Viscoelastic characterization of polymers using instrumented indentation. I. Quasi‐static testing*

The use of instrumented indentation to characterize the mechanical response of polymeric materials was studied. A model based on contact between a rigid probe and a linear viscoelastic material was used to calculate values for the creep compliance and stress relaxation modulus for two glassy polymeric materials, epoxy and poly(methyl methacrylate), and two poly(dimethyl siloxane) (PDMS) elastomers. Results from bulk rheometry studies were used for comparison with the indentation stress relaxation results. For the two glassy polymers, the use of sharp pyramidal tips produced responses that were considerably more compliant (less stiff) than the rheometry values. Additional study of the deformation remaining in epoxy after indentation creep testing as a function of the creep hold time revealed that a large portion of the creep displacement measured was due to postyield flow. Indentation creep measurements of the epoxy with a rounded conical tip also produced nonlinear responses, but the creep compliance values appeared to approach linear viscoelastic values with decreasing creep force. Responses measured for the unfilled PDMS were mainly linear elastic, with the filled PDMS exhibiting some time‐dependent and slight nonlinear responses in both rheometry and indentation measurements. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1794–1811, 2005     

Flat‐punch indentation of viscoelastic material

The indentation of standard viscoelastic solids, that is, the three‐element viscoelastic material, by an axisymmetric, flat‐ended indenter has been investigated theoretically. Under the boundary conditions of flat‐punch indentation of a viscoelastic half‐space, the solutions of the equations of viscoelastic deformation are derived for the standard viscoelastic material. Their generality resides in their inclusion of compressible as well as incompressible solids. They cover the two transient situations: flat‐punch creep test and load‐relaxation test. In experimental tests of their applicability, nanoindentation and microindentation probes under creep and relaxation conditions yielded a modulus from 0.1 to 1.1 GPa and viscosity from 1 to 37 Gpa · s for a crosslinked glassy polyurethane coatings. For bulk polystyrene, the values vary from 1 to 2 GPa and from 20 to 40 Gpa · s, respectively. The analysis here provides a fundamental basis for probing elastic and viscous properties of coatings with nanoindentation or microindentation tests. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 10–22, 2000     

Nanoindentation of polymers: an overview

In this paper, the application of instrumented indentation devices to the measurement of the elastic modulus of polymeric materials is reviewed. This review includes a summary of traditional analyses of load‐penetration data and a discussion of associated uncertainties. Also, the use of scanning probe microscopes to measure the nanoscale mechanical response of polymers is discussed, particularly with regard to the associated limitations. The application of these methods to polymers often leads to measurements of elastic modulus that are somewhat high relative to bulk measurements with potentially artificial trends in modulus as a function of penetration depth. Also, power law fits to indentation unloading curves are often a poor representation of the actual data, and the power law exponents tend to fall outside the theoretical range. These problems are likely caused by viscoelasticity, the effects of which have only been studied recently. Advancement of nanoindentation testing toward quantitative characterization of polymer properties will require material‐independent calibration procedures, polymer reference materials, advances in instrumentation, and new testing and analysis procedures that account for viscoelastic and viscoplastic polymer behavior.     

Viscoelastic modeling of nanoindentation experiments: A multicurve method

Nanoindentation is an increasingly used method of extracting surface mechanical properties of viscoelastic materials, especially polymers. Recently, Hutcheson and McKenna used a viscoelastic contact mechanics model to analyze the contact problem between a nanosphere and polystyrene surface. In nanoindentation experiments, the ramp loading test is a similar problem to the particle embedment experiment except that the indentation load function differs. The motivation in this work is to expand the Hutcheson and McKenna analysis to the nanoindentation problem. In particular, we illustrate the limitations of analyzing only a single load‐indentation curve, which does not provide enough information to determine the full range of the viscoelastic response of a polymer, and we show that performing a test sequence that includes multiple loading rates or indentation rates spanning two or more orders of magnitude greatly improves the extracted viscoelastic properties. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 633–639     

Temperature dependent relaxation of a “solid–liquid”

We have used the Interfacial Force Microscope to perform temperature dependent indentation measurements on a model viscoelastic material, Silly Putty. By transforming time dependent stress relaxations into frequency dependent modulus, we can identify the temperature dependence of the elastic and viscous response of an experimentally challenging material. This technique promises to be useful in determining the mechanical properties of composite materials with microscopic spatial resolution. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1285–1290, 2009     

Stretched polymer surfaces: Atomic force microscopy measurement of the surface deformation and surface elastic properties of stretched polyethylene

The surface structure and surface mechanical properties of low‐ and high‐density polyethylene were characterized by atomic force microscopy (AFM) as the polymers were stretched. The surfaces of both materials roughened as they were stretched. The roughening effect is attributed to deformation of nodular structures, related to bulk spherulites, at the surface. The surface‐roughening effect is completely reversible at tensile strains in the elastic regime and partially reversible at tensile strains in the plastic regime until the polymers are irreversibly drawn into fibers. AFM force versus distance interaction curves, used to measure changes in the stiffness of the surface and the surface elastic modulus as a function of elongation, show that the surfaces become softer as the polymers are drawn into fibers at high strains. At low elastic strains, however, the surface elastic modulus of HDPE increases—attributed to elastic energy stored by the amorphous regions. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2263–2274, 2001     

Nanoindentation creep of nonlinear viscoelastic polypropylene

Uniaxial tensile creep tests at various applied stresses were carried out to demonstrate that PP is nonlinear viscoelastic. A novel phenomenological model consisting of springs, dashpots, stress-locks and sliders was proposed to describe the nonlinear viscoelasticity. Indentation creep tests at different applied load levels were also performed on nonlinear viscoelastic PP. It was found that the shear creep compliance varies with the applied load level when the applied load is less than 5 mN, which means the indentation creep behavior was nonlinear. To find the real reason for the nonlinearity in indentation creep tests, the elastic modulus at various indentation depths was measured using continuous stiffness measurements (CSM). By analyzing the variation of elastic modulus with indentation depth, the nonlinearity of indentation creep behavior was proved to be caused by the non-uniform properties in the surface of the specimen rather than nonlinear viscoelasticity.     

AFM nanoindentation to determine Young’s modulus for different EPDM elastomers

AFM nanoindentation was investigated as a method for determining the micromechanical properties of polymer materials. It is generally accepted that the shape of the tip of the cantilever undergoes a change in a standard AFM setup. The shape defines the projected contact area, so it is a parameter directly proportional to the elastic modulus; any change in the shape thus affects the accuracy of the results. The method suggested in this paper relies on the introduction of an experimentally determined tip-area function. Values for Young’s modulus were calculated for EPDM samples with different degrees of cure and crystallinity. The degree of crystallinity has a greater impact on the mechanical properties of the material than the degree of cure. Depending on the amplitude of the indentation, the E-moduli determined by AFM are systematically higher. When studying different regions of polymer materials, the values of the E-modulus determined by AFM become identical to those measured by means of DMA on extrapolation of the modulus at zero indentation.     

Characterization of elastomeric blends by atomic force microscopy

The bulk mechanical properties of a blend of elastomers are found to depend on the micro and nano scale morphology of the phases of the materials in the blend. In this study, we examine the phase morphology of blends of incompatible elastomers using Atomic Force Microscopy (AFM). Specifically, nanoindentation and Tapping Mode AFM (TMAFM) imaging techniques are used as experimental tools for mapping the composition of unfilled elastomeric blends. Depending on the composition of the blend, either co‐continuous or discontinuous domain/matrix morphology is observed. To identify the different components in bromobutyl (BIIR)/natural rubber (NR) blends, nanoscale indentation measurements were made on the observed phase‐separated regions. Results from force mode AFM and mechanical measurements of bulk NR and BIIR are used to assist in the interpretation of the TMAFM results for the BIIR/NR blends. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 492–503, 2006     

The effects of pile-up,viscoelasticity and hydrostatic stress on polymer matrix nanoindentation

It is well known that a clear disparity exists between the elastic modulus determined using macroscopic tensile testing of polymers and those determined using nanoindentation, with indentation moduli generally overestimating the elastic modulus significantly. The effects of pile-up, viscoelasticity and hydrostatic stress on the indentation modulus of an epoxy matrix material are investigated. An analysis of residual impressions using scanning probe microscopy indicates that material pile-up is insignificant. Viscous effects are negated by increasing the time on the sample during the loading/hold segment phases of the indentation test, and by calculating the contact stiffness at a drift-insensitive point of the unloading curve. Removing the effects of viscous deformation reduces the modulus by 10–13%, while also significantly improving the non-liner curve fitting procedure of the Oliver and Pharr method. The effect of hydrostatic stress on the indentation modulus is characterised using relations from literature, reducing the measured property by 16%. Once viscous and hydrostatic stress effects are accounted for, the indentation modulus of the material compares very well with the bulk tensile modulus, and modifications to standard indentation protocols for polymers are proposed.     

Nanoindentation of biodegradable cellulose diacetate‐graft‐poly(L‐lactide) copolymers: Effect of molecular composition and thermal aging on mechanical properties

Nanoindentation of cellulose diacetate‐graft‐poly(lactide)s (CDA‐g‐PLLAs) synthesized by ring opening graft copolymerization of L ‐lactide in bulk onto the residual hydroxyl positions on CDA were conducted to investigate the effect of the molecular composition and thermal aging on mechanical properties and creep behavior. Continuous stiffness measurement (CSM) technique was used to obtained hardness and elastic modulus. These material properties were expressed as a mean value from 100 to 300 nm depths and an unloading value at final indentation depth. The hardness and elastic modulus in all CDA‐g‐PLLAs were higher than those in pure CDA, indicating that the introduction of PLLA increases the hardness and elastic modulus. With an increase of crystallinity by thermal aging, the hardness and elastic modulus were increased in both CDA‐g‐PLLA and PLLA. The creep test performed by CSM showed that the creep strain of CDA was decreased by the grafting of PLLA. Thermal aging decreased the creep strain of CDA‐g‐PLLA and PLLA. With an increase of holding time, hardness was decreased, whereas elastic modulus was kept almost constant. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1114–1121, 2007     

Investigation of Viscoelastic Properties of Amorphous Selenium near Glass Transition Using Depth‐Sensing Indentation

Abstract

New procedures involving depth‐sensing indentation are used to measure the submicron scale elastic modulus, hardness, viscosity, and activation energy and volume for creep of amorphous selenium below glass transition. The accurate measurement of Young's modulus in a highly viscoelastic situation using depth‐sensing indentation remains a challenge, and a creep correction procedure is employed here to measure the modulus. The measured Young's modulus exhibits a strong decreasing trend from ～10 GPa to 4.4 GPa as temperature increases from ～302 K to 309 K, in reasonably good agreement with bulk behavior. Two new procedures are also proposed here to measure the viscosity. The measured shear viscosity decreases from ～1×10¹² Pa‐s to ～2×10¹⁰ Pa‐s when the temperature increases over the same range, and the variation with temperature is found to obey an Arrehnius rate equation. The activation energy for the viscous creep process is found to be ～463 kJ/mol. Both the viscosity and the activation energy are lower than the bulk values, and this is thought to be due to the much higher stress levels of over 200 MPa involved in the nanoindentation experiments here. The apparent activation volume exhibits a rising trend from 1.04×10^?31 to 2.35×10^?30 m³ over the same temperature range.     

Instrumented Macroindentation Techniques for Polymers and Composites – Mechanical Properties,Fracture Toughness and Time-Dependent Behaviour as a Function of the Temperature

An innovative cooling and heating device has been successfully applied to an instrumented macrohardness testing machine in close collaboration with the company Zwick/Roell. The prototype allows the local time-dependent analysis of mechanical properties such as Martens hardness and indentation modulus, as well as fracture toughness and creep and relaxation behaviour at temperatures ranging from −100 °C to +100 °C. On the basis of load–indentation depth, load–time or indentation depth–time diagrams, the indentation behaviour as a function of test speed and/or temperature (which has rarely been done for polymers in the macro-range of loading) depending on matrix and materials composition (amorphous/semicrystalline thermoplastics, epoxy resins, micro- and nanocomposites) has been analysed. Martens-hardness, indentation modulus on the one hand and creep compliance and relaxation modulus on the other have been found to be strongly temperature dependent. Adequate methods of indentation fracture mechanics have been enhanced for polymers and applied to determine the fracture toughness of very different polymer-based materials.     

Surface elastic properties of human retinal pigment epithelium melanosomes

Atomic force microscope (AFM) imaging and nanoindentation measurements in water were used to probe the mechanical properties of retinal pigment epithelium melanosomes isolated from 14-year-old and 76-year-old donors. Topographic imaging reveals surface roughness similar to previous measurements on dry melanosomes. Force-indentation measurements show different types of responses that were catalogued into four different categories. In these measurements no permanent surface damage of melanosomes was observed as revealed by imaging before and after indentation measurements. The indentation measurements that exhibited nearly elastic responses were used to determine the Young's modulus of melanosomes. The average Young's modulus values are similar for 14-year-old and 76-year-old melanosomes with a somewhat narrower distribution for the 14-year-old sample. These elastic modulus values are considerably higher than the modulus of organelles with cytoplasm (<1 MPa) and approaching values of the modulus of protein crystals (approximately 100 MPa) indicating rather high packing density of biologic material in melanosomes. The width of the Young's modulus distributions is considerable spanning from few megapascals to few tens of megapascals indicating large heterogeneity in the structure. A fraction of the force curves cannot be described by the homogeneous elastic sample model; these force curves are consistent with approximately 10 nm structural heterogeneity in melanosomes. The approach-withdraw hysteresis indicates a significant viscoelasticity, particularly in the samples from the 14-year-old sample. Adhesion of the AFM probe was detected on approximately 3% and approximately 20% of the surface of 14-year-old and 76-year-old samples, respectively. In light of previous studies on these same melanosomes using photoelectron emission microscopy, this adhesion is attributed to the presence of lipofuscin on the surface of the melanosomes. This suggestion indicates that part of the difference in photochemical properties between the old and young melanosomes originates from surface lipofuscin.     

A discrete complex compliance spectra model of the nonlinear viscoelastic creep and recovery of microcellular polymers

The present work reports a discrete stress‐dependent, complex compliance spectra method that may be used to predict the mechanical response of nonlinear viscoelastic polymers during creep and recovery processes. The method is based on the observation that the real and imaginary parts of a discrete complex compliance frequency spectra obtained from creep and recovery measurements are smooth, easily fit functions of stress. The new method is applied to a set of microcellular polycarbonate materials with differing relative density. The nonlinear viscoelastic characteristics of a microcellular polycarbonate material system are very sensitive to relative density and therefore, this material system is a particularly difficult modeling challenge. However, the present model was able to exhibit excellent quantitative agreement with the basis creep and recovery measurements at all experimental stress levels for each of the experimental relative density material types. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 691–697, 2000     

Contact stiffness of initially stressed neo‐Hookean solids

This work, using the solution given by Dhaliwal and Singh, presents analytical expressions of the incremental stress and displacement fields for the axisymmetrical indentation of initially stressed, incompressible neo‐Hookean solids. A simple relation for the contact stiffness, contact area, elastic constants, and finite stretch can be obtained for the indentation by any rigid axisymmetric indenter, which can be described as a smooth function. The contact stiffness increases with the initial finite stretching; the finite stretching makes materials harder to deform. The results provide a basis for evaluating the effects of residual stresses on the nanoindentation of materials from the viewpoint of finite deformation. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2513–2521, 2004     

Measurement of viscoelastic properties for polymers by nanoindentation

A new method has been proposed and verified to measure the viscoelastic properties of polymers by nanoindentation tests. With the mechanical response of load–displacement curves at different loading rates, the parameters of creep compliance and relaxation modulus are calculated through the viscoelastic contact model. Dynamic thermomechanical analysis (DMA) tests are conducted to compare the results by the proposed technique. The results show that the correlation coefficients between DMA tests and the new method are above 0.9 in the entire range, which verified the feasibility of the method. The loading curves fitted by the model are identical to the experimental curves within the discrete points and so it shows that this technique is more suitable for general linear viscoelastic materials. Numerical creep tests are carried out to examine the effectiveness of the proposed method by input the Prony series calculated by the three-element Maxwell model and the viscoelastic contact model. The good agreement shows that the proposed technique can be applied in practice.     

Investigation of mechanical properties of insulin crystals by atomic force microscopy

Mechanical properties of protein crystals and aggregates depend on the conformational and structural properties of individual protein molecules as well as on the packing density and structure within solid materials. An atomic force microscopy (AFM)-based approach is developed to measure the elastic modulus of small protein crystals by nanoindentation and is applied to measure the elasticity of insulin crystals. The top face of the crystals deposited on mica substrates is identified as the (001) face. Insulin crystals exhibit a nearly elastic response during the compression cycle. The elastic modulus measured on the top face has asymmetric distribution with a significant width. This width is related to the uncertainty in the deflection sensitivity. A model that takes into account the distribution of the sensitivity values is used to correct the elastic modulus. Measurements performed in aqueous buffer on several crystals at different locations with three different AFM probes give a mean elastic modulus of 164 +/- 10 MPa. This value is close to the static elastic moduli of other protein crystals measured by different techniques that are usually measured in the range from 100 MPa to 1 GPa. The measured modulus of insulin crystals falls between the elastic modulus values of insulin amyloid fibrils measured previously at two orthogonal directions (a modulus of 14 MPa was measured by compressing the fibril in the direction perpendicular to the fibril axis, and a modulus of 3.3 GPa was measured in the direction along the fibril axis). This comparison indicates the heterogeneous structure of fibrils in the direction perpendicular to the fibril axis, with a packing density of the amyloid fibril core that is higher than the average packing density in insulin crystals. The mechanical wear of insulin crystals is detected during AFM measurements. In nanoindentation experiments on insulin crystal, the compressive load by the AFM tip ( approximately 1 nN, corresponding to a pressure of around 5 MPa) occasionally removes protein molecules from the top or the second top layer of insulin crystal in a sequential manner. The molecular model of this surface damage is proposed. In addition, the removal of the multiple layers of molecules is observed during the AC-mode imaging in aqueous buffer. The number of removed layers depends on the scan size.     

Effect of repetition nanoindentation of GaN epilayers on a‐axis sapphire substrates

In this work, gallium nitride (GaN) epilayers were deposited on a‐axis sapphire substrate by means of metal organic chemical vapor deposition (MOCVD). Berkovich nanoindentation was used to explore the repetition pressure‐induced impairment of the GaN film. The observation of load‐displacement vs stress‐strain curves concludes that basal slip is implicated in the deformation on the A plane GaN. The increase in the hardness (H) and elastic modulus (E) was determined from cyclic nanoindentation, and resulted in a crack due to the formation of incipient slip bands and/or the to‐and‐fro motion of mobile dislocation. It is indicated that the generation of individual dislocation and residual deformation of the GaN films are showed by CL mapping analysis. From the morphological studies, it is revealed that the crack was found by means of atomic force microscope (AFM) technique at nine loading/reloading cycles even after the indentation beyond the critical depth on the residual indentation impression. Copyright © 2010 John Wiley & Sons, Ltd.     

Viscoelastic properties of nanosilica‐filled epoxy composites investigated by dynamic nanoindentation

The viscoelastic properties of the epoxy filled with silica nanoparicles have been investigated by dynamic nanoindentation and characterized by the storage modulus and loss tangent. The materials studied are neat epoxy and silica/epoxy composites with silica volume fraction of 1, 3, 6, 10, and 14 vol %, respectively. The silica nanoparticles with an average diameter of 25 nm are found to disperse homogeneously in the epoxy matrix. The effect of the particle content, force frequency, and penetration load on the viscoelastic behavior is studied and discussed. The comparison with traditional testing methods such as tension, bending, and DMTA is made. Besides, theoretical results by using micromechanics models are also obtained and compared with the experimental results. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1030–1038, 2009