Large amplitude oscillatory shear rheology of three different shear-thickening particle dispersions

We present a large amplitude oscillatory shear rheology (LAOS) investigation of three different shear-thickening particle dispersions - fumed silica in polyethylene oxide (FLOC), fumed silica in polypropylene glycol (HydroC), and cornstarch in water (JAM). These systems shear-thicken by three different mechanisms - shear-induced formation of particle clusters flocculated by polymer bridging, hydrocluster formation, and jamming. The viscoelastic non-linearities of the three fluids were studied as a function of strain and strain-rate space through the use of Lissajous-Bowditch curves and local nonlinear viscoelastic moduli of an oscillatory shear cycle. The nonlinear behaviors of the three fluids were compared and contrasted to understand the nonlinear shear-thickening mechanism of each. Both HydroC and JAM dispersions were found to exhibit strong strain stiffening of the elastic moduli and strain thickening of the loss moduli behavior associated with possible hydrocluster formation and particle jamming. However, the FLOC dispersion, in contrast, showed strong strain softening and strain thinning behavior at large strain amplitudes associated with yielding of the microstructure. The expected thickening of the loss modulus of FLOC in LAOS with increasing strain was not observed even though viscosity of FLOC was found to shear-thicken in steady-shear measurements. This disagreement is likely due to very large strain amplitudes required for shear-thickening to occur by shear-induced polymer bridging mechanism. The hypothesis was confirmed through stress growth experiments. Conversely, the HydroC and JAM dispersions required relatively small applied strains for shear-thickening to occur by hydrocluster and jamming mechanism. The comparison of local intra-cycle nonlinearity through Lissajous-Bowditch plots and nonlinear viscoelastic parameters indicated that the elastic nonlinearities of all three systems are primarily driven by a strong dependence on the magnitude of the applied strain-rates within an oscillatory cycle rather than the amplitude of the applied strain. A close inspection of the LAOS data reveals strong differences in the viscoelastic nonlinearities of these three different shear-thickening dispersions which can be used to create a nonlinear rheological fingerprint for each and offers valuable new insights into the nonlinear dynamics associated with each of the shear-thickening mechanisms.     

An exploratory investigation of cumulative shock fatigue

A simple device for producing cumulative shock loading in solids is described. The device uses a ballistic-impact-driven projectile to introduce high-stress waves into a solid. The impact time and load amplitude can be varied to produce fracture in one or several impacts in PMMA rods. The wavefront approached a square wave shape. Materials other than PMMA were loaded to failure to demonstrate the versatility of the device. Fracture morphologies observed with optical and scanning-electron microscopy are described.     

Stress-concentration factors for semielliptical notches in beams under pure bending

Elliptical notches in rectangular beams under pure bending are examined photoelastically. Stress-concentration factors due to a single elliptical notch are obtained for wide ranges of 2a/h andd/h, where 2a, d, andh are the width of notch, depth of notch, and depth of beam, respectively. In particular, the geometries of the optimum elliptical notches producing the least stress concentrations are obtained. Almost the whole elliptical boundary of these notches are stressed to the same peak, which indicates that these notches will probably produce the least stress concentrations among all notches, elliptical or nonelliptical. The graphs herein will enable the designers to find the stress-concentration factors of elliptical notches and to pick out the geometry of the optimum notch which will give the least stress concentration for any given values of 2a/h andd/h. Stresses and the stress-concentration factors at the bottom of the beam opposite the notch are also obtained. These stresses, though smaller in magnitude, are of an opposite sign to the peak stress at the notch. For brittle materials, a smaller tensile stress may be more critical than a large compressive stress; therefore, these stress-concentration factors are also given.     

Determination of Chlorinated Solvent Sorption by Porous Material—Application to Trichloroethene Vapor on Cement Mortar

Experiments have been performed to investigate the sorption of trichloroethene (TCE) vapor by concrete material or, more specifically, the cement mortar component. Gas-flow experiments were conducted using columns packed with small pieces of cement mortar obtained from the grinding of typical concrete material. Transport and retardation of TCE at high vapor concentrations (500 mg L \(^{-1})\) was compared to that of a non-reactive gas tracer (Sulfur Hexafluoride, SF \(_{6})\) . The results show a large magnitude of retardation (retardation factor \(=\) 23) and sorption (sorption coefficient \(=\) 10.6 cm \(^{3}\)  g \(^{-1})\) for TCE, compared to negligible sorption for SF \(_{6}\) . This magnitude of sorption obtained with pollutant vapor is much bigger than the one obtained for aqueous-flow experiments conducted for water-saturated systems. The considerable sorption exhibited for TCE under vapor-flow conditions is attributed to some combination of accumulation at the air-water interface and vapor-phase adsorption, both of which are anticipated to be significant for this system given the large surface area associated with the cement mortar. Transport of both SF \(_{6}\) and TCE was simulated successfully with a two-region physical non-equilibrium model, consistent with the dual-medium structure of the crushed cement mortar. This work emphasizes the importance of taking into account sorption phenomena when modeling transport of volatile organic compounds through concrete material, especially in regard to assessing vapor intrusion.     

Flow past a suddenly cooled horizontal plate

The problem of unsteady laminar, incompressible free convection above a horizontal semi-infinite flat plate is studied theoretically. It is assumed that for timet<0 the plate is hotter than its surroundings and at timet=0 the plate is suddenly cooled to the same temperature of its surroundings. Three solutions of the momentum and energy equations are obtained, namely

1. an analytical solution which is valid for small time,
2. an asymptotic analytical solution which is valid for large time, and
3. a numerical solution which matches these two limiting analytical solutions.

It is found that the numerical solution matches the small and large time solutions accurately. Finally, the variation of the velocity, temperature, skin friction and heat transfer on the plate with time are discussed.     

Experimental and theoretical studies of explosive-induced large dynamic and permanent deformations of simple structures

Explosive-loading and structural-response measurement techniques are described for obtaining definitive large dynamic and permanent-deformation data on simple structures which undergo (a) two-dimensional deformations, or (b) general three-dimensional deformations. In the former category, explosively loaded structures discussed include freely suspended single-layer circular rings, freely suspended unbonded concentric rings, and flat circular plates with clamped edges. Representing category (b) is an explosively loaded cylindrical panel with clamped edges. To define the impulse which was imparted explosively to these structures, appropriate impulse-calibration tests were performed on high-explosive-loaded single-layer and unbonded double-layer specimens; these testing techniques and the results obtained are discussed. General numerical methods for predicting large elasticplastic dynamic and permanent deformations of structures which undergo either two-dimensional or general three-dimensional deformations are described briefly. Dynamic responses and permanent deformations predicted with these methods are compared with data from the present experiments. Certain problems, both experimental and theoretical, requiring further investigation are indicated.     

The Mixed Convection Boundary Layer on a Vertical Melting Front in a Non-Darcian Porous Medium

The effect of surface melting on the dual solutions that can arise in the problem of the mixed convection boundary-layer flow past a vertical surface embedded in a non-Darcian porous medium is considered. The problem is described by M, melting parameter, \(\lambda \), mixed convection parameter, and \(\gamma \), the flow inertia coefficient, numerical results being obtained in terms of these three parameters. It is seen that the melting phenomenon reduces the heat transfer rate and enhances the boundary-layer separation at the solid–liquid interface. Asymptotic solutions for the forced convection, \(\lambda =0\), and free convection, large \(\lambda \), limits are derived.     

Amplitude control contour in a hemispherical resonator gyro with automatic compensation for difference in <Emphasis Type="Italic">Q</Emphasis>-factors

For the normal operation of a hemispherical resonator gyro, its circuit must contain a control contour maintaining the resonator vibrations in the form of a standing wave with a prescribed amplitude. A turn of the basement leads to a turn of the standing wave, which permits using the resonator as a gyro. A turn of the standing wave may arise without a turn of the basement if the resonator has difference in Q-factors, i.e., if the damping constant of the standing wave depends on its orientation. This is one important source of device errors. Some information about the difference in Q-factors can be obtained by analyzing how the control signal maintaining the prescribed amplitude depends on the wave orientation. The larger the damping constant, the larger control signal is required to maintain the wave with the largest amplitude.In the present paper, we consider a version of the amplitude control contour in which the control signal maintaining the amplitude is supplemented with signal compensating for difference in Q-factors of the resonator. The compensating signals are produced by time integration of the control signal multiplied by certain trigonometric functions of the wave orientation angle. In this case, we decrease the level of dynamic errors of the amplitude maintenance contour, which arise in the usual circuit with each change of the wave orientation in the resonator, and simultaneously eliminate the drift caused by difference in Q-factors.     

Variable isochromatic/isopachic-fringe visibility in photoholoelasticity

This paper presents a new “hybrid” method whereby the ratio of the isochromatic-fringe visibility/isopachic-fringe visibility may be easily and continuously varied. This simple procedure merely combines a conventional polariscope with a holographic system. A variable beam splitter permits an incoherent superposition of the reconstruction of a doubly exposed hologram with real-time isochromatics, either dark or light field. By varying the ratios of the above two, in the image plane, numerous interesting results may be obtained including:

1. Isochromatics only, without errors in position
2. Isochromatics-isopachic fringes identical to those obtained through classical interferometry
3. Isochromatic-isopachic fringes whereby the amplitude modulation between the two may be minimized
4. Continuously variable isopachic/isochromatic-fringe visibility.

     

A thermodynamic approach to isotropic-nematic phase transitions in liquid crystals

We propose a dynamical model for (non-isothermal) phase transitions in liquid crystals. Macroscopic motions of the liquid crystal (LC) are neglected, while the coupling with the electromagnetic field is considered. The LC is described in terms of the classical order tensor Q, which is split as Q=s N, where N is a normalized tensor; two independent evolution laws are given for s and N. The model includes an evolutive equation for the temperature field obtained from an appropriate form of the energy balance, in which the internal powers associated to the equations for s and N are accounted for. The thermodynamic restrictions in the constitutive relations which ensure the Clausius–Duhem inequality have been pointed out.     

Darcy-Brinkman Flow Through a Bumpy Channel

The forced flow through a channel with bumpy walls which sandwich a porous medium is studied. The problem models micro-fluidics where, due to the small size of the channel width, the surface roughness of the walls is amplified. The Darcy-Brinkman equation is solved analytically through small perturbations on the ratio of bump amplitude to the half width of the channel. The first- order perturbation solutions give the three-dimensional velocity effects of the bumpiness and the second-order perturbation solutions give the increased resistance due to roughness. The problem depends heavily on the non-dimensional porous medium parameter $k$ which represents the importance of length scale to the square root of permeability. Our solutions reduce to the clear fluid limit when $k$ is zero and to the Darcy limit when $k$ approaches infinity.     

Temporal Homogenization of Linear ODEs,with Applications to Parametric Super-Resonance and Energy Harvest

We consider the temporal homogenization of linear ODEs of the form \({\dot{x}=Ax+\epsilon P(t)x+f(t)}\), where P(t) is periodic and \({\epsilon}\) is small. Using a 2-scale expansion approach, we obtain the long-time approximation \({x(t)\approx {\rm exp}(At) \left( \Omega(t)+\int_0^t {\rm exp}(-A \tau) f(\tau) {\rm d}\tau \right)}\), where \({\Omega}\) solves the cell problem \({\dot{\Omega}=\epsilon B \Omega + \epsilon F(t)}\) with an effective matrix B and an explicitly-known F(t). We provide necessary and sufficient conditions for the accuracy of the approximation (over a \({{\mathcal{O}}(\epsilon^{-1})}\) time-scale), and show how B can be computed (at a cost independent of \({\epsilon}\)). As a direct application, we investigate the possibility of using RLC circuits to harvest the energy contained in small scale oscillations of ambient electromagnetic fields (such as Schumann resonances). Although a RLC circuit parametrically coupled to the field may achieve such energy extraction via parametric resonance, its resistance R needs to be smaller than a threshold \({\kappa}\) proportional to the fluctuations of the field, thereby limiting practical applications. We show that if n RLC circuits are appropriately coupled via mutual capacitances or inductances, then energy extraction can be achieved when the resistance of each circuit is smaller than \({n\kappa}\). Hence, if the resistance of each circuit has a non-zero fixed value, energy extraction can be made possible through the coupling of a sufficiently large number n of circuits (\({n\approx 1000}\) for the first mode of Schumann resonances and contemporary values of capacitances, inductances and resistances). The theory is also applied to the control of the oscillation amplitude of a (damped) oscillator.     

Characterization of Viscoelasticity Due to Shear Wave Propagation: a Comparison of Existing Methods Based on Computational Simulation and Experimental Data

Shear wave propagation causes microvibrations within a medium; measuring the wave attenuation coefficient, α, and phase velocity, c _s , the medium shear modulus, μ, and shear viscosity, η, are determined based on a viscoelastic model that includes both c _s and α. The present work compares the performances of nine processing methods, based on cross-correlation and quadrature demodulation, used to extract the motion waveform from a sequence of radio-frequency (RF) echo signals from the medium. Kalman filtering determined the amplitude and the phase of the extracted motion waveform. The comparisons were done with regard to computational simulation and experiments with a gel phantom. Estimates obtained for μ and η of the medium considered different conditions for the vibration amplitude and the signal-to-noise ratio (SNR) of the RF echo signals and the waveform extracted by means of single frequency and shear wave dispersion ultrasound vibration (SDUV) methods. According to the simulated results, the cross-correlation-based processing techniques are more precise and accurate in comparison to quadrature demodulation techniques. The results for c _s , α, μ and η of the phantom and those obtained under the same setup conditions for experimental and computational tests agree with each other. Comparing the estimates based on single frequency and SDUV techniques, they presented similar performances at high SNR of the RF echo signal. On the other hand, the former technique prevailed for low SNR.     

Long-time Stability in Systems of Conservation Laws,Using Relative Entropy/Energy

We study the long-time stability of shock-free solutions of hyperbolic systems of conservation laws, under an arbitrarily large initial disturbance in L ²∩ L ^∞. We use the relative entropy method, a robust tool which allows us to consider rough and large disturbances. We display practical examples in several space dimensions, for scalar equations as well as isentropic gas dynamics. For full gas dynamics, we use a trick from Chen [1], in which the estimate is made in terms of the relative mechanical energy instead of the relative mathematical entropy.     

Oscillatory–ballistic motion regularities of a gravitational pendulum

We simulate the motion of a gravitational pendulum that has initial angular amplitude larger than 90\(^{\circ }\) and smaller than 180\(^{\circ }\), and loses energy at each change from ballistic to oscillatory motion when the string is suddenly tensed (we name this event collision). Simulation is based on a velocity Verlet algorithm that is implemented in a numerical code. The numerical simulation of motion as function of time is checked against an analytical code that describes the trajectory. The string tension expression that respects the velocity Verlet algorithm requirements is identified and a criterion for collision occurrence is introduced. An interesting band-like structure of the number of collisions as function of the initial amplitude and damping modelling is obtained.     

Rheological behavior of composites made from linear medium-density polyethylene and hemp fibers treated by surface-initiated catalytic polymerization

This work presents different rheological methods to determine the effect of fiber surface treatment on their interaction with a polymer matrix. In particular, surface-initiated catalytic polymerization was investigated on hemp fibers to improve their adhesion with linear medium-density polyethylene (LMDPE). The selected rheological tests (creep-recovery (solid state), small and large amplitude oscillation shear, and transient rheology (melt state)) were used to compare the treated and untreated fiber composites with the neat matrix. The results showed a significant improvement of the treated hemp composite (LPHC) creep modulus with respect to its untreated counterpart (LNHC) leading to a reduction of the creep strain, especially as temperature increases. The transient viscosity was modeled using a modified Kohlrausch-Williams-Watt (KWW) equation showing an increase in the transient viscosity (\( {\eta}_0^{+} \)) and relaxation time (τ) with fiber addition and surface treatment. These results were confirmed by large amplitude oscillatory shear (LAOS) through the reduction of the relative third harmonic (I_3/1), intrinsic nonlinearity parameter (Q₀), and nonlinear viscoelastic ratio (NRL). The results clearly show that catalytic polymerization is a good surface modification technique to increase the compatibility between natural fibers and polymer matrices as to improve all their final properties.

Open image in new window

Graphical Abstract ?

     

Mixed Convection Boundary-Layer Flow on a Vertical Surface in a Porous Medium with a Constant Convective Boundary Condition

The mixed convection boundary-layer flow on a vertical surface heated convectively is considered when a constant surface heat transfer parameter is assumed. The problem is seen to be chararterized by a mixed convection parameter $\gamma $ γ . The flow and heat transfer near the leading edge correspond to forced convection solution and numerical solutions are obtained to determine how the solution then develops. The solution at large distances is obtained and this identifies a critical value $\gamma _c$ γ c of the parameter $\gamma $ γ . For $\gamma > \gamma _c$ γ > γ c a solution at large distances is possible and this is approached in the numerical integrations. For $\gamma <\gamma _c$ γ < γ c the numerical solution breaks down at a finite distance along the surface with a singularity, the nature of which is discussed.     

One-dimensional optical solitons in cubic–quintic–septimal media with $$\varvec{\mathcal {}}$$-symmetric potentials

A (\(1+1\))-dimensional inhomogeneous cubic–quintic–septimal nonlinear Schrödinger equation with \(\mathcal {PT}\)-symmetric potentials is studied, and two families of soliton solutions are obtained. From soliton solutions, the amplitude of soliton is independent of the \(\mathcal {PT}\)-symmetric potential parameter k; however, the phase depends on the parameter k. The phase of soliton alters from negative to positive values at the location of center. Moreover, the evolutional behaviors of these solitons are discussed.     

Q345低周疲劳性能与疲劳寿命预测分析

本文对结构用钢Q345的低周疲劳性能进行了试验研究。试验在常温下岛津电液伺服疲劳试验机上进行,采用轴向应变控制方法,恒定应变速率为0.005s-1,应变比为-1。试验结果表明,初始阶段,Q345在高应变幅值(0.6%)循环作用下出现循环硬化效应,而在低应变幅值(0.6%)作用下出现循环软化效应;随着加载应变幅的增加,硬化和软化率呈直线上升趋势。Q345疲劳裂纹萌生阶段占其整个寿命的60%以上,其裂纹萌生寿命与应变幅存在幂函数关系。根据Coffin-Manson公式得到了Q345的应变-寿命关系公式;采用能量预测法得到了材料的塑性应变能与疲劳寿命的关系表达式。上述结果对钢结构的设计、评估具有重要的工程应用参考价值。     

The interaction of creep and fatigue for a rotor steel

Twenty tests were performed on a 1 Cr?1 Mo?1/4 V rotor steel at 1000° F (538°C) to determine the interaction of creep and low-cycle fatigue. These tests involved five different types of strain-controlled cycling: creep at constant tensile stress; linearly varying strain at different frequencies; and hold periods at maximum compressive strain, maximum tensile strain, or both. The experimental data were then used to characterize the interaction of creep and fatigue by the:

1. Frequency-modified strain-range approach of Coffin;
2. Total time to fracture vs. the time of one cycle relation as proposed by Conway and Berling;
3. Total time to fracture vs. the number of cycles to fracture characterization of Ellis and Esztergar;
4. Summation of damage fractions obtained from tests using interspersed creep and fatigue as proposed by the Metal Properties Council;
5. Strain-range-partitioning method of Manson, Halford, and Hirschberg.

In order to properly assess the strain-range-partitioning approach, seven additional tests were performed at the NASA Lewis Research Center. Visual, ultrasonic, and acoustic-emission methods of crackinitiation determination were unsuccessful. An approximate indication of crack initiation was obtained by finding the cycle N_o where the stress-cycle curve first deviated from a constant slope. Predictive methods (based on monotonic tests) for determining the fatigue life in the creep range were examined and found deficient, though they may still be useful for preliminary comparison of materials and temperatures. The extension of the frequency-modified strain-range approach to notched members was developed and the results of notched-bar tests were shown to corroborate this approach, when crack initiation for the plain and notched bars was campared.