Six decades of the Hall–Petch effect – a survey of grain-size strengthening studies on pure metals

The strength of polycrystalline materials increases with decreasing grain size. Below a critical size, smaller grains might lead to softening, as suggested by atomistic simulations. The strongest size should arise at a transition in deformation mechanism from lattice dislocation activities to grain boundary-related processes. We investigated the maximum strength of nanotwinned copper samples with different twin thicknesses. We found that the strength increases with decreasing twin thickness, reaching a maximum at 15 nanometers, followed by a softening at smaller values that is accompanied by enhanced strain hardening and tensile ductility. The strongest twin thickness originates from a transition in the yielding mechanism from the slip transfer across twin boundaries to the activity of preexisting easy dislocation sources.

We used molecular dynamics simulations with system sizes up to 100 million atoms to simulate plastic deformation of nanocrystalline copper. By varying the grain size between 5 and 50 nanometers, we show that the flow stress and thus the strength exhibit a maximum at a grain size of 10 to 15 nanometers. This maximum is because of a shift in the microscopic deformation mechanism from dislocation-mediated plasticity in the coarse-grained material to grain boundary sliding in the nanocrystalline region. The simulations allow us to observe the mechanisms behind the grain-size dependence of the strength of polycrystalline metals.