摘要:

In rheology the use of the concepts of elasticity—or mechanical stored energy—or recoverable shear in steady flow has been used for some time, but by no means universally accepted. In this paper, the foundations of the statistical mechanics of polymer solutions, as developed by Kuhn, Rouse, and Zimm, together with numerous others, are reviewed for the purpose of developing the basic ideas of elasticity and birefringence in steady flow and investigating what assumptions and limitations the present theory has. The quantitative relations between a number of mathematical theories are tabulated and a survey of the experimental results is given. The questions still unsolved are formulated. Especially the correlation among viscosity, flow birefringence, dynamic properties, and normal stress measurements is emphasized.

ISSN:0148-6055    

DOI:10.1122/1.549039

出版商:The Society of Rheology    

年代:1966

数据来源: AIP

摘要:

Mechanical and birefringent properties of plasticized polyvinyl ehloride in the glass transition region were determined by means of quasistatic tests at different temperatures and sinusoidal oscillation tests at room temperature. In the former method, mechanical creep and photocreep tests were conducted at temperatures ranging from −80 to 115°F. The method of reduced variables (temperature‐time equivalence principle) was used to obtain continuous curves for relaxation modulus and stress fringe value corresponding to room temperature and extending up to 24 decades of time. The resulting curves show a broad transition region for the material. The shift function was plotted versus temperature and was found to be about the same for both mechanical and optical properties. Short‐time (dynamic) properties obtained by the temperature‐time equivalence principle were compared with those obtained at room temperature by direct sinusoidal oscillation tests at different frequencies. The complex modulus and complex stress fringe value were determined as functions of frequency and converted to a relaxation modulus and stress fringe value as functions of time by means of an approximate interrelationship. The validity of the temperature‐time equivalence principle in this case was proven by the good agreement between these results and those obtained from creep tests at different temperatures.

ISSN:0148-6055    

DOI:10.1122/1.549040

出版商:The Society of Rheology    

年代:1966

数据来源: AIP

摘要:

Bodner and Fitzgerald and Woodward have described dynamic tests on beams of aluminum alloy and polytetrafluoroethylene, respectively, in which the laterally vibrating bars were subjected to tension by coaxial wires. In both cases, the direct effect of the wires was disregarded. This paper presents an analysis of the wire‐bar systems, based on the theories of vibrating bars and strings. The calculations show that resonance patterns generally resembling those found experimentally should be expected.

ISSN:0148-6055    

DOI:10.1122/1.549041

出版商:The Society of Rheology    

年代:1966

数据来源: AIP

摘要:

As part of a continuing study of the mechanical behavior of materials with temperature‐dependent properties, dynamic responses of an ideal viscous material are considered. An electric analog circuit containing thermistors and ideal inductors is presented. The characteristics of this circuit simulate the highly nonlinear characteristics of the model of the material. The experiments show how the conversion of mechanical work to heat can lead to stress and time‐dependent apparent viscosities and to thermal instability in velocity‐driven Couette flow. When the boundary velocity is sinusoidal, the heating can lead to the appearance of a pseudo elasticity as well as to thermal instability. The thermal stability of the system is shown to depend on the frequency as well as the amplitude of the excitation. A group of similarity parameters are described which are ratios of characteristic times for heating, velocity diffusion, thermal diffusion, and loading. These provide a description of the model mechanical experiment and make the connection with the electrical analog.

ISSN:0148-6055    

DOI:10.1122/1.549042

出版商:The Society of Rheology    

年代:1966

数据来源: AIP

摘要:

The vertical and horizontal displacements are obtained for a time‐dependent moving load on a viscoelastic half space. The load is assumed to increase exponentially with time and its velocity to decrease exponentially with time. The problem is solved as a quasistatic problem since the velocity of the load is small compared to stress wave velocities in the half space. The half space is characterized in shear by the four‐parameter model and is assumed to be elastic in its volumetric behavior. The elastic viscoelastic analogy is used in the solution of the problem.

ISSN:0148-6055    

DOI:10.1122/1.549043

出版商:The Society of Rheology    

年代:1966

数据来源: AIP

摘要:

A general theory of linear viscoelasticity under complex stress is analysed by utilizing the Laplace transformation and is applied to Hertz's contact problem for measuring the creep recovery in the penetration of a steel ball. As in the similar method of uniaxial compression, the temperature dependence of characteristic relaxation times can be computed from the experimental results on (residual depth of penetration creep recovery) ∼θ (temperature) curves by using the analytical results. The temperature dependence is in good agreement with that obtained from the results in uniaxial compression. The method using the RN (Rockwell Number) ∼θ curves obtained at a constant rate of temperature rise(2°C min−1)by a conventional Rockwell testing machine, is recommended as the simplest method and may be successfully used for various polymer solids. The effect of differences in molecular structure on the temperature dependence of mechanical behavior can be demonstrated clearly by this method. The results on thermosetting laminates are also presented. Further, the merits of this creep recovery are discussed.

ISSN:0148-6055    

DOI:10.1122/1.549054

出版商:The Society of Rheology    

年代:1966

数据来源: AIP

摘要:

The analysis of stress and strain in an orthotropic heterogeneous linear viscoelastic cylinder which has a burning inner boundary and which is subjected to a time‐dependent internal pressure, has been worked out. The assumptions of isothermal conditions and infinitesimal strains are consistently made and the conditions of a quasistatic plane strain are adopted. Numerical solution for an orthotropic heterogeneous viscoelastic cylinder is established and which was anticipated to be quite stable. The established solution can be reduced to that of a homogeneous orthotropic cylinder. As special cases from the general problem, solutions for an isotropic compressible cylinder and an isotropic incompressible cylinder can also be derived. Numerical examples have been worked out to illustrate the influence of anisotropy, heterogeneity, and viscosity on the deformation of a burning cylindrical grain in a solid propellant rocket. The results for both short‐time and long‐time behavior are presented for a relaxation function of a form similar to that obtainable from a seven‐parameter Maxwell model which has been shown to represent the rheological behavior of a filled elastomer fairly well.

ISSN:0148-6055    

DOI:10.1122/1.549044

出版商:The Society of Rheology    

年代:1966

数据来源: AIP

摘要:

New data are presented for the shear behavior of solutions of polyisobutylene in toluene at 25°C. Five samples (viscosity‐average molecular weight range of105to5×106) were studied at shear rates from 1.0 to3×105 sec−1.Both Couette and capillary viscometers were used in the investigation. The results are correlated by a standard reduced variable plot and compared with earlier data. A method for predicting the viscosity of straight chain polymer solutions from minimal data is discussed.

ISSN:0148-6055    

DOI:10.1122/1.549055

出版商:The Society of Rheology    

年代:1966

数据来源: AIP

摘要:

A mathematical model was proposed recently which appears to correlate the flow curves for several polymers in aqueous solution over a wide range of shear rates and concentrations. New data for several nonaqueous systems as well as data from literature sources support the idea that the same equation can be applied to nonaqueous solutions. The equation relates relative viscosityηrat shear rateγ̇and shear stress τ to two parameters, the zero‐shear viscosityηroand the power input at the inflection pointBas follows:log ηr/log γro=0.68−0.32 erf[log(rγ̇/B)/2.272]whereerf(q)is the error function ofq. The parameterBappears to be a function of intrinsic viscosity but is not sensitive to polymer type or concentration. A comparison is made which indicates that the proposed model has advantages over other two‐parameter flow equations for real polymer systems where concentration is varied.

ISSN:0148-6055    

DOI:10.1122/1.549068

出版商:The Society of Rheology    

年代:1966

数据来源: AIP

摘要:

Application is made of Pao's theory for viscoelastic flow together with measurements of the relaxation spectrum to analyze the flow behavior of polymer melts. One result for linear polyethylene is that over a limited range of shear rate, the shear stress becomes a many‐valued function of shear rate. This behavior arises as a natural consequence of the viscoelastic nature of polymers and appears to unify many previous experimental observations of the behavior of polymer melts at high shear rates. The theory predicts an instability in the flow curve of linear polyethylene. It predicts that this discontinuity occurs at different values depending on whether the shear stress is increasing or decreasing. The recoverable strain is predicted to pass through a maximum and the velocity of a material particle in the unstable region can have a number of values at different instants in time. One interpretation of this would be that the flow can occur as a “stick‐slip” process. The effect of hydrostatic pressure on the flow curve is also discussed. All of the results of this analysis have been observed experimentally by others.

ISSN:0148-6055    

DOI:10.1122/1.549056

出版商:The Society of Rheology    

年代:1966

数据来源: AIP