Onset of nonlinearity and yield strain of a model soft solid

For soft solids with their low modulus, small stress already results in large strain, which may cause nonlinearity and yielding. These potentially competing effects were studied on a clay/polybutadiene (clay/sPB) composite, which is a soft physical gel. Structural changes were introduced by oscillatory shear using large amplitude (LAOS). LAOS beyond a critical limit reduced the internal connectivity. This softened the already soft solid even further, thereby moving it closer to its physical gel point. For clay/sPB, the shear-induced changes were irreversible so that they could get probed using small amplitude shear (SAOS) frequency sweeps. Sequences of SAOS-LAOS-SAOS (SLS) where repeated with increasing LAOS amplitude and increasing duration. The flow-induced structural changes in the soft solid were attributed to yielding, which began to occur at about the same stress/strain values as found for the onset of nonlinearity in traditional SAOS to LAOS (StL) stress amplitude sweeps. The onset of nonlinearity and the yielding seem to be a strain activated process since the characteristic strain amplitude is independent of frequency and temperature, but not so for the characteristic stress amplitude. The duration of LAOS in a SLS experiment beyond yielding is an important parameter since flow-induced structural changes require time to grow.     

Simulation of the linear rheological behavior of silica-filled,star-shaped SBR compounds

The rheological behavior of star-shaped SSBR/silica 60 phr compounds with different filler surface areas was experimentally studied and simulated using constitutive modeling. Rheological behavior was characterized in small amplitude oscillatory shear (SAOS) and stress relaxation after a small step shear. Unfilled SBR and SBR filled with four different silica grades with BET surface areas of 55, 135, 160, and 195 m²/g were used. A clear trend in rheological behavior was observed with surface area. A frequency sweep in the SAOS regime indicated an increase in dynamic properties with surface area. Additionally, linear stress relaxation tests at a strain level of 0.05 showed an increase in relaxation modulus with surface area and the presence of a plateau in the relaxation modulus at large times in compounds containing silica with high surface areas. The Leonov and Simhambhatla-Leonov models, modified to incorporate multimode particle network relaxation, were successfully used to simulate the frequency dependence of the storage modulus and the time evolution of the linear relaxation modulus for all samples. However, simulations of the frequency dependence of the loss modulus showed poor results in comparison with experimental data for the filled compounds.     

Nonlinear viscoelasticity of PP/PS/SEBS blends

The nonlinear viscoelastic behavior of polypropylene/polystyrene (PP/PS) blends compatibilized or not with the linear triblock copolymer (styrene-ethylene-/butylene-styrene, SEBS) was investigated. Start-up of steady-shear at rates from 0.1 to 10 s^–1 was carried out using a controlled strain rotational rheometer and a sliding plate rheometer for strain histories involving one or several shear rates. The shear stress and first normal shear stress difference were measured as functions of time, and the morphologies of the samples before and after shearing were determined. For each strain history except that involving a single shear rate of 0.1 s^–1 the blends showed typical non-linear viscoelastic behavior: a shear stress overshoot/undershoot, depending on the history, followed by a steady state for each step. The first normal stress difference increased monotonically to a steady-state value. The values of the stresses increased with the addition of SEBS. The shear stress overshoot and undershoot and the times at which they occurred depended strongly on the strain history, decreasing for a subsequent shear rate step performed in the same direction as the former, and the time at which stress undershoot occurred increased for a subsequent shear rate step performed in the opposite direction, irrespective of the magnitude of the shear rate. This behavior was observed for all the blends studied. The time of overshoot in a single-step shear rate experiment is inversely proportional to the shear rate, and the steady-state value of N₁ scaled linearly with shear rate, whereas the steady-state shear stress did not. The average diameter of the dispersed phase decreased for all strain histories when the blend was not compatibilized. When the blend was compatibilized, the average diameter of the dispersed phase changed only during the stronger flows. Experimental data were compared with the predictions of a model formulated using ideas of Doi and Ohta (1991), Lacroix et al. (1998) and Bousmina et al. (2001). The model correctly predicted the behavior of the uncompatibilized blends for single-step shear rates but not that of the compatibilized blends, nor did it predict morphologies after shearing.     

微拉曼光谱研究M55JB碳纤维/微滴的拉伸变形行为

使用评价纤维/基体界面力学性能的新方法纤维微滴拉伸测试,来研究M55JB碳纤维/环氧树脂基体之间的界面应力传递性能。使用自制的微加载装置对碳纤维/环氧树脂微滴试样进行对称式拉伸测试,用微拉曼光谱仪记录下不同应变下的嵌入微滴内纤维上的拉曼频移信号,经过应力/频移关系转换成纤维轴向应力。实验结果显示,微滴内纤维轴向应力随载荷而明显增加。根据界面力平衡模型得到相应的界面剪切应力呈反对称式分布,在纤维嵌入端存在剪应力集中。新测试方法能保证嵌入微滴内纤维上的应力呈对称式分布,而且能降低纤维嵌入端附近的应力奇异性。     

Slip-line modeling of machining with a rounded-edge tool—Part II: analysis of the size effect and the shear strain-rate

Part II of the present study quantitatively analyzes orthogonal metal cutting processes based on the new slip-line model proposed in Part I. The applicable range of the model is illustrated, followed by an explanation of the non-unique nature of the model. It is suggested that the tool edge roundness be comprehensively defined by four variables. Namely: tool edge radius, position of the stagnation point on the tool edge, tool-chip frictional shear stress above the stagnation point on the tool edge, and tool-chip frictional shear stress below the stagnation point on the tool edge. The effects of these four variables on eight groups of machining parameters are investigated. These include (1) cutting force, thrust force, resultant force, and the ratio of cutting force to thrust force; (2) ploughing force; (3) chip up-curl radius; (4) chip thickness; (5) tool-chip contact length; (6) thickness of the primary shear zone; (7) average shear strain in the primary shear zone; and (8) average shear strain-rate in the primary shear zone. The importance of tool edge roundness is further reinforced by a series of new research findings made in this paper. It is revealed that the size effect highly depends on the material constitutive behavior in machining. The dependence of the thickness of the primary shear zone and the dependence of the magnitude of shear strain-rate in the primary shear zone on the tool edge radius are well demonstrated. A surprisingly good agreement between theory and experiments is reached.     

Stress overshoots of organoclay nanocomposites in transient shear flow

Forward and reverse stress growth experiments have been conducted on polypropylene/organoclay nanocomposites containing the same clay loading but characterized by different microstructures. Stress overshoots have been observed for the initial start-up experiments and for the following reverse start-up experiments after a certain rest time. The amplitude of these overshoots increased with the applied shear rate and rest time, but the overshoots occurred at the same strain of about 1.7. The overshoots are related to the structure of the nanocomposites, in particular the magnitude of the overshoots increased with the degree of the clay exfoliation in the matrix. Two models, initially developed for colloidal suspensions and fiber suspensions, have been used to describe the observed phenomena. The overshoots are fairly well predicted by the first (structure network) model and explained by the competing effects of the structure breakdown under flow and reorganization during rest time. However, the model predicts that the shear stress following the overshoot decreases and reaches steady-state too rapidly. The second model developed for ellipsoid suspensions describes quite well the stress overshoots for the initial forward flow, but no effect of rest time is predicted. A modified version has been proposed by adding a molecular diffusivity contribution in the Folgar–Tucker equation. The effect of the particle disorientation is qualitatively predicted, but the kinetics is too slow compared to that deduced from experiments.     

A time dependent micro-mechanical fiber composite model for inelastic zone growth in viscoelastic matrices

In this work, a fiber composite model is developed to predict the time dependent stress transfer behavior due to fiber fractures, as driven by the viscoelastic behavior of the polymer matrix, and the initiation and propagation of inelastic zones. We validate this model using in situ, room temperature, micro-Raman spectroscopy fiber strain measurements. Multifiber composites were placed under constant load creep tests and the fiber strains were evaluated with time after one fiber break occurred. These composite specimens ranged in fiber volume fraction and strain level. Comparison between prediction and MRS measurements allows us to characterize key in situ material parameters, the critical matrix shear strain for inelastic zones and interfacial frictional slip shear stress. We find that the inelastic zone is predominately either shear yielding or interfacial slipping, and the type depends on the local fiber spacing.     

Extensional rheology of concentrated poly(ethylene oxide) solutions

The shear and extensional rheology of three concentrated poly(ethylene oxide) solutions is examined. Shear theology including steady shear viscosity, normal stress difference and linear viscoelastic material functions all collapse onto master curves independent of concentration and temperature. Extensional flow experiments are performed in fiber spinning and opposed nozzles geometries. The concentration dependence of extensional behavior measured using both techniques is presented. The zero-shear viscosity and apparent extensional viscosities measured with both extensional rheometers exhibit a power law dependence with polymer concentration. Strain hardening in the fiber spinning device is found to be of similar magnitude for all test fluids, irrespective of strain rate. The opposed nozzle device measures an apparent extensional viscosity which is one order of magnitude smaller than the value determined with the fiber spinline device. This could be attributed to errors caused by shear, dynamic pressure, and the relatively small strains developed in the opposed nozzle device. This instrument cannot measure local kinematics or stresses, but averages these values over the non-homogenous flow field. These results show that it is not possible to measure the extensional viscosity of non-Newtonian and shear thinning fluids with this device. Fiber spin-line experiments are coupled with a momentum balance and constitutive model to predict stress growth and diameter profiles. A one-mode Giesekus model accurately captures the plateau values of steady and dynamic shear properties, but fails to capture the gradual shear thinning of viscosity. Giesekus model parameters determined from shear rheology are not capable of quantitatively predicting fiber spinline kinematics. However, model parameters fit to a single spinline experiment accurately predict stress growth behavior for different applied spinline tensions.     

Interfacial rheology of coextruded elastomeric and amorphous glass thermoplastic polyurethanes

In this work, we report on the sensitivity of rheometrical techniques to the nature and size of the interface/interphase in coextruded thermoplastic urethanes (TPUs). In particular, the interphases developed during coextrusion of an amorphous glass (hard) TPU (Isoplast^? ETPU 301) with one of two elastomeric (soft) TPUs (Estane^? TPU 58277 and Estane^? TPU X1175) were studied. Differences in the thickness and nature of the interphase of the two coextruded bilayer films were observed by atomic force microscopy. In one case, the interphase is thicker and rough, and in the other case, it is thinner and flat. Rheology was used in order to probe the type and characteristics of the interphases, with coextruded films having been tested in steady shear, small-amplitude oscillatory shear (SAOS), uniaxial extension, and stress relaxation after a step strain in shear. The results were compared with theoretical predictions assuming zero-thickness interfaces and no interfacial slip. For SAOS and stress relaxation experiments, expressions were deduced in order to enable such a prediction to be made. Of all four rheometrical tests, only stress relaxation after a step shear did not follow the theoretical predictions and, thus, was sensitive enough to detect the presence of the interphase.     

A rheological criterion to determine the percolation threshold in polymer nano-composites

In this work, the effect of multi-walled carbon nanotube (CNT) and montmorillonite nanoclay on polymer chain dynamics is investigated around the percolation concentration for systems based on ethylene vinyl acetate (EVA) copolymer. Then, the results obtained are compared with literature data to determine if, regardless of particle characteristics, a universal rheological behavior can be detected at percolation. To do so, rheological analyses are performed under small amplitude oscillatory shear (SAOS), large amplitude oscillatory shear (LAOS), and transient shear step. SAOS data showed that, while the dynamics related to the Rouse relaxation time (τ _R) were not significantly influenced, the reptation relaxation time (τ _D) was strongly increased by the presence of nanoparticles. In step shear transient tests, the critical shear rate \( \left({\dot{\upgamma}}_{\mathrm{cr}}\right) \) for overshoot appearance was decreased due to chain confinement, and the formation of particle network strongly increased the level of stress overshoot. Particle networks increased significantly the nonlinear parameters (I ₃/I ₁ and Q ₀) obtained under LAOS and quantified by FT-rheology. In all measurements, due to the higher surface area associated to its size and density as well as hollow structure, CNT showed stronger effects compared to clay. Moreover, while the percolation concentration was different for CNT and clay, both systems showed similar behavior at percolation: a 0.5 scaling for G′ indicating a Rouse-dominated behavior.     

Non-linear viscoelastic response of magnetic fiber suspensions in oscillatory shear

This paper reports the first study on the large amplitude oscillatory shear flow for magnetic fiber suspensions subject to a magnetic field perpendicular to the flow. The suspensions used in our experiments consisted of cobalt microfibers of the average length of 37 μm and diameter of 4.9 μm, dispersed in a silicon oil. Rheological measurements have been carried out at imposed stress using a controlled stress magnetorheometer. The stress dependence of the shear moduli presented a staircase-like decrease with, at least, two viscoelastic quasi-plateaus corresponding to the onset of microscopic and macroscopic scale rearrangement of the suspension structure, respectively. The frequency behavior of the shear moduli followed a power-law trend at low frequencies and the storage modulus showed a high-frequency plateau, typical for Maxwell behavior. Our simple single relaxation time model fitted reasonably well the rheological data. To explain a relatively high viscous response of the fiber suspension, we supposed a coexistence of percolating and pivoting aggregates. Our simulations revealed that the former became unstable beyond some critical stress and broke in their middle part. At high stresses, the free aggregates were progressively destroyed by shear forces that contributed to a drastic decrease of the moduli. We have also measured and predicted the output strain waveforms and stress–strain hysteresis loops. With the growing stress, the shape of the stress–strain loops changed progressively from near-ellipsoidal one to the rounded-end rectangular one due to a progressive transition from a linear viscoelastic to a viscoplastic Bingham-like behavior.     

聚丙烯纤维加筋绍兴非饱和黏土的剪切特性研究

为了研究纤维加筋非饱和土的剪切特性,以绍兴地区广泛分布的非饱和黏土为研究对象,聚丙烯纤维为加筋材料,通过一系列非饱和直剪试验,探讨了纤维长度对加筋土剪切变形特性、抗剪强度及其指标的影响规律,并简要分析了聚丙烯纤维的增强机理,最后得出了0.2%掺量下补强效果最佳的纤维长度．研究结果表明：随着净法向应力的增大,土体的剪应力-剪切位移曲线由软化型逐渐向硬化型转化,纤维长度L为12 mm的加筋土样表现出的剪切硬化特性最明显;不同净法向应力下,纤维加筋非饱和土的抗剪强度均高于素土;随着纤维长度的增加,纤维加筋土的黏聚力呈先增加后减小,内摩擦角先增加后趋于平缓;当纤维长度L为12 mm时,聚丙烯纤维对土体抗剪强度指标的补强效果能够最大程度得到发挥．     

土剪破坏次声监测试验研究

土质滑坡临滑会产生次声波, 次声监测可以作为判断土质滑坡临滑的一种技术手段. 在考虑到滑坡的力学方式是以剪切破坏为主的前提下, 为了探明土质滑坡过程中的次声信号响应特征, 设计了土体直剪实验次声-力-位移联合监测系统, 开展了土体剪破坏次声监测试验, 在次声事件自动拾取的基础上, 结合黏性土渐进性破坏理论, 分析了剪切过程中的微观声学机理, 结果表明: (1)黏性土剪切破坏时发出的次声信号主要来源于弹性阶段中黏土颗粒的相互挤压、弹塑性阶段中以黏土胶体团粒本身的拉张破裂和应变软化阶段中土颗粒间的摩擦; (2)在土体剪切载荷的不同阶段, 次声信号的幅值大小呈现出应变软化阶段<弹性阶段<弹塑性阶段的规律; (3)剪切力与次声信号之间存在较强的相关性, 次声事件的峰值包络线与剪切力趋势线相当吻合, 并且次声信号的均方功率峰值都在推力峰值之前, 平均提前为22.95 s. 研究对进一步利用次声开展土质滑坡的监测和稳定性评价具有重要的理论参考价值.      

Measurement modes of the response time of a magneto-rheological fluid (MRF) for changing magnetic flux density

The response of a magneto-rheological fluid (MRF) to a change of magnetic flux density is investigated by using a commercial plate–plate magneto-rheometer MCR501 (Anton Paar GmbH) at constant shear rate. The instrument was modified to allow an online determination of the transient flux density in the MRF. Both current and voltage imposition to the magneto-cell were applied by using a power operational amplifier to drive the electromagnet. Assuming a Maxwell behavior with switching time λ and a linear increase in shear stress with flux density, analytic relations for the transient shear stress are derived for sinusoidal and single exponential flux densities vs time. True switching times of a few milliseconds are only obtained if the low pass filter in the original MCR501 torque signal is surpassed by a firmware allowing a sampling rate of 0.1 ms. For a sinusoidal flux density, the switching time is derived from the modulation depth of the shear stress. An upper bound of λ < 3 ms for a flux density of 0.8 T was found. For step coil current imposition of 1 T magnitude, switching times of 2.8 ms (start-up) and 1.8 ms (shutdown) allowed to fit the transient torque signal more than 2/3 of the total change. Finally, the effect of a sigmoidal characteristic on the switching time determination is addressed. This paper was presented at Annual European Rheology Conference (AERC) held in Hersonisos, Crete, Greece, April 27-29, 2006.     

Nonlinear viscoelastic response of asphalt binders: An experimental study of the relaxation of torque and normal force in torsion

Development of normal stress in the direction perpendicular to the plane of shear is an important feature of the nonlinear viscoelastic behavior of asphalt binders. Here, we study the significance of this phenomenon with the help of stress-relaxation experiments in torsion. We conducted these experiments using a dynamic shear rheometer on an unmodified binder and polymer modified binder, at different temperatures and aging conditions. The results not only illustrate the nonlinearity of the behavior but also show certain distinctive characteristics of the relaxation behavior (torque relax faster than normal force) and it is seen that new constitutive models are required to predict such behavior.     

Yield behavior of wood under combined static axial force and torque

We have examined the yield behavior of wood (Japanese cypress and Japanese beech) under combined static axial force and torque. In order to take the anisotropy of the wood into consideration, the specimen had a rectangular cross-section with one of its major axis lying in the fiber (longitudinal) direction. The axial force was applied in the fiber direction (along L) and torque was applied on an axis lying in the same direction as L. A combined loading test was performed according to the proportional deformation loading method. The results obtained are summarized as follows. (1) The yield condition of wood under combined axial-shear stress can be expressed by several well-known yield criteria. (2) The determinations of yield points are more influenced by torsion than axial force. (3) Japanese cypress deforms elastically compared with Japanese beech. (4) It is suggested that the equivalent stress-equivalent strain relation could be used at the determination of the yield point.     

Orientation distribution of fibers and rheological property in fiber suspensions flowing in a turbulent boundary layer

A model relating the translational and rotational transport of orientation distribution function （ODF） of fibers to the gradient of mean ODF and the dispersion coefficients is proposed to derive the mean equation for the ODE Then the ODF of fibers is predicted by numerically solving the mean equation for the ODF together with the equations of turbulent boundary layer flow. Finally the shear stress and first normal stress difference of fiber suspensions are obtained. The results, some of which agree with the available relevant experimental data, show that the most fibers tend to orient to the flow direction. The fiber aspect ratio and Reynolds number have significant and negligible effects on the orientation dis- tribution of fibers, respectively. The additional normal stress due to the presence of fibers is anisotropic. The shear stress of fiber suspension is larger than that of Newtonian solvent, and the first normal stress difference is much less than the shear stress. Both the additional shear stress and the first normal stress difference increase with increasing the fiber concentration and decreasing fiber aspect ratio.     

The normal stress behaviour of suspensions with viscoelastic matrix fluids

 We investigate the variations in the shear stress and the first and second normal stress differences of suspensions formulated with viscoelastic fluids as the suspending medium. The test materials comprise two different silicone oils for the matrix fluids and glass spheres of two different mean diameters spanning a range of volume fractions between 5 and 25%. In agreement with previous investigations, the shear stress–shear rate functions of the viscoelastic suspensions were found to be of the same form as the viscometric functions of their matrix fluids, but progressively shifted along the shear rate axis to lower shear rates with increasing solid fraction. The normal stress differences in all of the suspensions examined can be conveniently represented as functions of the shear stress in the fluid. When plotted in this form, the first normal stress difference, as measured with a cone and plate rheometer, is positive in magnitude but strongly decreases with increasing solid fraction. The contributions of the first and the second normal stress differences are separated by using normal force measurements with parallel plate fixtures in conjunction with the cone-and-plate observations. In this way it is possible for the first time to quantify successfully the variations in the second normal stress difference of viscoelastic suspensions for solid fractions of up to 25 vol.%. In contrast to measurements of the first normal stress difference, the second normal stress difference is negative with a magnitude that increases with increasing solid content. The changes in the first and second normal stress differences are also strongly correlated to each other: The relative increase in the second normal stress difference is equal to the relative decrease of the first normal stress difference at the same solid fraction. The variations of the first as well as of the second normal stress difference are represented by power law functions of the shear stress with an unique power law exponent that is independent of the solid fraction. The well known edge effects that arise in cone-and-plate as well as parallel-plate rheometry and limit the accessible measuring range in highly viscoelastic materials to low shear rates could be partially suppressed by utilizing a custom- designed guard-ring arrangement. A procedure to correct the guard-ring influence on torque and normal force measurements is also presented. Received: 20 December 2000 Accepted: 7 May 2001     

Experimental investigation of cyclic and time-dependent deformation of titanium alloy at elevated temperature

A novel cyclic deformation test program was undertaken to characterize macroscopic time dependent deformation of a titanium alloy for use in viscoplastic model development. All tests were conducted at a high homologous temperature, 650 °C, where there are large time dependent and loading rate dependent effects. Uninterrupted constant amplitude tests having zero mean stress or a tensile mean stress were conducted using three different control modes: strain amplitude and strain rate, stress amplitude and stress rate, and a hybrid stress amplitude and strain rate. Strain ratcheting occurred for all cyclic tests having a tensile mean stress and no plastic shakedown was observed. The shape of the strain ratcheting curve as a function of time is analogous to a creep curve having primary, steady state and tertiary regions, but the magnitude of the ratchet strains are higher than creep strains would be for a constant stress equal to the mean stress. Strain cycles interrupted with up to eight 2-h stress relaxation periods around the hysteresis loop, including hold times in each quadrant of the stress–strain diagram, were also conducted. Stress relaxation was path-dependent and in some cases the stress relaxed to zero. The cyclic behavior of these interrupted tests was similar even though each cycle was very complex. These results support constitutive model development by providing exploratory, characterization and validation data.     

Shear-thickening flow of suspensions of carbon nanofibers in aqueous PVA solutions

The suspensions of carbon nanofibers in aqueous poly(vinyl alcohol) solutions were prepared in the presence of spherical carbon black particles, and the steady-shear viscosity and dynamic viscoelasticity were measured for complex suspensions. Although the single suspensions of carbon black are highly stable, the flocculation of carbon nanofibers is promoted by the addition of carbon black particles. The complex suspensions show remarkable shear thickening in the steady-flow and strain hardening in oscillatory shear with large amplitude. The nonlinear responses strongly depend on the carbon black concentration, whereas the dynamic viscoelasticity at low strains in the linear ranges is not significantly influenced. As the highly elastic effects arise from the long-range motion of particles, the possible mechanism may be the orientation of nanofibers in strong shear fields. The suspensions show the time-dependent behavior of viscosity when the time-scale of measurements is shorter than that of structural recovery to the isotropic states.