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     

AFM nanoindentation of viscoelastic materials with large end‐radius probes

We used atomic force microscopy (AFM) nanoindentation to measure mechanical properties of polymers. Although AFM is generally acknowledged as a high‐resolution imaging tool, accurate quantification of AFM nanoindentation results is challenging. Two main challenges are determination of the projected area for objects as small as AFM tips and use of appropriate analysis methods for viscoelastic materials. We report significant accuracy improvements for modulus measurements when large end‐radius tips with appropriate cantilever stiffnesses are used for indentation. Using this approach, the instantaneous elastic modulus of four polymers we studied was measured within 30 to 40% of Dynamic Mechanical Analysis (DMA) results. The probes can, despite their size and very high stiffnesses, be used for imaging of very small domains in heterogeneous materials. For viscoelastic materials, we developed an AFM creep test to determine the instantaneous elastic modulus. The AFM method allows application of a nearly perfect stepload that facilitates data analysis based on hereditary integrals. Results for three polymers suggest that the observed creep in the materials has a strong plastic flow component even at small loads. In this respect, the spherical indenter tips behave like “sharp” indenters used in indentation studies with instrumented indenters. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1573–1587, 2009     

Elevated temperature nanoindentation characterization of poly(para-phenylene vinylene) conjugated polymer films

Temperature dependent mechanical properties of poly(p-phenylene vinylene) (PPV) were investigated using quasi-static (QS) and dynamic nanoindentation (NI) at temperatures over the range of 25 to 100 °C. The reduced modulus decreased from about 4.40 GPa to 3.64 GPa over this temperature range. The plasticity indices at all measurement temperatures were lower than the critical value of 0.875, characterizing material “sink-in”, rather than “pile-up” during measurements. The plasticity index showed a non-monotonic trend, with a minimum value at around 70 °C. Analysis of indentation stress relaxation data, obtained at different temperatures, was also performed using generalized Maxwell viscoelastic models. From these analyses, a relaxation mode, with a characteristic relaxation time of approximately 0.5 s, was evident. The characteristic time remained relatively unchanged over the temperature range of 25 to 100 °C. However, the relaxation modulus associated with this mode showed the expected decrease with increase in temperature.     

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.     

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     

High temperature creep behavior of phosphoric acid‐polybenzimidazole gel membranes

This work investigates the effects of polymer solids content and macromolecular structure on the high temperature creep behavior of polybenzimidazole (PBI) gel membranes imbibed with phosphoric acid (PA) after preparation via a polyphosphoric acid (PPA) mediated sol‐gel process Low‐solids, highly acid‐doped PBI membranes demonstrate outstanding fuel cell performance under anhydrous, ambient pressure, and high temperature (120–200 °C) operating conditions. However, PBI membranes are susceptible to creep under compressive loads at elevated temperatures, so their long‐term mechanical durability is a major concern. Here, we report results for the creep behavior of PBI membranes subject to compression at 180 °C. For para‐ and meta‐PBI homopolymers, increasing polymer solids content results in lower creep compliance and higher extensional viscosity, which may be rationalized by increasing chain density in the sol‐gel network. Comparing various homo‐ and copolymers at similar solids loading, differences in creep behavior may be rationalized in terms of chain–chain and chain‐solvent interactions that control macromolecular solubility and stiffness in the PA solvent. The results demonstrate the feasibility of improving the mechanical properties of PA‐doped PBI membranes by control of polymer solids content and rational design of PBI macromolecular structure. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1527–1538     

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     

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     

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.     

Viscoelastic properties of dilute polymer solutions: The effect of varying the concentration

Dynamic viscoelastic behavior was investigated for solutions of polystyrene in tricresyl phosphate, a good solvent, at concentrations, c, less than the coil‐overlapping concentration, c*. At the infinite dilution limit, the behavior was in accord with the theory of Doi and Edwards involving the excluded volume potential and hydrodynamic interaction (HDI). Thus, the viscoelastic functions were completely derived from the intrinsic viscosity–molecular weight relation. At finite c, the complex modulus was represented by the sum of two terms. One was a Rouse–Zimm (RZ) term conveniently represented by the Zimm theory with an arbitrarily chosen value of the HDI parameter. The other was a term with a single relaxation time, longer than the longest RZ relaxation time, and with a high‐frequency modulus proportional to the square of c [the long‐time (LT) term]. The behavior of the RZ term indicated the stronger screening of HDI with increasing c. Using the experimental c dependence of the longest RZ relaxation time to get the relevant parameter, we compared the RZ viscoelastic function with the Muthukumar–Freed theory. The agreement was good at low concentrations, c < c*. The contribution of the LT term, which was not included in the theory, was quite significant at low frequencies; about 60% of the Huggins coefficient was attributable to this term. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 211–217, 2001     

Stress-dependent dynamic compliance spectra approach to the nonlinear viscoelastic response of polymers

The present work reports a discrete, stress-dependent dynamic compliance spectra method which may be used to predict the mechanical response of nonlinear viscoelastic polymers during strain-defined processes. The method is based on the observation that the real and complex parts of the discrete dynamic compliance frequency components obtained from creep measurements are smooth, easily fit functions of stress. Comparisons between experimental measurements and model calculations show that the model exhibits excellent quantitative agreement with the basis creep measurements at all experimental stress levels. The model exhibits good quantitative agreement with stress relaxation measurements at moderate levels of applied strain. However, the model underestimates the experimental stress relaxation at an applied strain of 3.26%. The stress relaxation error appears to be a real material effect resulting from the different strain character of creep and stress relaxation tests. The model provides a good quantitative agreement with experimental constant strain rate measurements up to approximately 4% strain, after which the model underestimates the experimental flow stress. This effect is explained by the time dependence of the stress-activated configurational changes necessary for large strains in glassy polymers. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2301–2309, 1998     

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.     

Viscoelasticity of nanobubble‐inflated ultrathin polymer films: Justification by the coupling model

The nanobubble inflation method is the only experimental technique that can measure the viscoelastic creep compliance of unsupported ultrathin films of polymers over the glass–rubber transition zone as well as the dependence of the glass transition temperature (T_g) on film thickness. Sizeable reduction of T_g was observed in polystyrene (PS) and bisphenol A polycarbonate by the shift of the creep compliance to shorter times. The dependence of T_g on film thickness is consistent with the published data of free‐standing PS ultrathin films. However, accompanying the shift of the compliance to shorter times, a decrease in the rubbery plateau compliance is observed. The decrease becomes more dramatic in thinner films and at lower temperatures. This anomalous viscoelastic behavior was also observed in poly(vinyl acetate) and poly (n‐butyl methacrylate), but with large variation in the change of either the T_g or the plateau compliance. By now, well established in bulk polymers is the presence of three different viscoelastic mechanisms in the glass–rubber transition zone, namely, the Rouse modes, the sub‐Rouse modes, and the segmental α‐relaxation. Based on the thermorheological complexity of the three mechanisms, the viscoelastic anomaly observed in ultrathin polymer films and its dependence on chemical structure are explained in the framework of the Coupling Model. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013     

A detailed elastic analysis of the flat punch (tack) test for pressure‐sensitive adhesives

Detailed finite element calculations are carried out in order to study the mechanical response of a compliant layer sandwiched between a rigid cylindrical flat punch and a rigid substrate. Two cases of practical interest are considered: one in which the layer is perfectly bonded to the punch and the substrate and one in which the interface between the punch and the layer is frictionless. The substrate is assumed to be perfectly bonded to the adhesive layer in both cases. Analytic expressions are obtained for the stresses away from the edges, and the effect of lateral constraint is examined. The compliances of the loading systems for both cases are obtained numerically, and accurate analytic expressions are determined based on these numeric results. The nature of the stress fields near the contact edge are explored, and their connections with the energy release rate are determined. The relevance of these calculations to two recent adhesion tests is discussed. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2769–2784, 2000     

Anomalous aging in two-phase systems: Creep and stress relaxation differences in rubber-toughened epoxies

From time–aging time superposition principles, similar to time–temperature superposition, one would expect similar shifting or superposition behaviors for both creep and stress relaxation responses. In particular, for isotropic homogeneous systems, in the linear viscoelastic regime, consideration of superposition in rheology by Markowitz¹ or the discussion by Ferry² from the Kramers–Kronig relation would seem to demand that creep and stress relaxation shift in the same way. Here we report on results from creep and stress relaxation measurements in two-phase, rubber-toughened epoxies that exhibit Boltzman additivity of creep or relaxation behaviors and follow the time–aging time superposition behavior in creep, but not in stress relaxation. While the lack of superposition in stress relaxation is, perhaps, not surprising, the finding that the creep responses at different aging times superimpose while the stress relaxation responses do not, presents an anomalous behavior that has not been previously reported. In addition, our findings show that the stress relaxation responses show short time “softening” upon aging. Possible reasons for the anomalous behaviors are briefly considered. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1167–1174, 1997     

The mechanics of tack: Viscoelastic contact on a rough surface

This work considers the mechanics of tack in viscoelastic materials. We study a particular tack test in which a flat, rigid probe is brought into contact with the rough surface of a viscoelastic material. The rough surface is modeled as consisting of many spherical asperities of varying heights but all having the same radius. Because of the asperities, the apparent contact area can be much greater than the actual contact area, which is regarded as the key parameter that controls tack. We show how this actual contact area evolves with time under different loading conditions. Our formulation is different from previous theories in that it explicitly accounts for the fact that asperities of different heights are subjected to different loading histories. Explicit solutions are given for the cases of a constant load test, a load relaxation test, and a constant displacement rate test. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1485–1495, 2000     

Influence of Material Properties on the Damage-Reporting and Self-Healing Performance of a Mechanically Active Dynamic Network Polymer in Coating Applications

We conducted a detailed investigation of the influence of the material properties of dynamic polymer network coatings on their self-healing and damage-reporting performance. A series of reversible polyacrylate urethane networks containing the damage-reporting diarylbibenzofuranone unit were synthesized, and their material properties (e.g., indentation modulus, hardness modulus, and glass-transition temperature) were measured conducting nanoindentation and differential scanning calorimetry experiments. The damage-reporting and self-healing performances of the dynamic polymer network coatings exhibited opposite tendencies with respect to the material properties of the polymer network coatings. Soft polymer network coatings with low glass-transition temperature (~10 °C) and indentation hardness (20 MPa) exhibited better self-healing performance (almost 100%) but two times worse damage-reporting properties than hard polymer network coatings with high glass-transition temperature (35~50 °C) and indentation hardness (150~200 MPa). These features of the dynamic polymer network coatings are unique; they are not observed in elastomers, films, and hydrogels, whereby the polymer networks are bound to the substrate surface. Evidence indicates that controlling the polymer’s physical properties is a key factor in designing high-performance self-healing and damage-reporting polymer coatings based on mechanophores.     

Relaxation of polymer thin films in isothermal temperature‐jump measurements

The dynamic behavior of thin polymer films is of interest in the fabrication of microelectronics and optoelectronics and in the coatings industry. It is known that polymer relaxation is affected by film thickness and the particular substrate/polymer pair. We previously used a spectroscopic ellipsometer to investigate the glass transition in thin films. In addition to information on the modification of thermal transitions such as the glass‐transition temperature, the speed of data acquisition in an automated, spectroscopic ellipsometer, operated at a single wavelength of 780 nm, allows for the direct observation of the isothermal dimensions of a thin polymer film as a function of time after a rapid temperature change. In this article, we discuss recent results from the observation of the time dependence of film‐normal thickness and normalized, in‐plane, lateral dimension as well as simple fits to this relaxation behavior in terms of a normalized viscosity and relaxation time. The results support a highly asymmetric initial thermal expansion normal to the film followed by close to isotropic relaxation and anisotropic “flow” (the flow in response to the vanishingly small shears of thermal expansion). These features may clarify issues involving the observation of chain confinement in thin polymer films in terms of potential differences between equilibrium and dynamic measurements. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2929–2936, 2000     

Full‐chain dynamics of entangled linear and star polymers

The full‐chain dynamics and the linear viscoelastic properties of monodisperse, entangled linear and star polymers are simulated consistently via an equilibrium stochastic algorithm, based on a recently proposed full‐chain reptation theory 1 that is able to treat self‐consistently mechanisms of chain reptation, chain‐length fluctuations, and constraint release. In particular, it is the first time that the full‐chain simulation for star polymers is performed without subjecting to the great simplifications usually made. To facilitate the study on linear viscoelasticity, we employ a constraint release mechanism that resembles the idea of tube dilation, in contrast to the one used earlier in simulating flows, where constraint release was performed in a fashion similar to double reptation. Predictions of the simulation are compared qualitatively and quantitatively with experiments, and excellent agreement is found for all investigated properties, which include the scaling laws for the zero‐shear‐rate viscosity and the steady‐state compliance as well as the stress relaxation and dynamic moduli, for both polymer systems. The simulation for linear polymers indicates that the full‐chain reptation theory considered is able to predict very well the rheology of monodisperse linear polymers under both linear viscoelastic and flow conditions. The simulation for star polymers, on the other hand, strongly implies that double reptation alone is insufficient, and other unexplored mechanisms that may further enhance stress relaxation of the tube segments near the star center seem crucial, in explaining the linear viscoelasticity of star polymers. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 248–261, 2000