An attempt to determine the true stress-strain curves of amorphous polymers by nanoindentation

We have made an attempt to identify the true material stress-strain curves of some amorphous polymers (PC, PMMA, CR39 (diethylene glycol bis(allyl carbonate)) from nanoindentation experiments by using non-self similar tip shapes, i.e. tips promoting an increasing strain with an increasing indentation depth. We firstly found that, for a defined strain rate, the relationship linking the contact pressure to the ratio between the contact depth and the contact radius is intrinsic to the material, i.e. it doesn’t depend on the tip shape used. From this relationship, for each material, we calculated the evolution of the average stress with the average strain beneath the tip, by using the theoretical background developed for elasto-perfectly plastic materials. By comparing to compression test results, we concluded that this approach works well for PC and PMMA only for an average strain below 12%. This approach is inapplicable for the CR39 material even at low strains. We assumed that this is mainly due to the occurrence of a significant strain hardening, that doesn’t allow us to neglect the strain gradient existing beneath the tip.