Stress strain measurement

Choosing the best conditions of dynamic stress and strain is often difficult when creating mechanical analysis methods for a series of samples. Since sample behaviour will often change when the stress or strain imposed on a sample is increased or decreased, a curve of stress versus strain is very valnable. The Newtonian or linear region for a material can be measured with the stress scan mode of the DMTA. This is the region in which quantitative data can be obtained. 

The stress scan [dynamic stress (10 Pa) versus strain (%)] of an rmvnlcanised rubber material depicted the linear region of this material to be within 0.08-0.27% strain and 2,000-4,200 Pa stress. Without this capability, this linear region of stress and strain can only be approximated. 

A stress scan [i.e., dynamic stress (Pa) versus strain (%) plots] will show the effect of increasing stress on a polymer. There is usually an initial region where the strain is proportional to stress. Then, with increasing strain there can be deviations from linearity due to various molecular effects. Calculations can determine proportional limits, yield modulus, draw strength and ultimate modulus. 

The prevailing tension divided by the smallest cross-section Fq of the test specimen at the beginning of the experiment gives the corresponding stress a, which is thus the tension per unit cross-section (1 mm ). The ultimate tensile strength Og is obtained by dividing the maximum load P ,ax t y the initial cross-section Fq measured in N/mm or MPa  

The elongation is generally understood to be the extension with respect to the original length. The elongation at yield is accordingly the extension, Al = I- 

The second group exhibits the phenomenon of drawability. This manifests itself in the stress-strain behavior (curve II in Fig. 2.21) as follows At first these materials behave in a similar way to those of curve I. The proportionality limit lies at low values, and the deformation with increasing load is also quite small. Then, suddenly, a large extension occurs, even though the load remains constant or becomes smaller. The material begins to flow and the stress-strain curve sometimes runs nearly parallel to the abscissa. The point at which the 

Finally, the modulus of elasticity E (Young s modulus), which is a measure of the stiffness of the polymer, can be calculated from the stress-strain diagram. According to Hooke s law there is a linear relation between the stress o and the strain e  

the elastic modulus corresponds in principle to the force per square millimeter that is necessary to extend a rod by its own length. Materials with low elastic modulus experience a large extension at quite low stress (e.g., rubber, = 1 N/mm ). On the other hand, materials with high elastic modulus (e.g., polyoxymethylene, s 3500 N/mm ) are only slightly deformed under stress. Different kinds of elastic modulus are distinguished according to the nature of the stress applied. For tension, compression, and bending, one speaks of the intrinsic elastic modulus ( modulus). For shear stress (torsion), a torsion modulus (G modulus) can be similarly defined, whose relationship to the modulus is described in the literature. 

In a stretching experiment a test specimen is placed under tension, causing the length to increase and the cross-sectimi to decrease, until finally it breaks. For these stress-strain measurements the test specimen has shoulders at both ends, such that the break occurs in the desired place, namely at the position of lowest cross-section. 

The specimen is held at its broader parts in the clamps of the testing machine. The machine then puUs the clamps apart at constant speed, whereby a force is transmitted to the test specimen. The latter is plotted continuously against the change of length by means of a coupled recorder. The maximum tension Pmax during the experiment is not always the same as the tension at break. 

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In particular it can be shown that the dynamic flocculation model of stress softening and hysteresis fulfils a plausibility criterion, important, e.g., for finite element (FE) apphcations. Accordingly, any deformation mode can be predicted based solely on uniaxial stress-strain measurements, which can be carried out relatively easily. From the simulations of stress-strain cycles at medium and large strain it can be concluded that the model of cluster breakdown and reaggregation for prestrained samples represents a fundamental micromechanical basis for the description of nonlinear viscoelasticity of filler-reinforced rubbers. Thereby, the mechanisms of energy storage and dissipation are traced back to the elastic response of tender but fragile filler clusters [24]. 

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. 

Plots of G at 0.5 Hz and the reduced stress ore(j obtained from stress-strain measurements at small strains against temperature, give almost identical straight lines (Figure 5). This similarity was expected because no frequency dependence of G had been observed. Hence G equals the equilibrium modulus G G moreover equals the reduced stress ore(j, if the latter is measured in the vicinity of X= 1. The measurements were always performed at X = 1.02 - 1.04, so that this requirement is fulfilled. 

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. 

Relative energy part of the modulus at T = 298K, from stress-strain measurements with X = 1.02-1.04 (ored u red and from torsional vibration experiments (G y/G 5... 

In order to check this prediction, stress-strain measurements were made up to moderate strains at room temperature. The obtained data are plotted in the usual manner as a versus 1/X in Figure 8. Table V gives the Mooney-Rivlin constants 2C and 2C calculated from these plots and also the ratio C./Cj. 

Networks were prepared in all cases using the amount of endlinking agent necessary to give a minimum Mc. Values of Mc were calculated from the Mooney-Rivlin elasticity coefficient Cj, determined from tensile stress-strain measurements (10),... 

The results of stress-strain measurements can be summarized as follows (1) the reduced stress S (A- A ) (Ais the extension ratio) is practically independent of strain so that the Mooney-Rivlin constant C2 is practically zero for dry as well as swollen samples (C2/C1=0 0.05) (2) the values of G are practically the same whether obtained on dry or swollen samples (3) assuming that Gee=0, the data are compatible with the chemical contribution and A 1 (4) the difference between the phantom network dependence with the value of A given by Eq.(4) and the experimental moduli fits well the theoretical dependence of G e in Eq.(2) or (3). The proportionality constant in G for series of networks with s equal to 0, 0.2, 0.33, and 0. Ewas practically the same -(8.2, 6.3, 8.8, and 8.5)x10-4 mol/cm with the average value 7.95x10 mol/cm. Results (1) and (2) suggest that phantom network behavior has been reached, but the result(3) is contrary to that. Either the constraints do survive also in the swollen and stressed states, or we have to consider an extra contribution due to the incrossability of "phantom" chains. The latter explanation is somewhat supported by the constancy of in Eq.(2) for a series of samples of different composition. 

Residual radiation, from nuclear power facilities, 17 553-554 Residual stress/strain measurement diffractometers in, 26 428—430 Residual thermal stresses ceramics, 5 632-633... 

C. Galiotis and J. Parthenios, Stress/strain measurements in fibers and composites using Raman spectroscopy, in Vibrational Spectroscopy of Biological and Polymeric Materials, V.G. Gregoriou and M.S. Braiman (Eds), CRC Press, Boca Raton, 2006. 

Figure 10. Dependence of the reduced equilibrium modulus of POP triol - MDI networks prepared in the presence of diluent. POP triol Mu= 708 stress-strain measurements in the presence of diluent (o) and after evaporation of the diluent ( ). Flory theory for the values of the front factor A indicated, theoretical dependence including trapped interchain constraints Numbers at curves Indicate the value of ry.

FIGURE 14.11 Typical dumbbell- or dog-bone-shaped sample used for stress-strain measurements. 

Many of the rheological properties of materials are determined using stress-strain measurements. 

The phenomenological ordering of polymers projected for use as constructing materials is not an easy matter. Sometimes the temperature stability is used as a criterion, i.e., the temperature up to which the mechanical properties remain more or less constant. Another attempt for classification, uses the E modulus or the shape of the curve of stress-strain measurements (see Sect. 2.3.5.1). In general one can say that semicrystalline thermoplastics are stiff, tough, and impact-resistant while amorphous thermoplastics tend to be brittle. Their E... 

Stress-strain measurements were carried out on molded films ( 1 mm thickness) at room temperature by the use of microdumbell-shaped samples and an Instron tensile tester (model No. 1130, crosshead speed of 5 cm/min). The samples were premolded between Mylar sheets for 10 min at 162 °C at about 5000 psi, then remolded at 165 °C and 7000 psi for 20 min, and slowly cooled ( 1 °C/min) to 50 °C. Select samples were solvent extracted by MEK using a Soxhlet extractor before molding. 

The cross-link density can be determined by equilibrium swelling or from equilibrium stress-strain measurements at low strain rate, elevated temperature, and sometimes in the swollen state3 °... 

When using equilibrium stress-strain measurements, the cross-link density is determined from the Mooney-Rivlin equation ... 

The value of Ci is obtained from the plot of o/2(X - A ) vs. 1A and extrapolating to 1A = 0. By comparison with the theory of elasticity, it has been proposed that Cl = 1/2 NRT, where N is cross-link density, R the gas constant, and T the absolute temperature (of the measurement). To assure near-equilibrium response, stress-strain measurements are carried out at low strain rate, elevated temperature, and sometimes in the swollen state. °... 

The most commonly reported physical properties of radiation cross-linked natural rubber and compounds made from it are modulus and tensile strength, obtained from stress-strain measurements. Figure 5.5 illustrates some of the results obtained from gum rubber and from a natural rubber compound reinforced by HAF carbon black. In Figure 5.6 the tensile strength of radiation cured gum is compared to that of vulcanizates cured by sulfur and by peroxide. ... 

The information on physical properties of radiation cross-linking of polybutadiene rubber and butadiene copolymers was obtained in a fashion similar to that for NR, namely, by stress-strain measurements. From Table 5.6, it is evident that the dose required for a full cure of these elastomers is lower than that for natural rubber. The addition of prorads allows further reduction of the cure dose with the actual value depending on the microstructure and macrostructure of the polymer and also on the type and concentration of the compounding ingredients, such as oils, processing aids, and antioxidants in the compound. For example, solution-polymerized polybutadiene rubber usually requires lower doses than emulsion-polymerized rubber because it contains smaller amount of impurities than the latter. Since the yield of scission G(S) is relatively small, particularly when oxygen is excluded, tensile... 

In the simplest study of this type, Al-ghamdi and Mark [138] studied reinforcement of PDMS by two zeolites of different pore sizes. The zeolites were a zeolite 3A (pore diameter 3 A) and a zeolite 13X (pore diameter 10 A), both with a cubic crystalline structure. They were simply blended into hydroxyl-terminated chains of PDMS which were subsequently end-linked with tetraethoxysilane to form an elastomeric network. These elastomers were studied by equilibrium stress-strain measurements in elongation at 25°C. Both zeolites increased the modulus and related mechanical properties of the elastomer, but the effect was larger for the zeolite with the larger pore size. 

The relaxation behavior of the trapped chains Iras been studied by means of stress strain measurements on dry networks and on networks swollen in bad solvents63. ... 

In any case, if this polymerized form of elemental sulfur is quenched (cooled rapidly), it becomes a solid. This solid is glassy at very low temperatures, but becomes highly elastomeric above its glass-transition temperature of approximately -30 °c.6 8 14 30 The situation is complicated by the presence of unpolymerized S8 molecules which would certainly act as plasticizers. So far, attempts to cross-link the elastomeric form into a network structure suitable for stress-strain measurements have not been successful. The polymer is unstable at room temperature, gradually crystallizing, and eventually reverting entirely to the S8 cyclics. 

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