Dynamic mechanical properties of particulate-filled composites

The relative shear moduli of composites containing glass spheres in a rubbery matrix obey the Mooney equation, analogous to the relative viscosity of similar suspensions in Newtonian liquids. However, when the matrix is a rigid epoxy, the relative shear moduli are less than what the Mooney equation predicts but greater than what the Kerner equation predicts. Relative moduli are less for rigid matrices than for rubbery matrices because (1) the modulus of the filler is not extremely greater compared to that of the rigid matrix; (2) Poisson's ratio is less than 0.5 for a rigid matrix; (3) thermal stresses in the matrix surrounding the particles reduce the apparent modulus of the polymer matrix because of the nonlinear stress—strain behavior of the matrix. This latter effect gives rise to a temperature dependence of the relative modulus below the glass transition temperature of the polymer matrix. Formation of strong aggregates increases the shear modulus the same as viscosity is increased by aggregation. Torsion or flexure tests on specimens made by casting or by molding give incorrect low values of moduli because of a surface layer containing an excess of matrix material; this gives rise to a fictitious increase in apparent modulus as particle size decreases. The mechanical damping can be markedly changed by surface treatment of the filler particles without noticeable changes in the modulus. The Kerner equation, which is a lower bound to the shear modulus, is modified and brought into closer aggrement with the experimental data by taking into account the maximum packing fraction of the filler particles.     

Rheology of a low‐filled polyamide 6/montmorillonite nanocomposite

The rheological properties of a polyamide 6/clay nanocomposite with a low loading of clay (1 wt %) were studied. Linear viscoelastic measurements in oscillatory and steady shear with small strain amplitudes were carried out. The nanocomposite exhibited a higher elastic modulus, viscous modulus, and complex viscosity than neat polyamide 6 during dynamic and steady shear tests. Moreover, the addition of clay resulted in a reduction of the critical strain amplitude, an increase of the loss angle, and a reduction of the frequency at the intersection of the elastic and viscous moduli. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci 2008     

Dynamic moduli change of aluminum hydroxide sol during sol-gel transition

Aluminum hydroxide sol was prepared by the sol-gel method. Dynamic moduli such as storage and loss moduli were measured to investigate the relative dominance of elastic and viscous contributions to the viscoelastic response of aluminum hydroxide sol during sol-gel transition. The loss modulus, a measure of viscous response. is larger than the storage modulus, a measure of elastic response, for the sols of low particle concentrations. But at a high particle concentration above 15.3 wt%, the storage modulus is found to be larger than the loss modulus. This inversion from a viscous to an elastic response with the increase of particle concentration is attributable to the formation of gel structures by the aggregation of dispersed particles     

Constrained Densification of Alumina/Zirconia Hybrid Laminates, II: Viscoelastic Stress Computation

To analyze the inhibited densification during sintering and differential shrinkage during cooling of Al₂O₃/ZrO₂symmetric and asymmetric laminates, viscoelastic formulations, in which the viscosity and elastic modulus vary with time, have been developed. The viscoelastic mismatch stresses have been numerically computed over the entire processing cycle, including the heating period, the isothermal period, and the cooling period. The viscosity and free sintering rates that are needed for stress computation have been obtained by modifying the parameters that are measured for a normal isotropic densifying compact using cyclic loading dilatometry. The modification is based on the available sintering models to account for the effect of strain history on compact viscosity and sintering rates. The stress calculation shows that, with the exception of the initial heating period, the viscoelastic stress is identical to the viscous stress that is calculated solely from the strain rate mismatch. Sintering damage in the laminates is shown to occur during densification under conditions where the differential sintering stress is smaller than the intrinsic sintering pressure. The magnitude of residual stress in hybrid laminates on cooling is dependent on the cooling rate, and slower cooling rates are capable of almost completely relaxing the expansion mismatch stress at temperatures of >1200°C.     

Evolution of rheological properties of the nanofluids composed of laponite particles and Mg-Fe layered double hydroxide nanosheets

The thixotropic clay suspensions composed of laponite particles and Mg-Fe layered double hydroxide nanosheets were examined. By adding a very small amount of the layered double hydroxide nanosheets overall rheological properties of the host laponite suspension have been changed. Though the particle concentration of the mixture suspension is only about 1 wt%, the mixture quickly becomes a gel in a day by the electrostatic attraction between nano-materials. When a constant shear rate is applied to the mixture gel suspension, at short time, stress increases linearly with elastic deformation of the mixture. Beyond the maximum of stress, while the solid-like gel structure is being broken down with time of shearing, the stress increases again by reflecting shear enhanced association of solid phase. This is likely that the mixture suspension shows partially the behavior of memory effect.     

Rheology of aging aqueous muscovite clay dispersions

In hydrometallurgical mineral processing, time and pH dependent rheology of dispersions comprising reactive particles can exert a striking influence on material processability and handleability. Rheological studies of 0.32 solid volume fraction (57 wt% solid) aqueous dispersions of muscovite clay mineral aging at pH 7 and 1 for 4 h were undertaken to investigate the temporal, pulp chemistry-mediated particle interactions. In particular, the dispersions’ flow and deformation behaviour in tandem with viscoelastic structure changes over time were probed. Dispersions at both pH 7 and 1 displayed non-Newtonian, Bingham plastic behaviour and strong time-dependent viscosities and yield stresses. Fresh dispersions showed a weak rheology at pH 7 initially, accompanied by thixotropy which transformed to anti-thixotropic and rheopectic behaviour upon aging. Furthermore, the viscosities, yield stresses and both the viscous (G″) and elastic (G′) moduli accentuated dramatically with time, reflecting an elastic to a more sol-like viscoelastic gel transformation. In contrast to pH 7, the particle interactions at pH 1 initially led to the formation of a highly networked gel structure which displayed thixotropic and predominantly elastic behaviour. Upon aging however, systematic attenuation of thixotropy, suspension viscosity, shear yield stress and viscoelasticity occurred. Above certain shear stresses, viscoelastic gel to sol structure transformation occurred, the creep behaviour being distinctly pH and time dependent. Differing pH-mediated pulp chemistries which prevailed at pH 7 and 1 upon aging were responsible for the contrasting, temporal particle interactions and microstructure evolution.     

Relaxation of the axial strain induced stresses in double–coated optical fibers

The axial strain induced stresses in double‐coated optical fibers are analyzed by the viscoelastic theory. A closed form solution of the axial strain induced viscoelastic stresses is obtained. The viscoelastic stresses are a function of the radii, Young's moduli, relaxation times and Poisson's ratios of the polymeric coatings. If the applied axial strain linearly increases, the induced stresses increase with the time. On the other hand, if the axial strain is fixed, besides the axial stress in the glass fiber, the stresses exponentially decrease with the time. The relaxation of stresses is strongly dependent on the relaxation times of the polymeric coatings. If the relaxation time of the polymeric coating is very long, the viscous behavior of the polymeric coatings will not appear, and the axial strain induced stresses solved by the viscoelastic theory are the same as those solved by the elastic theory. On the other hand, if the relaxation time of the polymeric coating is very short, the relaxation of stresses is very apparent. A compressive radial stress at the interface of the glass fiber and primary coating will result in an increase of the transmission losses, and a tensile interfacial radial stress will possibly produce debonding at the interface of the glass fiber and primary coating. To minimize this interfacial radial stress, the radius, Young's modulus and Poisson's ratio of the polymeric coatings should be appropriately selected, and the relaxation time of the primary coating should be shortened. Finally, the stresses in single‐coated and double‐coated optical fibers are discussed.     

Thermal,mechanical, and rheological characterization of polypropylene/layered double hydroxide nanocomposites

Polypropylene (PP)/organomodified layered double hydroxide (LDH) nanocomposites were prepared in order to examine the influence of LDH content on thermal, mechanical, and rheological properties. The nanostructure examinations by X‐ray diffraction (XRD) and transmission electron microscopy (TEM) confirmed the exfoliated/intercalated dispersion of LDH. Incorporation of the LDH resulted in a noteworthy improvement in the thermal stability of PP. It was shown that the addition of LDH contributed to the reinforcement effect by increasing the elastic modulus. The mechanical performance, as evaluated by stress–strain curves, reveal that PP/LDH hybrid materials showed significant contribution toward increment in elastic modulus, tensile strength but at the expense of impact strength. The rheological response showed a strong influence of LDH particles on the flow behavior of the PP/LDH melt which resulted in enhancement of storage, loss of moduli, and complex viscosity of nanocomposites. Therefore, the nanocomposites have higher moduli but better processibility compared with pure PP. Overall, the results indicated that the LDH particles in nanometer size might act as potential reinforcing agent for polypropylene. POLYM. ENG. SCI., 52:2006–2014, 2012. © 2012 Society of Plastics Engineers     

Characterization of a glycidyl azide polymer composite propellant: Strain rate effects and relaxation response

Uniaxial tension tests were completed on a developmental GAP/PSAN solid rocket propellant at constant strain rates ranging over three decades and at five different temperatures. An analysis of the maximum stress (strength) and the strain at maximum stress showed that there is a relatively narrow range of temperatures and strain rates that give rise to strains at maximum stress that exceed 18%. The long-term equilibrium strain capability (strain endurance) appears to be between 10% and 12%. The trend of the strength and initial deformation moduli were log-linear with the reciprocal of the strain rate across three decades. However, the shifted master curves were log-curvilinear in form. The relationship between the strength and the initial modulus can be approximated by a power law. A series of stress relaxation tests was completed at a level of 4% strain and at five different temperatures. The initial portion of the shifted master relaxation curve is concave-up with correspondingly high stresses and moduli. It decays with time approaching a log-constant slope. Tensile moduli derived from constant strain rate tests were found to be consistently higher in value than the moduli as a function of time determined from relaxation tests, for an equivalent shifted time. Preliminary evidence suggests that the tensile modulus as a function of the reciprocal of shifted strain rate can be equated to the relaxation modulus as a function of shifted time through an adjustment factor. This relationship extends the relaxation modulus results back a further three and one-half decades of shifted time. © 1995 John Wiley & Sons, Inc.     

Viscoelastic measurements of PVC plastisol during gelation and fusion

This work is concerned with the change of viscoelastic properties of poly(vinyl chloride) (PVC) plastisol during heating. The system changes from a suspension of solid particles in a liquid medium to a swollen gel and further to a fused state as the temperature is raised. The Rheometrics mechanical spectrometer was used in the oscillatory mode at 0.1 Hz. The temperature of the sample was raised in a controlled manner to 195°C. During gelation, the viscosity increased rapidly about three decades. There was a similar increase of the elastic modulus. After reaching a maximum, both viscosity and elastic modulus decreased rapidly with the progress of fusion. The viscoelastic properties depended somewhat on the heating rate. At 170-195°C, it took a few minutes for the moduli to reach steady values. Continued heating, for several minutes at 195°C, did not change the moduli any further. The temperature range of the decomposition of a blowing agent in the plastisol foam formulation was determined. Over this temperature range, the viscoelastic properties change very rapidly. Quantitative estimates were made for the decrease of moduli during this period.     

Rheometric and ultrasonic investigations of viscoelastic properties of fresh Portland cement pastes

The paper investigates the possibility of using a shear wave reflection technique to monitor the viscoelastic behavior (represented by storage shear modulus and viscosity) of Portland cement paste at very early age. Three cement pastes with water/cement ratios equal to 0.4, 0.5 and 0.6 cured under water at a constant temperature of 25 °C were studied. By measuring the wave reflection coefficients and the phase angles of reflected ultrasonic waves, the dynamic storage shear moduli and the viscosity of the cement paste can be calculated. The calculated results of the storage modulus were compared with the results obtained directly from the oscillatory rheometric measurement. In addition, the viscosity calculated from the wave reflection measurements was compared with results obtained directly from the step rheometric method and a qualitative agreement was found. The results show that as a non-destructive method, the ultrasonic wave reflection method provides useful information about both the elastic and viscous behavior of cement pastes at very early age.     

Toughening of Glasses by Metallic Particles

The role of elastic, thermoelastic, and interfacial properties in the toughening of a brittle matrix by metallic second-phase particles was studied. Two composites were studied: glass+partly oxidized Ni particles (thermal expansion coefficient of the glasses lower than, equal to, and higher than that of Ni) and glass+partly oxidized Al particles (thermal expansion and elastic moduli equal). Weak interfacial bonding between the nickel and its oxide and developed stress concentrations are the major toughness limitations found in the glass/Ni composites. When the thermal expansion coefficient and elastic modulus of the second phase are sufficiently greater than that of the glass matrix, a propagating crack will bypass the particles. When the thermal and elastic stresses are minimized and satisfactory bonding is achieved (glass/Al composites), a 60x toughness increase was realized.     

Steady-State and dynamic properties of concentrated fiber-filled thermoplastics

Rheometric data for short-fiber-filled thermoplastics are presented using a parallel-plate viscometer. Polypropylene tensile bars contain short and long fibers with glass weight percentages of 0%, 5%, 10%, 20%, and 30%, polycarbonate tensile bars with glass percentages of 0%, 5%, and 10% long fibers, and nylon 6/6 tensile bars with 0%, 15%, 30%, and 45% short fibers. The short fibers were initially 3 mm in length and 12.7 microns in diameter. The long fibers were initially 6 mm in length and 10 microns in diameter. In the steady-state experiments, the fibers increase the viscous stresses and the normal stresses in proportion to the concentration of fibers. At low shear rates, the viscosity is increased by the addition of the fibers, but at high shear rates the viscosity approaches that of the neat resin. In dynamic testing, the fibers increase the viscous and elastic components as measured by the complex viscosity and modulus. The fibers increase the viscous and elastic nature of the fiber-filled composite at low frequencies and to a lesser extent at higher frequencies. The fibers increase the elastic component more than the viscous component at low frequencies and less at higher frequencies as demonstrated by tan δ.     

Synthesis of exfoliated acrylonitrile-butadiene-styrene copolymer (ABS) clay nanocomposites: role of clay as a colloidal stabilizer

Acrylonitrile-butadiene-styrene copolymer (ABS) clay nanocomposites were synthesized using two clays (sodium montmorillonite, laponite). Both colloidal stability and mechanical properties of the nanocomposites were dependant on aspect ratios of clays. Laponite, a low aspect ratio clay, reduced particle sizes of ABS clay nanocomposite latexes, enhanced colloidal stabilities, and increased viscosity of the latexes. The colloidal stability of ABS clay latexes may result from four factors. Firstly, the electrostatic repulsion forces originated from surface charges of clays and anionic surfactant contribute to colloidal stability. Secondly, laponite layers separate sodium montmorillonite layers and polybudadiene latex particles preventing the coagulation. Thirdly, the laponite layers adsorbed on latexes act like steric barriers against coagulation. Fourthly, increased viscosity reduces latex mobility, lowering collision possibility among latex particles. Resultant ABS clay nanocomposites showed exfoliated structures, and their mechanical properties related to the relative weight ratio of sodium montmorillonite to laponite: as portions of sodium montmorillonite increased, dynamic moduli of the nanocomposites increased, because sodium montmorillonite has higher aspect (length/thickness) ratio than laponite.     

Effect of temperature and age on the relationship between dynamic and static elastic modulus of concrete

This study investigates the effects of cement type, curing temperature, and age on the relationships between dynamic and static elastic moduli or compressive strength. Based on the investigation, new relationship equations are proposed. The impact-echo method is used to measure the resonant frequency of specimens from which the dynamic elastic modulus is calculated. Types I and V cement concrete specimens with water-cement ratios of 0.40 and 0.50 are cured isothermally at 10, 23, and 50 °C and tested at 1, 3, 7, and 28 days.Cement type and age do not have a significant influence on the relationship between dynamic and static elastic moduli, but the ratio of static to dynamic elastic modulus approaches 1 as temperature increases. The initial chord elastic modulus, which is measured at low strain level, is similar to the dynamic elastic modulus. The relationship between dynamic elastic modulus and compressive strength has the same tendency as the relationship between dynamic and static elastic moduli for various cement types, temperatures, and ages.     

The missing parameter in rheology: hidden solid‐like correlations in viscous liquids,polymer melts and glass formers

BACKGROUND: Determination of dynamic relaxation consists of measuring the viscous and the elastic components of a material by generally applying a small (oscillatory) deformation. The shear stress is transmitted to the material via contact with a substrate. Dating at least back to Stokes, the no‐slip boundary condition between the fluid and the substrate is supposed to be fulfilled during this measurement. We show that the viscoelastic parameters of fluids are usually not determined under no‐slip boundary conditions and do not originate from the first linear regime. Viscous and viscoelastic fluids (entangled and unentangled polymers, glass formers) measured under no‐slip conditions exhibit a fundamentally different response with a dominant terminal solid‐like response. RESULTS: We show that the terminal behaviour of fluids such as liquid polymers or glass formers measured at the sub‐millimetre scale and far above the glass transition is not viscous but solid‐like. Instead of a viscoelastic behaviour scaling as ω and ω² (ω is the frequency) for the viscous and the elastic moduli, respectively, the dynamic response is simplified; for low gap thickness, both viscous and elastic moduli are invariant with respect to the frequency (with the elastic modulus being larger than the viscous modulus) and enhanced by two to four orders of magnitude compared to the conventional viscoelastic response. Over a critical strain amplitude, the solid‐like response decreases and is progressively replaced by the conventional viscoelastic behaviour. We discuss the implications of this observation and reconsider the assumptions inherent to a rheology measurement. CONCLUSION: The identification of so far neglected macroscopic elasticity in the fluidic state far above the glass transition temperature in entangled and unentangled polymers and glass formers shows that the liquid state is dominated by long range intermolecular interactions. This information is fundamental to understand and to foresee dynamic behaviour; it sheds further light on nonlinear phenomena such as large time scale relaxations, rheo‐thinning, violation of the no‐slip boundary condition and spectacular shear‐induced instabilities (spurt effect, ‘shark‐skin’ instabilities, gross melt fracture, etc.) that are unpredictable in the frame of the conventional viscoelastic approach. It also implies that the viscoelastic times (reptation, Rouse) in polymers are not the longest relaxation times of these materials. Copyright © 2009 Society of Chemical Industry     

Effects of a strong polyelectrolyte on the rheological properties of concentrated cementitious suspensions

Strong polyelectrolytes, referred to as superplasticizers, are known to improve the initial fluidity of concentrated cement suspensions. To quantify how the polyelectrolytes affect the fluidity, we have studied the effect of a strong anionic polyelectrolyte, melamine formaldehyde sulfonate (MFS), on the zeta potential of cement particles and on the steady-shear and low-amplitude rheological properties of cement suspensions. Adsorption of low concentrations of MFS onto the cement particles leads to an inversion in the sign of the surface potential, causing the electrostatically flocculated particles to become electrostatically dispersed and giving rise to a corresponding decrease in the steady-shear viscosity and storage modulus. At an intermediate MFS concentration, the steady-shear viscosity and the storage modulus each display a minimum. This concentration corresponds to that at which the zeta potential becomes constant. Larger concentrations of MFS result in an increase in the viscosity and storage modulus, which is attributed to depletion flocculation. These results thus relate the interaction between particles to the suspension fluidity through the analysis on the surface potential of particles and microstructure of suspension.     

Yielding in Surfactant Suspension Pastes: Effect of Surfactant Type

In this work, we study the rheological properties and the yielding behavior of cleaning pastes containing surfactant and abrasive particles, for three different types of surfactants, namely linear alkyl benzene sulfonate (LAS), alpha olefin sulfonate (AOS) and sodium lauryl ether sulfonate (SLES). All the pastes were observed to have soft solid-like consistency with their elastic modulus significantly greater than the viscous modulus. With around 36 volume percent of particulate matter, the high stiffness of the pastes suggests that particles form a space spanning network. Interestingly, when subjected to oscillatory shear deformation with increasing strain amplitude, the elastic modulus undergoes a decrease in two steps thereby showing a two-step yielding behavior. It is observed that the first yield stress does not show frequency dependence, and for LAS-containing paste was the largest followed by AOS- and SLES-containing pastes, respectively. The second yield stress, on the other hand, for all the three pastes is observed to increase with frequency. Careful assessment of the experimental data suggests that the first yielding event is due to rupture of the network which leads to formation of particulate aggregates. The second yielding event is attributed to breakage of aggregates. In both yielding phenomena, surfactants play an important role. Since, the phase behavior of surfactant in water determines the inter-particle interaction and network density, the nature of surfactant has a pivotal influence on both the yielding phenomena in surfactant suspension pastes used for cleaning purposes.     

The glass transition temperature of filled polymers and its effect on their physical properties

The glass transition temperature, dynamic shear moduli, and bulk viscosities of Phenoxy PKHH (a thermoplastic polymer made from bisphenol-A and epichlorohydrin) filled with glass beads and Attapulgite clay were investigated. The glass temperature of the polymer increased with increasing filler concentration and with increasing specific surface area of the filler. The data were interpreted by assuming that interactions between filler particles and the polymer matrix reduce molecular mobility and flexibility of the polymer chains in the vicinity of the interfaces. From the measured moduli and the viscosities of the filled and unfilled materials, the modulus reinforcement ratio in the glassy state and the relative viscosity in the viscous state were obtained as functions of the filler type and concentration. The relative modulus for the glass bead composite system follows the Kerner equation, while the clay-filled systems exhibit slightly greater reinforcement. The relative viscosities are strongly temperature dependent and do not follow conventional viscosity predictions for suspensions. It is suggested that the filler has a twofold effect on the viscosity of the composite materials; one is due to its mechanical presence and the other is due to modifications of part of the polymer matrix caused by interaction. Using the WLF equation to express all modifications of the matrix, one can isolate a purely mechanical contribution to the viscosity reinforcement. This mechanical part is approximately bounded by the theoretical predictions of Kerner,³² Mooney, ³⁶ and Brodnyan,⁴¹ for suspension viscosities.     

The effect of interlayers on the transverse stresses in fiber composites

Numerical results are given of calculations of the radial, transverse, and shear stresses in the matrix surrounding a cylindrical inclusion in plane strain perpendicular to the cylinder axis, this being taken as a model of a fiber composite under transverse loading. It is shown that the presence of an interlayer on the fiber at a thickness which is a small fraction of the fiber diameter can significantly affect the stress concentrations in the matrix. The interlayer-fiber ‘composite’ can be ‘matched’ to the matrix by suitable choice of interlayer elastic moduli. In particular, if the shear modulus of the interlayer is smaller than that of the matrix and its Poisson's ratio is very small, the stress concentrations in the matrix are considerably reduced and the composite should be less subject to failure by delamination.