Index of content:
Volume 15, Issue 2, July 1971
Polymer Melt Flow Instabilities in Extrusion: Investigation of the Mechanism and Material and Geometric Variables15(1971); http://dx.doi.org/10.1122/1.549207View Description Hide Description
A comprehensive study of the effect of material, geometric, and operating variables on the onset of melt flow instabilities in extrusion was made. Primary objectives were to compare such melt instabilities for a variety of materials and to correlate instability criteria with independent rheological parameters. Seven polymer melts were studied: two polyethylenes, polypropylene, polystyrene, two polybutadienes, and an SBR copolymer. Two distinct extrusion apparatuses were used: a die fed by a screw extruder system and a die fed by an Instron rheometer. The variables studied were temperature, entry cone angle, length/diameter ratio of the die, and flow rate. Independent rheological measurements were performed. These consisted of the evaluation of normal stresses on the Weissenberg rheogoniometer, entrance pressure drop measurements on the Instron rheometer, and viscosity measurements on both instruments and the screw extruder. In a companion study, flow visualization studies were made in the die entry region of the Instron rheometer, for most of the above materials and also a solution of polyisobutylene and glycerine. Distinctively different patterns were observed for the various materials, ranging from severe channeling with corner eddies to nonchanneling flow. Interrelationships between the onset of instabilities with other measurements were noted. In comparing a variety of materials, a decrease in the critical shear rate is generally associated with an increased tendency of the material to channel, an increased normal stress/shear stress ratio and an increased entrance pressure drop/shear stress ratio. It is argued that the instability phenomena are strongly associated with the elastic properties of the materials.
15(1971); http://dx.doi.org/10.1122/1.549209View Description Hide Description
The energy required to form a unit of new surface in the fracture of a polyurethane elastomer is determined. The rate sensitivity of the material has been reduced by swelling it in toluene. This paper primarily describes the experimetal work of measuring the lower limit of the fractureenergy. With this value and the creep compliance as a basis, the rate dependence of fractureenergy for the unswollen material has been determined. It is thus shown that the dependence of the fractureenergy on the rate of crack propagation can be explained by energy dissipation around the tip of the crack. Good agreement between the theoretically and experimentally determined relationships for the rate‐sensitive fractureenergy is demonstrated.
15(1971); http://dx.doi.org/10.1122/1.549210View Description Hide Description
The unique thermoplastic elastomerproperties of A‐B‐A triblock polymers, where A is polystyrene and B is polybutadiene or polyisoprene, are analyzed by means of an adsorption‐interdiffusion (A‐I) model for the interfacial phase. The model defines the size, shape, and connectivity of the domain microstructure based upon free energy balances for the interfacial phase. The interfacial phase model is utilized to predict the phase relationships: and consequent mechanical properties based upon the volume fractions and of A and B components. The filler‐reinforcing function of polystyrene is isolated in terms of the A‐Iinterfacial phase model and analyzed by means of the Takayanagi series‐parallel (S‐P) analog model of mechanical response. Triblock polymers of A‐B‐A type are distinguished from (a) elastomers with rigid fillers, (b) incompatible polyblends, and (c) semi‐crystalline polymers based upon the A‐Iinterfacial phase model.
15(1971); http://dx.doi.org/10.1122/1.549211View Description Hide Description
A theoretical approach, relating cotton fiber tenacity to macromolecular geometrical parameters, follows. Assumptions as to the changes in fibril orientation within the secondary wall of the fiber and as to radial stress distributions resulting from axial strains are based on convolutions induced. Effects of tenacity are calculated on the basis of these assumptions and compared with experimental values.
15(1971); http://dx.doi.org/10.1122/1.549233View Description Hide Description
A theoretical model for cavitation in viscoelastic media is developed which incorporates both interfacial and rheological arguments. The properties of interfacial and bulk cavities are correlated, and the influence of time‐dependent cavityvapor pressure or hydrostatic tension are correlated with the extension ratio of the cavitysurface in a stress relaxation model. Experimental data are analysed for cavitation by peeling, tensile loading of butt joints, and superheating of swollen elastomers. For each case an agreement between theory and experiments is obtained which identifies the specific mode of cavitation and indicates for all cases the presence of prenucleated cavities with radii microns. The direct correlation of peeling stresses with viscoelastic restraints to interfacialcavitation provides a new type of experimental confirmation for the applicability of rate‐temperature superposition to peeling data. The implicit assumption that the interfacial failure stress depends upon frequency or strain rate in the same fashion as cohesive failure stress is confirmed by cavitation theory for the general case where surface tension constraints are negligible compared to viscoelastic constraints.
15(1971); http://dx.doi.org/10.1122/1.549212View Description Hide Description
The behavior of rigid and deformable particles suspended in pseudoplastic and elasticoviscous liquids undergoing tube flow was studied. The velocity profiles were more blunted than those obtained for Newtonian fluids and, as in Couette flow, the measured angular velocities of rigid spheres, rods, and discs were in accord with the theory for Newtonian liquids. There was also a drift in the orbit of the cylinders to limiting values corresponding to minimum energy dissipation in the flow. In elasticoviscous liquids, rigid particles migrated across the planes of shear towards the tube axis whereas in pseudoplastic liquids, the opposite was observed, rigid spheres actually coming in contact with the wall. The lateral migration of deformed liquid drops in elasticoviscous fluids was, as in Newtonian systems, towards the tube axis whereas in pseudoplastic liquids the drops attained an equilibrium position between the tube wall and axis. An accumulation of rigid spheres behind an advancing suspension‐air meniscus was observed in elasticoviscous media at all initial volume concentrations, the rates of accumulation increasing with flow rate and particle size. In the pseudoplastic fluids, however, there was a dilution at concentrations less than 10% followed by an accumulation at higher values but the rates of accumulation decreased with increasing flow rate and particle size. As in the Couette flow of non‐Newtonian suspension, it was not possible to interpret the observed radial migration of the particles in terms of the known rheological properties of the suspending fluids.
15(1971); http://dx.doi.org/10.1122/1.549213View Description Hide Description
Stress overshoot at the start of a flow,stress relaxation after the stoppage of a flow, and superposition of a small oscillation upon a steady shear flow are treated by the use of the concept of a deformation rate‐dependent relaxation spectra. These analyses are used as the basis of methods to determine the spectrum of relaxation times. Although the treatment is restricted to specific types of constitutive equations in which the response function depends on the rate of deformation invariants, it is not necessary to specify any functional form of the response function. Experimental determination of the rate‐dependent spectrum may play an important role in the discussion of the relative applicability of different forms of constitutive equations recently proposed in the literature.
15(1971); http://dx.doi.org/10.1122/1.549214View Description Hide Description
15(1971); http://dx.doi.org/10.1122/1.549215View Description Hide Description
Expressions were obtained for the Young's modulus,E, and the shear modulus,G, of an elastic material, resulting from a small extension, twist, or shear, respectively, superposed on a finite uniaxial stretch. The expressions are given in terms of the stretch ratio, λ, and the partial derivatives of the strain‐energy function with respect to λ. The predictions of the theory arising from several proposed forms of the strain‐energy function are calculated and compared. If the small deformation is imposed after the stress resulting from the finite stretch in a viscoelastic material has relaxed, substitution of the time‐ or frequency‐dependent viscoelastic functions for the elastic constants describes viscoelastic behavior in the small deformation when the finite stretch is within the region in which strain and time effects can be factored.
15(1971); http://dx.doi.org/10.1122/1.549208View Description Hide Description
An apparatus is designed for the determination of the axial pressure distributions of molten polyethylene and polypropylene, both in a capillary and in a reservoir. Experimental results reveal that the pressure at the tube exit, termed “exit pressure,” is above atmospheric and it is found to be shear dependent for a given ratio. The authors suggest a modified Bagley plot corrected for “exit pressure.” Such plots show curvature at the entrance region. The plots of entrance‐correction vs. wall shear stress also show curvature, thus indicating that Hooke's law in shear is not obeyed by the polymers under study. The “exit pressure” is further used to correlate with the total pressure drop at the entry to the tube.