Static stress-strain measurements

On poly(dimethylsiloxane) (PDMS) networks having comb-like crosslinks, torsional vibration experiments and static stress-strain measurements at small deformations were performed as a function of temperature, torsional vibrations also as a function of frequency. 

Static stress-strain measurements are usually needed for estimating the appropriate pretension. In these measurements, one deforms the fiber or the film in the tension mode at a constant deformation rate, and then plots the resulting stress as a function of strain. The pretension needs to be selected such that the total stress during the subsequent DMA measurements falls onto the initial linear portion of the stress-strain curve (refer to Fig. 5.7 of this chapter—the initial portion of the curve below the yield point). It should be noted that the information presented here on pretensioning apphes to tension measurements on any type of sample. 

Being a very sensitive quantity, however, the relative energy part of the modulus is different for some of the samples, if calculated from static or dynamic data, respectively. (For the calculation method, compare ref. 2J3, K ) Table III gives the values for the relative energy part. ore(j u/ored the ener9Y part calculated from stress-strain measurements Gy/G is the corresponding number obtained from dynamic data at 0.5 Hz. 

Dynamic properties are more relevant than the more usual quasi-static stress-strain tests for any application where the dynamic response is important. For example, the dynamic modulus at low strain may not undergo the same proportionate change as the quasi-static tensile modulus. Dynamic properties are not measured as frequently as they should be simply because of high apparatus costs. However, the introduction of dynamic thermomechanical analysis (DMTA) has greatly widened the availability of dynamic property measurement. 

It is demonstrated that the quasi-static stress-strain cycles of carbon black as well as silica filled rubbers can be well described in the scope of the theoretic model of stress softening and filler-induced hysteresis up to large strain. The obtained microscopic material parameter appear reasonable, providing information on the mean size and distribution width of filler clusters, the tensile strength of filler-filler bonds, and the polymer network chain density. In particular it is shown that the model fulfils a plausibility criterion important for FE applications. Accordingly, any deformation mode can be predicted based solely on uniaxial stress-strain measurements, which can be carried out relatively easily. 

The compressive stress-strain measurements are performed in an Instron Universal Test Machine. Pad specimens (Figure 1) are loaded to the bottomed deflection (Figure 2) at 1.1 in. and unloaded without pause. A cross-head rate of 2.0 in./min which is sufficiently slow as to give essentially a static loading condition is employed. Compressive stress data are reported for deflections of 0.2, 0.4 and 0.6 in. 

Detailed stress-optical measurements have been analyzed to yield further information [4]. In Fig. 10 the birefringence (order parameter) was plotted as a function of reduced temperature for several nominal stresses <7 . These results were combined with the predictions of the Landau model and static stress-strain curves and led to a number of interesting consequences. In Fig. 11 the shift in the phase transition temperature is plotted as a function of nominal stress and shifts of up to 7.5 K were found compared to maximum displacements by electric and magnetic fields of about 5 mK in low molecular weight materials. In Fig. 12 the birefringence An is shown as a function of strain X=L/Lq at constant nominal stress f7n = 2.11xlO Nmm. A strictly... 

Gibson, A.G. at al. (1978). Dynamic mechanical behaviour and longitudinal crystal thickness measurements on ultra-high modulus linear polyethylene a quantitative model for the elastic modulus. Polymer, Vol. 19 (1978), pp. 683-693 Hong, K. et al. (2004). A model treating tensile deformation of semi-crystalline polymers Quasi-static stress-strain relationship and viscous stress determined for a sample of... 

Characterization of the viscoelastic properties of polymers are classified into two categories static and dynamic measurements. The static mechanical tests involve creep, stress relaxation, and stress-strain measurements. In a creep test, a constant stress is applied to the specimen, and its deformation is measured as a function of time. In a stress relaxation test, the specimen is deformed a fixed amount, and the change in the stress is measured as a function of time. The stress-strain measurement is carried out by stretching the sample at constant tensile speed and then recording the load and deformation simultaneously. 

Fig. 10.5. Stretching curve measured for PEVA12 with a strain rate ch = 0.005 s (continuous line). Quasi-static stress-strain relationship (squares) [124]...

Young s modulus can be deterrnined by measuring the stress—strain response (static modulus), by measuring the resonant frequency of the body... 

Sol fraction 17, 25, 35, 39, 50 Soluble fractions 123,130 Spanning tree approximation 22 Stable fracture 134 Static light-scattering 7 Statistical links 126 Stick-slip fracture 133, 135 Strain hardening 145 Stress intensity factor 133 —strain measurement 42 Substitution effect 21, 28, 30... 

In addition, other measurement techniques in the linear viscoelastic range, such as stress relaxation, as well as static tests that determine the modulus are also useful to characterize gels. For food applications, tests that deal with failure, such as the dynamic stress/strain sweep to detect the critical properties at structure failure, the torsional gelometer, and the vane yield stress test that encompasses both small and large strains are very useful. 

From previous statistical studies on similar systems which Include the combination of errors Involved in sample preparation and measurement of static compressive stress-strain characteristics, the following reproducibility results were obtained (4,5, ) ... 

The buffering action of a coating in this situation is determined by the relaxation modulus of the coating material. The relaxation modulus may be measured on a film cast from the material by carrying out tensile-stress relaxation measurements with a suitable apparatus such as a Rheovibron dynamic viscoelastometer operated in a static mode. Figure 13 (inset) displays such measurements for the four coating materials used on the fibers measured in Figure 12. The measurements were carried out at 23 °C at small tensile strains, where the materials exhibit linear viscoelastic behavior. 

If a creep test is continued for long enough, complete failure of the test piece can be induced. Such a test is termed static stress rupture or static fatigue and is essentially a creep test with the bother of measuring strain removed. 

Static mechanical measurements to evaluate the stress-strain relationship in cholesteric sidechain LCEs have been described [71, 72]. In [72] it has been found, for example, thatfor0.94nominal stress Cn is nearly zero as the poly domain structure must be converted first into a monodomain structure. For deformations A < 0.94, the nominal stress increases steeply. Similar results have also been reported elsewhere [71]. The nominal mechanical stress as a function of temperature for fixed compression has also been studied for cholesteric sidechain elastomers [71]. It turns out that the thermoelastic behavior is rather similar as that of the corresponding nematic LCE [2, 5]. 

In order to describe the elastic behavior of a body, the values of the elastic constants are needed. Thus, it is important to understand the experimental techniques that are used to measure these constants. The most obvious approach is to apply a stress and measure the resulting strain held (static loading). For such approaches, strain gages are often used to measure the strain. These gages are usually electrical resistors that are calibrated such that changes in resistance can be converted to strain. Newly developed optical techniques, such as laser exten-someters, are allowing strains to be measured without specimen contact. 

Viscoelastic characteristics of polymers may be measured by either static or dynamic mechanical tests. The most common static methods are by measurement of creep, the time-dependent deformation of a polymer sample under constant load, or stress relaxation, the time-dependent load required to maintain a polymer sample at a constant extent of deformation. The results of such tests are expressed as the time-dependent parameters, creep compliance J t) (instantaneous strain/stress) and stress relaxation modulus Git) (instantaneous stress/strain) respectively. The more important of these, from the point of view of adhesive joints, is creep compliance (see also Pressure-sensitive adhesives - adhesion properties). Typical curves of creep and creep recovery for an uncross-Unked rubber (approximated by a three-parameter model) and a cross-linked rubber (approximated by a Voigt element) are shown in Fig. 2. 

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