Indentation size effects in polymers and related rotation gradients

Similar to metals, the hardness of many polymers increases with decreasing indentation depths at depth ranges from several microns down to several nanometers. While for metals such phenomena are commonly attributed to geometrically necessary dislocation densities, such an explanation cannot be applied to polymers. To provide a micromechanically motivated model for the indentation size effect in polymers, here we propose an elasto-plastic extension of the higher order elasticity model recently developed by the authors. In this model, size effects in polymers (as well as in nematic liquid crystals) are related to Frank elasticity arising from bending distortions of the polymer chains and their interactions. On the basis of this theory, we derive a simple model for indentation size effects in polymers. Unlike other models, our model includes only elastic size effects due to rotational gradients. It is shown that the proposed model can explain the experimentally observed size effects in polymers. Together with the existing experimental data mentioned here, new experimental data for silicon rubber are also presented and discussed.