Analysis of the stress distribution in two-dimensional bins by the method of characteristics

The method of characteristics, as outlined by Sokolovski [8], is used to calculate the stress distribution in two-dimensional parallel-sided bins containing granular material under either a uniform or zero surcharge. Both active and passive states are considered and the analyses are extended to include cohesive as well as cohesionless materials.In the active state, a continuous stress distribution is generated. The method of computing this has been investigated by many workers [3, 8, 9]. In the passive state, however, a discontinuity is shown to emanate from the top comer and be “reflected” at the centreline and wall, thus proceeding down the bin. The numerical method of computation is outlined.Wall stresses by this method are compared with those by the Janssen—Walker method [5]. There are large discrepancies, especially in the passive state, although the somewhat oscillatory plot of stresses by the method of characteristics does seem to be about the corresponding Janssen—Walker curve.     

Estimating time and temperature dependent yield stress of cement paste using oscillatory rheology and genetic algorithms

A controlled shear stress–shear rate rheometer was used to determine the viscoelastic behavior of cement paste incorporating various superplasticizers and subjected to prolonged mixing at high temperature. At a low applied shear stress range, the oscillatory shear strain/stress curve of cement paste was characteristic of a linear elastic solid; while the higher stress range was characteristic of a viscous liquid exhibiting a linear strain increase with increasing applied shear stress. The transition from solid-like to liquid-like behavior occurred over a very narrow stress increment. This transition stress corresponded to the yield stress parameter estimated from conventional flow curves using the Bingham model. The yield stress from oscillatory shear stress tests was estimated using the intersection between the viscous part of the oscillatory shear strain/stress curve and the oscillatory shear stress axis. In this study, equations describing the variation of shear strain versus shear stress beyond the solid–fluid transition for cement pastes incorporating various superplasticizers at different ambient temperatures and mixing times were developed using genetic algorithms (GA). The yield stress of cement pastes was subsequently predicted using the developed equations by calculating the stress corresponding to zero strain. A sensitivity analysis was performed to evaluate the effects of the mixing time, ambient temperature, and superplasticizer dosage on the calculated yield stress. It is shown that the computed yield stress values compare well with corresponding experimental data measured using oscillatory rheology.     

振动剪切作用下聚合物熔体的非仿射网络结构模型 Ⅱ．非仿射网络结构模型

假设聚合物熔体的缠结网络形变是非仿射的，运用瞬态网络结构原理，采用在本课题第一部分^[1]中所建立的动态速率方程，并对上随体Maxwell本构方程加以修正来建立一个非仿射网络结构模型，利用这一模型来研究振动剪切作用下LDPE熔体的流变行为，研究表明，随着应变振幅和频率的增加，LDPE熔体的剪切应力也增加，同时指出了非仿射网络结构模型的精确变比仿射结构模型有较大提高，这表明在振动力场作用下，网络形变发生了非仿射形变，因此在建立振动力场作用下聚烯烃熔体本构方程时，不能假设其网络是仿射形变的。     

注射成型中模腔内振动剪切流动的理论模型

采用Ｌｅｏｎｏｖ本构模型,首次研究了在注射成型中模腔内聚合物熔体的振动剪切流动时所产生的振动剪切应力。结果表明,振动剪切应力的振幅随着聚合物熔体的粘度,振动频率和应变振幅的增加而增加,随着熔体温度的增加而减小。     

A study on bicomponent two-layer slot cast coextrusion

Extensional flow of a bicomponent two-layer slot cast coextrusion process has been studied. A Newtonian and an upper-convected Maxwell fluid were considered to be the two layers, respectively, and the two-layer flow was assumed to be steady and isothermal. This choice was made as a simple model for a system which consists of two distinctly different fluids in terms of their extensional behaviors. Present study considered only the draw-down region where the film thickness changes slowly with the distance from the die exit. For this region, asymptotic solutions could be obtained for two limiting cases in which the elasticity effect of the Maxwell fluid layer is small and the applied tension at the take-off is large, respectively. When the elasticity effect is small, the melt thickness and the velocity profiles are exponential as in the case of a Newtonian single-layer flow. When the applied tension is large, on the other hand, the velocity profile is shown to be near linear. Furthermore, the viscoelasticity effect of the Maxwell fluid layer becomes so dominant that it dictates the mechanics of the coextrusion flow even when its flow rate and shear viscosity may be much smaller than those of the Newtonian layer.     

Viscoelastic modeling of natural and synthetic textile yarns

Viscoelastic models were employed to analyze the stress–strain behavior of cotton, acrylic, and polyester yarns. The potential model and the modified Maxwell model gave the best fits as regards the stress–strain behavior of these yarns. The results of the potential model resembled those of the modified Maxwell model with an infinite relaxation time. The potential model is suitable for explaining the rearrangement undergone by the yarns when no slippage between fibers under strain occurs. When slippage occurs, Maxwell models are able to explain the stress–strain behavior of the yarns. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 76: 2062–2067, 2000     

Recovery rheology via rheo-SANS: Application to step strains under out-of-equilibrium conditions

Stress relaxation from a step strain test provides important information about constituent dynamics, but if a material has experienced a complex shear history, the underlying physics is not straightforward to access. We use recovery rheology and rheo-small-angle neutron scattering to probe the nonlinear dynamics of an entangled wormlike micelle solution by applying step strains after complex shear histories enforced by large-amplitude oscillatory shear (LAOS) flow. We show that a universal relaxation modulus can be obtained from step strain tests with complex shear histories, as long as the modulus is defined in terms of the recoverable strain. The shear and normal stresses, as well as the alignment of micellar Kuhn segments, are shown to be positively correlated with the recoverable strain. We identify re-entanglement of polymeric chains after cessation of LAOS and show that this process occurs over the same timescales as linear-regime stress relaxation. This work, therefore, lays the foundation of how to accurately probe out-of-equilibrium rheology in a consistent manner.     

Investigation of Unsteady Elongational Flow of Polymer Melts

Abstract

A method for estimation of the viscoelastic characteristics of polymer melts in the prestationary elongational flow is given. The experimental data show that at specific strain rates the polymer starts to respond to dynamic deformation as a highly elastic material. The viscoelastic characteristics of the polymer in the prestationary extensional flow can be described by a modified Maxwell equation.     

Polarization-optical investigation of polymers in fluid and high-elastic states under oscillatory deformation

The relationship was investigated between birefringence and oscillatory shear deformation of linear high molecular mass polymers exemplified by narrow- and broad-distribution polybutadienes and polyisoprenes. Polymer deformation at different frequencies and amplitudes was carried out in an annular gap. The stress field uniformity was not below 95%. It was shown that in oscillatory deformation of polymers in the fluid and high-elastic states, birefringence contains a time-independent steady component and an oscillatory component with a frequency equal to that of the assigned oscillation. A linear interrelation was found to exist between the amplitude of the oscillatory component of birefringence and that of the shear stresses, with a proportionality factor equal to the stress-optical coefficient of the polymers. The phase of the oscillatory component of birefringence coincides with that of the shear stresses. Measurements of the steady component of the birefringence make it possible to find the steady component of the first normal stress difference resulting from the assignment of shear oscillations to the polymer. On the basis of the experimental data obtained for polybutadienes and polyisoprenes, and the literature data for polystyrene solutions, a master curve was constructed that generalizes the dependence of the steady component of the first normal stress difference in the linear and nonlinear deformation regimes on the product of the square of the deformation amplitude and the storage modulus measured at low amplitudes. This dependence is valid in the linear and nonlinear deformation regimes. It is invariant with frequency, amplitude deformation, molecular mass, and molecular mass distribution of the polymers. It is shown by visual observation of deformation that the abrupt drop in resistance of polymer to shear in large-amplitude deformation is due to polymer rupture near the surface of the inner cylinder and is accompanied by a slip-stick process. This is the phenomenon of spurt early observed in capillary viscometers at high shear stresses and recently investigated in coaxial cylinder devices at large amplitude deformation.     

Nonlinear tensile behavior of cotton fabric reinforced polypropylene composites

From the perspectives of elastoplasticity (nontime-dependent) and viscoelasticity (time-dependent), the Ramberg–Osgood relation and time-varying viscosity Maxwell (TVM) models were used to model and analyze the stress–strain behavior of cotton fabric-reinforced polypropylene composites (CFRLs), respectively. The Ramberg–Osgood relation could well describe the tensile behavior of CFRLs as an elastoplastic behavior, while the tensile behavior could also be described as a nonlinear viscoelasticity behavior by Maxwell model. The fitting results showed that the Maxwell model accurately described the tensile behavior of different CFRLs samples under low strain, but there was a considerable gap between the test data and model values when the strain was greater than 5%. Therefore, a time-varying viscosity fluid damper was used instead of a Newtonian fluid damper to modify the Maxwell model, namely the TVM model. The TVM model closely described the stress–strain behavior during the entire tensile process.     

基于变温下圆管内润滑脂流动特性的表征

为研究温度对润滑脂圆管流动特性的影响规律,采用旋转流变仪分析了润滑脂的流变特性,并基于流变特性研究结果和理论分析建立了润滑脂圆管流的速度场和应力场变化模型。结果表明：润滑脂具有高的屈服剪应力,表现出良好的黏温特性和剪切稀化特性,温度升高润滑脂的屈服应力和表观黏度均下降,表现为更好的流动性;利用MATLAB编程绘图对速度场和应力场分析,给出了润滑脂圆管流动特性规律的影响因素及变化关系;揭示了温度对润滑脂圆管流动特性的影响规律,提高输送介质温度利于润滑脂的输送。     

Using creep and recovery to study flow behavior of fresh cement paste

A controlled stress rheometer has been used to determine the creep and recovery behavior of flocculated cement pastes. The behavior was found to depend on the level of applied stress. At a lower applied stress, the creep curve of each paste was characteristics of a nonlinear viscoelastic solid, with an instantaneous strain superimposed on an elastic strain; the recovery, on the other hand, was characteristics of a viscoelastic liquid, with little or no instantaneous strain, but some retarded strain and a substantial unrecovered strain. At a higher applied stress the behavior was strikingly different. In this case, the behavior was characteristics of a viscous liquid, with a nearly linear increase in strain throughout the duration of the stress and no recovery when the stress was released. This transition from solid-like behavior to liquid-like behavior occurred over a very narrow stress increment, and the transition stress corresponded to the yield stress estimated from flow curves and from oscillatory shear measurements.     

Three-Dimensional Modeling of Microsphere Contact/Impact with Smooth,Flat Surfaces

A three-dimensional (3D) simulation model of a microsphere in contact with a nominally-smooth, flat surface is established. The model is based on Hertzian contact stresses, an idealized ring force distribution of adhesion, nonlinear damping, and friction. Although originally developed for the study of oblique impact, the model also is shown to describe the motion of a microsphere in sustained contact with a flat surface, including nonlinear normal oscillatory motion in the presence of sliding and rolling. Nonlinear, normal oscillatory motion is illustrated using conventional phaseplane techniques. Methods for the determination of damping coefficients associated with normal motion from impact experiments are discussed. The significance and modeling of rolling resistance and implications of asymmetric contact stress distributions are presented. Simulations show that energy exchange between translation and rotation can play an important role during oblique impact. The effects of complex initial conditions on the rebound and capture of a microsphere are significant as are the effects of contact friction. Results show that the inability to measure and the failure to account for rotational velocities in experimental measurements can limit the intepretation of the results.     

Numerical simulation on dense phase pneumatic conveying of pulverized coal in horizontal pipe at high pressure

A kinetic–frictional model, which treats the kinetic and frictional stresses in an additive manner, was incorporated into the two fluid model based on the kinetic theory of granular flow to simulate three dimensional flow behaviors of dense phase pneumatic conveying of pulverized coal in horizontal pipe. The kinetic stress was modeled by the kinetic theory of granular flow, while the friction stress is from the combination of the normal frictional stress model proposed by Johnson and Jackson [1987. Frictional–collisional constitutive relations for granular materials, with application to plane shearing. Journal of Fluid Mechanics 176, 67–93] and the modeled frictional shear viscosity model proposed by Syamlal et al. [1993. MFIX documentation and theory guide, DOE/METC94/1004, NTIS/DE94000087. Electronically available from http://www.mfix.org], which was modified to fit experimental data. For the solid concentration and gas phase Reynolds number was high, the gas phase and particle phase were all treated as turbulent flow. The experiment was carried out to validate the prediction results by three kinds of measurement methods. The predicted pressure gradients were in good agreement with experimental data. The predicted solid concentration distribution at cross section agreed well with electrical capacitance tomography (ECT) image, and the effects of superficial velocity on solid concentration distribution were discussed. The formation and motion process of slug flow was demonstrated, which is similar to the visualization photographs by high speed video camera.     

Determination of the rheological properties of thermoplastic composites for compression flow molding

The influence of the fiber mat structure and the matrix rheology on the squeeze flow behavior of thermoplastic composites for compression flow molding has been investigated. An analytical model for isothermal squeeze flow has been developed and experimentally confirmed. The model is based on the role of the matrix at local fiber interaction points. The squeeze flow rheology of the composite can be evaluated from the shear flow of the pure matrix as expressed by a Carreau equation, using two micromechanical‐based shift factors. It was found that the fiber mat structure influences the yield stress of the composite, but has a minor influence on the squeeze flow in comparison to the influence of the matrix.     

Compression molding of Carbon/Polyether ether ketone composites: Squeeze flow behavior of unidirectional and randomly oriented strands

Compression molding of randomly oriented strands (ROS) of thermoplastic composite is a new process that enabled the formation of complex shapes with high fiber volume fraction. During compression molding of ROS, several deformation mechanisms occurred. This article focused on the macroscopic squeeze flow mechanism. It ruled how the material will flow and fill intricate features of the mold. The squeeze flow behavior under large strain was investigated for Unidirectional (UD) and ROS. An experimental characterization was performed using an instrumented hot press. Also, to predict the associated thickness reduction, existing models using equivalent viscosity and lubrication assumptions were used. The results showed that large deformation of UD and ROS composite materials is mainly governed by two regimes: a Non‐Newtonian fluid behavior at low strain followed by a yielded phase at large strain. Quantitative indicators were defined to analyze these two phases. They showed that current models available in the literature fail to predict accurately the squeeze flow of thermoplastic composites under high strain (>50%). Also, strands size (especially strand length) has a large effect on the squeeze flow mechanism. This article provided basic process window guidelines in terms of minimum pressure and achievable strain for compression molding of ROS parts. POLYM. COMPOS., 38:1828–1837, 2017. © 2015 Society of Plastics Engineers     

Cyclic deformations of polypropylene with a strain‐controlled program

Experimental data are reported on isotactic polypropylene in uniaxial tensile cyclic tests with a strain‐controlled program (oscillations between fixed minimum and maximum strains). The following characteristic features of stress–strain diagrams are observed: (i) logarithmic decay in maximum and minimum stresses with number of cycles (cyclic softening), (ii) more pronounced reduction in minimum stress than in maximum stress (cyclic strengthening), (iii) independence of rates of decrease in maximum and minimum stresses of strain rate, (iv) decrease in hysteresis energy with number of cycles. To rationalize these observations, a constitutive model is derived in cyclic viscoelasticity and viscoplasticity of semicrystalline polymers. Numerical simulation demonstrates that the model correctly describes experimental stress–strain curves and quantitatively predicts evolution of maximum and minimum stresses with number of cycles. POLYM. ENG. SCI., 2012. © 2012 Society of Plastics Engineers     

Simulation of dense granular flows: Comparison with experiments

A comparison of the predictions of a rheological model that we recently developed with experimental results of stress and flow profiles in a pilot scale silo is presented in this work. Experiments were performed to collect information on the flow field by means of a tracer method and on wall normal stresses at several different positions along the vessel. The silo (2.5 m high, 0.5 m wide) had the possibility of inserting internal devices; the model was first validated on data without internals and then used to predict the profiles for the case with them. Both stress and flow profiles with and without internals agree with the experimental results within the experimental error that locally could be rather significant due to the difficulty of large scale experiments with granular materials.     

Stress relaxation behavior after cyclic preloading in polypropylene

The viscoelastic behavior of polypropylene before and after cyclic preloading was investigated by stress relaxation tests. The relaxation tests were performed after a simple uniaxial tension (number of cycles N = 0) and after the cyclic preloading (N = 50) by use of a closed loop, electrohydraulic, servocontrolled testing machine. The tests were conducted under different sets of strain rate, number of cycles, and strain amplitude. The experimental data were compared with theoretical results analyzed by use of a linear viscoelastic model. The three-element model consists of a Maxwell unit and a Hookean spring in parallel. The calculated results agree well with the experimental ones; in particular, in the relaxation tests after the cyclic preloading (N = 50), the calculated results agree very well with the experimental ones at both the predetermined strain rates of 1,000 μ/s and 10,000 μ/s, at a strain amplitude of ±5%. It can be seen that the linear viscoelastic model explains the viscoelastic characteristics of polypropylene despite the solution of the constitutive equation constructed by the simple three-element model.