Viscoelastic State Research Articles

Modelling procedures and properties of rubber in rolling contact

Rubber covered cylinders in rolling contact are studied in two cases; rolling over a flat surface and rolling over a groove. In the first case, two different finite element procedures are compared for the purpose of investigating if computational savings can be made when taking amplitude dependent effects into account by using a modified viscoelastic steady state rolling procedure. This procedure is compared with using a more expensive overlay method with an elastoplastic-viscoelastic material model. The two procedures and material models are shown two give equal results in the flat surface case. For the case of rolling over a groove, it is shown how the non-linear dynamic material characteristics of the rubber layer influence the rolling contact. The groove filling capacity of the rubber is shown to be strongly dependent on the material model. It is shown that amplitude dependent rubber materials have better ability to fill out contact surface irregularities such as a groove.

Load-Relaxation Properties of the Human Trunk in Response to Prolonged Flexion: Measuring and Modeling the Effect of Flexion Angle

Experimental studies suggest that prolonged trunk flexion reduces passive support of the spine. To understand alterations of the synergy between active and passive tissues following such loadings, several studies have assessed the time-dependent behavior of passive tissues including those within spinal motion segments and muscles. Yet, there remain limitations regarding load-relaxation of the lumbar spine in response to flexion exposures and the influence of different flexion angles. Ten healthy participants were exposed for 16 min to each of five magnitudes of lumbar flexion specified relative to individual flexion-relaxation angles (i.e., 30, 40, 60, 80, and 100%), during which lumbar flexion angle and trunk moment were recorded. Outcome measures were initial trunk moment, moment drop, parameters of four viscoelastic models (i.e., Standard Linear Solid model, the Prony Series, Schapery's Theory, and the Modified Superposition Method), and changes in neutral zone and viscoelastic state following exposure. There were significant effects of flexion angle on initial moment, moment drop, changes in normalized neutral zone, and some parameters of the Standard Linear Solid model. Initial moment, moment drop, and changes in normalized neutral zone increased exponentially with flexion angle. Kelvin-solid models produced better predictions of temporal behaviors. Observed responses to trunk flexion suggest nonlinearity in viscoelastic properties, and which likely reflected viscoelastic behaviors of spinal (lumbar) motion segments. Flexion-induced changes in viscous properties and neutral zone imply an increase in internal loads and perhaps increased risk of low back disorders. Kelvin-solid models, especially the Prony Series model appeared to be more effective at modeling load-relaxation of the trunk.

Thermoreversible viscoelastic to weak gel transition in a micellar ionic liquid with salt

Rheological measurements as a function of temperature have been carried out on a micellar-ionic liquid (4.45wt% sodium dodecylsulfate (SDS) in 1-butyl-3-methylimidazolium chloride (BmimCl)) with 18.7wt% lithium chloride (LiCl). We report here for the first time, the formation of a “weak gel” state at high temperatures (>80°C) based on elastic and loss moduli behavior and yield stress measurements. Below 80°C, the sample is identified to be in a viscoelastic liquid state. The transition from viscoelastic liquid to weak gel state is found to be thermoreversible. From the rheological evolutions, small angle neutron scattering measurements and turbidity measurements, we argue that the weak gel state arises due to the winning of the micellar network structures over the association structure of BmimCl in the presence of lithium chloride and is responsible for the viscoelastic liquid to weak gel transformation observed in the micellar-ionic liquid.

Microrheological consequences of attractive colloid-colloid potentials in a two-dimensional Brownian fluid

By using microrheological methods commonly employed in videomicroscopy experiments, we study the rheology of a two-dimensional computational fluid formed by Brownian disks with the aim of exploring the influence of some effective colloid-colloid attractive interactions. The model of fluid is developed by Brownian dynamics simulations without hydrodynamical interactions, and it is characterized by calculating its equation of state from the pair distribution function. Micromechanical properties, relative and intrinsic viscosity and freezing are discussed. Then, we include attractive forces such a Asakura-Oosawa depletion force or an empiric expression proposed by Grier and Hal (GH) for an anomalous electrostatic potential observed in confined and charged colloids. By using both potentials, viscosity is clearly increased, but when the GH potential is included, viscoelastic gel state is reached for intermediate values of surface concentration. Finally, we analyse the influence of the attractive potentials in the breaking-up by thermal fluctuations of linear chains formed by 2D particles, finding that the GH potential reduces the characteristical time at which the disks can be considered as disaggregated. In this work, we employ an experimental-like methodology for the study of a Brownian hard-disk fluid, providing a very useful link with experimental procedures.

Effect of Physical States of Binders on High-Shear Wet Granulation and Granule Properties: A Mechanistic Approach Toward Understanding High-Shear wet Granulation Process, Part 3: Effect of Binder Rheological Properties

Ternary blends consisting of efavirenz (a model drug compound), lactose monohydrate, and a polymeric binder were investigated to verify the "physical state theory" in which granulation occurs only when binders undergo transition from glassy state to rubbery solution state. Furthermore, it was found that the rheological properties of the binders can significantly affect the granulation process. The blends with binders of viscous flow [polyvinylpyrrolidone (PVP) K17, PVP K25, and PVP K29/32 after exposure to 96% RH] showed an increase in particle size with both binder concentration and mixing time. On the contrary, binders with viscoelastic properties, such as hydroxypropylcellulose (HPC) EXF and PVP K90, did not flow well and thereby, the blends with HPC and PVP K90 did not show much effect of binder concentration and mixing time on their granule size. Moreover, the friability of granules made with HPC EXF and PVP K90 is low, indicating that the strength of the granules largely depends on the viscosity of the binders, as the binders of higher viscosity tend to produce stronger granules. Finally, the viscoelastic state of the polymeric binders upon absorbing water was analyzed using the glass-rubber transition model, which shows five regions with different viscoelastic properties.

Mechanical Properties of Anisotropic Conductive Adhesive Film Under Hygrothermal Aging and Thermal Cycling

Mechanical properties of anisotropic conductive adhesive film (ACF) were investigated experimentally under various environmental conditions. The temperature sweep test was conducted to investigate the effects of temperature on dynamical mechanical properties of the ACF. The ACF exhibited transitions to the glass state, viscoelastic state, and rubber state with increasing temperature, and its glass-transition temperature (Tg) was determined to be 149°C. The creep-recovery behaviors of the ACF were investigated, and it was found that the initial strains, instantaneous strains, and creep or recovery rates increased with increasing temperature. No obvious creep phenomenon was observed at low temperatures (≤0°C). The creep strain and creep rates at any time decreased with increasing hygrothermal aging time. The uniaxial tensile behaviors of the ACF were also investigated under hygrothermal aging and thermal cycling. The results show that the Young’s modulus and tensile strength of the ACF decrease with increasing hygrothermal aging time; however, they increase at first and then decrease with increasing thermal cycling time. Tg decreases slightly for the ACF after hygrothermal aging; however, it increases after thermal cycling.

A new spectral calculation scheme for long‐term deformation of Maxwellian planetary bodies

Viscoelasticity plays an important role in long‐term deformation of large‐scale topographies on small planetary bodies, such as the Moon. Although we should consider increases in viscosity due to secular cooling during long‐term deformation, previous spectral calculation schemes for a Maxwellian viscoelastic body have problems in calculating deformation with temporal and radial variation in viscosity. To resolve these problems, we propose a new formulation of the constitutive equation of a Maxwell body. Compared with conventional time domain spectral schemes, our scheme, with its second‐order approximation in time, demonstrates significant improvement in both accuracy and stability for long time steps. As a result, the computational costs for time‐consuming calculations, such as the long‐term evolution of surface topography, are greatly reduced. Using this scheme, we investigate the effect of planetary cooling on the deformation of an initially hot but monotonically cooling Moon. Our calculation results show that the effective elastic thickness depends on the wavelength of deformation for loads emplaced at very early times (<20 Myr). The results of our calculations also show that without additional heat sources other than initial accretion heat, hardening due to secular cooling prevents substantial isostatic compensation and crustal lateral flow underneath large impact basins. This result indicates that small planetary bodies, such as the Moon, do not retain the memory of their initial state during the accretion phase for very long and that their current viscoelastic states reflect sustained heat production and/or transport from their deep interior.

A new ultrasonic precise bonding method with ultrasound propagation feedback for polymer MEMS

With the advantage of local heating, no foreign materials introduced and high efficiency, etc., ultrasonic bonding was attempted in micro assembly. A new ultrasonic precise bonding method based on ultrasound propagation was proposed. The principle was based on the different propagation efficiencies of ultrasound in the polymer components in different mechanical state. During ultrasonic bonding, local polymer components were heated up and changed from glassy state to viscoelastic state. The propagation of ultrasound though polymer components attenuated, the fusion degree was obtained by detecting the attenuation of ultrasound propagation in real time, which is meaningful for the precise control of ultrasonic bonding. Ultrasonic bonding system was established based on this mechanism. Piezoelectric sensor was fixed in the anvil to detect the ultrasound from horn through polymer components to the bottom. Amplitude attenuation ratio was set as the parameter to control ultrasonic bonding process. Bonding experiments of PMMA (polymethyl methacrylate) micro connectors and substrates were carried out and different fusion degrees were obtained at different parameters. This method is easy to take act at different bonding machine by adjust the amplitude attenuation ratio based on primary experiments and realizes the precise joining of the micro connector with low shape deformation and good appearance in bonding interface, which has significance in micro assembly.

Mathematical simulation and calculation of the soil compaction under dynamic loads

The deformation and compaction of loamy sandy soddy-podzolic soils under linear dynamic changes in the compressive stresses and in the course of the soil creeping were studied in field experiments. The rheological properties of these soils occurring in the viscoelastic state were described by a first-order differential equation relating the compressive stresses, the rates of their changes, and the velocities of the relative vertical compressive deformation. Regression equations were derived for the viscoelastic properties of the studied soil as functions of its density, moisture, and linear compaction velocity. Methods were proposed for the calculation of indices of the stress-strain state and the compaction of soils under specified conditions of changes in their compressive stresses with time and in the course of the soil creeping after the initial linear increase in load. Corresponding computer programs were developed. The effect of the main factors due to the linear increase in the compressive loads and in the course of the soil creeping on the rheological properties, the stress-strain state, and the density of soils was quantitatively estimated. The calculation showed that the values of the soil deformation and the density under compressive stresses lower than the ultimate strength were stabilized with time, and the properties of the viscoelastic soil approached elastic ones.

An ex-situ state-based approach using rheological properties to measure and model cure in polymer composites

In this paper, studies of measurement and modeling of viscoelastic properties of two commercial prepregs, MTM45 and MTM45-1 manufactured by ACG, have been carried out using an encapsulated sample rheometer. The key variables of cure process directly correlated with the viscoelastic states of the material during the cure cycle. The viscoelastic properties (storage modulus, loss modulus, and tan δ) and glass transition temperature of the prepregs were measured using an oscillatory shear rheometry with different isothermal cure cycles below the final glass transition temperature (Tg∞ ). A semi-empirical curing model based on the viscoelastic properties of the prepreg was developed and compared with the experimental data collected at a constant frequency. The model can be used by a process engineer to monitor, control, and optimize a process and to aid in the curing of parts that have time and temperature history discrepancies. The model can be statistically correlated to critical composite properties and it can be validated with time and temperature feedback. Therefore, the primary in-situ sensor remains a temperature sensor and there is no need for additional material state sensors to be placed inside the autoclave or other process unit.

Reversible Photorheology in Solutions of Cetyltrimethylammonium Bromide, Salicylic Acid, and trans-2,4,4′-Trihydroxychalcone

We show photorheology in aqueous solutions of weakly entangled wormlike micelles prepared with cetyltrimethylammonium bromide (CTAB), salicylic acid (HSal), and dilute amounts of the photochromic multistate compound trans-2,4,4'-trihydroxychalcone (Ct). Different chemical species of Ct are associated with different colorations and propensities to reside within or outside CTAB micelles. A light-induced transfer between the intra- and intermicellar space is used to alter the mean length of wormlike micelles and hence the rheological properties of the fluid, studied in steady-state shear flow and in dynamic rheological measurements. Light-induced changes of fluid rheology are reversible by a thermal relaxation process, at relaxation rates which depend on pH and which are consistent with photochromic reversion rates measured by UV-vis absorption spectroscopy. Parameterizing viscoelastic rheological states by their effective relaxation time τ(c) and corresponding response modulus G(c), we find the light and dark states of the system to fall onto a characteristic state curve defined by comparable experiments conducted without photosensitive components. These reference experiments were prepared with the same concentration of CTAB, but different concentrations of HSal or sodium salicylate (NaSal), and tested at different temperatures.

Long-term toughness of photopolymerizable (meth)acrylate networks in aqueous environments

Photopolymerizable (meth)acrylate networks are potentially advantageous biomaterials due to their ability to be formed in situ, their fast synthesis rates and their tailorable material properties. The objective of this study was to evaluate how immersion time in phosphate-buffered saline (PBS) affects the toughness of photopolymerizable methyl acrylate (MA)–co-methyl methacrylate–co-poly(ethylene glycol) dimethacrylate networks containing various concentrations of MA. Stress–strain behavior was determined by performing tensile strain to failure testing after soaking in PBS for different periods (1 day up to 9 months). In tandem, differential scanning calorimetry and PBS content measurements were undertaken at each time point in order to determine whether time-dependent changes in toughness were related to changes in T g or PBS absorption. The effect of immersion time on network toughness was shown to be dependent upon composition in a manner related to the viscoelastic state of the polymer upon initial immersion in PBS. The results demonstrate that tough acrylate-based materials may not maintain their toughness after several months in PBS. In addition, decreasing the PBS content by changing the network hydrophobicity resulted in better toughness maintenance after 9 months. The results provide a possible means to toughen various amorphous acrylate-based implant materials that are being explored for load-bearing biomedical applications, beyond the systems considered in this work.

Rheological Properties of Polypropylene/Attapulgite Nanocomposite

The rheological properties of nanocomposites consisting of organic modified attapulgite and polypropylene are investigated. The morphology of the nanocomposites was studied with scanning electron microscopy and X-ray diffraction. Linear dynamic viscoelasticity and steady state flow step of the nanocomposites are presented. For the nanocomposites, the deviation from linear behavior occurs earlier than pure polypropylene at the strain. The storage moduli, loss moduli and dynamic viscosities of the nanocomposites increase monotonically with organoclay concentration. However, the nanocomposites show greater shear thinning tendency than pure polypropylene because of the orientation of the organoclay fibers. Therefore, the nanocomposites have higher moduli but better processibility compared with pure polypropylene.

Viscoelasticity and morphological modulation of silicon alkoxide-based systems by selective catalysts

We have studied the formation of three-dimensional silicon alkoxide-based network resulting from an inorganic polycondensation based on hydrolysis and condensation reactions. Using mechanical spectroscopy, small-angle X-ray scattering, and penetration measurements, we have shown that viscoelastic and morphological properties of gelling soft matter systems can be modulated according to the nature of a catalyst by modifying the rate of the hydrolysis and condensation reactions. The description of the network build up in terms of a continuous transition between three viscoelastic states leads us to obtain new information on the viscoelastic properties determined up to now only at the sol–gel transition.

Determination of the viscoelastic state of an anisotropic plate with rigid inclusions

A method for the determination of the viscoelastic state of multiconnected anisotropic plates with absolutely rigid inclusions is proposed. As an example, we consider the solution of the problem of viscoelasticity for a plate with an elliptic inclusion which, in a special case, turns into a linear one. For the case of tension of the plate, results of numerical investigations of the stress state depending on geometric parameters of the inclusion and on the time of application of load are described.

Stress Relaxation Analysis of Polyurethane Foam Preloaded Structures

Based on the nonlinear finite element analysis method, FEA models which describe the viscoelastic friction contact state of the polyurethane foam preloaded structures are created. In the simulations, the general Maxwell viscoelastic constitutive relation is introduced and a seven-parameter general Maxwell viscoelastic model is used to fit the experimental stress relaxation curve of polyurethane foam. During the nonlinear contact analysis, coulomb friction law is adopted, and the effects of the coulomb friction coefficient on the reaction force in the axial direction are analyzed. The FE results show that the change tendencies of relation curves of the structures are similar to which of the polyurethane foams. In the end, the influences of stiffness ratio of polyurethane foam to the outer component on the structural relaxed force are discussed, and the FE results indicate that the stiffness ratios affect the stress (force) relaxation degree remarkably. That is to say a good structure design could optimize the mechanical performance of the complicated structures greatly.

Modelling of viscoelastic material behaviour close to the glass transition temperature

AbstractIn this contribution we investigate the mechanical behaviour of polyurethane over a range of different but constant temperatures from the glass to the viscoelastic state. Therefore uniaxial tension tests are performed on dogbone specimens under different isothermal conditions. In this manner an experimental data set is provided. As a theoretical basis we present the well known thermomechanically coupled one dimensional linear viscoelastic material model which is able to display the experimentally observed material behaviour. For this we adopt temperature dependent relaxation times. The introduced model parameters are identified via a standard parameter identification tool. Finally, the experimental results are compared with the ones of simulations of the identified model parameters. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Characterization of the Tensile Viscoelastic Properties of an Undamaged Asphalt Mixture

All characterization of asphalt mixtures must begin with the properties of the mixture in an undamaged state. Subsequent tests of the mixture in different stress or strain states at a level to cause damage can be referred to this undamaged state to assess the degree to which the mixture has been changed. All forms of such change from an original state by such damaging processes as fatigue, plasticity, healing, moisture damage, and aging can only be properly assessed by comparison with an accurately measured undamaged state. This is particularly the case with the use of pseudostrain dissipated energy to characterize the departure of a material from an original linear viscoelastic state. This paper presents a new test and data analysis protocol based on linear viscoelasticity theory to characterize the master curves of the viscoelastic properties of an asphalt mixture. Instead of running a relaxation modulus test in which controlling the test apparatus is a serious challenge, the proposed test protocol applied a uniaxial monotonically increasing tensile stress to the test specimen. The axial and radial deformations of the specimen were recorded and used to calculate the axial and radial strains. The uniaxial tensile loading rate and time were carefully controlled to assure that the strain of the specimen was limited to the small-strain condition 100 under which the specimen was assumed not to be damaged during the test. The applied stress and measured strain were fitted with functions of time. Applying the Laplace transform to the stress and strain functions, the relaxation modulus as a function of time was determined using the Boltzmann superposition principle and the convolution theorem. The relation between the relaxation modulus and the complex modulus was used to determine the complex modulus as a complex function of frequency. Then the magnitude and phase angle of the complex modulus were obtained from the real part and imaginary part of the complex modulus. The proposed test and data analysis protocol were performed on the same specimen at three temperatures, 10, 20, and 30°C, so master curves of the magnitude and phase angle of the complex modulus were constructed using the time-temperature superposition principle. The master curves of the magnitude and phase angle of the complex modulus were fitted with mathematical functions that were reported in the literature and were modified to be more comprehensive. The parameters in the mathematical functions were searched simultaneously using the Solver Function built into the Microsoft Excel. Compared to the traditional relaxation modulus and the dynamic modulus test protocols, the newly developed test protocol was more efficient to characterize the viscoelastic properties of asphalt mixtures. The newly developed test method did not introduce any damage to the specimen so the same specimen may be retested for its fatigue, healing, and other properties.

Viscoelastic state of a semi-infinite medium with multiple circular elastic inhomogeneities

This paper is concerned with the problem of an isotropic, linear viscoelastic half-plane containing multiple, isotropic, circular elastic inhomogeneities. Three types of loading conditions are allowed at the boundary of the half-plane: a point force, a force uniformly distributed over a segment, and a force uniformly distributed over the whole boundary of the half-plane. The half-plane is subjected to farfield stress that acts parallel to its boundary. The inhomogeneities are perfectly bonded to the material matrix. An inhomogeneity with zero elastic properties is treated as a hole; its boundary can be either traction free or subjected to uniform pressure. The analysis is based on the use of the elastic-viscoelastic correspondence principle. The problem in the Laplace space is reduced to the complementary problems for the bulk material of the perforated half-plane and the bulk material of each circular disc. Each problem is described by the transformed complex Somigliana’s traction identity. The transformed complex boundary parameters at each circular boundary are approximated by a truncated complex Fourier series. Numerical inversion of the Laplace transform is used to obtain the time domain solutions everywhere in the half-plane and inside the inhomogeneities. The method allows one to adopt a variety of viscoelastic models. A number of numerical examples demonstrate the accuracy and efficiency of the method.

Multiple nonergodic disordered states in Laponite suspensions: A phase diagram

We study the time evolution of different Laponite suspensions from a low-viscosity ergodic state to a viscoelastic nonergodic state over a wide range of volume fractions and salt contents. We find that the evolution of nonergodicity parameter (Debye-Waller factor) splits into two branches for all the samples, which correspond to two distinct dynamically arrested states. At moderately high salt concentrations, on the other hand, a third nonergodic state appears that is different from the above two nonergodic states. Measurement of the conductivity of Laponite solutions in pure water shows that the contribution of counterions in the ionic strength is considerable and their role should be taken into account in interpretations of aging dynamics and the phase diagram. Based on these data and available data in the literature, we propose a (nonequilibrium) phase diagram for Laponite suspensions.