Volume 36, Issue 1, January 1992
Index of content:
36(1992); http://dx.doi.org/10.1122/1.550338View Description Hide Description
Starting from the idea of equilibration, i.e., assuming that all molecular tensions are evenly distributed onto short and long chains in polydisperse polymer melts, we derive a general strain measure from a slip‐link model. By specifying disentanglement and slip of polymer chains, the strain measures of Lodge, Wagner, Doi, and Marrucci are shown to be special cases of this general strain measure. Predictions are compared to experimental data of uniaxial, planar, ellipsoidal, and equibiaxial extensions of a well‐characterized polydisperse polyisobutylene melt. The data do not support Doi’s assumption that the tube diameter remains unchanged by deformation. The relative tube diameter and its inverse, the molecular stress function, can be extracted directly from the data. The tension of the average polymer chain increases with increasing deformation, i.e., the polymer chain is stretched. At small strains, the relative cross section of the tube is inversely proportional to the average stretch of the tube.
36(1992); http://dx.doi.org/10.1122/1.550340View Description Hide Description
Earlier studies on the molecular orientation developed during the solid‐state compression of cylindrical polypropylene disks revealed a high degree of anisotropy both across the thickness and along the radius of the disk. Tracer deformation experiments reported in the present work suggest that this anisotropy is related to the complex deformation kinematics developed during the disk compression. Finite‐element simulations of the disk compression are also presented, based on a strain‐rate and temperature‐dependent viscosity. Numerical tracking of tracer elements duplicates well the experimentally observed tracer deformation. It is shown that the flow rearrangement (fountain flow) behind the spreading disk front is responsible for the observed deformation patterns.
36(1992); http://dx.doi.org/10.1122/1.550341View Description Hide Description
In a compressed in‐series array of bodies having the same cross‐sectional area, the force is the same and the deformation the sum of that of the individual components. This concept, with certain simplifying assumptions, was used to develop a simple mathematical model with which the compressive force–deformation relationships of a finger–object array can be predicted on the basis of the compressive behavior of the individual components. The models’ applicability is demonstrated with experimental compression data of a human’s index finger and thumb and food specimens having concave upward or downward force–deformation curves (hot dog, cheddar cheese, and cream cheese), tested alone and in an in‐series array. This was done by representing the force–deformation curve of each component by a two‐parameter mathematical model whose form had been specially selected so that the force–deformation relationship of the array could be calculated by an explicit algebraic expression.
36(1992); http://dx.doi.org/10.1122/1.550342View Description Hide Description
Time‐dependent volume changes are important in polymer processing because the material is frequently cooled rapidly from a rubbery melt to a nonequilibrium glassysolid. The present work uses a generalized constitutive equation of the authors, in which time‐dependent compressibility effects have been included. Its use is illustrated by two examples: (1) simultaneous pulling and cooling near the glass transition temperature, for which we present our own data; and (2) simulation of the packing and cooling steps in injection molding, for which we use literature data. Our experimental data, involving the pulling and cooling of fiber‐like samples of polystyrene near T g , were fit satisfactorily in all runs, although we note that there is considerable adjustability in a key function (the modulus–temperature relation). This example illustrates clearly the need to couple the mechanical and thermal effects in the theoretical formulation. In a separate analysis the packing and cooling steps in injection molding were simulated (by making certain simplifications in the temperature profiles) and compared with literature data.
36(1992); http://dx.doi.org/10.1122/1.550343View Description Hide Description
We describe and determine the static and dynamic (Bingham) yield stresses in an electrorheological (ER) fluid from a microstructural model. The model relates both these yield stresses to the electrostatic energy determined from the suspensioncapacitance matrix, which we developed previously for the dynamic simulation of an ER fluid. The static yield stress is determined from nonlinear elasticity strain‐energy theory applied to an ER fluid for a variety of volume fractions and particle‐to‐fluid dielectric constant ratios. The static yield stress increases with the dielectric constant ratio and exhibits a maximum at 40 Vol % particles for dielectric constant ratios of 4 or less. From the capacitance of the suspension we also compute the zero‐frequency birefringence of the ER fluid and show that it follows a nonlinear stress‐optical rule. The dynamic yield stress, as we have observed in our previous simulations, dominates the rheology of the ER fluid at large electric field strengths. At the same time the electrostatic energy of the suspension undergoes repeated slow increases, followed by rapid decreases or jumps. The connection between the dynamic yield stress and these energy jumps observed in the simulations is derived from a total energy balance of a sheared ER suspension. At low Mason number, Ma, the ratio of viscous forces to electrostatic forces, the dynamic yield stress is found to be equal to the product of the average energy jump and its frequency, and the theory is successfully tested using our dynamic simulation. Using this theory, a simple model is developed that predicts the effects of volume fraction and particle‐to‐fluid dielectric constant ratio on the dynamic yield stress. We find that the dynamic yield stress, like the static yield stress, increases with dielectric constant ratio and there is a maximum for a volume fraction of 40% particles as is indeed observed experimentally. With this understanding of the origin of the dynamic yield stress, we are able to predict the maximum yield stress obtainable with an ER fluid.
36(1992); http://dx.doi.org/10.1122/1.550357View Description Hide Description
The time‐dependent structure development of sealants changes drastically when subjecting the materials to selective degradation. By passing sealants through a Graco pump several times, the rheological properties affecting end use performance change appreciably. After only two passes in the pump the sealant is no longer classified as a ‘‘usable’’ product. This selective degradation lowers viscosity (lesser effect), elasticity, and yield stress, all due to a change in the structure of the material. The viscoelasticity of the sealant compounds was studied using a Rheometrics Controlled Stress Rheometer. By monitoring the creep and elastic recovery of the selectively degraded compounds, a correlation was developed between performance properties (end use applications) and time‐dependent structure formation. Creep and recovery results indicate that the sealants behave as viscoelastic materials. Results obtained at low stresses show elastic deformation and high viscosity. At higher stresses structural breakdown occurs resulting in lower viscosity with little or no elasticity. After two passes through the Graco pump the sealant drastically loses structure properties related to the end use performance. Viscosity,elasticity, and yield stress are lowered due to a breakdown in the time‐dependent structure development. The recoverable strain, which relates directly to elasticity, decreases appreciably with increasing passes. The degradation of the sealant changes the structure development which relates directly to the viscoelasticproperties.
The effect of shear on the yield stress and relationship to the viscoelastic nature of a thixotropic sealant36(1992); http://dx.doi.org/10.1122/1.550358View Description Hide Description
The effects of shearing a commercial thixotropic sealant using a Graco pump were studied using a Carri‐Med Stress Rheometer and a Rheometrics Mechanical Spectrometer. For a nonsag sealant, depending on the particular thickening mechanism, there is a gradual deterioration of the nonsag character once the sealant is passed through a Graco pump (a dispensing equipment for commercial cartridge filling operation). The gradual loss of nonsag character is attributed to the breakdown of the thixotropic structure and is nonrecoverable. The breakdown of the structure fundamentally changes the viscoelasticity of the sealant to a more viscous nature, which imparts resistance to crack development prior to cure. A balance between minimum yield stress and a more viscous nature is necessary for commercial application of nonsag sealants. The elastic component, G’, is proposed to be indirectly related to the yield stress of the sealant. The shearing process results in a reduction of the yield value as well as G’.
36(1992); http://dx.doi.org/10.1122/1.550359View Description Hide Description
Experimental measurements of the rheology, morphology, and flow characteristics of polymer melts containing suspended glass fibers were interpreted by employing the Doi–Doraiswamy equations for rigid rod (liquid crystalline) suspensions. The fibers were found to be generally aligned along the streamlines of the flow even at very low deformation rates. The diagonal elements of the second‐order orientation parameter tensor, which describe the perfection of the orientation, were generally predicted well by the theory using parameters obtained from rheological measurements only. Extraordinary surface irregularities were observed for suspensions extruded from circular dies, and a number of factors were examined in detail to formulate a mechanism for this flow behavior. The two most important factors affecting extrudate morphology appear to be the flexing of fibers at the surface of the extrudate and rotation of fibers in the rearranging velocity profile at the die exit.
36(1992); http://dx.doi.org/10.1122/1.550360View Description Hide Description
The recently developed generalized bracket formulation of transport phenomena (a Helmholtz free energy‐based approach) is used to predict the rheological behavior of high molecular weight, dilute polymer solutions near planar, smooth, noninteracting solid surfaces. A boundary‐value problem (passage to a stochastic differential equation) is set up in order to estimate the entropy reduction caused by the presence of the solid barrier. Under flow, in addition to diffusionaleffects, such an entropy reduction results in different conformations of the macromolecules next to the wall, which in turn causes a different than the bulk rheological behavior. The resulting continuum equations account for wall effects under arbitrary flow conditions provided the confining flow boundary is smooth. For the steady‐state simple shear flow, two limiting cases, corresponding to a uniform and a nonuniform (fully developed) concentration profile, have been examined. In both cases, calculated apparent slip velocities are found to depend almost linearly on the wall shear stress, corresponding, however, to different proportionality (slip) coefficients. Moreover, both the chain conformation and the first normal stress are found to change appreciably near the wall in a fashion moderately dependent on the applied shear stress. Assuming fully developed concentration profiles, the corresponding depletion layer is found to decrease with increasing shear stress in agreement with the molecular simulation results of Duering and Rabin.
36(1992); http://dx.doi.org/10.1122/1.550339View Description Hide Description