Constant stress experiments

In contrast to creep, which is a constant stress experiment, stress relaxation is a constant strain experiment (and is usually somewhat easier to perform than a creep experiment)—Figure 13-76. A sample is deformed instantaneously (well, almost instantaneously) to a given value of the strain and the stress required to maintain that deformation is measured as a function of time. As the sample relaxes (i.e., as the chains change their conformations, disentangle and slide over one another) this stress decreases. 

The log (V ) versus log (to) plot is a straight line, with a slope of — 1, if the activation enthalpy of the craze growth and breakage are the same in a constant stress experiment at variable temperatiues. 

Once t(o) Is determined from constant stress experiments, equation (1) can be used to predict the time to fall under any stress history. The form of T(a) which we found describes our data is ... 

D(t) can only be measured directly from constant-stress experiments. Conversions from other experiments are often troublesome and can easily lead to considerable error. 

Middleman [M24], Goldstein [G8], Furuta et al. [Fll], Lobe and White [LI4], Toki and White [T7], Montes et al. [M37], Osanaiye et al. [OlO], and K. J. Kim and White [K8a]. The apparatus (with constant-temperature chamber) may be placed in a tensile tester and operated in a mode with a fixed velocity V giving a constant shear rate. It may, on the other hand, be used in a creep mode with hanging weights. This provides constant stress experiments. At low stress levels one needs to compensate for the weight of the central member which exerts a gravitational stress [OlO]. At very low stresses one may accurately determine the yield value of rubber-carbon black compounds. Osanaiye et al. [OlO] have made measurements at shear stresses below the yield value. 

It has been observed that steady state is achieved substantially faster in a constant stress experiment than in a constant strain rate experiment, and this is advantageous because of the very large sample length and very small diameter that are involved in continuing a constant rate experiment to steady state. If the extensional viscosity is the property of interest, the use of tensile creep is therefore advantageous. However, most of the data that have been reported were measured at constant strain rate. 

In Chapter 4, the response of these models to dynamic (i.e., sinusoidal) loads or strains is illustrated. In Chapter 5, the stress-strain response in constant rate experiments is described. Models with nonlinear springs and nonlinear dashpots (i.e., stress not proportional to strain or to strain rate)... 

The transition from ideal elastic to plastic behaviour is described by the change in relaxation time as shown by the stress relaxation in Fig. 66. The immediate or plastic decrease of the stress after an initial stress cr0 is described by a relaxation time equal to zero, whereas a pure elastic response corresponds with an infinite relaxation time. The relaxation time becomes suddenly very short as the shear stress increases to a value equal to ry. Thus, in an experiment at a constant stress rate, all transitions occur almost immediately at the shear yield stress. This critical behaviour closely resembles the ideal plastic behaviour. This can be expected for a polymer well below the glass transition temperature where the mobility of the chains is low. At a high temperature the transition is a... 

Figure H3.3.1 A creep experiment where a small constant stress (0) is applied to a food sample (step 1) for a period of time. Afterwards the applied stress is removed (step 2). The degree of deformation (strain, y) is measured during the experiment, and a typical response is shown. ...

We can distinguish between two types of stresses on an interface a shear stress and a dilatational stress. In a shear stress experiment, the interfacial area is kept constant and a shear is imposed on the interface. The resistance is characterized by a shear viscosity, similar to the Newtonian viscosity of fluids. In a dilatational stress experiment, an interface is expanded (dilated) without shear. This resistance is characterized by a dilatational viscosity. In an actual dynamic situation, the total stress is a sum of these stresses, and both these viscosities represent the total flow resistance afforded by the interface to an applied stress. There are a number of instruments to study interfacial rheology and most of them are described in Ref. [1]. The most recent instrumentation is the controlled drop tensiometer. 

The same molecular mechanisms as in tensile drawing are observed, of course, in constant load experiments. Depending on the stress-time-temperature regime essentially four different failure modes are observed with thermoplastic materials ... 

When subjected to a step constant stress, viscoelastic materials experience a time-dependent increase in strain. This phenomenon is known as viscoelastic creep. 

Fig. 13.84c, known as the Smith failure envelope, is of great importance because of its independence of the time scale. Moreover, investigations of Smith, and Landel and Fedors (1963,1967) proved that the failure envelope is independent of the path, so that the same envelope is generated in stress relaxation, creep and constant-rate experiments. As such it serves a very useful failure criterion. Landel and Fedors (1967) showed that a further generalisation is obtained if the data are reduced to ve, i.e. the number of elastically active network chains (EANCs). The latter is related to the modulus by... 

FIGURE 13-76 Stress relaxation—a constant strain experiment. 

If we now perform a creep experiment, applying a constant stress, a0 at time t = 0 and removing it after a time f, then the strain/ time plot shown at the top of Figure 13-89 is obtained. First, the elastic component of the model (spring) deforms instantaneously a certain amount, then the viscous component (dashpot) deforms linearly with time. When the stress is removed only the elastic part of the deformation is regained. Mathematically, we can take Maxwell s equation (Equation 13-85) and impose the creep experiment condition of constant stress da/dt = 0, which gives us Equation 13-84. In other words, the Maxwell model predicts that creep should be constant with time, which it isn t Creep is characterized by a retarded elastic response. 

If we now want to model a creep experiment we apply a constant stress, o0, hence we obtain Equation 13-89 ... 

Three types of experiments are used in the study of viscoelasticity. These involve creep, stress relaxation, and dynamic techniques. In creep studies a body is subjected to a constant stress and the sample dimensions are monitored as a function of lime. When the polymer is lirst loaded an immediate deformation occurs, followed by progressively slower dimensional changes as the sample creeps towards a limiting shape. Figure 1-3 shows examples of the different behaviors observed in such experiments. 

Since the polymer is semicrystalline, trans-cis azo isomerization must be restricted to the amorphous regions. Measurements at constant stress carried out at 200 °C indicate a deformation of about 0.6%. On the other hand, in experiments at constant length the... 

In a constant strain-rate experiment, the rapid multiplication of dislocations following the yield point can produce more mobile dislocations than are necessary to maintain the imposed strain-rate and consequently the stress drops. The deformation will continue at a constant stress provided any decrease in u is compensated by an increase in iom, or vice versa. However, in general, the stress rises with increasing strain. The slope (dajdt) of the stress-strain curve is determined by the competition between two dislocation processes namely, work-hardening and recovery, which we now consider briefly. 

Basically, a constant stress cr is applied on the system and the compliance J(Pa ) is plotted as a function of time (see Chapter 20). These experiments are repeated several times, increasing the stress in small increments from the smallest possible value that can be applied by the instrament). A set of creep curves is produced at various applied stresses, and from the slope of the linear portion of the creep curve (when the system has reached steady state) the viscosity at each applied stress, //, can be calculated. A plot of versus cr allows the limiting (or zero shear) viscosity /(o) and the critical stress cr (which may be identified with the true yield stress of the system) to be obtained (see also Chapter 4). The values of //(o) and <7 may be used to assess the flocculation of the dispersion on storage. 

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