On the origin of indentation size effects and depth dependent mechanical properties of elastic polymers

Indentation size effects have been observed in both polymers and metals but, unlike in metals, the origin of size effects in polymers is not well understood. To clarify the role of second order gradients of displacements, a model polymer is examined with spherical and Berkovich tips at probing depths between 5 and 25 μm. Applying different theories to determine the elastic modulus, it is found that with a pyramidal tip, the elastic modulus increases with decreasing indentation depth, while tests with the spherical tip yielded essentially constant values for the elastic modulus independent of indentation depth. The differences between these tips are attributed to second order displacement gradients, as they remain essentially constant with a spherical tip while they increase in magnitude with decreasing indentation depth applying a Berkovich tip.