On the propagation of elastic waves through composite media

Summary With the aid of an ultrasonic pulse technique, the propagation of elastic waves (longitudinal as well as transverse) through polyurethane rubbers filled with different amounts of sodium chloride particles was studied. The velocity of both longitudinal and transverse waves was found to increase with filler content. From the measured wave velocities, the effective modulus for longitudinal waves,L, bulk modulus,K, and shear modulus,G, were calculated according to the relations for a homogeneous isotropic material. All three moduli appear to be monotonously increasing functions of the filler content over the whole experimentally accessible temperature range (–70 °C to + 70 °C forL andK;}-70 °C to about –20 °C forG) and they, moreover, reflect the glassrubber transition of the binder.Poisson's ratio,, was found to decrease with increasing filler content and show a rise at the high temperature side of the experimentally accessible temperature range (about –20 °C) as a result of the approach of the glass-rubber transition.In addition to the velocities, the attenuation of both longitudinal and transverse waves was measured in the temperature ranges mentioned. It was found that in the hard region tan _L as well as tan _G are independent of the filler content within the accuracy of the measurements. In the rubbery region, however, tan _L, increases with increasing filler content.Finally, the experimental data are compared with a simple macroscopic theory on the elastic properties of composite media.     

Behaviour of unfilled and filled rubbers in shear in the glass-rubber transition region

Summary Rubbers filled with high amounts of a hard inorganic filler still show the typical mechanical properties of a high polymer, viz. a glass-rubber transition region, a glassy state and a rubbery state. The influence of filler characteristics on the glass-rubber transition is discussed, chiefly on the basis of the course of shear modulus at constant frequency as a function of temperature.The influence of volume content of filler on the glass-rubber transition of composite materials consists chiefly in a change of the levels of the shear modulus in the glassy and in the rubbery state. This change may be described by a simple macroscopic model due toVan der Poel. Predictions by this theory could be confirmed for rubbers filled with single filler fractions in the range of filler size between 30–500 m, and in the range of filler content between 0–50 vol.%.At smaller particle sizes, an influence of filler size was observed, which points to an increase in the transition temperature and to an increase in the level of modulus in the rubbery state with decreasing filler size.The preparation of composite materials with high filler contents (> 55 vol.%) is only possible by using a filler with a bimodal size distribution.In this case, moduli depend on filler content and mixing ratio of coarse to fine filler fraction; theVan der Poel theory then gives predictions which are too high in comparison with experimental results.     

Temperature Dependent Viscoelastic Properties of Polymers Investigated by Small-Scale Dynamic Mechanical Analysis

The temperature-dependent viscoelastic properties of polymers were investigated by small-scale dynamic mechanical analysis in the range of −100°C to 200°C. The polymers tested included glassy polymer (atactic polystyrene), semicrystalline polymer (high-density polyethylene) and rubbery polymer (polyisobutylene). The small-scale dynamic mechanical analyses were performed by using a flat-tip indenter with an oscillating displacement of amplitude 36 nm. The force amplitude and phase angle were measured, from which the storage modulus E′ and loss tangent tanδ were calculated. The results obtained from indentation experiments are consistent with those obtained from conventional dynamic mechanical analyzer (DMA). It is thus demonstrated that the indentation technique can quantitatively measure the temperature-dependent viscoelastic properties of polymers at small dimensions.     

A New Device for Mechanical Testing of Blood Vessels at Cryogenic Temperatures

As part of an ongoing program to study the thermo-mechanical effects associated with cryopreservation via vitrification (vitreous in Latin means glassy), the current study focuses on the development of a new device for mechanical testing of blood vessels at cryogenic temperatures. This device is demonstrated on a bovine carotid artery model, permeated with the cryoprotectant cocktail VS55 and a reference solution of 7.05M DMSO, below glass transition. Results are also presented for crystallized specimens, in the absence of cryoprotectants. Results indicate that the elastic modulus of a specimen with no cryoprotectant, at about −140°C (8.6 and 15.5°C below the glass transition temperature of 7.05M DMSO and VS55, respectively), is 1038.8 ± 25.2 MPa, which is 8 and 3% higher than that of a vitrified specimen permeated with 7.05M DMSO and VS55, respectively. The elastic modulus of a crystallized material at −50°C is lower by ∼20% lower from that at −140°C.     

Rheological properties of poly(vinyl chloride)/plasticizer systems—relation between sol–gel transition and elongational viscosity

Poly(vinyl chloride) (PVC)/di-isononyl phthalate systems with PVC content of 45.5 (PVC8) and 70.4 wt% (PVC6) were prepared by a hot roller at 150 °C and press molded at 180 °C. The dynamic viscoelasticity and elongational viscosity of PVC8 and PVC6 were measured in the temperature range from 150 to 220 °C. We have found that the storage and loss shear moduli, G′ and G″, of PVC8 and PVC6 exhibited the power-law dependence on the angular frequency ω at 190 and 210 °C, respectively. Correspondingly, the tan δ values did not depend on ω. These temperatures indicate the critical gel temperature T _gel of each system. The critical relaxation exponent n obtained from these data was 0.75 irrespective of PVC content, which was in agreement with the n values reported previously for the low PVC concentration samples. These results suggest that the PVC gels of different plasticizer content have a similar fractal structure. Below T _gel, the gradual melting of the PVC crystallites takes place with elevating temperature, and above T _gel, a densely connected network throughout the whole system disappears. Correspondingly, the elongational viscosity behavior of PVC8 and PVC6 exhibited strong strain hardening below T _gel, although it did not show any strain hardening above T _gel. These changes in rheological behavior are attributed to the gradual melting of the PVC crystallites worked as the cross-linking domains in this physical gel, thereby inapplicability of the of time–temperature superposition for PVC/plasticizer systems.     

An experimental study of dynamic tensile properties of glass fiber at low-temperatures

Tensile impact experiments of EC8.0−24×7 glass fiber bundles at different low temperaturesT(14°C, −40°C and −10°C) and strain rates ɛ were carried out, and complete stress-strain curves were obtained. Within the range of the experiment temperatures and strain rates, it is found that the initial modulusE, the ultimate strength σ_max and the unstable strain ɛ _b of the glass fiber bundles all increase with ɛ at an identicalT. At an identical ɛ, with the decrease ofT, E and σ_max increase; but ɛ _b increases when 10°C>T>−40°C and decreases when −40°C>T>−100°C. The strain-rate- and temperature-dependent bimodal Weibull statistical constitutive theory was adopted for the statistical analysis of the experimental results, and the Weibull parameters of single fiber were obtained. The results show that the bimodal Weibull distribution function is suitable to represent the strength distribution of the glass fiber at low temperature and different strain rates. The differences in the mechanical properties between EC8.0−24×7 and EC5.5−12 ×14 glass fiber bundles were also discussed. Project supported by the National Natural Science Foundation of China (No. 19772058).     

Thermoreversible gels in oil/EVA systems

In this work we investigate the gel formation of EVA/recycled motor oil systems as a route to obtain synthetic binders which could be used instead of natural bitumen, as well as mixed with natural bitumen to modify adequately its viscoelastic response. The EVA copolymer studied in this work has a vinyl acetate content of 18 wt% and solutions of EVA/motor oil have been prepared up to a concentration of 50 wt%. Dynamic viscoelastic frequency sweeps between 10⁻² Hz and 10² Hz have shown that above 3 wt%, at 25 °C, EVA/motor oil systems form gels. It has been possible to define an elastic equilibrium modulus, G_e, for each gel. The dependence of G_e on concentration has been compared with that of PVC/DOP and SBS/oil gels on the basis of the De Gennes model. Thermal stability of EVA/motor oil gels has also been analyzed, indicating that for the highest polymer concentrations gel point is above 80 °C. Received: 23 December 1999 Accepted: 13 June 2000     

On the perturbational global attractivity of nonautomous delay differential equations

Consider the perturbed nonautonomous linear delay differential equation x(t) = - a(t)x(t-τ) + F(t, x₁, t ⩾ 0 where x₁(s)=x(t+s) for −δ≤s≤0. Suppose that a(t) ∈ C([0,∞), (0,∞)), τ≥0,F:[0, ∞) x C[−δ,0] → R is a continuous functions and F(t,0) ≡ 0. Here C[−δ,0] is the space of continuous functions Φ: [−δ,0] → R with ∥Φ∥<H for the norm | Φ |, where |·| is any norm in R and 0<H≤+∞. Most of the known papers [1–5,7] have been concerned with the local or global asymptotic behavior of the zero solution of Eq. (*) when a(t) is independent of t i. e., a(t) is autonomous. The aim in this paper is to derive the sufficient conditions for the global attractivity of the zero solution of of Eq. (*) When a(t) is nonautomous. Our results, which extend and improve the known results, are even “sharp”. At the same time, the method used in this paper can be applicable to the perturbed nonlinear equation. Project supported by the Natural Science Foundation of Hunan     

Rheological behavior of dilute solutions of a side-chain liquid-crystalline polysiloxane in 4,4′-n-octylcyanobiphenyl

The electrorheological (ER) behavior and stress transient response of dilute solutions of a side-chain liquid-crystalline polysiloxane (LCP) in 4,4′-n-octylcyanobiphenyl (8CB) is studied. In the flow-tumbling regime of 8CB, i.e. from T = 34–38 °C, the stress transients of both 8CB and LCP/8CB solutions show oscillatory responses, but with shorter oscillation periodicities for the solution. In the flow-aligning regime of 8CB, i.e. at 39 and 40 °C, a transformation to flow-tumbling is observed in the stress transients of the LCP/8CB solution. In both cases, analysis of the transient responses indicates that the change in Leslie viscosity coefficients on dissolving the LCP are δα₂ < 0 and δα₃ > 0. The amplitude of the ER response, defined as the viscosity difference between the on and off states, Δη = η_on − η_off, is only weakly affected by the dissolution of LCP. These rheological results can be interpreted consistently using a modified version of a hydrodynamic theory by Brochard, provided an additional dissipation mechanism is included, which derives from the presence of an elastic torque between director rotation and LCP orientation. Received: 8 September 1999/Accepted: 13 December 1999     

Vorticities in a LES Model for 3D Periodic Turbulent Flows

This paper is devoted to the study of a LES model to simulate turbulent 3D periodic flow. We focus our attention on the vorticity equation derived from this LES model for small values of the numerical grid size δ. We obtain entropy inequalities for the sequence of corresponding vorticities and corresponding pressures independent of δ, provided the initial velocity u₀ is in L_x² while the initial vorticity ω₀ = ∇ × u₀ is in L_x¹. When δ tends to zero, we show convergence, in a distributional sense, of the corresponding equations for the vorticities to the classical 3D equation for the vorticity.     

Isothermal viscoelastic properties of PMMA and LDPE over 11 decades of frequency and time: a test of time–temperature superposition

Many instruments used to measure viscoelastic properties are only capable of subjecting a sample to a limited range of loading frequencies. For thermorheologically simple materials, it is assumed that a change in temperature is equivalent to a shift of the viscoelastic behavior on the log frequency or time axis. For many materials, time–temperature superposition appears to work well for modulus or compliance curves over three decades of time or frequency, but some deviations are known if the window is expanded to five or six decades. To apply a more stringent test of the validity of time–temperature superposition, broadband viscoelastic spectroscopy is used to isothermally study polymethylmethacrylate and low-density polyethylene at several temperatures in the glassy region. Shear modulus and damping (tan δ) are measured isothermally over a wide range (up to 11 decades) of time and frequency. Results indicate that, while modulus curves can be approximately superimposed, the damping (tan δ) curves change in height and shape with temperature.     

Oscillating flow in a 2-D diffuser

Separating oscillating flows in an internal, adverse pressure gradient geometry are studied experimentally. Simultaneous velocity and pressure measurements demonstrate that the minor losses associated with oscillating flow in an adverse pressure gradient geometry can be smaller or larger than those for steady flow. Separation is found to begin high in the diffuser and propagate downward. The flow is able to remain attached further into the diffuser with larger Reynolds numbers, small displacement amplitudes, and smaller diffuser angles. The extent of separation grows with L ₀/h. The minor losses grow with increasing displacement amplitude in the measured range 10 < L ₀/h < 40. Losses decrease with increasing Re _δ in the measured range of 380 < Re _δ < 740. It is found that the losses increase with increasing diffuser angle over the measured range of 12° < θ < 30°. The nondimensional acoustic power dissipation increases with Reynolds number in the measured range and decreases with displacement amplitude.     

A study of loop heat pipe with biporous wicks

The purpose of this study is to investigate the effects of various bimodal pore size distributions of biporous wicks for a loop heat pipe (LHP). The study was conducted following a statistical method using a two-level factorial plan involving three variables (particle size of pore former:74–88 and 125–149 μm Na₂CO₃, pore former content:20% by volume and 25% by volume, sintering temperature:700 and 750°C). Finally, the heat transport capability of the LHP between monoporous wicks and biporous wicks has been investigated. Experimental results show that, at the sink temperature of 10°C and the allowable evaporator temperature of 80°C, the heat transfer capacity of the better biporous wick achieved 200 W and the total thermal resistance was 0.31°C/W. The performance is enhanced about 60%, compared to a monoporous wick for 125 W and 0.53°C/W. Therefore, LHPs with biporous wicks are very attractive for high heat flux applications in the future.     

Irradiation-Induced Solute Clustering in a Low Nickel FeMnNi Ferritic Alloy

Understanding the radiation embrittlement of reactor pressure vessel (RPV) steels is required to be able to operate safely a nuclear power plant or to extend its lifetime. The mechanical properties degradation is partly due to the clustering of solute under irradiation. To gain knowledge about the clustering process, a Fe−1.1 Mn−0.7 Ni (at.%) alloy was irradiated in a test reactor at two fluxes of 0.15 and 9 ×10¹⁷ n _E > 1MeV .m^− 2.s^− 1 and at increasing doses from 0.18 to 1.3 ×10²⁴ n _E > 1MeV .m^− 2 at 300°C. Atom probe tomography (APT) experiments revealed that the irradiation promotes the formation in the α iron matrix of Mn/Mn and/or Ni/Ni pair correlations at low dose and Mn–Ni enriched clusters at high dose. These clusters dissolve partially after a thermal treatment at 400°C. Based on a comparison with thermodynamic calculations, we show that the solute clustering under irradiation can just result from an induced mechanism.     

Aerodynamics of intermittent bounds in flying birds

Flap-bounding is a common flight style in small birds in which flapping phases alternate with flexed-wing bounds. Body lift is predicted to be essential to making this flight style an aerodynamically attractive flight strategy. To elucidate the contributions of the body and tail to lift and drag during the flexed-wing bound phase, we used particle image velocimetry (PIV) and measured properties of the wake of zebra finch (Taeniopygia guttata, N = 5), flying at 6–10 m s⁻¹ in a variable speed wind tunnel as well as flow around taxidermically prepared specimens (N = 4) mounted on a sting instrumented with force transducers. For the specimens, we varied air velocity from 2 to 12 m s⁻¹ and body angle from −15° to 50°. The wake of bounding birds and mounted specimens consisted of a pair of counter-rotating vortices shed into the wake from the tail, with induced downwash in the sagittal plane and upwash in parasagittal planes lateral to the bird. This wake structure was present even when the tail was entirely removed. We observed good agreement between force measures derived from PIV and force transducers over the range of body angles typically used by zebra finch during forward flight. Body lift:drag (L:D) ratios averaged 1.4 in live birds and varied between 1 and 1.5 in specimens at body angles from 10° to 30°. Peak (L:D) ratio was the same in live birds and specimens (1.5) and was exhibited in specimens at body angles of 15° or 20°, consistent with the lower end of body angles utilized during bounds. Increasing flight velocity in live birds caused a decrease in C _L and C _D from maximum values of 1.19 and 0.95 during flight at 6 m s⁻¹ to minimum values of 0.70 and 0.54 during flight at 10 m s⁻¹. Consistent with delta-wing theory as applied to birds with a graduated-tail shape, trimming the tail to 0 and 50% of normal length reduced L:D ratios and extending tail length to 150% of normal increased L:D ratio. As downward induced velocity is present in the sagittal plane during upstroke of flapping flight, we hypothesize that body lift is produced during flapping phases. Future efforts to model the mechanics of intermittent flight should take into account that flap-bounding birds may support up to 20% of their weight even with their wings fully flexed.     

Maximum density effects on convective instability of horizontal plane poiseuille flows in the thermal entrance region

A linear stability analysis is used to study the conditions marking the onset of secondary flow in the form of longitudinal vortices for plane Poiseuille flow of water in the thermal entrance region of a horizontal parallel-plate channel by a numerical method. The water temperature range under consideration is 0∼30°C and the maximum density effect at 4°C is of primary interest. The basic flow solution for temperature includes axial heat conduction effect and the entrance temperature is taken to be uniform at far upstream location jackie=−∞ to allow for the upstream heat penetration through thermal entrance jackie=0. Numerical results for critical Rayleigh number are obtained for Peclet numbers 1, 10, 50 and thermal condition parameters (λ ₁, λ ₂) in the range of −2.0≤λ ₁≤−0.5 and −1.0≤λ ₂≤1.4. The analysis is motivated by a desire to determine the free convection effect on freezing or thawing in channel flow of water.     

Transfer model and kinetic characteristics of $${\rm NH}_{4}^{+}$$ –K+ ion exchange on K-zeolite

Based on the mass transfer theory, a new mass transfer model of ion-exchange process on zeolite under liquid film diffusion control is established, and the kinetic curves and the mass transfer coefficients of –K⁺ ion-exchange under different conditions were systemically determined using the shallow-bed experimental method. The results showed that the –K⁺ ion-exchange rates and transfer coefficients are directly proportional to solution flow rate and temperature, and inversely proportional to solution viscosity and the size of zeolite granules. It also showed that the transfer coefficient is not influenced by the ion concentrations. For a large ranges of operational conditions including temperatures (10 − 75°C), flow rates (0.031 m s⁻¹ −0.26 m s⁻¹), liquid viscosities (1.002 × 10⁻³ N s m⁻² − 4.44 × 10⁻³ N s m⁻²), and zeolite granular sizes (0.2 − 1.45 mm), the average mass transfer coefficients calculated by the model agree with the experimental results very well.     

Micro Scale Tensile Behaviour of Thin Bitumen Films

The tensile behaviour of two types of viscoelastic bituminous films confined between mineral aggregates or steel as adherends, was investigated in the brittle and ductile regimes. Uniaxial specimens were fabricated employing a prototype set up allowing construction of micro-scale thin films and visualization of failure phenomena. The effect of key parameters, namely, temperature (23°C and −10°C), binder type (straight run and polymer modified), adherend type (stainless steel and mineral aggregate), and water conditioning were investigated sequentially. The results show that water sensitive aggregate-binder combinations in macro (150 mm diameter) and mega (in service) scales also displayed reduced tensile strength in the micro scale when water conditioned. At 23°C ductile failure and at −10°C brittle fracture were observed. At 23°C phenomena, such as formation of striations during tensile mechanical loading, void nucleation and growth, filamentation and large ductile flow before fracture could be witnessed. When using proper surface preparation procedures, in all types of specimen investigated at 23°C only cohesive failure and at −10°C predominantly adhesive-cohesive failure were found.     

Measurement of thermal expansion coefficients of composites using strain gages

The measurement of the coefficients of thermal expansion (CTEs) of composite materials using electrical resistance strain gages is addressed. Analytical expressions for the CTEs of an orthotropic lamina are derived, accounting for the effects of transverse sensitivity and possible misalignment of the gages. Experiments are performed for the characterization of the thermal expansion behavior of a fiber-glass-reinforced epoxy unidirectional lamina using an invar specimen as reference material. Preliminary training cycles are performed for the determination of an optimal heating rate for the measurements, which ensures thermal equilibrium conditions. Three measurement cycles yield the principal CTEs of the lamina α₁, α₂ and α₁₂ with repeatability within ±0.34×10⁻⁶, ±0.85×10⁻⁶ and ±2.8×10⁻⁶/°C, respectively. It is noted that inhomogeneity of the specimen and variation in thermomechanical properties of the gages can cause a noticeable spead in the measurements.     

Temperature and rate effects on stable crack growth in a particulate composite material

In this study, edge cracked sheet specimens made from polybutadiene rubber embedded with hard particles were used in crack propagation tests. Crack propagation tests were conducted under two crosshead speeds (2.54 mm/min and 12.7 mm/min) at three temperatures (−53.9°C, 22.2°C and 73.9°C). The experimental data were analyzed and the crack growth resistance curves and the crack growth rate versus the Mode I stress intensity factor were plotted. Based on these experimental results, the effects of temperature and loading rate on the crack growth behavior were investigated and the results are discussed.