Modeling nano-indentation tests of glassy polymers using finite elements with strain gradient plasticity

It is widely reported that when an indentation test is carried out at the submicron level, the materials display strong size effects, which alter the mechanical properties from their bulk characteristics. Classical plasticity theory is unable to account for this phenomenon. It has been shown that introducing the strain gradient plasticity theory in the analysis is able to capture successfully the size effects of various materials. The present study adopts a constitutive model for the viscoelastic-plastic deformation of glassy polymers, incorporates the effects of strain gradient plasticity and implements them via user subroutines in the commercial general purpose finite element package, ABAQUS. It is demonstrated that the strain gradient effect has to be considered into the adopted constitutive model in order to better describe the viscoelastic-plastic response of polymers at submicron indentations. The study also covers the two approaches of deriving the values of the effective strain gradient (i) via indentation geometry and (ii) directly from finite element nodal displacement parameters. Comparison of results obtained from both approaches show good agreement with existing experimental values in all cases covered in the present study. The latter, as expected, provides slightly more accurate solutions as compared to the test results than the former but at marginally higher computing time and resources.