A micromechanical approach to the stress–strain relations, strain-rate sensitivity and activation volume of nanocrystalline materials

This review highlights a secant viscosity approach that has wide applicability for the determination of mechanical properties of nanocrystalline materials. Along the way we also add some new elements and provide fresh perspectives. This approach was originally proposed for the nonlinear, time-dependent, work-hardening creep of dual-phase composites (Li and Weng, J Mech Phys Solids 45:1069–1083, 1997a), but by conceiving a nanocrystalline material as a composite of the stronger grain interior and the softer grain-boundary (GB, or grain-boundary affected zone GBAZ), it becomes possible to extend it to calculate the grain-size dependence of their flow stress, strain-rate sensitivity, and activation volume. We also use it to explain how the flow stress first increases and then decreases as the grain size decreases from the coarse grain to the nanometer range, leading to the Hall–Petch and the inverse Hall–Petch relations. The critical state at which the slope of the strength variation with respect to the grain size becomes zero also yields the strongest material state. In this way the two most important parameters for material design—the maximum strength and the critical grain at which it occurs—can be obtained. The strain-rate sensitivity parameters are also shown to follow a similar pattern as the flow stress, but the activation volume varies in an exactly reverse way.