Modeling the indentation size effects of polymers, based on couple stress elasticity and shear transformation plasticity

Abstract

This work attempts to construct models which can describe the size effects in modulus and hardness of polymers measured by indentation tests. Firstly, the origin of size effects in the procedure of nanoindentation is analyzed. The finding of the literature that the indentation size effects of polymers are of significant elastic nature is further discussed and confirmed. The elastic size effects are described by a model, through introducing a model of elastic unloading load with consideration of couple stress elasticity into the Oliver-Pharr indentation approach. The accordingly proposed modulus model and hardness model agree excellently with a large amount of experimental data obtained from literatures. The models show that the elastic size effects of polymers and their experimental observations are mainly determined by the molecular structures. The fitting results verify that the size effects in indentation hardness of polymers with complex molecular structures are significantly elastic. It is postulated that the plastic size effects in indentation hardness of polymers are only derived from their glassy components. A shear transformation plasticity formula of glassy polymers recently proposed by literature is slightly extended to characterize the size dependent deformations in indentation tests. A hardness model with consideration of size effects is accordingly obtained and agrees well with related experimental data.