congresos y reuniones científicas
Hard problems with Soft Materials: Nanoindentation of Polymers
Encuentro; III Encuentro Nacional de Materia Blanda - III MAB; 2010
Depth-sensing indentation (DSI, also called “nanoindentation”), in which the load and displacement are continuously monitored during a contact test, has developed into a standard technique for measurement of local mechanical responses of engineering materials such as metals, glasses and ceramics. The two mechanical properties measured most frequently are the elastic modulus, E, and hardness, H. In a commonly used method, data obtained from a complete cycle of loading and unloading are analyzed for properties deconvolution. The Oliver-Pharr approach is the most accepted analysis technique [W.C. Oliver, G.M. Pharr, J. Mater. Res. 7 (1992)] and it has been incorporated into a number of commercial systems largely due to its robustness and simplicity. This technique relies on the isotropic time-independence of indentation response in the experimental timeframe. DSI techniques are increasingly being used to probe the mechanical response of polymers. In contrast to engineering materials, polymers behave in a visco-elastic fashion, exhibit non-linear behavior at relatively small strains and their responses to tension, compression and shear can be quite different. Thus, a number of challenges exists when applying DSI methods to characterize polymers. This essay summarizes the state of the art of nanoindentation of polymers based on the knowledge available in literature, and our own experimental and finite element simulation results. Polymers exhibit substantial time-dependent nanoindentation responses in an experimentally-relevant timeframe: creep at fixed load, stress relaxation at fixed displacement, and rate-dependent behavior. If the load history has a holding period, creep is shown as a displacement of the tip even tough the load remains unchanged or depending on the degree of creeping, the unloading curve may present a “nose”. Creep effects lead to the overestimation of elastic modulus values due to high contact stiffness and to the underestimation of hardness values due to large viscous displacements. Popular experimental approaches use a long hold time at peak load, aspiring to unload elastically after saturating the creep. Another post-experiment approach and consists in the correction of the unloading contact stiffness by accounting for the creep rate at maximum load [A.H.W. Ngan, H.T. Wang, B. Tang, K.Y. Sze, Int. J. Solids Struct. 42 (2005)]. The disadvantage of such approaches is that the viscoelastic response is discarded and not measured, although time dependence is clearly a feature of the polymer’s mechanical behavior. Directly accounting for the time dependence with phenomenological modeling allows isolation of the elastic response while also directly measuring an experimental time-constant. Soft polymers can also develop substantial adhesive forces at the tip-sample interface, which largely affect elastic modulus determination [S. Grupta, F. Carrillo, C. Li, L. Pruitt, C. Puttlitz, Materials Letters 61 (2007)]. A false decreasing trend in E values is observed with increasing penetration depth in the presence of adhesive forces. Adhesive forces can be measured and included in E determination analysis by taking into account the JFK model. When a polymer deforms elasto-plastically beneath the indenter tip, some material is displaced and push out to the side of the indenter forming a pile-up. The actual contact area is higher than the one determined by the Oliver-Pharr approach, and hence the elastic modulus and hardness data results to be overestimated. Finite element simulations can be used to account for the estimation of the actual contact area. Several examples of indentation tests on different polymers such as UHMWPE, PVC and PMMA are shown and analyzed for illustrative purposes. Prospective works will be directed toward the understanding of the intrinsic deformation behavior and the development of ad-hoc constitutive equations of polymeric systems.