Interpreting the inverse Hall-Petch relationship and capturing segregation hardening by measuring the grain boundary yield stress through MD indentation

The inverse Hall-Petch relationship, which occurs below a critical grain size, is attributed to the high interface to volume ratio that characterizes nanocrystalline metals. This has led some theoretical models to treat nanocrystals as composite materials in which the grains and grain boundaries behave as two separate phases, which follow their own yield behavior. The present study provides first estimates of a grain boundary yield stress, by employing molecular dynamics indentation. The case system considered was that of nanocrystalline Fe with a Σ5 symmetric boundary and indentations were performed either in the grain interior or on the grain boundary illustrating that grain boundaries yield at less than half the stress that grains do. This can interpret the inverse Hall-Petch relationship, since as the grain size decreases below a critical value, the grain boundary thickness is not negligible and its low yield stress dominates the material behavior. To stabilize the boundary from migration/sliding and capture the effect of segregation the simulations were repeated when 0.008% C impurities were added into the sample. This low C content resulted in a higher grain boundary yield stress, without however increasing the grain interior yield stress, illustrating the sensitivity of grain boundaries to segregant atoms. In addition to shear strain maps, a new visual representation was done by using different colors to indicate the orientation of atoms during indentation, as would be done experimentally with electron backscatter diffraction. It was therefore possible to reveal the occurrence of twinning, in addition to dislocation nucleation.