Farid Alisafaei

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

Abstract 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.

Indentation Depth Dependent Mechanical Behavior in Polymers

Various experimental studies have revealed size dependent deformation of materials at micro and submicron length scales. Among different experimental methods, nanoindentation testing is arguably the most commonly applied method of studying size effect in various materials where increases in the hardness with decreasing indentation depth are usually related to indentation size effects. Such indentation size effects have been observed in both metals and polymers. While the indentation size effects in metals are widely discussed in the literature and are commonly attributed to geometrically necessary dislocations, for polymer the experimental results are far sparser and there does not seem to be a common ground for their rationales. The indentation size effects of polymers are addressed in this paper, where their depth dependent deformation is reviewed along with the rationale provided in the literature.

Length Scale Dependent Deformation in Polymers

Length scale dependent deformation of polymers has been observed in different experiments including micro-beam bending and indentation tests. Here the length scale dependent deformation of polydimethylsiloxane is examined in indentation testing at length scales from microns down to hundreds of nanometers. Strong indentation size effects have been observed in these experiments which are rationalized with rotation gradients that can be related to Frank elasticity type molecular energies known from liquid crystal polymers. To support this notion additional experiments have been conducted where Berkovich and spherical indenter tips results have been compared with each other.© 2012 ASME

INDENTER TIP DEPENDENCE IN THE DETERMINATION OF ELASTIC MODULUS IN POLYMERS

The two most common outputs of nanoindentation experiment are hardness and elastic modulus. Length scale dependent deformation in polymers has however been observed in different experiments such as microbeam bending, torsional thin wires and indentation testing which may affect the mechanical testing. Unlike in metals where the size dependency is attributed to necessary geometry dislocations, the origin of length scale dependent deformation in polymers is not well understood. In this study, elastic modulus of polydimethylsiloxane (PDMS) is determined using both Berkovich and spherical tips. Observing different trends for elastic modulus upon the change of indentation depth using these two different tips brings up the question which tip should be used to get the real mechanical properties of PDMS which is discussed here. Surface roughness, surface effects and the imperfection of the Berkovich indenter tip are negligible at the studied length scale.Copyright

ON THE TIME DEPENDENCE OF SIZE EFFECT IN POLYDIMETHYLSILOXANE

Nanoindentation tests at the nano-micrometer scales are conducted to investigate the depth and time dependent deformation mechanisms of polydimethylsiloxane (PDMS). Astonishing indentation size effects observed in these experiments are analyzed with an existing theoretical hardness model, and the effects of loading time on the hardness and indentation stiffness of PDMS are studied. The change in the indentation recovery with respect to indentation depth and loading time are analyzed. Furthermore, it is shown that the stiffness of PDMS obtained at the maximum applied force can be efficiently applied to validate the applied theoretical hardness model with the experimental results.Copyright