Zero creep experiments

Fig. 3a, b. Schematic of a zero creep experiment, (a) Fine Cu wires (0 0.07 mm) are loaded with different weights of the same material of up to 100 mg and heated in a vacuum oven, (b) The strain of the wires after heating for 72 h... 

Techniques to measure the surface tension of solids are notoriously difficult and known for their inaccuracies. Reliable surface tension data requires not only a reliable measurement technique but careful control over parameters such as sample purity and the gaseous atmosphere in which the experiments are conducted. TTie zero creep technique is considered one of the most accurate and reliable of these techniques since it requires only a simple length measurement(8). Samples can be either wires or thin foils. Hondros(9) has postulated that the use of thin foils increases the sensitivity of the technique and thus allows more accurate measurements. The thinner the foil, the more it approximates a surface. Wire gauges are limited due to the loads required to strain the sample. Table I lists some of the results obtained using the zero creep foil technique. It should be pointed out that the terms surface tension and surface free energy are often used interchangeably, though they are not equivalent(9,10). 

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... 

In a tensile test, for example. Eq. (11-10) relates the strain and stress in a creep experiment when the stress Tq is applied instantaneously at time zero. If this loading... 

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... 

Strain from a creep experiment with constant applied stress a for a viscoelastic solid (lower curve) and a viscoelastic liquid (upper curve). The slope at long times is the steady shear rate 7, from which the viscosity is calculated as = cr/7 (the viscosity of any solid is infinite, corresponding to zero slope). The extrapolation of this straight line to zero time (dotted line) gives the elastic part of the strain, from which the recoverable compliance is determined. 

A stress-relaxation experiment is carried out by stretching the sample to some definite length at zero time and by measuring the force necessary to maintain that length as a function of time. The stress-relaxation measurements tend to yield the same sort of information that is obtained in creep experiments, but the results can be expressed in different ways. It is also possible, in principle, to calculate the stress-relaxation data from cre measurements, but this is rather complicated and not often d[Pg.929]

The measurement of rheological properties for non-Newtonian, lipid-based food systems, such as dilatant, pseudoplastic, and plastic, as depicted in Figure 4.1, are much more difficult. There are several measurement methods that may involve the ratio of shear stress and rate of shear, and also the relationship of stress to time under constant strain (i.e., relaxation) and the relationship of strain to time under constant stress (i.e., creep). In relaxation measurements, a material, by principle, is subjected to a sudden deformation, which is held constant and in many food systems structure, the stress will decay with time. The point at which the stress has decayed to some percentage of the original value is called the relaxation time. When the strain is removed at time tg, the stress returns to zero (Figure 4.8). In creep experi-... 

Given a sufficiently long time of creep, the velocity of creep will decelerate to zero and y t) attains an equilibrium limit if a viscoelastic solid is being measured. On the other hand, if the material is a viscoelastic liquid, the velocity of creep will decelerate to a finite constant value. Viscoelastic steady state is achieved, and y t) increases indefinitely. The creep experiment has a second part when the stress is set to zero after a period of creeping. A portion or all of the strain accumulated during creeping is then recovered as a function of time for a viscoelastic liquid or solid, respectively.For a viscoelastic liquid, the portion that is permanent deformation and irrecoverable reflects the contribution of viscous flow to the total deformation accumulated during creep. Since a viscoelastic solid does not flow, all of its creep deformation is recoverable. 

Figure 4.156 illustrates the detailed technical drawing of a dynamic mechanical analyzer by TA Instraments. The sample is enclosed in a variable, constant-temperature environment, not shown, so that the recorded parameters are stress, strain, time, frequency, and temperature. This instrument can be used for resonant and defined-frequency operation. Even creep and stress relaxation measurements can be performed. In creep experiments, a constant stress is applied at time zero and the... 

Instead of imposing a constant stretch rate on a sample and measuring the steady-state stress, one may impose a constant stress and determine the resulting extensional strain. This is a creep experiment, and if the strain, initially zero, begins to increase linearly with time, a constant stretch rate is achieved. The extensional viscosity is again obtained as the ratio of the imposed stress to the resulting constant stretch rate. 

The roles of stress and strain are reversed in a creep experiment stress is the disturbance and strain the response. In simple shear, a constant shear stress cxq is imposed and the time dependence of strain y(t) is recorded. In the creep recovery phase, the sample is unloaded (the shear stress is set to zero), and the strain at subsequent times is recorded. Because the stress is constant, the creep strain y t) would be a constant, y t) = Oq/G, for the Hookean solid and directly proportional to time, y t) = (oo/r))t, for the Newtonian liquid. In the recovery phase, the strain recoils immediately to zero for the solid and remains fixed at (cTo/v)ti for the liquid, ti being the time at which recovery began. 

These relationships mean that we can extend any oscillatory plot if steady-state data such as zero-shear-rate viscosity from a creep experiment is available (or vice versa). This then dictates the G curve, at least to the shear rate where the viscosity departs from r o, which in turn prescribes the frequency at which G" departs from t o< . 

The solution of the relaxation equation for the creep experiment, i.e. a step-like application of a stress at zero time, can be written down directly. It is given by... 

In a creep experiment, the stress, rather than the strain, is increased suddenly from zero to a constant value (Tq at time t = 0. The resulting data are interpreted in terms of the creep compliance / = y t)lretardation spectrum . All these terms are defined later in this section. Plazek and Echeverria [5] have argued that compliance data are more useful than stress relaxation data in revealing various relaxation mechanisms. 

If, at time, tg, the creep experiment has reached a steady-state (constant shear rate) then the recovered strain no longer depends on tg, and it is convenient to set tg equal to zero, thus resetting the clock . This leads to ... 

Most experiments on the surface free energy which have been discussed in the preceding sections have been performed on polycrystalline material. One exception is the zero creep technique when applied to foils which can be prepared as single crystal surfaces [67Hon], Absolute values for the surface free energy of a specific orientation have also been obtained by the cleavage technique, see data in section 4.4.7.1. 

---