摘要:

A variety of quantitative theories for the large elastic deformations of rubbers have been proposed. Most useful for applications in engineering, for example, because they most readily lead to the presentation of computed results in dimensionless form, are those which involve one elastic constant only (such as Young's modulus) in addition to Poisson's ratio (0.5 for incompressible rubbers). Two such theories (referred to as the Neo‐Hookean and the Varga, Dickie‐Smith elasticities) are considered here and applied to the analysis of large deformations of thick cylindrical rubber tubes. Predictions are compared to experimental results. The deformations considered are basically divided into two types: 1) longitudinal extension under constant inside pressure in which the tube is longitudinally extended by applying a variable longitudinal force while a constant pressure is maintained inside; 2) inflation under constant longitudinal force in which the tube is inflated by applying a variable pressure while a constant longitudinal force is exerted. Simple extension is a special case of type 1 when the constant pressure is zero and simple inflation is a special case of type 2 when the constant longitudinal force is zero.

ISSN:0148-6055    

DOI:10.1122/1.549461

出版商:The Society of Rheology    

年代:1977

数据来源: AIP

摘要:

Based on the integral constitutive equation and using a specific functional form of the response function which is shear rate dependent, the dynamic moduli and the first normal stress difference are quantitatively predicted from the steady‐flow viscosity for linear polyethylene melts of varying molecular weight and molecular weight distribution. No arbitrary constant is involved in the procedure. The significance of the prediction is that at least for linear polyethylene melts, the elastic properties are obtained exclusively from knowing the manner in which the viscous parameter, namely the steady‐flow viscosity, changes with shear rate.

ISSN:0148-6055    

DOI:10.1122/1.549442

出版商:The Society of Rheology    

年代:1977

数据来源: AIP

摘要:

New criteria for testing integral constitutive equations are proposed. The constitutive models studied are generalized models with stress‐, strain‐, and rate‐dependent memory functions, as well as the BKZ and Bogue‐White (BW) models. On the basis of these models, the critical relations for the test of constitutive equations are derived for five types of experiments: single‐ and double‐step stress relaxation under finite shear strain, stress overshoot, interrupted flow, and stress relaxation after cessation of steady shear flow. Among the models examined in this study, the predictions as to the time‐dependent stress or relaxation modulus in single‐ and double‐step stress relaxation are quite different, and therefore these relaxation experiments are very useful for testing the models. The Van Es‐Christensen function is monotone increasing in time for strain‐dependent models as well as for rate‐dependent models. On the other hand, it is possible that the function overshoots for the stress‐dependent model. New critical tests are proposed using interrupted flow. It is demonstrated that relations between shear and normal stress relaxation after cessation of steady shear flow are very useful for testing the models.

ISSN:0148-6055    

DOI:10.1122/1.549465

出版商:The Society of Rheology    

年代:1977

数据来源: AIP

摘要:

Well‐defined, uniaxial extensional experiments were carried out using a new apparatus which appears to be well suited as a “primary standard” for such measurements on molten polymers over a significant range of experimental conditions. Results are reported for two materials whose rheological properties in shearing flows had also been determined precisely. A polystyrene having a broad molecular weight distribution and a low‐density polyethylene were chosen as representative test materials and were studied at 165°C and 150°C, respectively, over a decade of stretch rates between about 0.04 and0.69 sec−1.Very simple constitutive descriptions, which suffice in steady shearing flows, are shown to describe the stress‐strain rate‐time behavior of polystyrene in extensional deformations of substantial complexity, as well as in constant deformation rate experiments. In the case of polyethylene, on the other hand, a “strain‐hardening” phenomenon occurs during extension. This would appear to require, except at low strain levels, the use of constitutive equations which consider explicitly the evolving melt structure in order to avoid spurious predictions when the kinematics are changed.

ISSN:0148-6055    

DOI:10.1122/1.549443

出版商:The Society of Rheology    

年代:1977

数据来源: AIP

摘要:

This paper was presented, in part, as a plenary lecture at the Seventh International Congress on Rheology at Gothenburg, Sweden on August 23, 1976 in observance of the centenary of Boltzmann's superposition principle.

ISSN:0148-6055    

DOI:10.1122/1.549444

出版商:The Society of Rheology    

年代:1977

数据来源: AIP

摘要:

The shear‐wave field generated in a linear viscoelastic medium confined between parallel plates (one fixed, the other oscillating sinusoidally in its own plane) has been evaluated and presented in a graphical form convenient for determination of the role of wave propagation effects in dynamic rheological measurements. The transition from closely spaced planes (“gap loading”) to the freely propagating plane wave (“surface loading”) limit is examined; the importance of deviations in magnitude and phase of the gradient profile from the gap loading limit is discussed in terms of high precision dynamic rheological experiments; significant deviations occur for shear wavelength to gap width ratios of 30 or less.

ISSN:0148-6055    

DOI:10.1122/1.549445

出版商:The Society of Rheology    

年代:1977

数据来源: AIP

摘要:

The process of transition from laminar to turbulent flow on a flat plate in the presence of drag‐reducing polymer additives has been investigated. In particular, the effect of polymer concentration and plate inclination on the formation of turbulent spots and their subsequent growth has been studied. It is observed that polymer addition causes a delay in both onset of turbulence and complete transition. The turbulent spots are seen to move at a lower velocity in the presence of the polymer additives. Further, the pressure gradient affects the transition in polymer solutions in the same way that it does in pure water.

ISSN:0148-6055    

DOI:10.1122/1.549446

出版商:The Society of Rheology    

年代:1977

数据来源: AIP

摘要:

The apparent uniaxial extensional viscosity or elongational viscosity,ηE,of several polymer melts in a wide range of temperatures was determined as a function of strain rate, ε̇, using Cogswell's analysis of converging flow at the die entry. In particular,ηEwas derived from knowledge of the dependence of the steady‐flow viscosity as well as the entrance pressure drop,δP0,on shear rate. Quantitative agreement was found inηE−ε̇dependence derived from the convergent flow analysis (CFA) along with that measured from isothermal melt-spinning experiments for melts of high‐density and low‐density polyethylene, polypropylene, and polystyrene. Further support of CFA comes from the finding here that the normalized entrance pressure drop,δP0/τ,is uniquely related to the vortex angle in a manner similar to that determined from flow visualization studies by Ballenger and White. Here τ is the shear stress at the die wall. Additionally, the flow activation energy in extension is found to be equal to that in shear for melts of low‐density polyethylene, polypropylene, and polystyrene. Such observations are in line with the earlier results of Munsted on polystyrene melts. An anomaly exists for high‐density polyethylenes sinceηEincreased with increases in temperature above a critical temperature. Finally, the shapes of extensional flow curves are found to be similar to the published data, although an exception such as low‐melt‐index, low‐density polyethylene, whereηEdecreases with ε̇, is cited.

ISSN:0148-6055    

DOI:10.1122/1.549468

出版商:The Society of Rheology    

年代:1977

数据来源: AIP

ISSN:0148-6055    

DOI:10.1122/1.549447

出版商:The Society of Rheology    

年代:1977

数据来源: AIP