Volume 20, Issue 2, July 1976
Index of content:
20(1976); http://dx.doi.org/10.1122/1.549421View Description Hide Description
The Bird‐Carreau single‐integral constitutive equation is considered with an unspecified and unrestricted form of non‐linear memory function, and with an arbitrary strain measure,I, in place of the normally used Finger and Cauchy strain tensors. It is shown that the form of the shear component of the strain measure, can be derived from experimental results obtained in the start‐up of steady shear flow; and that normal stresses can be predicted from shear stresses. In contrast to the Finger and Cauchy tensors, the form of obtained from experiment is decidedly non‐linear in the amount of shear, and this results in markedly improved normal stress predictions. It is concluded that some of the previous failures of the Bird‐Carreau type of equation have been due to a poor choice of strain measure, and not (as has been suggested) to the use of an inappropriate form of memory function. The new strain measure might usefully be applied to other flows.
A Note on the Predictions from Polar Fluid Theory Which Are Independent of the Spin Boundary Condition20(1976); http://dx.doi.org/10.1122/1.549409View Description Hide Description
20(1976); http://dx.doi.org/10.1122/1.549410View Description Hide Description
The large axisymmetric deformation of a plane circular membrane into surfaces of revolution by a lateral pressure is considered. The material is taken to be a styrene‐butadiene rubber for which a nonlinear integral type constitutive equation incorporating measured properties has been presented by McGuirt and Lianis [Trans. Soc. Rheol., 14, 117, (1970)]. The formulation is reduced to a two‐point boundary value problem governed by a system of nonlinear partial differential‐integral equations of Volterra type for principal stretch ratios and a related kinematic variable. A numerical procedure is outlined which reduces at each time step to solving a system of equations having the same general structure as that for the corresponding problem assuming the membrane to be elastic. Stretch ratio and stress variation and deformed profile histories are computed for prescribed pressure histories, the latter being most useful for comparison of predictions and experiment.
20(1976); http://dx.doi.org/10.1122/1.549411View Description Hide Description
The torque and forces normal to the end surfaces of cylinders of natural rubber were measured as a function of the angle of twist. The measurements were repeated on small cylinders cut from the larger cylinders to insure that the tests were on identical material. Plots of reduced torque and of reduced normal force versus reduced twist for the different sized cylinders coincide to within 1%. This result supports the simple material assumption of the classical theory of finite elastic deformations. An interesting instability was observed, and derivatives of the strain energy function were calculated.
20(1976); http://dx.doi.org/10.1122/1.549412View Description Hide Description
A new device has been built and tested which provides for pressure‐driven flow at high shear rates in the angular direction within the annulus between two concentric cylinders. Analysis of this viscometric flow demonstrates that the measured difference between the normal stresses at the inner and outer surfaces of the annulus is related to the first normal stress function. The data interpretation corrects for pressure hole errors and inertial effects. First normal stress function data for aqueous polymeric solutions are presented and discussed. Significant advantages over commonly used testing procedures are realised. These include the ability to conduct tests on both polymer solutions and melts over a broad range of shear rates (comparable to that realized in capillary flows), improved temperature control, and the minimization of changes in the sample due to solvent evaporation and polymer degradation. Surmountable difficulties include the need for relatively large sample size, the possibility of secondary flows under some conditions, and data analysis that requires inversion of an integral.
20(1976); http://dx.doi.org/10.1122/1.549413View Description Hide Description
Developing centerline velocity and reattachment lengths were measured for viscoelasticpolymer solutions in an abrupt 2‐to‐1 expansion. Test fluids were characterized for shear stress and first normal stress difference using a Weissenberg Rheogoniometer. The deviation from inelastic behavior is examined for and No deviation from inelastic behavior was observed for while significant predevelopment of the flow field relative to inelastic behavior was observed for A flow instability was observed for The conditions for unstable flow are compared to the reversed contraction flow and to criteria suggested in the literature.
20(1976); http://dx.doi.org/10.1122/1.549430View Description Hide Description
Elongational and shear flow experiments on solutions of polybutadiene in dekalin and polyacrylonitrile in dimethyl formamide have been examined. It has been found that by using the total strain in elongation rather than strain rate the data obtained at different rates of extrusion and take‐up rate in the elongational flow experiments can be correlated. The use of the concept of total strain can be shown to allow the data to be considered in terms of constant macromolecular entanglement. Moreover, by plotting the variation of the normalized elastic modulus in elongation, against the normalized elongational viscosity, it becomes possible to obtain the total strain at which the elongational response of a polymer solution changes from mainly viscous to mainly elastic. The results have been considered in terms of a set of constitutive equations developed by Marrucci et al. Remarkable similarity exists between their theoretical predictions and the experimental results, in elongational flow, on the above solutions. These are discussed on the molecular level and it is proposed that the anomalous situation that exists between the proposal that chain entanglement decreases and the change in response of the fluid from viscous to elastic as elongation progresses, can be resolved. This is achieved by postulating the existence of a network of very‐long‐lifetime entanglements between the macromolecules.
20(1976); http://dx.doi.org/10.1122/1.549414View Description Hide Description
A semi‐quantitative method for studying the composition dependence of the non‐Newtonian melt viscosity of commercial grades of polypropylene‐linear‐polyethylene blends is presented and its effectiveness illustrated with data for two sets of blends differing widely in the molecular weight of the components. The usefulness of the composition dependence of the molten blend's specific volume in gauging their rheological behavior is also demonstrated. Melt elasticity is estimated from extrudate swell. A technique is developed for estimating the influence of the blends composition on their melt elasticity in the nonlinear range. This technique is proposed as an extension of the relaxation spectrometry widely employed for the study of solid polymers. Finally, the terminal zone of the relaxation spectra for the blends is determined from dynamic measurements using the Weissenberg rheogoniometer.
20(1976); http://dx.doi.org/10.1122/1.549415View Description Hide Description