent developments which permit analyses of fatigue crack growth involving the direct coupling of disparate size scales. Although no analyses have been carried out directly coupling size scales from the atomic to the conventional continuum, the ingredients to do so are in place. We provide background that illustrates the key role played by the intermediate discrete dislocation size scale and review steps that have been taken to permit direct size scale coupling. The prospects and modeling needs for further developments are also discussed.