A geometric approach to modeling microstructurally small fatigue crack formation: III. Development of a semi-empirical model for nucleation

It has been observed during fatigue cracking of AA 7075-T651 that a small percentage of Al7Cu2Fe particles crack during manufacturing or very early in their life. Some of the cracked particles eventually nucleate cracks into the surrounding microstructure, and among these the number of cycles required for nucleation varies widely. It is important to comprehend the mechanics underpinning the observed variation so that the subsequent propagation stage can be accurately modeled. To this end, finite element models of replicated grain and particle geometry are used to compute mechanical fields near monitored cracked particles using an elastic-viscoplastic crystal plasticity model that captures the effect of the orientation of the grains near each monitored particle. Nonlocal, slip-based metrics are used to study the localization and cyclic accumulation of slip near the cracked particles providing mechanics-based insight into the actuation of the nucleation event. A high slip localization and cyclic accumulation rate are found to be a necessary, but not sufficient, condition for nucleation from cracked particles. A sufficient local driving stress must also be present, which is strongly dependent on the local microstructure and accumulated slip. Furthermore, the simulation results elucidate a quantitative relationship between the slip accumulated during fatigue loading and a consequential reduction of the critical local driving stress for nucleation, providing a physical basis for the fatigue damage concept. The observed nucleation direction is orthogonal to the computed local maximum tangential stress direction, as expected for this alloy. The main result is a semi-empirical model for the number of cycles required for nucleation, which is dependent on the maximum tangential stress and cyclic slip-accumulation rate near a cracked particle.