Hall–Petch revisited at the nanoscale

During the past decade it has been documented that nanomaterials behave differently than their bulk counterparts. From a mechanical point of view the inverse Hall–Petch phenomenon that has been observed for nanocrystalline metals, such as for Cu, is of particular interest. In the present study three different theoretical approaches will be used to model this inverse Hall–Petch phenomenon, which occurs for nanocrystalline materials with grain sizes less than 100 nm. Although the underlying mechanisms leading to this inverse behavior have not yielded to precise physical interpretation, it is qualitatively attributed to the presence of a high interfacial area, and also to the existence of nanopores. To account for interfaces a gradient plasticity formulation that accounts specifically for interface energies is used as a first step towards this direction. In continuing, a simplified gradient plasticity model, that does not contain interfacial terms, is coupled with wavelet analysis; while in concluding, a model involving the concept of nano-porosity, is utilized in order to capture this behavior at the nanoscale. The theoretical predictions are then compared with available experimental data from tensile tests on nanocrystalline Cu as well as hardness measurements on nanocrystalline Fe samples.