Stress relaxation measurement

Another resonant frequency instmment is the TA Instmments dynamic mechanical analy2er (DMA). A bar-like specimen is clamped between two pivoted arms and sinusoidally oscillated at its resonant frequency with an ampHtude selected by the operator. An amount of energy equal to that dissipated by the specimen is added on each cycle to maintain a constant ampHtude. The flexural modulus, E is calculated from the resonant frequency, and the makeup energy represents a damping function, which can be related to the loss modulus, E". A newer version of this instmment, the TA Instmments 983 DMA, can also make measurements at fixed frequencies as weU as creep and stress—relaxation measurements. 

Stress-relaxation measurements, where stress decay is measured as a function of time at a constant strain, have also been used extensively to predict the long-term behavior of styrene-based plastics (9,12). These tests have also been adapted to measurements in aggressive environments (13). Stress-relaxation measurements are further used to obtain modulus data over a wide temperature range (14). 

All tensile and stress-relaxation measurements were done using an Instron Tensile tester. The samples were cut into the dumbbell shape corresponding to the ASTM D412 type C model (total length 4.5 in. straight part 1.5 in. width 0.25 in.). 

The samples were tested at a deformation rate of 1 in./min. for the simple tension experiments. In the case of stress-relaxation measurements, the samples were prestrained to 7% elongation at e = 5 in./min. then allowed to stress relax over a 20 minute period. All mechanical testing were carried out at room temperature. 

At the highest temperature we performed stress relaxation measurements to extend the experimental frequency range. From these relaxation experiments, the corresponding oscillatory data were calculated with the well-known approximate relationships of Schwarzl (13). More details on the preparation of the networks and on the measurements were published previously (14). 

The reduction in stress which takes place in a test strip of rubber held at constant elongation. Stress relaxation measurements are used in the study of the ageing of rubber vulcanisates, the degradation of the network structure resulting in a reduction of the tension. 

Stress-relaxation measurements of styrene-based plastics, 23 362 on tempering, 23 285-286... 

Crosslinking yields can also be derived from the extent of swelling of the irradiated polymer (if the hydrodynamic interaction factor, X, between the polymer and the solvent is known accurately), or from stress relaxation measurements on elastomers. 

Stress relaxation measurements [Figure 3.1 (3)] are obtained by employing similar equipment. Here the force (weights, etc.) is rapidly applied... 

Scission yields are determined by stress relaxation measurements during irradiation of specimens. Permanent and temporary chain scissions are measured by this technique in contrast to gel measurements, which provide data only on permanent scissions. 

Stress relaxation measurements can be made in compression, shear or tension, but in practice a distinction is made as regards the reason for making the test which is generally related to the mode of deformation. The most important type of product in which stress relaxation is a critical parameter is a seal or gasket. These usually operate in compression and, hence, stress relaxation measurements in compression are used to measure sealing efficiency. 

Stress relaxation measurements can also be used as a general guide to ageing, and it is particularly relaxation due to chemical effects which is then studied. Such measurements are normally made in tension and will be considered in Chapter 15 as an ageing test. Hence, in this section, only relaxation tests in compression will be discussed as this mode of deformation is the only one commonly used and standardised to directly estimate the relaxation of rubbers in service. For an application in tension, the methods described in Chapter 15 could, of course, be adapted. It must be appreciated that the methods in compression do not only measure relaxation due to physical effects, especially when elevated temperatures and liquid environments are used, so that the distinction is a little blurred. 

Experience with compression stress relaxation measurement was not particularly widespread when the ISO standard was first formulated, a variety of apparatus was in use and reproducibility was not good. Birley et al ° studied a number of factors and made recommendations for change,... 

DSC measurements showed that the crystallization ability of this interphase region was reduced by the silane modification of the glass beads. Despite an increase in the amount of amorphous material with increasing number of silane layers, a decrease in the intensity of the fourth lifetime was observed. This decrease in the free volume is in accordance with the earlier observed reduced mobility in the interphase region measured by dynamic-mechanical spectroscopy in the melt state [9,10] and creep and stress relaxation measurements in the solid state [12]. 

Creep measurements involve the application of a constant stress (usually a shearing stress) to the sample and the measurement of the resulting sample deformation as a function of time. Figure 9.6 shows a typical creep and recovery curve. In stress-relaxation measurements, the sample is subjected to an instantaneous predetermined deformation and the decay of the stress within the sample as the structural segments flow into more relaxed positions is measured as a function of time. 

Tonami et al.179) studied atactic-PMAA (at-PMAA)-PEO complex membranes by means of infrared spectroscopy, stress relaxation measurement and torsional analysis of dynamic-mechanical properties. They pointed out that the polymer complex was formed through hydrogen bonds between the ether... 

Preparation of the Samples. Blends of different composition were prepared by freeze drying dioxane solutions. Sheets were compression molded at 249°C and cut into samples of desired dimensions. Rectangular samples were used for the stress-relaxation measurements and dumbbellshaped samples were used for the tensile stress-strain experiments. The compositions by weight of the PC-PST blends studied are as follows 95/5, 90/10, 80/20, 75/25, 50/50, and 25/75. 

For HDPE this gives Eact/R = 2.31 x 1265 /0.11 = 2.66 x 104 K, in good agreement with the experimental value obtained by Seitz and Balazs in stress relaxation measurements, viz. 28,000 (Eact = 235 kj/mol). 

The rate of chemical degradation can often be measured by means of physical quantities, e.g. stress relaxation measurements. 

Figure 7 Infrared spectra of succinylated woods after stress relaxation measurement in solution at various pH values. (From Ref. 29.)...

If the above discussion is valid, G, should decrease rapidly when we replace low-pH solution with high-pH solution during the stress relaxation measurement. Stress relaxation was measured in solutions of varying pH from 2.97 to 10.10 at log t = 3. The results of untreated and succinylated wood are shown in Fig. 9 and 10. As would be expected, untreated wood changes slightly by the replacement, whereas succinylated wood does remarkably. This is because the numbers of ionizative side chains differ from one another. A slight decrease for the untreated wood appears due to the ionization of... 

Figure 16 shows relationships between the number of introduced side chains and relaxation rigidity (G,) at 900 s for carboxymethylated wood binding various metal ions [341. Wood specimens were prepared from Japanese linden Tilia japonica Smik.). Carboxymethylation and the introduction of metal ions was the same procedure as mentioned in the previous section [32,33]. Stress relaxation measurements were carried out in an aqueous solution at 30°C. The relaxational property of carboxymethylated wood without metal ions is first discussed. For carboxymethylated wood (a broken line in Fig. 16), Gf (900) decreases with an increase in the number of introduced side chain. This rapid decrease appears to be caused by two factors. One is the effect of sodium hydroxide (NaOH). Young s modulus of wood treated with an aqueous solution of NaOH decreases remarkably under wet conditions, especially at concentrations above 10% NaOH [35]. The other factor is the electrostatic repulsion of ionized carboxymethyl groups in carboxymethylated wood, as mentioned in the above section [291. For example, conformation of polypeptide is influenced by the ionization of the side chains, and the structural change of the helix-coil transition has been interpreted as a reversible transformation. Theoretical treatment of the transformation has been reported to explain the mechanism [23-25, 36-43]. The conformation of component molecules in wood, however, cannot change markedly by ionization in comparison with soluble polyelectrolytes in water, because carboxymethylated wood is not dissolved in water. Only space among the main chains is expanded by the electrostatic repulsion due to negatively charged side chains. For these reasons, G (900) of carboxymethylated wood decreases with an increase in the number of introduced side chains.

Consider two experiments carried out with identical samples of a viscoelastic material. In experiment (a) the sample is subjected to a stress CT for a time t. The resulting strain at f is ei, and the creep compliance measured at that time is D t) = e la. ln experiment (b) a sample is stressed to a level CT2 such that strain i is achieved immediately. The stress is then gradually decreased so that the strain remains at f for time t (i.e., the sample does not creep further). The stress on the material at time t will be a-i, and the corresponding relaxation modulus will be y 2(t) = CT3/C1. In measurements of this type, it can be expected that az> 0 > ct and Y t) (D(r)) , as indicated in Eq. (11-14). G(t) and Y t) are obtained directly only from stress relaxation measurements, while D(t) and J(t) require creep experiments for their direct observation. Tliese various parameters can be related in the linear viscoelastic region described in Section 11.5.2. 

A complete description of the viscoelastic properties of a material requires information over very long times. Creep and stress relaxation measurements are limited by inertial and experimental limitations at short times and by the patience of the investigator and structural changes in the lest material at very long times. To supplement these methods, the stress or the strain can be varied sinusoidally in a dynamic mechanical experiment. The frequency of this alternation is u cycles/s or m(= 27ri ) rad/s. An alternating experiment at frequency w is qualitatively equivalent to a creep or stress relaxation measurement at a time t = (I /w) sec. 

Stress-relaxation measurements confirm Burley s interchange hypothesis. Fibers pretreated with iodine or nitrous acid, both of which oxidize disulfide groups and probably also thiol groups (Sookne and Harris, 1937 Cockbum etal., 1948 Crewtherand Dowling, 1961a), were characterized by... 

Stress Relaxation. In a stress-relaxation measurement, the specimen is deformed by a fixed strain and the stress required to maintain this deformation is measured for a specific time. The degree of stress relaxation is highly temperature-dependent in the region of Tg and very sensitive to interacting solvents as well as other factors which alter chain mobility. Therefore, stress relaxation is useful in determining the influence of solvents on the viscoelastic properties of corneum. 

A reported dependence of on M - for narrow distribution polystyrenes recently reported by Tobocsky et al. 209a) deduced from stress relaxation measurements has not been confirmed by extensive studies of Plazek and O Rourke (180b) on the creep and recovery behavior of similar polymers. The latter found jjr cc over the interval Z, to Z 1.6 x 10, as reported in Fig. 1,... 

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