Correlation between interfacial interactions and internal stresses in filled high density polyethylene

The stress relaxation and the creep behaviour of high density polyethylene (HDPE) filled with glass fibres, clay (plate-like particles) or CaCO₃ (particles with irregular shape) were measured in uniaxial extension at room temperature. It was observed that the addition of filler increased the internal stress level, as evaluated from stress relaxation data. This increase was larger than the corresponding increase in the (short-term) elastic modulus. This behaviour may be attributed to a reduced macromolecular mobility in the matrix material close to the filler surface, i.e. to formation of an interphase region in the HDPE-matrix. From the internal stress values, the thickness of this interphase region around each filler particle was estimated, assuming a uniform coverage of the particles. It was suggested that the amount of matrix material with reduced mobility (or the thickness of the interphase region) reflected the degree of adhesion between the filler and HDPE. The change in the internal stress level due to the incorporation of different fillers, which were surface treated in some cases, was also consistent with the observed creep behaviour.     

An extended micromechanics method for probing interphase properties in polymer nanocomposites

Inclusions comprised on filler particles and interphase regions commonly form complex morphologies in polymer nanocomposites. Addressing these morphologies as systems of overlapping simple shapes allows for the study of dilute particles, clustered particles, and interacting interphases all in one general modeling framework. To account for the material properties in these overlapping geometries, weighted-mean and additive overlapping conditions are introduced and the corresponding inclusion-wise integral equations are formulated. An extended micromechanics method based on these overlapping conditions for linear elastic and viscoelastic heterogeneous material is then developed. An important feature of the proposed approach is that the effect of both the geometric overlapping (clustered particles) and physical overlapping (interacting interphases) on the effective properties can be distinguished. We apply the extended micromechanics method to a viscoelastic polymer nanocomposite with interphase regions, and estimate the properties and thickness of the interphase region based on experimental data for carbon-black filled styrene butadiene rubbers.     

The peculiarities of the rheological behaviour of coal tars

The results are discussed of rheological studies of coal tars with different concentrations of substances insoluble in toluene at periodical, steady-state and combined periodical-steady shear deformations in a wide range of deformation frequencies, rates and amplitudes in the temperature region from 223 to 333 K. The temperatures of structural and mechanical glassingT _g , the activation energies of viscous flow and initial viscoelastic constants of these systems have been determined. Temperature and temperature-frequency dependencies of dynamical parameters have been obtained, the pre-steady-state and the steady-state flow modes of permanent deformation have been studied and thixotropic parameters have been evaluated at the combined action of vibration and permanent deformation.     

A theoretical model for the prediction of thermal expansion behaviour of particulate composites

The thermal expansion coefficient of particle-reinforced polymers was evaluated using a theoretical model which takes into account the adhesion efficiency between the inclusions and the matrix — an important factor affecting the thermomechanical properties of a composite. To measure the adhesion efficiency a boundary interphase, i.e. a layer between the matrix and the fillers having a structure and properties different from those of the constituent phases, was considered. This layer is assumed to have varying properties.To obtain information concerning the properties and extent of the interphase, an experimental study of the thermal behaviour of aluminium-epoxy composites was undertaken. Differential Scanning Calorimetry (DSC) measurements were performed to evaluate heat capacity with respect to temperature. In addition, the effects of different factors, such as heating rate and filler concentration on the glass transition temperature of the composite, were examined. The sudden changes in heat capacity values in the glass transition region were used to estimate the extent of the boundary interphase according to an existing theory.Finally, the values of the thermal expansion coefficient, predicted by this model, were compared with theoretical results obtained by other authors and with experimental results.     

The nonlinear viscoelastic response of carbon black-filled natural rubbers

Three series of tensile relaxation tests are performed on natural rubber filled with various amounts of carbon black. The elongation ratio varies in the range from λ=2.0 to 3.5. Constitutive equations are derived for the nonlinear viscoelastic behavior of filled elastomers. Applying a homogenization method, we model a particle-reinforced rubber as a transient network of macromolecules bridged by junctions (physical and chemical cross-links, entanglements and filler clusters). The network is assumed to be strongly heterogeneous at the meso-level: it consists of passive regions, where rearrangement of chains is prevented by surrounding macromolecules and filler particles, and active domains, where active chains separate from temporary nodes and dangling chains merge with the network as they are thermally agitated. The rate of rearrangement obeys the Eyring equation, where different active meso-domains are characterized by different activation energies. Stress–strain relations for a particle-reinforced elastomer are derived by using the laws of thermodynamics. Adjustable parameters in the constitutive equations are found by fitting experimental data. It is demonstrated that the filler content strongly affects the rearrangement process: the attempt rate for separation of strands from temporary nodes increases with elongation ratio at low fractions of carbon black (below the percolation threshold) and decreases with λ at high concentrations of filler.     

Anomalous steady flows in a tube

Tube flow of a viscoelastic liquid of the multiple integral type driven by periodic forcing is investigated. It is shown that mean longitudinal and secondary flows exist, independently of the explicit form of the constitutive functions, due to frequency cancellation when the forcing oscillates around a zero mean. Closed form expressions are given for these non-trivial flows at the lowest order of the algorithm where nonlinear effects appear.Presented at the Third European Rheology Conference, Edinburgh, UK, Sept. 3–7, 1990.     

Propagation of nonlinear waves along a viscoelastic bar

Various types of nonlinear waves propagating along a viscoelastic bar are considered. The rheological equation of state has strong physical and geometric nonlinearities, and nonisothermal effects are included. Both weak (isentropic) and shock waves of loading and unloading are investigated. It is shown that, for certain rubber-like materials, stable shock waves of extension can exist along with the shock waves of compression at very large strains. We then consider the strike of a viscoelastic bar of finite length against a rigid obstacle. Numerical solutions to this problem illustrate the influence of stress relaxation on nonlinear wave processes. A model for sticking and bouncing off is formulated and the mass-averaged velocity of the bar at the moment when it bounces off the obstacle is calculated.     

Rheology of columnar-grained ice

Creep of columnar-grained ice, under uniaxial compressive force normal to the columns, is shown to be composed of an instantaneous elastic response followed by a delayed elastic and viscous deformation. Both the delayed elastic and viscous strains are shown to have equal activation energies. Thus, this ice can be considered as a thermorheologically simple material with a nonlinear stress dependence. A simple phenomenological relationship has been developed that can be used for further analysis of the creep compliance function presented in a normalized form.     

Impact of mixing procedure on phase morphology and fracture mechanical properties of carbon black-filled NR/SBR blends

Based on a viscoelastic model, the filler distribution and the amount of interphase of carbon black-filled blends of natural rubber (NR) with styrene-butadiene rubber (SBR) are evaluated. Hereby, the total dissipated energy \(G''\) during dynamical straining is decomposed into the contributions of the different polymer phases and the interphase. For the NR/SBR blends, we find a higher filling of the SBR phase and the interphase and a lower filling of the NR phase. The filler distribution itself depends not only on the affinity of the polymer to the filler but also on the mixing procedure. This is investigated by studying NR/SBR blends prepared by two different mixing procedures. In the standard mixing procedure, the polymers are mixed first, and then, the filler is added. In the batch mixing procedure, the filler is previously mixed in the NR only and then blended with SBR. Batch mixing is resulting in an increase in the filling of the interphase due to filler transfer from NR to SBR. The results for the filler distribution are compared to fatigue crack propagation rates under pulsed excitation. The crack propagation is accelerated when substituting NR with SBR. The batched samples show higher crack propagation rates at higher tearing energies due to a worse dispersion of the carbon black and/or higher filler loading of the interphase.     

Break-up of a viscoelastic liquid jet

Applying Green's continuum theory of a slender body, the process of liquid jet break-up is analysed for a viscoelastic upper-convected Jeffreys fluid. In contrast to a Newtonian liquid an enforced growth of the perturbation is received from a linear analysis. A non-linear numerical analysis shows the viscosity-dependent filament formation between growing droplets of the viscoelastic liquid. The radius of these filaments decreases in an uniaxial extensional flow.     

Filled elastomers: A theory of filler reinforcement based on hydrodynamic and interphasial effects

Experimental evidence has by now established that (i) the hydrodynamic effect and (ii) the presence of stiff interphases (commonly referred to as bound rubber) “bonding” the underlying elastomer to the fillers are the dominant microscopic mechanisms typically responsible for the enhanced macroscopic stiffness of filled elastomers. Yet, because of the technical difficulties of dealing with these fine-scale effects within the realm of finite deformations, the theoretical reproduction of the macroscopic mechanical response of filled elastomers has remained an open problem.The object of this paper is to put forward a microscopic field theory with the capability to describe, explain, and predict the macroscopic response of filled elastomers under arbitrarily large nonlinear elastic deformations directly in terms of: (i) the nonlinear elastic properties of the elastomeric matrix, (ii) the concentration of filler particles, and (iii) the thickness and stiffness of the surrounding interphases. Attention is restricted to the prominent case of isotropic incompressible elastomers filled with a random and isotropic distribution of comparatively rigid fillers. The central idea of the theory rests on the construction of a homogenization solution for the fundamental problem of a Gaussian elastomer filled with a dilute concentration of rigid spherical particles bonded through Gaussian interphases of constant thickness, and on the extension of this solution to non-Gaussian elastomers filled with finite concentrations of particles and interphases by means of a combination of iterative and variational techniques.For demonstration purposes, the theory is compared with full 3D finite-element simulations of the large-deformation response of Gaussian and non-Gaussian elastomers reinforced by isotropic distributions of rigid spherical particles bonded through interphases of various finite sizes and stiffnesses, as well as with experimental data available from the literature. Good agreement is found in all of these comparisons. The implications of this agreement are discussed.     

Stokes' first problem for linear viscoelastic fluids with finite memory

We consider Stokes' first problem for a viscoelastic fluid. The memory of the fluid is truncated to a finite time interval and discontinuities in the stress relaxation modulus or its derivatives are allowed at the point of truncation. We investigate secondary waves which are generated by the interaction of these singularities in the memory with earlier waves.Dedicated to Prof. Hanswalter Giesekus on the occasion of his retirement as Editor of Rheologica Acta.     

History-dependent dimensional stability of paper

History-dependent dimensional behavior of paper has been formulated within the framework of the general linear theory of viscoelasticity and the classical lamination theory. The effect of the drying history of the papermaking process was incorporated by introducing the residual stress in the reference configuration which was taken at the final drying stage in this study. This permits us to account for complex dimensional and form changes of paper in the converting and end use processes.In order to determine the prediction performance of the computer simulation model developed, in-plane and out-of-plane dimensional responses under cyclic humidity changes were predicted on the basis of hygroviscoelastic data of paper. The simulation examples demonstrated typical irreversible dimensional responses of paper both for the in-plane dimensional change and the curvature change (curl). The computer code can easily deal with the non-uniform distribution of 1) anisotropic viscoelastic properties, 2) hygrothermal properties, and 3) moisture and temperature through the thickness.     

A model for the thermorheological behavior of viscoelastic fluids

Using a power-law ansatz for the temperature dependence of the shear modulus on the level of internal variables, the thermorheological behavior is modeled for viscoelastic fluids of a special group of rheological constitutive equations (rate-type models). The model parameter introduced characterizes thermoelastic contributions. The relation between the model parameter and the physical quantities appearing in deformation processes is discussed. Based on the chosen temperature dependence of the shear modulus, thermodynamically consistent equations like the nonlinear rheological constitutive equation and the temperature equation are derived. The special cases of entirely entropy and energy elastic fluids are also considered. The thermorheological behavior (exo-, - or endothermal processes) of a viscoelastic fluid in a stress-growth experiment followed by relaxation is analyzed with respect to the model parameter.     

Nonlinear viscoelasticity of polymer melts in different types of flow

The nonlinear viscoelastic properties of a fairly large class of polymeric fluids can be described with the factorable single integral constitutive equation. For this class of fluids, a connection between the rheological behaviour in different flow geometries can be defined if the strain tensor (or the damping function) is expressed as a function of the invariants of a tensor which describes the macroscopic strain, such as the Finger tensor. A number of these expressions, proposed in the literature, are tested on the basis of the measuring data for a low-density polyethylene melt. In the factorable BKZ constitutive equation the strain-energy function must be expressed as a function of the invariants of the Finger tensor. The paper demonstrates that the strain-energy function can be calculated from the simple shear and simple elongation strain measures, if it is assumed to be of the shape proposed by Valanis and Landel. The measuring data for the LDPE melt indicate that the Valanis-Landel hypothesis concerning the shape of the strainenergy function is probably not valid for polymer melts.     

Linear rheology of viscoelastic emulsions with interfacial tension

Emulsions of incompressible viscoelastic materials are considered, in which the addition of an interfacial agent causes the interfacial tension to depend on shear deformation and variation of area. The average complex shear modulus of the medium accounts for the mechanical interactions between inclusions by a self consistent treatment similar to the Lorentz sphere method in electricity. The resulting expression of the average modulus includes as special cases the Kerner formula for incompressible elastic materials and the Oldroyd expression of the complex viscosity of emulsions of Newtonian liquids in time-dependent flow.     

Finite rise time step strain modeling of nearly monodisperse polymer melts and solutions

The step shear strain experiment is one of the fundamental transient tests used to characterize the rheology of viscoelastic polymer melts and solutions. Many melts and solutions exhibit homogeneous deformation and stress relaxation; in these cases the transient dynamics can be modeled by completely ignoring momentum effects and imposing singular kinematics. Recently, however, it has been observed that there are certain classes of nearly monodisperse melts and solutions that exhibit anomalous nonhomogeneous deformation and stress relaxation (Morrison and Larson (1990), Larson, Khan, and Raju (1988), Vrentas and Graessley (1982), and Osaki and Kurata (1980)). We demonstrate that, for these classes, a finite rise time must be incorporated, some source of inhomogeneity must be present, and a small amount of added Newtonian viscosity is necessary. We examine five nonlinear and quasilinear models; the Johnson-Segalman, Phan Thien Tanner, Giesekus, White-Metzner, and Larson models. We determine which mathematical features of the models are necessary and/or sufficient to describe the observed experimental behavior.     

Viscoelastic properties of polymerlike reverse micelles

A dramatic increase in the viscosity of reverse micellar solutions of lecithin in a variety of organic solvents of up to a factor of 10⁶ upon the addition of a small amount of water can be observed. The formation of viscoelastic solutions can be explained by a water-induced aggregation of lecithin molecules into flexible cylindrical reverse micelles and the subsequent formation of a transient network of entangled micelles. The viscoelastic properties of these solutions are characterized as a function of water content and temperature for different organic solvents by means of dynamic shear viscosity measurements. The results are interpreted by making analogies to the behavior of semidilute polymer solutions and living polymers.Dedicated to Prof. Dr. J. Meissner on the occasion of his 60th birthday.     

Viscoelastic plastic rheological model for particle filled polymer melts

A viscoelastic plastic model for suspension of small particles in polymer melts has been developed. In this model, the total stress is assumed to be the sum of stress in the polymer matrix and the filler network. A nonlinear viscoelastic model along with a yield criterion were used to represent the stresses in the polymer matrix and the filler network, respectively. The yield function is defined in terms of differential equations with an internal parameter. The internal parameter models the evolution of structure changes during floc rupture and restoration. The theoretical results were obtained for steady and oscillatory shear flow and compared with experimental data for particle filled thermoplastic melt. The experimental data included the steady state shear strress over a wide range of shear rates, the transient stress in a start up shear flow, stress relaxation after cessation of a steady state shear flow, the step shear and the oscillatory shear flow at various amplitudes.