摘要:

The pendulum consists of a circular viscoelastic rod fixed at one end and attached to a disk at the other end. The disk, initially at rest, is subjected to a step function of torque. The subsequent motion is analyzed in terms of normal modes and normal coordinates. The normal modes are found by separation of variables. The characteristic numbers associated with these modes depend only on the moments of inertia of the disk and rod. The normal coordinates satisfy integro‐differential equations of the Volterra type. The mechanical properties of polyisobutylene at 25°C were represented in differential operator form. The Volterra integral equations were then solved by means of the Laplace transforms. An analysis of the numerical results shows that only the oscillatory part of the fundamental mode should persist after a short time. This result is in qualitative agreement with observations. This method of analysis may be applied to other dynamic problems in linear viscoelasticity provided the characteristic equation can be reduced to a form that does not involve the mechanical properties of the material.

ISSN:0148-6055    

DOI:10.1122/1.548998

出版商:The Society of Rheology    

年代:1965

数据来源: AIP

摘要:

The physical and mathematical similarity of the resistance‐temperature relation in thermistors to the viscosity‐temperature relation in typical liquids makes it possible to simulate the essential nonlinearity of the flow of model Newtonian liquids by the use of an electric analog. Simple measurements of current and voltage take the place of detailed computation. Circuits containing a thermistor and capacitor provide a model for nonlinear viscoelastic materials. A transmission line containing thermistors would be applicable where inertial terms are important and both the time and space variation of the stress would be significant. The behavior of simple analogs described here agrees with available numerical computations. In addition, it duplicates experimentally observed temperature effects and apparent departures from Newtonian behavior in liquids as well as necking, yield, fracture, creep, strain hardening, and stick‐slip effects in solids. This electric analog literally simulates the model mechanical system. In contrast, the widely discussed simulation of linear viscoelasticity by electric networks is figurative. That is, there, the well‐developed mathematics of linear circuits was applied to the mechanical system. The new simulation is effective over wide ranges of stress, strain, and time even with a single thermistor.

ISSN:0148-6055    

DOI:10.1122/1.548999

出版商:The Society of Rheology    

年代:1965

数据来源: AIP

摘要:

The test fluids were three aqueous solutions of Natrosol 250 H hydroxyethyl cellulose. Their nominal concentrations were 0.3, 0.5, and 0.7%. Viscosity data for each solution wee filled with a generalized Newtonian viscosity model which properly describes the zero‐shear viscosity. The test geometries were two conical sections. Their vertex angles were approximately 14 and 21°. Laminar flow rate vs. pressure drop data were taken for each Natrosol solution in each conical section. Approximate expressions relating flow rate and pressure drop were derived for the limiting cases of very low and very high flow rates. The low flow rate (non‐Newtonian flow) expression was of form: pressuredrop=functionof (flow rate, geometry, viscosity model parameters). The high flow rate (inviscid flow) expression was of form: pressuredrop=functionof (flow rate, geometry, fluid density). These two expressions were in excellent agreement with data at low and high flow rates. The sum of these two expressions was in good agreement with data over the entire range of flow rates. This superposition expression in no way accounts for normal stresses, time‐dependent elastic effects, or the effect of the third invariant on viscosity. Its success in describing the data implies that these phenomena were not important. For engineering purposes generalized Newtonian viscosity models will probably be adequate for characterizing the flow of dilute polymer solutions in conical sections.

ISSN:0148-6055    

DOI:10.1122/1.549024

出版商:The Society of Rheology    

年代:1965

数据来源: AIP

摘要:

A method is suggested for characterizing viscoelastic fluids in an approximate but useful way for the description of flow in complicated geometries. This method rests on the determination of a zero‐shear limiting viscosity, a characteristic time, and a dimensionless parameter relating to the slope of a log‐log plot of viscosity vs. shear rate in the “power law” region. It is then shown how such parameters can be used in correlating experimental data on pressure drops through packed beds at constant volumetric flow rate. This is done by a combination of a porous medium model calculation and dimensional analysis. It is shown how the characteristic time of the fluid can be used to designate regions of behavior where elastic effects are important.

ISSN:0148-6055    

DOI:10.1122/1.549000

出版商:The Society of Rheology    

年代:1965

数据来源: AIP

摘要:

In the study of the flow of shear‐sensitive fluids through porous media, fourteen different aqueous solutions of polyethylene glycol, polyvinyl alcohol, and hydroxy‐ethylcellulose were investigated. The shear‐sensitive viscosities of these fluids were characterized by the three‐parameter Ellis model. Two different types of flow behavior were observed: (1) When the volumetric flow rates were held constant, the results were both steady and reversible. The flow data were successfully correlated by a modified Darcy's law. It is shown that the characteristic time of the fluid can be used to designate regions of behavior where elastic effects are important. (2) When the pressure drop across the porous medium was held constant, the results were both unsteady and irreversible. In this case, polymer adsorption and gel formation were believed to have occurred throughout the bed.

ISSN:0148-6055    

DOI:10.1122/1.549023

出版商:The Society of Rheology    

年代:1965

数据来源: AIP

摘要:

An axial annular flow device has been utilised to determine the secondary normal stress differenceτ22−τ33[where the velocity field isv1=v1(x2)] for several aqueous polymer solutions. Data are presented on the radial pressure difference, at a fixed axial position, between inner and outer walls of the annulus vs. the axial pressure gradient. The data are analyzed by numerically integrating the radial component of the equation of motion using a nonlinear generalized Maxwell model proposed by Spriggs to obtain a trial function forτ22−τ33.Results indicate that the secondary normal stress difference, while not zero, is considerably smaller than the primary normal stress difference,τ11−τ33,for the solutions studied.

ISSN:0148-6055    

DOI:10.1122/1.549025

出版商:The Society of Rheology    

年代:1965

数据来源: AIP

摘要:

The results of an experimental study of rheological properties of typical lubricating greases are reported in this paper. Viscosity‐shear rate relations are compared for steady‐state shear and for transient shear conditions of stress relaxation and creep. In steady‐state shear the systems are non‐Newtonian, but under transient conditions of shear stress relaxation, they are linear viscoelastic for strains approaching their ultimate yield strain. The linear viscoelastic nature of two greases was confirmed by studies of the damping of a torsion pendulum for small strains. A sodium soap grease is shown to be linear viscoelastic by an analysis of creep data from the literature. Recognition of the wide range of strains for linear viscoelastic behavior simplifies the study of the flow and deformation of greases.

ISSN:0148-6055    

DOI:10.1122/1.549001

出版商:The Society of Rheology    

年代:1965

数据来源: AIP

摘要:

A multiple integral functional relationship has been employed as a constitutive equation for nonlinear creep of viscoelastic material under combined stress. The kernel functions of this representation for first, second and third order stress terms have been determined from tests on a single tubular specimen of polyvinyl chloride copolymer. Tests needed to determine kernel functions adequate to describe multiaxial creep under constant stress were found to be three pure tension tests at different stress levels, three pure torsion tests at different stress levels, and two combined tension‐torsion tests. Experiments include twenty tests under various combinations of tension and torsion of the same specimen. The use of only one specimen was made possible by the fact that following 2 hr of creep the recovery in 4 days was almost complete. Agreement between the multiple integral representation and experimental results was very satisfactory. Agreement with a hyperbolic sine representation of stress dependence was less satisfactory owing in part to the fact that the synergistic effect of tension plus torsion in the nonlinear range was not accounted for.

ISSN:0148-6055    

DOI:10.1122/1.549002

出版商:The Society of Rheology    

年代:1965

数据来源: AIP

摘要:

Energy storage and energy dissipation characteristics of a cohesive soil are studied in the frequency domain using strain‐controlled vibratory uniaxial compression tests. Such characteristics are important considerations in earthquake phenomena, machine foundation design, and soil‐structure interaction under dynamic loading. The soil response is expressed in terms of the storage, loss, and complex moduli as well as the loss tangent. Dynamic stress‐strain amplitude response is nonlinear even at small values of dynamic strain. Storage, loss, and complex moduli decrease with increased dynamic strain amplitude. The energy dissipation expressed in terms of the loss tangent decreases with increases in moisture content, frequency, and dynamic strain amplitude. Loss tangent values determined by the direct method are compared with those obtained by transformation of stress relaxation test data. Effects of concentration (moisture content) are presented in terms of a non‐dimensional dynamic stress‐strength parameter using the ultimate compressive strength in uniaxial compression as a consistency index. Static stress level about which the dynamic perturbations take place has no apparent effect on the dynamic stress‐strain response for the range studied.

ISSN:0148-6055    

DOI:10.1122/1.549003

出版商:The Society of Rheology    

年代:1965

数据来源: AIP

摘要:

Storage(G′)and loss(G″)shear moduli of supercooled glucose have been measured at thirteen temperatures from 27.4 to 41.1°C in the frequency range from 0.3 to 1.8 cps. Shear creep has been measured at four temperatures from 41.1 to 47.6°C. The temperature dependence of the storage moduli and the creep compliance was described by reducing the time and frequency scales with shift factors calculated from the WLF equation, the constants corresponding to a fractional free volume of 0.026 at 41.1°C and a free volume expansion coefficient of3.6×10−4 deg−1.The loss moduli plotted against reduced frequency did not give a single composite curve, however. Conversion of the dynamic measurements to creep compliance by approximation methods provided the latter function over ten decades of logarithmic time except for a gap of three decades in the middle of the range. At long times, the creep was indistinguishable from viscous flow; the viscosity at 41.1°C was1.82×1010 poise.At short times, the limiting creep compliance appeared to be0.32×10−16 cm2/dyne,and there was an additional time‐dependent compliance of at least this magnitude with a broad distribution of retardation times. The relaxation and retardation spectra were calculated for this region.

ISSN:0148-6055    

DOI:10.1122/1.549026

出版商:The Society of Rheology    

年代:1965

数据来源: AIP