Mechanics of creep resistance in nanocrystalline solids

Summary In a nanocrystalline solid a significant portion of atoms resides in the grain boundary and the nearby outer grain. This combined region, known as the grain-boundary affected zone (GBAZ), is plastically softer than the grain interior, and it are the combined contributions of the grain interior and GBAZ that give rise to the overall response. In this spirit a two-phase composite model is developed to study the high-temperature creep resistance of nanocrystalline materials. Here the rate equation of each phase is represented by a power law and the Arrhenius function, but that of the grain interior is further taken to scale with the Hall–Petch relation whereas that of the GBAZ remains independent of grain size. This unified constitutive equation in turn leads to the concept of secant viscosity. Then a homogenization theory is developed by means of a transition from linear viscoelasticity to nonlinear viscoplasticity with the Maxwell viscosity constantly replaced by the secant viscosity. Subsequently a field-fluctuation method is called upon to determine the effective stress of both phases. The developed theory is applied to model the creep behavior of nanocrystalline Cu, NiP alloy, and Ni at various levels of stress, temperature, and grain size, with results that reflect good agreement with available experiments. We then applied the theory to examine the nature of creep resistance as the grain size decreases in the nanometer range in some detail, and it was discovered that creep resistance in the Hall–Petch like plot undergoes a transition from a positive slope to leveled off, and then to a negative slope. The leveled-off value in effect represents the maximum creep resistance that a material can attain, and it is found that this occurs at a critical grain size, d crit , that exists in the nanometer range.