Constant Stress Creep Experiments

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. 

If flocculation occurs on storage (without any Ostwald ripening or coalescence), the values of //(o) and may show a gradual increase with increase in storage time. As discussed in the previous section on steady-state measurements, the trend becomes complicated if Ostwald ripening and/or coalescence occur simultaneously, as both have the effect of reducing //(o) and cr.  

The above measurements should be supplemented by particle size distribution measurements of the diluted dispersion (ensuring that no floes are present after dilution) to assess the extent of Ostwald ripening and/or coalescence. Another complication may arise from the nature of the flocculation, however. If the latter occurs in an irregular fashion, so as to produce strong and tight floes, //(o) may 

To carry out creep experiments and ensure that a steady state is reached can be time-consuming. Typically, a stress sweep experiment is carried out whereby the stress is gradually increased within a predetermined time period to ensure that the steady state is almost attained, after which plots of versus a can be established. 

The above experiments are carried out at various storage times (perhaps every two weeks) and temperatures. From the change in rj o) and ct with storage time and temperature, information may be obtained on the degree and the rate of flocculation of the system. Clearly, the interpretation of these rheological results requires an expert knowledge of rheology, as well as measurements of particle size distribution as a function of time. 

As discussed in the previous section (on steady-state measurements), the trend becomes complicated if Ostwald ripening occurs simultaneously (both have the effect of reducing and er ). 

The above measurements should be supplemented by particle size distribution measurements of the diluted suspension (making sure that no floes are present after dilution) to assess the extent of Ostwald ripening. 

The above experiments are carried out at various storage times (say every two weeks) and temperatures. From the change of ctcj with storage time and 

---

Ot, is a parameter which is related directly with the stressed state as used here in the theory, we have a problem that the creep experiments done here are not constant true stress creep but a constant engineering stress creep experiment, and this will disturb the simple stress history expected. That is, is not... 

In constant stress (creep) measurements, one applies the stress (that is kept constant at each measurement) in small increasing increments. If the stress applied is below the yield stress, the system behaves as a viscoelastic solid. In this case, the strain shows a small increase at zero time and this strain remains virtually constant over the duration of the experiment (near zero shear rate). When the stress is removed, the strain returns back to zero. This behaviour will be the same at increasing stress values, provided the applied stress is stiH below the yield stress. Any increase in stress will be accompanied by an increase in strain at zero time. However, when the stress exceeds the yield stress, the system behaves as a viscoelastic liquid. In this case, the strain rapidly increases at zero time, giving a rapid elastic response characterised by an instantaneous compliance Jo (the compliance is simply the ratio between the strain and applied stress, Pa ). At time larger than zero, the strain shows a gradual and slow increase with time. This is the region of retarded response (bonds are broken and reformed at different rates). Ultimately,... 

The creep test probes the time-dependent nature of a sample. Creep and recovery tests allow the differentiation between viscous and elastic responses when the viscoelastic material is subjected to a step constant stress (creep) and then the applied stress is removed (recovery). A standard creep experiment provides critical parameters such as zero shear viscosity (qo) and equilibrium compliance (Jeo), which measures the elastic recoil of a material. 

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. ...

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

In a creep experiment the Voigt-Kelvin element is instantaneously subjected to a stress [Pg.414]

Let s start with creep, which is the easiest to understand. In a creep experiment you simply subject a sample to a constant (non-destructive) load or stress and watch it deform (i.e., measure the strain) as a function of time (Figure 13-72). The first systematic studies of this type were conducted by the German physicist, Weber, in 1835, who noted that silk fibers exhibited an immediate deformation upon loading, behavior that we call elastic, followed by an extension that gradually increased with time. Similarly, upon removing- the load both an immediate and delayed contraction were observed. In many... 

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. 

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 ... 

The Zero Creep Technique. The zero creep technique was developed by Udin, Shaler, and Wulff(8) to measure the surface energy of Cu wires. The technique was later extended for use with thin foils by Hondros(16). Very thin foils, approximating a surface, are readily available. When shaped into a cylinder, the sample will tolerate large loads without necking. Since necking does not occur, the stress can be considered constant throughout the experiment. Figure 1 shows a schematic of a foil and the associated stress under an applied load... 

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. 

The Maxwell body is appropriate for the description of stress relaxation, while the Voigt element is more suitable for creep deformation. In a stress relaxation experiment, a strain yo is imposed atr = Oand held constant thereafter (dy/r// = 0) while r is monitored as a function of t. Under these conditions, Eq. (11-29) for a Maxwell body behavior becomes... 

A simple creep experiment involves application of a stress tq at time t = 0 and measurement of the strain while the stress is held constant. The Voigt model (Eq, 11-28) is then... 

Much important information about deformation mechanisms has come from creep experiments, in which the stress is kept constant and the strain is measured as a function of time, producing a creep curve (Figure 9.5). In general, the creep curve exhibits three stages of deformation (i) transient creep, in which the strain-rate changes with time (this stage may be... 

The dislocation nucleation just discussed is a preyield phenomenon in any deformation experiment, it may occur (i) during any preconditioning treatment at temperature and pressure before the shear stress is applied, (ii) during the incubation period in a creep test, or (iii) during the nominally elastic region in a constant strain-rate experiment. Thus, the microstructure of the crystal immediately prior to the onset of deformation may not be the same as the microstructure of the as-grown crystal. 

The yield point, work-hardening, and recovery. The yield stress, whether in a creep or a constant strain-rate experiment, is determined by the onset of dislocation mobility, usually glide. The subsequent deformation depends on the density mobile dislocations and their speed v. Provided the dislocations are distributed reasonably homogeneously in the specimen, the deformation is described by the Orowan equation... 

The Kelvin-Voigt elements are used to describe data from a creep experiment and the retardation time (t2) is the time required for the spring and the dashpot to deform to (1 — 1 /e), or 63.21 % of the total creep. In contrast, the relaxation time is that required for the spring and dashpot to stress relax to 1 /e or 0.368 of a (0) at constant strain. To a first approximation, both z and Z2 indicate a measure of the time to complete about half of the physical or chemical phenomenon being investigated (Sperling, 1986). 

Creep-compliance studies conducted in the linear viscoelastic range also provide valuable information on the viscoelastic behavior of foods (Sherman, 1970 Rao, 1992). The existence of linear viscoelastic range may also be determined from torque-sweep dynamic rheological experiments. The creep-compliance curves obtained at all values of applied stresses in linear viscoelastic range should superimpose on each other. In a creep experiment, an undeformed sample is suddenly subjected to a constant shearing stress, Oc. As shown in Figure 3 1, the strain (y) will increase with time and approach a steady state where the strain rate is constant. The data are analyzed in terms of creep-compliance, defined by the relation ... 

In a shear creep experiment of this type, the material undergoes a stress cr = shear strain with time is registered. As shown in Figure 5.4b, the shear strain for an ideal solid is instantaneous [e(0 = eoFT(0], remaining constant with time. However, the strain for ideal liquids is a linear function of time (Fig. 5.4c). As Eq. (4.135) suggests, the shear strain for an ideal liquid is given by... 

Figure 5.4 Response of ideal solids (b) and ideal liquids (c) to a constant shear stress (a) in creep experiments.

Figure 5.5 Response of real solids (a) and real liquids (b) to a constant shear stress in creep experiments.

This is the Boltzmann superposition principle for creep experiments expressed in continuous form. If the stress is a continuous function of time in the interval —oo < < 8i, constant in the interval 0i < / < 02, and again a continuous function for t > 02 (see Fig. 5.14), then Eq. (5.35) cannot be used to obtain e because the contribution of the stress to the strain in the interval 0i < t < 02 would be zero. The response for this stress history is given by... 

---