Measurements of Two Independent Viscoelastic Functions by Nanoindentation

Current nanoindentation measurement techniques normally assume that one material function (such as the Poisson's function) is a constant, and measures just one material function, such as the creep compliance in shear. For materials with significant viscoelastic effects and unknown viscoelastic functions, assuming a constant for one material function is not satisfactory. Accurate measurements require simultaneously determining two independent material functions. This paper provides a method to use nanoindentation to measure both bulk and shear relaxation functions. Two different nanoindenter tips, namely Berkovich and spherical indenters, are used for nanoindentation on polymers. Any two independent viscoelastic functions, such as bulk relaxation modulus and shear relaxation modulus, have different representations in the load–displacement curves obtained with these two indenters so that the two independent viscoelastic functions can be separated and determined. Two polymers, poly(vinyl acetate) (PVAc) and poly(methyl methacrylate) (PMMA) were used in nanoindentation. Nanoindentation measurements were conducted on PVAc above glass transition temperature (Tg) and on PMMA below Tg. Both shear and bulk relaxation functions determined from nanoindentation were found in a reasonably good agreement with data obtained from conventional tests, providing validation of the method presented. The new method can be applied in measurements of two independent viscoelastic functions at sub-micron scale of very small amounts of materials such as polymeric films on a substrate, heterogeneous materials such as bones, tissues, and nanocomposites.     

Dynamic bulk and shear moduli due to grain-scale local fluid flow in fluid-saturated cracked poroelastic rocks: Theoretical model

Grain-scale local fluid flow is an important loss mechanism for attenuating waves in cracked fluid-saturated poroelastic rocks. In this study, a dynamic elastic modulus model is developed to quantify local flow effect on wave attenuation and velocity dispersion in porous isotropic rocks. The Eshelby transform technique, inclusion-based effective medium model (the Mori–Tanaka scheme), fluid dynamics and mass conservation principle are combined to analyze pore-fluid pressure relaxation and its influences on overall elastic properties. The derivation gives fully analytic, frequency-dependent effective bulk and shear moduli of a fluid-saturated porous rock. It is shown that the derived bulk and shear moduli rigorously satisfy the Biot-Gassmann relationship of poroelasticity in the low-frequency limit, while they are consistent with isolated-pore effective medium theory in the high-frequency limit. In particular, a simplified model is proposed to quantify the squirt-flow dispersion for frequencies lower than stiff-pore relaxation frequency. The main advantage of the proposed model over previous models is its ability to predict the dispersion due to squirt flow between pores and cracks with distributed aspect ratio instead of flow in a simply conceptual double-porosity structure. Independent input parameters include pore aspect ratio distribution, fluid bulk modulus and viscosity, and bulk and shear moduli of the solid grain. Physical assumptions made in this model include (1) pores are inter-connected and (2) crack thickness is smaller than the viscous skin depth. This study is restricted to linear elastic, well-consolidated granular rocks.     

X-ray scattering measurements of particle orientation in a sheared polymer/clay dispersion

We report steady and transient measurements of particle orientation in a clay dispersion subjected to shear flow. An organically modified clay is dispersed in a Newtonian polymer matrix at a volume fraction of 0.02, using methods previously reported by Mobuchon et al. (Rheol Acta 46: 1045, 2007). In accord with prior studies, mechanical rheometry shows yield stress-like behavior in steady shear, while time dependent growth of modulus is observed following flow cessation. Measurements of flow-induced orientation in the flow-gradient plane of simple shear flow using small-angle and wide-angle X-ray scattering (SAXS and WAXS) are reported. Both SAXS and WAXS reveal increasing particle orientation as shear rate is increased. Partial relaxation of nanoparticle orientation upon flow cessation is well correlated with time-dependent changes in complex modulus. SAXS and WAXS data provide qualitatively similar results; however, some quantitative differences are attributed to differences in the length scales probed by these techniques.     

Development of High Temperature Nanoindentation Methodology and its Application in the Nanoindentation of Polycrystalline Tungsten in Vacuum to 950 °C

The capability for high temperature nanoindentation measurements to 950 °C in high vacuum has been demonstrated on polycrystalline tungsten, a material of great importance for nuclear fusion and spallation applications and as a potential high temperature nanomechanics reference sample. It was possible to produce measurements with minimal thermal drift (typically ~0.05 nm/s at 750–950 °C) and no visible oxidative damage. The temperature dependence of the hardness, elastic modulus, plasticity index, creep, creep strain, and creep recovery were investigated over the temperature range, testing at 25, 750, 800, 850, 900 and 950 °C. The nanoindentation hardness measurements were found to be consistent with previous determinations by hot microhardness. Above 800 °C the hardness changes relatively little but more pronounced time-dependent deformation and plasticity were observed from 850 °C. Plasticity index, indentation creep and creep recovery all increase with temperature. The importance of increased time-dependent deformation and pile-up on the accuracy of the elastic modulus measurements are discussed. Elastic modulus measurements determined from elastic analysis of the unloading curves at 750–800 °C are close to literature bulk values (to within ~11 %). The high temperature modulus measurements deviate more from bulk values determined taking account of the high temperature properties of the indenter material at the point (850 °C) at which more significant time-dependent deformation is observed. This is thought to be due to the dual influence of increased time-dependency and pile-up that are not being accounted for in the elastic unloading analysis. Accounting for this time-dependency by applying a viscoelastic compliance correction developed by G. Feng and A.H.W. Ngan (J. Mater. Res. (2002) 17:660–668) greatly reduces the values of the elastic modulus, so they are agree to within 6 % of literature values at 950 °C.     

Nano-Indentation Device for Investigating the Mechanics of Compliant Materials

Indentation testing has long been used to measure the mechanical properties of a wide range of materials from metals and ceramics to brain tissue and hydrogels. The purpose of this study was to build and validate a Nano-Tissue Indenter (NTI) capable of performing indentation testing on micro-scale structures within the liver’s extracellular matrix. Two silicone-based tissue simulant materials were selected with elastic properties similar to hydrogels used for liver cell cultures. Samples of each material formulation, EcoFlex0030 (EF30) and EcoFlex0010 (EF10), were indented with NTI and also tested in unconfined compression to provide benchmark shear moduli. The resulting force and displacement measurements from NTI with resolutions of 300 nN and 700 nm respectively were analyzed using the Pietrement-Troyon model of adhesive contact. Using this method, NTI was able to distinguish a 10 kPa difference in shear modulus between EF30 and EF10 with comparable significance as unconfined compression (p?<?0.001). General agreement between the results of the two test methods is evidenced by the overlapping of the mean ± S.D. range for the NTI-indentation and benchmark unconfined compression shear moduli measured for both formulations. NTI was used successfully to perform nano-indentation tests on samples of compliant material undergoing adhesive contact, similar to the extracellular matrix of organs such as the liver.     

Linear viscoelastic models: Part II. Recovery of the molecular weight distribution using viscosity data

The constitutive models for the viscoelasticity of polymers are presented for determining molecular weight distributions (MWDs) from viscosity measurements. The inversion of this model derived from control theory and melt calibration procedure connects the relaxation modulus, viscosity, and other flow properties of a polymer. The linear principle enables simultaneous and accurate modelling of the relaxation modulus and of viscosity flow curves over a wide range. Starting from viscosity measurements, the new model is used to determine the MWD, linear viscoelastic relaxation moduli, and the relaxation spectra of polyethylene of different grades. In addition, two benchmark analyses of bimodal polystyrene are reported, and the capability of the model is proven by the two-box test of Malkin. The error of the modelled viscosity is smaller than that for previously reported models. One of the main features of this work is that no relaxation time or spectrum procedures were used to generate and model linear viscoelasticity.     

Rheology of molecular liquids and concentrated suspensions by microscopic dynamical simulations

The rheology and the associated changes that arise in sheared molecular and colloidal liquids are investigated by Molecular and Brownian Dynamics Computer Simulation. Significant shear thinning and normal pressure effects occur in all liquids when the shear rate approximately equals an inverse characteristic relaxation time for the material. The shear and bulk moduli, and self-diffusion coefficients increase with shear rate for all liquids and stable dispersions. The importance for rheology of hydrodynamic coupling between macromolecule trajectories at high packing fractions is demonstrated. The infinite frequency moduli depend on the packing fraction to a power which is effectively the same for all materials, i.e. ca. 3.5, above a percolation transition at a packing fraction 0.25. The suspending fluid enhances the degree of shear thinning above that of the corresponding single component fluid consisting of pure macroparticles.     

Tailored heterogeneity increases overall stability regime of composites having a negative-stiffness inclusion

Recent theoretical and experimental results have shown the possibility of enormous increases in composite material overall elastic stiffness, damping, thermal expansion, piezoelectricity, etc., when the composite contains a tuned non-positive-definite (i.e., negative stiffness) constituent. For such composite materials to have practical utility, they must be stable. Recent research has shown they can be, for a limited range of constituent negative stiffness. This research has treated linear elastic composite materials with homogeneous phases, via the energy method and full dynamic stability analyses.In the present work, we first show how to analyze the composites previously treated by the comprehensive but simpler static stability approach, obtaining closed-form results. We then employ this approach to show that permitting heterogeneity of the positive-definite phase can substantially increase the range of constituent negative stiffness while maintaining overall composite stability. We first treat the positive-definite phase heterogeneity as piecewise homogeneous, and then treat it as continuously-varying. In the continuously-varying heterogeneity case, we seek the radially optimal distribution of the elastic moduli in the coatings, under constant coating average moduli constraint, to permit the most negative possible inclusion stiffness while maintaining overall composite stability. This is accomplished for three coating cases: constant bulk modulus but arbitrarily radially-varying shear modulus; constant shear modulus but arbitrarily radially-varying bulk modulus; and both moduli arbitrarily radially varying. We find the optimal coatings to be: a heterogeneous one with shear modulus being a specific continuously decreasing function of radius for the first case; a homogeneous one for the second case; and a heterogeneous one with both moduli being either Dirac-delta or Heaviside-step decreasing functions of radius for the last case (if the coating moduli are unrestricted in magnitude or have upper limits, respectively). The results show a substantial increase in the permissible inclusion negative stiffness range is provided by coating heterogeneity, while maintaining overall composite stability. Such an increased range of constituent negative stiffness provides an enlarged tuning parameter range for the development of novel, high-performance composite materials.     

Effective elastic properties of porous materials: Homogenization schemes vs experimental data

In this paper, we focus on the prediction of elastic moduli of isotropic porous materials made of a solid matrix having a Poisson's ratio vm of 0.2. We derive simple analytical formulae for these effective moduli based on well-known Mean-Field Eshelby-based Homogenization schemes. For each scheme, we find that the normalized bulk, shear and Young's moduli are given by the same form depending only on the porosity p. The various predictions are then confronted with experimental results for the Young's modulus of expanded polystyrene (EPS) concrete. The latter can be seen as an idealized porous material since it is made of a bulk cement matrix, with Poisson's ratio 0.2, containing spherical mono dispersed EPS beads. The Differential method predictions are found to give a very good agreement with experimental results. Thus, we conclude that when vm=0.2, the normalized effective bulk, shear and Young's modulus of isotropic porous materials can be well predicted by the simple form (1 − p)² for a large range of porosity p ranging between 0 and 0.56.     

Rheological behaviour of vitreous humour

The vitreous humour (VH) is a complex biofluid that occupies a large portion of the eyeball between the lens and the retina, and exhibits non-Newtonian rheological properties that are key for its function in the eye. It is often possible to distinguish two different phases in VH, known as liquid and gel phases (Sebag J Eye 1: 254–262, 1987). In this work, we present a detailed rheological characterisation of the two phases of the VH under shear and extensional flow conditions. Healthy New Zealand rabbit eyes were used to measure the surface tension and the shear and extensional rheological properties of VH in different phase conformations and at different times after dissection. The results show that VH liquid phase exhibits a surface tension of 47.8 mN/m, a shear thinning behaviour reaching a viscosity plateau around 10^?3 Pa s for shear rates above ~1000 s^?1, and an average relaxation time of 9.7 ms in extensional flow. Interestingly, both VH phases present higher storage modulus than loss modulus, and the measurements performed with VH gel phase 4?±?1 h after dissection exhibit the highest moduli values. The compliance measurements for the gel phase show a viscoelastic gel behaviour and that compliance values decrease substantially with time after dissection. Our results show that the two VH phases exhibit viscoelastic behaviour, but with distinct rheological characteristics, consistent with a gel phase mostly composed of collagen entangled by hyaluronan and a second phase mainly composed of hyaluronan in aqueous solution.     

On the Measurement of two Independent Viscoelastic Functions with Instrumented Indentation Tests

In the present paper, a methodology for complete characterization of linear isotropic viscoelastic material with spherical instrumented indentation test is proposed. The developed method allows for measuring two independent viscoelastic functions, shear relaxation modulus and time-dependent Poisson’s ratio, from the indentation test data obtained at non-decreasing loading, but otherwise arbitrary. Finite element modelling (FEM) is relied upon for validating the proposed methodology and for quantifying the influence of experimental variables on the measurements accuracy. Spherical indentation experiments are performed on several viscoelastic materials: polyoxymethylene, bitumen and bitumen-filler mastics. The viscoelastic material functions obtained with the indentation tests are compared with the corresponding results from the standard mechanical tests. Numerical and experimental results presented indicate that the methodology proposed allows mitigating the machine compliance and loading rate effects on the accuracy of the viscoelastic indentation tests.     

Dynamic shear properties of a technical polystyrene melt

A dynamic viscometer of the Couette type is described which permits the determination of storage and loss shear modulus of polymer melts with high accuracy. For a technical polystyrene, results of measurements of storage and loss moduli are reported in the temperature interval between the rubbery plateau and degradation. From these data, the courses of storage and loss compliances and the course of the time-dependent shear compliance are derived and compared with the results of creep measurements.The frequency dependence of the storage compliance shows clearly the presence of the so-called network transition between the end of the glass transition and the onset of flow. The time-temperature shifting laws for the flow process and for the network transition are shown to obey the WLF shift equation, but with different sets of parameter values. Consequently, the complete data do not obey the time-temperature superposition law.Comparison with non-Newtonian viscosities, measured by means of a slit and a capillary viscometer attached to an extruder, shows the excellent validity of the Cox-Merz rule, provided either the absolute dynamic viscosity or the stressing viscosity are used for this comparison.Dedicated to Prof. Dr. Josef Schurz, University Graz, Austria, on the occasion of his 60th birthday     

The total creep of viscoelastic composites under hydrostatic or antiplane loading

The problem of bounding the total creep (or total stress relaxation) of a composite made of two linear viscoelastic materials and subjected to a constant hydrostatic or antiplane loading is considered. It is done by coupling the immediate and the relaxed responses of the composite, which are pure elastic. The coupled bounds provide the possible range of the total deformation at infinite time as a function of the initial deformation of the composite. For antiplane shear existing bounds for coupled two-dimensional conductivity yield the required coupled bounds, and these are attained by doubly coated cylinder assemblages. The translation method is used to couple the effective bulk moduli of a viscoelastic composite at zero and infinite time. A number of microgeometries are found to attain the bulk modulus bounds. It is shown that the Hashin's composite sphere assemblage does not necessarily correspond to the maximum or minimum overall creep, although it necessarily attains the bounds for effective bulk moduli. For instance, there are cases when the doubly coated sphere microstructure or some special polycrystal arrangements attain the bounds on the total creep.     

DETERMINATION OF EFFECTIVE MODULI FOR FOAM PLASTICS BASED ON THREE PHASE SPHEROIDAL MODEL

The relations of bulk modulus,shear modulus,Young's modulus and the Poisson's ra-tio with porosity of foam plastics are determined by a three phase spheroidal model commonly used inComposite Mechanics.The results are compared with those using differential scheme.It is shownthat the material properties derived from the present model normally are larger than those obtained bydifferential scheme for foam plastics with identical porosity.The differences in shear moduli andYoung's moduli obtained by the two methods are small,but they are larger for bulk moduli of incom-pressible matrix and Poisson's ratios.The Young's moduli of high density foam plastics derived by thepresent model agree better with experimental ones.     

<Emphasis Type="Italic">In-situ</Emphasis> Measurement of Crystalline Lattice Strains in Polytetrafluoroethylene

Strain measurements by neutron diffraction are employed as an in situ technique to obtain insight into the deformation modes of crystalline domains in a deformed semi-crystalline polymer. The SMARTS (Spectrometer for MAterials Research at Temperature and Stress) diffractometer has been used to measure the crystalline lattice displacements in polytetrafluoroethylene (PTFE) for crystalline phase IV (at room temperature) in tension and compression and for crystalline phase I (at 60°C) in compression. The chemical structure of PTFE, -(C₂F₄)-_n, makes it ideally suited for investigation by neutron methods as it is free of hydrogen that results in limited penetration depths and poor diffraction acquisition in most polymers. Deformation parallel to the prismatic plane normals is shown to occur by inter-polymer chain compression with a modulus ∼10× bulk, while deformation parallel to the basal plane normal occurs by intra-polymer chain compression with a modulus ∼1000× bulk, corresponding with theoretical values for a PTFE chain modulus. Deformation parallel to the pyramidal plane normals is accommodated by inter-polymer chain shear.     

基于三相球模型确定泡沫塑料有效模量

通过复合材料三相球模型确定泡沫塑料的体积模量、剪切模量、杨氏模量和泊松比等材料等参数与材料孔隙比的关系，并将该文结果同微分法得到的结果进行了对比；结果表明：三相球模型确定的材料参数在相同孔隙比情况下，一般都高于微分法确定的结果，两种方法得到的有效剪切模量和杨氏模量差异较小，而体积模量和泊松比则差异较大，然而，由三相球模型确定的泡沫塑料杨氏模量仍可与实验较好地符合。此外，该文结果也同现有的理论及实验     

Rheology of concentrated microgel solutions

Viscosity, modulus, and yield stress for 0–6 wt% aqueous solutions of Carbopol 941 were investigated using constant shear rate, constant shear stress, and dynamic oscillatory experiments. The microgel character of the polymer was evident from the solid-like behavior of the solutions above 1 wt%. Yield stress increased with concentration, but yield occurred at a critical shear strain of 40%, independent of concentration. The static stress-strain relationship became non-linear at ~ 25% strain, in fair agreement with the onset of non-linear response in the storage modulus at ~ 10% strain. Small strain moduli from static and low frequency measurements agreed rather well; modulus values obtained from the recoverable strain after yielding were 30–40% smaller. Solutions flowed at near-constant stress in the low shear rate regime; at higher rates the stress increases with shear rate more rapidly. The viscosity did not obey the Cox-Merz rule. Steady-state viscosity scaled with polymer concentration to the 3/4 power. Results were interpreted using a cellular, deformable sphere model for the polymer, in analogy to emulsions and foams.     

一种适用于低体模量材料的被动围压SHPB实验设计

基于动态三轴被动加载实验技术,建立了一种可测量吉帕量级及以下低体模量材料压强-体应变关系的被动围压SHPB实验设计方法。在该实验设计中确定了样品、封装垫块、围压套管的尺寸以及尺寸间的匹配,并对实验压强进行了限制。通过比较传统SHPB实验和被动围压SHPB实验测量LC4铝合金等效应力的方式,验证了被动围压SHPB实验压强测量的有效性;通过实验和数值模拟分析,验证了体应变测量的有效性。将设计的被动围压SHPB实验方法应用于铈,得到了铈在伽马→阿尔法相变区间完整显示的压强-体应变演化信息,且相变起始和终止压强、相变体积变化量均与静高压实验结果基本一致。这说明设计的被动围压SHPB实验方法适用于测量低体模量材料的压强-体应变关系。     

A MODIFIED TORSION PENDULUM FOR MEASURING THE SHEAR MODULUS OF A SINGLE MICRO-SIZED FILAMENT

A modified torsion pendulum apparatus is developed for measuring the shear modu- lus of single filaments with uniform micro-sized diameter. A single filament fixed at both ends and with a ring-shaped mass attached at the middle is used as a clamped-clamped torsion pendulum. The shear modulus of single filaments can be expressed as a function of the oscillation frequency of the torsion pendulum. The oscillation motion is measured with a CCD laser displacement sensor, and its frequency is determined by the Fast Fourier Transform （FFT） method. The shear moduli of three types of filaments： copper wires, tungsten wires and carbon fibers are accurately measured with this technique. It is found that the size effect in shear moduli of both copper wires and tungsten wires is minor. Finally, the error analysis of our measurement technique is presented in detail.     

Linear rheology of compressible soft nanocomposites

The influences of interfacial tension and compressibility to the linear viscoelastic properties of nanocomposite and nanoporous materials are considered theoretically. The effective bulk and shear moduli of the systems are calculated within the generalized composite sphere model which takes into account the effect of interfacial tension. It is found that frequency dependence of the effective dynamic shear and bulk moduli of nanocomposites with the compressible elastic matrix and viscous inclusions may be represented in terms of the Zener model comprising of the viscoelastic Kelvin element in series with the elastic spring. The relations of the Zener model parameters with the material characteristics are revealed. The physical interpretation of the frequency behavior of the dynamic shear and bulk moduli against the interfacial tension, component compressibility, viscosity, and inclusion volume fraction is discussed. Victor G. Oshmyan deceased.