Constant strain rate

A method for measuring the uniaxial extensional viscosity of polymer soHds and melts uses a tensile tester in a Hquid oil bath to remove effects of gravity and provide temperature control cylindrical rods are used as specimens (218,219). The rod extmder may be part of the apparatus and may be combined with a device for clamping the extmded material (220). However, most of the mote recent versions use prepared rods, which are placed in the apparatus and heated to soften or melt the polymer (103,111,221—223). A constant stress or a constant strain rate is appHed, and the resultant extensional strain rate or stress, respectively, is measured. Similar techniques are used to study biaxial extension (101). 

The parameters for the model were originally evaluated for oil shale, a material for which substantial fracture stress and fragment size data depending on strain rate were available (see Fig. 8.11). In the case of a less well-characterized brittle material, the parameters may be inferred from the shear-wave velocity and a dynamic fracture or spall stress at a known strain rate. In particular, is approximately one-third the shear-wave velocity, m has been shown to be about 6 for various brittle materials (Grady and Lipkin, 1980), and k can then be determined from a known dynamic fracture stress using an analytic solution of (8.65), (8.66) and (8.68) in one dimension for constant strain rate. 

The predicted strain variation is shown in Fig. 2.43(b). The constant strain rates predicted in this diagram are a result of the Maxwell model used in this example to illustrate the use of the superposition principle. Of course superposition is not restricted to this simple model. It can be applied to any type of model or directly to the creep curves. The method also lends itself to a graphical solution as follows. If a stress is applied at zero time, then the creep curve will be the time dependent strain response predicted by equation (2.54). When a second stress, 0 2 is added then the new creep curve will be obtained by adding the creep due to 02 to the anticipated creep if stress a had remained... 

J7 In a tensile test on a plastic, the material is subjected to a constant strain rate of 10 s. If this material may have its behaviour modelled by a Maxwell element with the elastic component f = 20 GN/m and the viscous element t) = 1000 GNs/m, then derive an expression for the stress in the material at any instant. Plot the stress-strain curve which would be predicted by this equation for strains up to 0.1% and calculate the initial tangent modulus and 0.1% secant modulus from this graph. 

Controlled Strain-rate Tests Controlled strain-rate tests were first developed by Parkins (see Ugiansky and Payer ) for the study of stress-corrosion cracking. These took the form of constant strain-rate tests (also known, perhaps more accurately, as constant extension-rate tests). Since then alternative forms of test have been developed to modify the conditions under which the specimen is exposed. 

Master curves are important since they give directly the response to be expected at other times at that temperature. In addition, such curves are required to calculate the distribution of relaxation times as discussed earlier. Master curves can be made from stress relaxation data, dynamic mechanical data, or creep data (and, though less straightforwardly, from constant-strain-rate data and from dielectric response data). Figure 9 shows master curves for the compliance of poly(n. v-isoprene) of different molecular weights. The master curves were constructed from creep curves such as those shown in Figure 10 (32). The reference temperature 7, for the... 

If the applied shear stress varies during the experiment, e.g. in a tensile test at a constant strain rate, the relaxation time of the activated transitions changes during the test. This is analogous to the concept of a reduced time, which has been introduced to model the acceleration of the relaxation processes due to the deformation. It is proposed that the reduced time is related to the transition rate of an Eyring process [58]. The differential Eq. 123 for the transition rate is rewritten as... 

The uniaxial failure envelope developed by Smith (95) is one of the most useful devices for the simple failure characterization of many viscoelastic materials. This envelope normally consists of a log-log plot of temperature-reduced failure stress vs. the strain at break. Figure 22 is a schematic of the Smith failure envelope. Such curves may be generated by plotting the rupture stress and strain values from tests conducted over a range of temperatures and strain rates. The rupture locus moves counterclockwise around the envelope as the temperature is lowered or the strain rate is increased. Constant strain, constant strain rate, and constant load tests on amorphous unfilled polymers (96) have shown the general path independence of the failure envelope. Studies by Smith (97) and Fishman (29) have shown a path dependence of the rupture envelope, however, for solid propellants. 

Figure 29. Plot of storage data for three propellant formulations at various temperatures. Critical storage time is defined as the time required for the strain at maximum stress or the maximum stress itself, to change by a factor of 2. Uniaxial constant strain rate data at 0.74 in./min. and 77°F. (44)...

The strain-control test has the advantage that information on the strain capacity is obtained, as well as the maximum stress that can be sustained, the latter value being similar to that obtained in a conventional test with constant loading rate. In the following we shall discuss behaviour in compression in tests with a constant strain rate. 

Tensile tests involve either stretching a sample and monitoring the load or loading it while monitoring the extension. The simplest test uses a tensile testing machine (e.g. an Instron) where the sample is stretched at a constant rate while the load is measured using a (usually hard) load cell. Variations on this test allow the specimen to be extended at a constant strain rate or to be loaded at a constant load, or stress rate. These latter tests are usually carried out on servo hydraulic machines. 

One major consequence of the Ml project was the development of a modified filament stretching instrument by Sridhar. In this device, the test sample is held horizontally between two Teflon discs and pulled equally at both ends at a programmable exponential rate such that a constant strain rate is achieved and the stress growth at a constant stretch rate is obtained (40). It appears though that the test sample has to adhere to the plates as the technique does not use aids to clamp samples. Consequently, it is not clear if the technique can be applied to products that are non-sticky or exhibit slip, which could be limiting factors for testing food products. 

A second device that is also able to generate truly extensional flow field has been developed by Meissner (41) utilizing the concept of rotary clamps. At a constant strain rate this instrument can measure stress growth and thus allow the steady state flow measurements. 

In order to calculate, for a considered polymer under defined experimental conditions (constant strain rate or temperature), the occurrence of the micromechanism transition, one has to plot the temperature or strain rate dependence of the various critical stresses. Hereafter, we will assume that experiments are performed as a function of temperature at constant strain rate. 

At a constant strain rate, the crack propagation is brittle-stable at low temperatures and becomes of the stick-slip type at high temperatures, with an increase of KIci (Kinloch, 1985). 

The influence of temperature and strain rate can be well represented by Eyring s law physical aging leads to an increase of the yield stress and a decrease of ductility the yield stress increases with hydrostatic pressure, and decreases with plasticization effect. Furthermore, it has been demonstrated that Structure-property relationships display similar trends e.g., chain stiffness through a Tg increase and yielding is favored by the existence of mechanically active relaxations due to local molecular motions (fi relaxation). 

A constant strain rate of 10% per minute was employed. Polymers were isolated by air drying or freeze drying and molded at 150°C into dumbbell speciments for the tensile measurements. Glass transition temperatures (Tg) were measured by differential scanning calorimetry. 

Figure 2.37 presents plots of elongational viscosities as a function of stress for various thermoplastics at common processing conditions. It should be emphasized that measuring elongational or extensional viscosity is an extremely difficult task. For example, in order to maintain a constant strain rate, the specimen must be deformed uniformly exponentially. In addition, a molten polymer must be tested completely submerged in a heated neutrally buoyant liquid at constant temperature. 

If the elastic modulus is obtained from the slope of the elastic stress-strain curve, then we can evaluate the first term on the right-hand side in Equation (8.3) from experimental data elastic stress-strain curves. The second term on the right-hand side in Equation (8.3) can be evaluated from the product of the strain rate, which is set in a constant strain-rate experiment, and the viscosity. As we discussed in Chapter 3, the viscosity of a macromolecule is related to the shape factor v, therefore we can evaluate the second term on the right-hand side of Equation (8.3) from the product of the shape factor and the strain rate. 

IR Dichroism. Two types of IR-dichroism experiments were used in this study to follow segmental orientation. First, dynamic differential dichroism was used to follow chain orientation while the sample was elongated at a constant strain rate. This experiment was performed with different IR peaks which allowed a comparison of the molecular orientations for each blend constituent. Second, a cyclic experiment was used where the film was strained to a predetermined elongation, relaxed at the same strain rate until the stress was reduced to zero, and then elongated to a higher level of strain, and so forth. 

Superimposed on these fields are contours of constant strain rate, e. The heavy broken lines correspond to the contour at a strain rate of 10 12 s The region of cold drawing by adiabatic heating is shown as a shaded zone, bounded by the conditions of adiabatic heating ... 

Fig. 41. Stress as a function of log (strain rate). Constant strain rate tests A A (.yield,...

T. Kato, What is the Characteristic Time of Measurement of jt-A Isotherms - Necessity of a Constant Strain Rate of Compression of Insoluble Monolayer for Ji-k Measurements , Langmuir, 6, 870 (1990)... 

---