Constant-strain-rate rheometer

The major advantage of a constant-stress rheometer over a constant-strain-rate rheometer is that, for a given polymer, a steady state is frequently achieved in the former mode but not in the latter one.(28) Even when a steady state is obtained with the use of both instruments, the total strain needed to achieve a steady state is lower for the constant stress viscometer. This extends the range of strain rates at which the extensional viscosity can be determined for an apparatus of a given size. Finally, it has been observed(4 20) that the stress tends to decrease slightly in a constant stretch rate experiment even after a plateau appears to have been reached. The physical significance of this last observation is not entirely clear. (29)... 

Commercial instruments are available the Brabender Plastograph, and Plasticorder, this latter allowing use of an extruder head the RAPRA variable torque rheometer [5]. The advantages of these instruments are based on the similarity of their action to full-scale extrusion equipment and on the fact that they can be operated at shear rates appropriate for factory equipment. But because of the difficulty of matching exactly the range of shear rates which exist in full-scale plant, successful scaling-up is difficult. Elongation flow measurements have been reported by several workers, in which a sample is stretched in uniaxial tension at a constant strain rate [6]. 

Since the invention of the rotary damp rheometer (Figure 1(a)) by Meissner [1], the elongational viscosity of linear and branched polyethylene (PE) melts has l n studied extensively. For polypropylene (PP), only a few studies have been published. The measurement of elongational viscosity at constant strain rate or constant tensile stress is of great importance for characterizing the structure of the pol5uner melt. 

FIG. 15.24 Schematic representation of the four roller extensional rheometer, designed by Meissner (1972) to attain high Hencky strains. Two sets of rotary clamps are individually driven by two motors at constant rotation rates. The force in the sample is measured by a transducer F mounted on a leaf spring. From Barnes, Hutton and Walters (Gen Ref 1993). Courtesy Elsevier Science Publishers. 

Many of the earlier commercial viscometers have been of the constant shear rate design where the speed of rotation was the controlled variable and the resulting shear stress was measured. However, viscometers and rheometers in which the shear stress is controlled and resulting shear rate or strain can be measured are available now. Because they provide an opportunity to conduct studies related to yield stress, creep-compliance, stress relaxation, and rate of breakdown of weak structures, it seems... 

Rheology is a powerful method for the characterization of HA properties. In particular, rotational rheometers are particularly suitable in studying the rheological properties of HA. In such rheometers, different geometries (cone/plate, plate/plate, and concentric cylinders) are applied to concentrated, semi-diluted, and diluted solutions. A typical rheometric test performed on a HA solution is the so-called "flow curve". In such a test, the dynamic viscosity (q) is measured as a function of the shear rate (7) at constant strain (shear rate or stress sweep). From the flow curve, the Newtonian dynamic viscosity (qo), first plateau, and the critical shear rate ( 7 c), onset of non-Newtonian flow, could be determined. 

Fig. 15.20. The build-up of modulus in disentangled polymer melts with time. Samples compressed at 50 C, having diameter of 8mm, thickness 1mm, were heated with varing heating rate (10°C/min till 0.1 C/min) from 125°C to 138°C and then heated fast (30°C/min) to 180°C in the rheometer(inlay). A constant strain of 0.5% was applied at a fixed frequency of lOOrad/s. The frequency was chosen to be in the plateau region...

These working equations, along with the limitations and utility of fiber spinning measurements, are summarized in Table 7.5.1. The major problem is that typically is not constant, so the force, which is measured over the entire fiber, is an integration of stresses due to various strain rates and even the upstream shear histmy in the die. For these reasons, the fiber spinning experiment is not a true rheometer, but gives only an iq>paient uniaxial extensional viscosity. 

Measuring yield stress of concentrated suspensions can be carried out using various rheological techniques that can be broadly classified under two categories the controlled rate rheometry and the controlled stress rheometry. A controlled rate rheometer deforms a specimen at a constant shear rate and measures the shear stress. On the other hand, a controlled stress rheometer imposes a constant shear stress on a specimen and then measures the corresponding strain. The latter approach involves a more sophisticated control system and is only introduced in the last ten years. These techniques can be further classified as direct (or static) or indirect methods (or dynamic). The indirect determination of yield stress involves the extrapolation of experimental shear stress - shear rate data to obtain a yield stress, which is the shear stress at zero shear rate. This is illustrated in Figure 9. It is evident that the choice of the model or methods yield differing values of yield stress. 

Melt behavior has been studied using uniaxial (also called simple or tensile), biaxial, and planar extensional flows [9, Ch. 6]. However, only the first two of these are in general use and will be discussed here. A uniaxial extensional rheometer is designed to generate a deformation in which either the net tensile stress Tg or the Hencky strain rate e (defined by Eq. 10.89) is maintained constant. The material functions that can, in principle, be determined are the tensile stress growth coefficient / (f, ), the tensile creep compliance, andthetensile... 

We have seen that rheometers capable of accurate measiuements of extensional flow properties are limited to use at low Hencky strain rates, usually well below 10 s . In order to reach higher strain rates, the drawdown of an extruded filament ( melt spinning ) and the converging flow into an orifice die or capillary have been used to determine an apparent extensional viscosity . Since the stress and strain are not imiform in these flows, it is necessary to model the flow in order to interpret data in terms of material functions or constants. And such a simulation must incorporate a rheological model for the melt under study, but if a reliable rheological model were available, the experiment would not be necessary. This is the basic problem with techniques in which the kinematics is neither controlled nor known with precision. It is necessary to make a rather drastically simplified flow analysis to interpret the data in terms of some approximate material function. 

Extensional viscosity was measured at 170°C on a Sentmanat Extensional Rheometer (SER) fixture (Xpansion Instruments).[1] The SER is based on a dual drum system. It is designed as a fixture of a standard rotational rheometer which consists of a master and slave wind-up dmms coupled via intermeshing gears. A constant Hencky strain rate is obtained simply by setting a constant winding speed. The SER fits inside the environmental chamber of an Advanced Rheometric Expansion System (ARES) rheometer. Tests were carried out on strips cut out of a 0.5 mm thick compression molded sheet. Constant Hencky strain rates (1 and 10 s ) were applied and the time-dependent stress was determined from the measured torque and the sample time-dependent cross-section. The extensional viscosity, tie, was obtained by dividing the stress by the Hencky strain rate. 

Thus, to predict sedimentation, one has to measure the viscosity at very low stresses (or shear rates). These measurements can be carried out using a constant stress rheometer (Carrimed, Bohlin, Rheometrics or Physica). A constant stress very small torques and using an air bearing system to reduce the frictional torque) is applied on the system (which may be placed in the gap between two concentric cylinders or a cone-plate geometry) and the deformation [strain y or compliance J = (y/cr) Pa ] is followed as a function of time [39-41]. 

The best designs of rheometers use geometries so that the forces/ deformation can be reduced by subsequent calculation to stresses and strains, and so produce material parameters. It is very important that the principle of material independence is observed when parameters are measured on the rheometers. The flow within the rheometers should be such that the kinematic variables and the constitutive equations describing the flow must be unaffected by any rigid rotation of both body and coordinate system - in other words, the response of the material must not be dependent upon the position of the observer. When designing rheometers, care is taken to see that the rate of deformation satisfies this principle for simple shear flow or viscometric flow. The flow analyzed can be considered as viscometric (simple shear) flow if sets of plane surfaces (known as shear planes) are seen to exist and each is moving past the other as a solid plane, i.e. the distance between every two material points in the plane remains constant. 

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