Length scale effects in epoxy: The dependence of elastic moduli measurements on spherical indenter tip radius

Significant increases in the measured elastic moduli with decreasing indentation depth have been previously found in various polymers by indentation tests with a Berkovich tip at micro-to nanometer length scales. These increases in the determined elastic moduli were related to second order displacement gradients which increase with decreasing depth when a conical tip is applied. When a spherical tip is applied, such depth dependence should not be present as the second order displacement gradients remain essentially unchanged with indentation depth. However, these gradients should be proportional to the radius of the spherical tip. To examine the notion of second order displacement gradient dependence in measurements of elastic moduli, indentation experiments are conducted on epoxy with spherical tips of different nominal radii. Accounting for tip imperfections, an increase in the determined elastic moduli is found with decreasing tip radius, which corroborates the notion of second order displacement gradient dependence.