摘要:

This study defines experimentally the steady flow of a partially crystalline polyethylene. The polymer has been exposed to high and variable shear rates at temperatures from about 40°C above to about 40°C below the polymer melting point. The polymer tested was a branched polyethylene, specific gravity 0.92 (20°C), melting point 103°C with a viscosity‐average molecular weight of 2800. Viscosities measured above the melting point were independent of shear over the experimental shear rate range,30–10,000 sec−1.Viscosities measured below the melting point became progressively more shear dependent with decreasing test temperature. A rotational concentric cylinder viscometer and a pressure capillary viscometer were used. The results have been interpreted in terms of temperature and shear dependence in order to evaluate possible mechanisms in flow such as orientation and destruction of crystalline regions. Estimates of the magnitude of molecular associations from several approaches have been made. Flow activation energies were calculated for the melt and as a function of shear rate for the partially crystalline state.

ISSN:0148-6055    

DOI:10.1122/1.549081

出版商:The Society of Rheology    

年代:1967

数据来源: AIP

摘要:

Viscosity was measured as a function of shear rate for a series of concentrated solutions of polystyrene inn‐butyl benzene, using a plate‐cone viscometer. The polymers had narrow distributions of molecular weight(Mw/Mn=1.01–1.20)withMwranging from 19,800 to 2,400,000. Polymer concentrations ranged from 0.20 to 0.55 g/cc and temperatures from 30 to 60°C. A master curve of reduced viscosity versus reduced shear rate was prepared and found to be similar to one recently predicted for monodisperse entangling polymers. An experimental relaxation timeτ0was deduced for each solution by superposition with the theoretical master curve. The values ranged from 0.0024 to 9.1 sec and were always of the order of the Rouse relaxation time,τr=(6/π2)(η0M/cRT),calculated for the solution. Residual variations in the ratioτ0/τrwith both concentration and molecular weight were noted however, although a single curve was formed whenτ0/τrwas plotted as a function of the productcM. This suggested that the number of chain entanglements per molecule influences the course of the relaxation process. A very simple equation correlated all the data, yieldingτ0=(const.)η0M/cTat low values of the entanglement density andτ0=(const.)η0/c2Tat high values.

ISSN:0148-6055    

DOI:10.1122/1.549089

出版商:The Society of Rheology    

年代:1967

数据来源: AIP

摘要:

The propagation of small amplitude stress discontinuities in linear viscoelastic media with differential stress‐strain laws is considered. The theory of weak solutions is used to determine the curves of discontinuity and the jumps in the stress and the velocity and their successive derivatives on the discontinuity. A Taylor series expansion is then used to approximate the stress and the velocity behind and sufficiently near the discontinuity. These results are applied to study the propagation of longitudinal impact waves in semi‐infinite and finite viscoelastic rods.

ISSN:0148-6055    

DOI:10.1122/1.549090

出版商:The Society of Rheology    

年代:1967

数据来源: AIP

摘要:

The applicability of a functional polynomial of third degree for the constitutive equation of a nonlinear viscoelastic polymer has been investigated. A method for the determination of the kernel functions appearing in the one‐dimensional creep formulation has been discussed. Creep measurements of tension and compression in low density polyethylene under single step, two step, and three step loading histories are described. The analysis of this data has provided a basis for determination of the creep kernel functions. For the loading range used in the test, the Volterra‐Fréchet multiple integral expansion of the constitutive functional of low density polyethylene has been found to be adequately represented by the three‐term integral representation. A number of cases of general load histories was investigated. A close comparison between the experimental response to these loading histories and the response predicted by the three‐term integral representation was obtained.

ISSN:0148-6055    

DOI:10.1122/1.549082

出版商:The Society of Rheology    

年代:1967

数据来源: AIP

摘要:

Gross features of linearly viscoelastic flow are related to corresponding features of Newtonian viscous flow. A step change in pressure gradient produces particle displacements that are asymptotic (fort→∞) to those in a Newtonian flow startingTunits of time earlier.Tis the mean relaxation time of the fluid. A step change in flux requires a pressure loss that is asymptotic to the loss in a Newtonian flow startingTunits of time later. Results are independent of cross‐sectional shape, but require flow slow enough that terms of third order in shear per relaxation time are negligible.

ISSN:0148-6055    

DOI:10.1122/1.549083

出版商:The Society of Rheology    

年代:1967

数据来源: AIP

摘要:

Experimental problems arising in the measurement of the second normal stress difference are discussed. An approximate method (with error estimates) for inversion of experimental data is given. A potentially exact numerical approach for data inversion is also suggested. Some results on polyisobutylene‐cetane solutions are shown to be in close agreement with previously published work. Finally, an adaptation of the given technique for finding the first normal stress difference without the use of rotating parts is considered.

ISSN:0148-6055    

DOI:10.1122/1.549084

出版商:The Society of Rheology    

年代:1967

数据来源: AIP

摘要:

A modified superposition principle has been employed to describe creep in the nonlinear range under combined stresses which change abruptly from time to time. The stress functionfijemployed is derived from three integrals of the multi‐integral theory for constant stress. Several means of treating the nonlinearity in stress when the stress changes are investigated. The most satisfactory of these considers that after a change in stress fromσkl(1)toσkl(2)the creep may be described as the sum of the recovery resulting from removal ofσkl(1)and the creep from application ofσkl(2),the recovery being computed on the basis of superposition. Thus for a power function of timetwhere the strainε=ε0+ε+tnandnis a constant the creep following a change in stress at timet1is given byεij(t)=fij0(σkl(1))+[fij0(σkl(2))−fij0(σkl(1))]+fij+(σkl(1))tn+[fij+(σkl(2))−fij+(σkl(1))] (t−tl)n. Experiments on an unplasticized poly(vinyl chloride) include tension creep followed by multiple‐step unloading; combined tension and torsion creep followed by multiple‐step unloading; combined tension and torsion creep with several abrupt changes in combination of tension and torsion; and tension creep with partial unloading and reloading. The method describes the time dependence reasonably well in all cases, but the total strain following partial unloading from high combined stresses in the nonlinear range was substantially larger than predicted.

ISSN:0148-6055    

DOI:10.1122/1.549091

出版商:The Society of Rheology    

年代:1967

数据来源: AIP

摘要:

A rheological equation for viscoelastic fluids is derived as an expansion of Noll's functional for simple fluids. The present expansion is developed in terms of the deformation rate referred to a co‐rotational material frame. The resulting series of approximations for the stress differs significantly from those proposed previously by Green and Rivlin and by Coleman and Noll. Applications to both simple‐extensional and viscometric flows are considered. For viscometric flows the present model exhibits non‐Newtonian effects similar to those observed in real fluids, with relatively few terms in the functional expansion. The first term in the expansion yields a “first‐order” fluid similar to the model proposed by Pao. Expressions are also given for the viscometric material functions of the present “third‐order” fluid. As with higher‐order fluids, these functions areFourierintegrals of certain hereditary or memory functions for the fluid.

ISSN:0148-6055    

DOI:10.1122/1.549085

出版商:The Society of Rheology    

年代:1967

数据来源: AIP