Exposing the nonlinear viscoelastic behavior of asphalt-aggregate mixes

In this study asphalt-aggregate mixes are treated as both viscoelastic and viscoplastic. Following a damage mechanics approach, a nonlinear viscoelastic constitutive formulation is generated from a linear formulation by replacing ‘applied stresses’ with ‘effective viscoelastic stresses’. A non-dimensional scalar entity called ‘relative viscoelastic stiffness’ is introduced; it is defined as the ratio of applied to effective viscoelastic stress and encapsulates different types of nonlinearities. The paper proposes a computational scheme for exposing these nonlinearities by uncovering, through direct analysis of any test data, changes experienced by the ‘relative viscoelastic stiffness’. In general terms, the method is based on simultaneous application of creep and relaxation formulations while preserving the interrelationship between the corresponding time functions. The proposed scheme is demonstrated by analyzing a uniaxial tension test and a uniaxial compression test (separately). Results are presented and discussed, unveiling and contrasting the character of viscoelastic nonlinearities in both cases. A conceptual viewpoint is offered to explain the observations, illustrating the requirements from any candidate constitutive theory.     

Hot pressing ‘window’ for (P2O5, B2O3)-containing magnesium aluminosilicate reinforced with SiC fibres

Unidirectional magnesium aluminosilicate (MAS) glass-ceramic matrix/silicon carbide (SiC) fibre composites were produced, employing the slurry infiltration-hot pressing technique. The densification and crystallisation behaviour of the (P₂O₅, B₂O₃)-containing MAS glass-ceramic matrix was studied in depth. The major result of the matrix study was the construction of a two-dimensional hot pressing ‘window’ within which MAS/SiC composites were successfully processed. The ‘window’ dimensions, namely temperature and time, were shown to depend on each other. This revised version was published online in September 2006 with corrections to the Cover Date.     

Quantitative deformation model for two-phase composites including concrete

New rheological models are presented that can reproduce the load-induced deformations of two-phase composite materials from their compositions. The models are extensions of the earlier published ‘composite average’ concept. The mathematical forms of the rheological models are obtained first by considering the composite as a linearly viscoelastic, nonageing material. For ageing materials, such as concrete, the modulus of elasticity and viscosity of the hardened cement paste were estimated by suitable formulas from the cement type, water-cement ratio and age, and substituted into the nonageing solution (Equation 19). It is shown by two examples that Equation 19 can reproduce the creep of normal weight concrete quite well in terms of concrete composition, modulus of elasticity of aggregate and age of concrete, as well as age and duration of loading.     

Miscibility analysis,viscoelastic properties and morphology of cyclic olefin copolymer/polyolefin elastomer (COC/POE) blends

Miscibility of cyclic olefin copolymer/polyolefin elastomer (COC/POE) blends over full composition range was investigated through determination of viscoelastic characteristics both at melt and solid state as well as by direct morphological analysis using experimental and theoretical approaches. The melt viscosity, storage modulus and Han diagrams were used for analyzing the rheological behavior. It was found that the storage modulus of neat COC was higher than that of neat POE, while the modulus of the blends were in between the modulus of the neat components. Palierne and Gramspacher–Meinssner models were used in order to predict the storage and loss moduli of COC and POE. Better correspondence of Palierne model with the experimental results was observed as compared to the other model. Contrary to the Veenstra model, the calculated modulus via Coran model was reasonably in good agreement with the experimental results for blends with co-continuous morphology. Dynamic mechanical investigations have revealed that COC/POE blends were immiscible which firmly supported the morphological and rheological findings.     

A combined experimental and modelling approach to aortic valve viscoelasticity in tensile deformation

The quasi-static mechanical behaviour of the aortic valve (AV) is highly non-linear and anisotropic in nature and reflects the complex collagen fibre kinematics in response to applied loading. However, little is known about the viscoelastic behaviour of the AV. The aim of this study was to investigate porcine AV tissue under uniaxial tensile deformation, in order to establish the directional dependence of its viscoelastic behaviour. Rate dependency associated with different mechanical properties was investigated, and a new viscoelastic model incorporating rate effects developed, based on the Kelvin-Voigt model. Even at low applied loads, experimental results showed rate dependency in the stress–strain response, and also hysteresis and dissipation effects. Furthermore, corresponding values of each parameter depended on the loading direction. The model successfully predicted the experimental data and indicated a ‘shear-thinning’ behaviour. By extrapolating the experimental data to that at physiological strain rates, the model predicts viscous damping coefficients of 8.3 MPa s and 3.9 MPa s, in circumferential and radial directions, respectively. This implies that the native AV offers minimal resistance to internal shear forces induced by blood flow, a potentially critical design feature for substitute implants. These data suggest that the mechanical behaviour of the AV cannot be thoroughly characterised by elastic deformation and fibre recruitment assumptions alone.     

The gelation behaviors of the reactive blends of nylon1212 and functional elastomer

Studies on the gelation behaviors of the reactive blends of nylon1212 and functional elastomer were carried out. The results show that the curves of the storage modulus(G′)–frequency (ω) exhibit a gel plateau in the low ω region, and the transition from liquid-like to solid-like viscoelastic behaviors emerges with the concentration of SEBS-g-MA increasing. There exist the gelation behaviors in the blending process similar to those of crosslinking polymer. Based on Winter’s method, the gel point of blends is determined to be, φ_g = 17.45 wt%, and the corresponding value of tanδ is 1.44. The gel index n calculated is 0.61 and the gel strength S _g is 1.08 × 10⁴ Pa s^0.61. However, the non-reactive blends of nylon1212 and elastomer have no emergence of gelation behaviors. The morphology analysis shows that the gel point for the reactive blends is a threshold of cocontinuous morphology, and morphology analysis can also be a method to determine the gel point.     

Materials behaviour and intermetallics characteristics in the reaction between SnAgCu and Sn–Pb solder alloys

The paper compares theoretical calculations with experimental data, to identify the metallurgical mechanisms with respect to the rework or repair that may be encountered in the transition period from Sn–Pb to Pb-free soldering. Thermodynamic calculations have been carried out to study material behaviour and possible formation of intermetallic precipitates during the reaction between Sn–Pb and Sn–Ag–Cu Pb-free alloys. Two Sn–Ag–Cu alloys that are relevant to current industrial interests, namely Sn–3.9Ag–0.6Cu* (known as ‘405 alloy’ in Europe and North America), and Sn–3.0Ag–0.5Cu (known as ‘305’ alloy in Asia), were reacted with different contamination levels of eutectic Sn–37Pb solder. The variables examined included those related to both the materials and processes, such as composition, temperature and cooling rate. Together these are the primary drivers with respect to the resultant solder microstructures, which were studied using scanning electron microscopy (SEM). Nanoindentation, which is suitable for the ultra-fine and complex microstructures, was also used to investigate the micromechanical properties, including hardness and elastic modulus, at both ambient and elevated temperatures. The results from this work provide guidance as to the consequence for microstructural evolution and hence mechanical integrity when small amounts of Pb exist in Pb-free alloys. The composition of alloys in this paper is in weight percentage (wt%)     

Time dependent properties of thermoreversible gels

Rheological properties of the system gelatin + water at a polymer concentration of 5.0% by wt at a temperature of 301 K and an angular frequency of 0.628 rads^–1 are presented and evaluated by use of the percolation theory. A frequency power law has been found close to the gel point from which a critical time range could be deduced in which the powers of the loss and storage modulus are the same. The times needed for the gelation from the percolation relations are close to the range where the exponents of the frequency power law relations are identical. The scaling coefficient Δ for physical gelation agrees very well with that found for chemical gelation by Durand and coworkers. Received: 9 October 2000 / Reviewed and accepted: 10 October 2000     

Towards a theory of granular plasticity

A theory of granular plasticity based on the time-averaged rigid-plastic flow equations is presented. Slow granular flows in hoppers are often modeled as rigid-plastic flows with frictional yield conditions. However, such constitutive relations lead to systems of partial differential equations that are ill-posed: they possess instabilities in the short-wavelength limit. In addition, features of these flows clearly depend on microstructure in a way not modeled by such continuum models. Here an attempt is made to address both short-comings by splitting variables into ‘fluctuating’ plus ‘average’ parts and time-averaging the rigid-plastic flow equations to produce effective equations which depend on the ‘average’ variables and variances of the ‘fluctuating’ variables. Microstructural physics can be introduced by appealing to the kinetic theory of inelastic hard-spheres to develop a constitutive relation for the new ‘fluctuating’ variables. The equations can then be closed by a suitable consitutive equation, requiring that this system of equations be stable in the short-wavelength limit. In this way a granular length-scale is introduced to the rigid-plastic flow equations.     

Viscoelastic properties of hybrid copolymers based on methacryloxypropyl-grafted nanosilica and methyl methacrylate

The linear viscoelastic behavior of “model” hybrid materials based on methyl methacrylate and methacryloxypropyl-grafted nanosilica was investigated. As unique features, the materials under study present an excellent dispersion of silica within the polymer matrix and are almost free of uncross-linked chains. In addition, very progressive changes in network architecture are available, resulting from changes in particle diameter, d, volume fraction of filler, Φ, number of methacryloyl units grafted per surface unit of silica particle, n, and nature of the grafting agent. The influence of these parameters on the characteristics of the mechanically active relaxations α and β was examined. Emphasis was put on the storage modulus, E′, on the loss modulus, E′′, and on their dependence on filler volume fraction. E′′ values were shown to simply account for the reduction of the mechanical energy lost within the material, in connection to the occurrence of polymer molecular motions. Analysis of E′ variations as a function of Φ was based on the theoretical models available in the literature to account for the contribution of the spherical filler particles. In the glassy state, Kerner’s and Christensen and Lo’s models yielded comparable results. In the rubbery state, Guth and Gold’s model was shown to prevail on Kerner’s model.     

Interlocking hexagons model for auxetic behaviour

A 2D ‘Rough Particle’ model consisting of interlocking hexagons is reported. Analytical expressions for the in-plane Poisson’s ratios and Young’s moduli due to particle translation along the geometrically matched male and female interlocks are derived for the model. The dependency of the mechanical properties on each of the model (geometrical and stiffness) parameters is provided, and it is shown that the assembly of interlocking hexagons deforming by particle translation along the interlocks displays auxetic (negative Poisson’s ratio) behaviour. The model predictions are compared with experimental mechanical properties for auxetic polypropylene (PP) films and fibres. The model predicts the experimental Poisson’s ratio values very well (model: ν_xy = −1.30, ν_yx = −0.77; experiment (PP films): ν_|| = −1.12, ). The model generally overestimates the Young’s moduli of the films, but is in reasonable agreement with the axial Young’s modulus of the fibres.     

Influence of crystallographic textures on tensile properties of 316L austenitic stainless steel

Role of cold rolling texture on the tensile properties of the cold rolled and cold rolled and annealed AISI 316L austenitic stainless steel is described here. The solution-annealed stainless steel plates were unidirectionally cold rolled to 50, 70 and 90% of reduction in thickness. The cold rolled material was annealed at 500–900 °C annealing temperatures. X-ray diffraction technique was employed to study the texture evolution in cold rolled as well as cold rolled and annealed conditions. The texture components that evolved were translated into slip transmission number ‘λ’ and Schmid factor ‘μ’. These two parameters were correlated with the tensile properties of the material. The tensile properties were evaluated under all processing conditions. Softening of the cold rolled material was observed after annealing with increasing annealing temperatures. From the stress–strain curves, strain hardening coefficient ‘n’ and strain hardening rate ‘θ’ were determined. It was found that the effect of texture on tensile behaviour could be understood clearly by strain hardening rate. Out of the two parameters, ‘n’ and ‘θ’, strain hardening rate was found to be more sensitive to type of texture in the material.     

Fatigue crack growth behaviour of gamma base titanium aluminides under different loading conditions

Static and cyclic fatigue crack growth behaviour of gamma base titanium aluminides with three different microstructures were investigated. Influence of cyclic test frequency on fatigue crack growth behaviour was also studied at room temperature under a controlled humidity condition. The crack growth behaviour both under static and cyclic loading was strongly influenced by the microstructure. The threshold stress intensity and crack growth behaviour under cyclic loading were much inferior than that under static loading indicating the ‘true-cyclic fatigue’ effect exhibited in gamma base titanium aluminides. No significant effect of test frequency on the crack growth behaviour was observed for the equiaxed and duplex microstructure materials.     

Rheological behaviour of LDPE/EVAc blends. II. Linear viscoelasticity and extrusion properties

This study was designed to determine the linear viscoelastic and extrusion properties of a series of LDPE/EVAc blends. Newtonian viscosity was found to show strong positive deviation from the double reptation model, which assumes miscibility or, at least, cooperative relaxation between the mixed species. The blends also showed enhanced steady-state compliance and elastic indices compared to those of the pure components. These features, typical of emulsion-like polymer blends, seem to be attributable to additional relaxation processes at low frequencies associated with dispersed phase deformability. Good agreement with experimental dynamic results was shown by the Palierne model for emulsions of two viscoelastic liquids, for values of α/R = 3.5 × 10³ Pa across the whole frequency range examined. The double reptation model, usually applied to miscible blends, showed good agreement with experimental data for frequencies higher than 10⁻² rad s⁻¹. This could lead to erroneous conclusions on the miscibility of certain systems, for which a complete set of experimental data is lacking.     

Wood viscoelastic compliance determination with special attention to measurement problems

A new experimental technique has been developed for the determination of wood viscoelastic compliance in tension. It associates tensile creep tests parallel to, and off the material symmetry axes with a strain measurement system using a rosette gauge. Particular attention has been paid to accurate strain measurement, and to hydrothermal and mechanical disturbance factors. Application is restricted to the determination of the four compliances which characterize the viscoelastic behaviour of spruce in the LR (radial) plane, at 21°C and 12% equilibrium moisture content. The time-dependent strain induced by load level up to 58% of the ultimate strength, and applied during 4 to 10 days, is largely recoverable. As proposed by Schniewind and Barrett, the compliances are represented by time power functions. The experimental results support earlier observations that the creep level is much higher in tension in the radial direction than parallel to the grain, and that the creep level in shear over the LR plane is an intermediate between the above two cases. Finally, the experimental results illustrate the validity of the superposition principle under the test conditions examined, which is the basis of the linear viscoelastic model introduced here.

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Resume On présente une méthode d’essais originale pour la détermination des complaisances viscoélastiques du bois sans défaut en traction. Elle combine des essais de fluage en traction d’éprouvettes taillées suivant les axes d’anisotropie et taillées avec un angle de désorientation (essais ‘hors axes’). Le mesurage des déformations est effectué par des jauges d’extensométrie (rosettes). Préalablement aux essais, il a été réalisé une réflexion méthodologique portant sur les essais de traction sur bois sans défaut et une analyse expérimentale de la stabilité au cours du temps des systèmes de mesurage (jauge/colle). Ce dernier point, lié aux effets mécaonosorptifs, nous a permis de préconiser l’utilisation des jauges KFC en association avec celle de la colle époxy.

     

Dynamic mechanical behavior of polymer modified bitumen

The dynamic mechanical behaviour of bitumen (BIT) modified with styrene/butadiene/styrene block copolymer (SBS) were investigated. Dynamic mechanical analysis (DMA) were performed in the temperature range –80 to 60 °C. The primary viscoelastic functions were determined at the traffic frequency, 5 Hz. The BIT+SBS blends were investigated in creep fatigue regime at temperature 10, 20, 30, 40 and 50 °C. Dynamic mechanical behaviour of BIT+SBS blends depends on their morphological characteristics, number of phases, phase compositions and phase content in blend, as well as time and temperature. The curves of primary viscoelastic functions, storage modulus (E′), loss modulus (E′′) and loss tangent (tg δ) vs. temperature of polymer modified bitumen differ from unmodified bitumen and indicate the presence of the swollen polybutadiene and polystyrene phases in bitumen phase. The curve E′ vs. temperature of polymer modified bitumen show the rubbery plateau. With the increment of SBS content the rubbery plateau is shifted to high temperatures. At the constant load the creep values of BIT-SBS blends increase and those of creep modulus decrease over a period of time. These effect are more pronounced in samples with higer content of SBS. The time-temperature correspondence principle was applied to create master curves for the reference temperature 10 °C for the creep modulus of BIT + SBS blends. The data were analysed using WLF and Arrhenius equations. Electronic Publication     

Two-fluid pressure-driven channel flow with wall deposition and ageing effects

Two-fluid, stratified pressure-driven channel flow is studied in the limit of small viscosity ratios. Cases are considered in which the core fluid undergoes phase separation that results in the ‘precipitation’ of a distinct phase and the formation of a wall layer; these situations are common in the oil industry where ‘fouling’ deposits are formed during the flow. The thickness of this layer increases as a result of continual deposition through Stefan-like fluxes, which are related to the phase behaviour of the core fluid through a chemical equilibria model that treats the fluid as a bi-component mixture. The deposit also undergoes an ‘ageing’ process whereby its viscosity increases due to the build-up of internal structure; the latter is modelled here via a Coussot-type relation. Lubrication theory is used in the wall layer and an integral balance in the core fluid wherein inertial effects are important. By choosing appropriate semi-parabolic velocity and temperatures closures for the laminar flow in the channel core, and a closure relation for the wall layer rheology, evolution equations are derived that describe the flow dynamics. In the presence of ageing but absence of deposition, it is demonstrated how the time-varying deposit rheology alters the wave dynamics; for certain parameter ranges, these effects can give rise to the formation of steep waves and what appears to be finite-time ‘blow-up’. With both ageing and deposition, the spatio-temporal evolution of the deposit is shown together with the increase in the deposition rate with increasing temperature difference between the wall and the inlet.     

Asymptotic analysis on nonlinear vibration of axially accelerating viscoelastic strings with the standard linear solid model

Nonlinear parametric vibration of axially accelerating viscoelastic strings is investigated via an approximate analytical approach. The standard linear solid model using the material time derivative is employed to describe the string viscoelastic behaviors. A coordinate transformation is introduced to derive Mote’s model of transverse motion from the governing equation of the stationary string. Mote’s model leads to Kirchhoff’s model by replacing the tension with the averaged tension over the string. An asymptotic perturbation approach is proposed to study principal parametric resonance based on the two models. The amplitude and the existence conditions of the steady-state responses are determined by locating the nonzero fixed points in the modulation equations resulting from the solvability condition. Numerical results are presented to highlight the effects of the material parameters, the axial-speed fluctuation amplitude, and the initial stress on steady-state responses.     

Is surface chemical composition important for orthopaedic implant materials?

Ti-6Al-7Nb (NS) in its ‘standard’ implant form has been previously shown to be detrimental to fibroblast growth and colonisation on its surface. Specific aspects of the NS topography have been implicated, however, the contribution of its unique surface chemistry to the cell behaviour was unknown. By evaporating either gold or titanium on the surface of standard NS, two different model surface chemistries could be studied with the same characteristic standard NS topography. Two other ‘standard’ orthopaedic topographies, that of stainless steel (SS) and of ‘commercially pure’ titanium (TS) were also treated in a similar manner. All materials elicited behaviour similar to their uncoated counterparts. For coated SS and TS, cell proliferation was observed, cells were well spread and displayed mature focal adhesion sites, and associated cytoskeletal components. For coated NS, cell proliferation was compromised, cells remained rounded, filopodia attached and seemed to probe the surface, especially the β -phase particles, and both the focal adhesion sites and the microtubule network were disrupted by the presence of these particles. These results confirmed, that in the instance of NS, the topography was the primary cause for the observed stunted cell growth. For biomaterials studies, the standardisation of surface chemistry used here is a valuable tool in allowing vastly different materials and surface finishes to be compared solely on the basis of their topography.     

Fracture mechanisms in a stoichiometric 3Al2O32SiO2 mullite

The mechanical behaviour from room temperature up to 1400°C (strength, toughness, Young’s modulus) of a 3Al₂O₃·2SiO₂ dense mullite material containing 0.2 wt% alkali has been studied. Microstructure has been characterized by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Toughness, bend strength and static Young’s modulus have been determined from room temperature up to 1400°C. The influence of strain rate on fracture behaviour has been investigated and a correlation of the mechanical parameters to fractographic observations by SEM has been stated. A strong influence of loading rate on microstructural modifications during fracture at 1300°C has been found. This revised version was published online in November 2006 with corrections to the Cover Date.