Distribution effects of secondary twin lamellae on the global and local behavior of hierarchically nanotwinned metals

Twin lamellae in hierarchical nanotwinned metals (HNMs) typically exhibit a random distribution of thickness. Here, a self-consistent model using a micro–macro transition method has been proposed to understand the distribution effects of secondary twin lamellae on the global and local mechanical behaviors of HNMs. The representative volume element (RVE) of this model is composed of secondary twin lamellae with a lognormal distribution. Each RVE in the HNMs follows an elastic–viscoplastic behavior. A mechanism-based strain gradient theory is adopted based on different dislocation densities in twin boundary dislocation pileup zones and grain interiors. Numerical simulation results reveal that not only the mean size of secondary twin lamellae thickness contributes to the global mechanical behaviors, but the variance of the distribution will also affect the material strength, especially for a relatively small mean twin thickness. Additionally, local stress/strain fields are explored under given macroscopic fields. The discrepancy between micro- and macro-fields for two different mean twin lamellae thicknesses is thoroughly discussed. Furthermore, the influence of dispersion, which increases the local stress field while decreasing the local strain field, is also highlighted. This proposed model can help us design functional HNMs by considering the size distribution and local mechanical behaviors caused by size dispersion.