Stress-strain data

The molecular orientation of the polymer in a fabricated specimen can significantly alter the stress—strain data as compared with the data obtained for an isotropic specimen, eg, one obtained by compression mol ding. For example, tensile strengths as high as 120 MPa (18,000 psi) have been reported for PS films and fibers (8). PS tensile strengths below 14 MPa (2000 psi) have been obtained in the direction perpendicular to the flow. 

Rheological parameters, such as relaxation time, shear modulus, and stored elastic energy, are determined from the extrudate swell and stress-strain data as previously described. Representative examples of the variation of these parameters with blend ratios for both blends are shown in Figs. 16-18. Figure 16 shows that relaxation time for both preblends without heating and... 

Brittleness Brittle materials exhibit tensile stress-strain behavior different from that illustrated in Fig. 2-13. Specimens of such materials fracture without appreciable material yielding. Thus, the tensile stress-strain curves of brittle materials often show relatively little deviation from the initial linearity, relatively low strain at failure, and no point of zero slope. Different materials may exhibit significantly different tensile stress-strain behavior when exposed to different factors such as the same temperature and strain rate or at different temperatures. Tensile stress-strain data obtained per ASTM for several plastics at room temperature are shown in Table 2-3. 

Table 2-2 Examples of specific room temperature shear stress-strain data and Poisson s ratio for several plastics and other materials...

In general, the compressive strength of a non-reinforced plastic or a mat-based RP laminate is usually greater than its tensile strength. The compressive strength of a unidirectional fiber-reinforced plastic is usually slightly lower than its tensile strength. Room-temperature compressive stress-strain data obtained per ASTM for several plastics are shown in Table 2-5. 

Shear stress-strain data can be generated by twisting (applying torque) a material specimen at a specified rate while measuring the angle of twist between the ends of the specimen and the torque load exerted by the specimen on the testing machine. Maximum shear stress at the surface of the specimen can be computed from the measured torque that is the maximum shear strain from the measured angle of twist. 

Designers of most structures specify material stresses and strains well within the pro-portional/elastic limit. Where required (with no or limited experience on a particular type product materialwise and/or process-wise) this practice builds in a margin of safety to accommodate the effects of improper material processing conditions and/or unforeseen loads and environmental factors. This practice also allows the designer to use design equations based on the assumptions of small deformation and purely elastic material behavior. Other properties derived from stress-strain data that are used include modulus of elasticity and tensile strength. 

The process of design for static loads involves a great deal more than the mechanical operation of the stress-strain data to determine the performance of a section. The results obtained from the stress analysis are used to determine the functionality of the product and then, combined with the other factors involved to decide on a suitable design. 

FIGURE 6.1 A set of consistent stress-strain data for P-plastomers with ethylene content between 8.2 wt% (highest) and 16.0 wt% (lowest). The data for P-plastomers with intermediate composition is intermediate within these extremes. 

It is also possible to estimate the cross-link density from the stress-strain data, using the statistical theory of rubber-like elasticity [47,58]. For a swollen rubber the relationship is... 

FIGURE 22.11 Uniaxial stress-strain data (up-cycles) of solution-based styrene-butadiene rubber (S-SBR) samples with 60 phr silica at different prestrains s =100%, 150%, 200%, 250%, and 300% (symbols) and fittings (lines) with the stress-softening model Equations 22.19-22.24. The fitting parameters are indicated. The insert shows a magnification of the small-strain data. (From Kliippel, M. and Heinrich, G., Kautschuk, Gummi, Kunststojfe, 58, 217, 2005. With permission.)... 

It has been found that in the case of many metals the observed stress-strain data approximately follow the empirical relationship o = k1 s " (n < 1), where kj and n are constants that vary from material to material. Taking logarithms one can write... 

Table IV lists the mechanical stress-strain data for a series of hybrid TEOS-PTMO materials containing different levels of Ti-isop in the starting reaction mixture. These materials, with the exception of the first one, were all made using a modified reaction scheme (see experimental section) in order to incorporate the titanium into the network. The starting reaction mixtures in all cases contained 50% by weight of the glass precursors (TEOS and Ti-isop) and 50% by weight of PTMO(2000) (endcapped with triethoxysilane). One set of samples without titanium was made in order to compare the effects of the reaction scheme on the observed mechanical properties.

Data Interpretation. Often the same stress-strain data is utilized by two different research groups as evidence to both support and deny the existence of a trapped entanglement contri-... 

Figure 11 shows plots according to equation(lO) of stress-strain data for triol-based polyester networks formed from the same reactants at three initial dilutions (0% solvent(bulk), 30% solvent and 65% solvent). Only the network from the most dilute reactions system has a strictly Gaussian stress-strain plot (C2 = 0), and the deviations from Gaussian behaviour shown by the other networks are not of the Mooney-Rivlin type. As indicated previously, they are more sensibly interpreted in terms of departures of the distribution of end-to-end vectors from Gaussian form. 

Figure 11. Mooney-Rivlin plot of stress-strain data (32) for three triol-based polyester networks prepared from sebacoyl chloride and LHT240 at various initial dilutions in diglyme as solvent. Conditions P100 is 0% solvent P130 is 30% solvent PI 65 is 65% solvent.

Studies have been made of the elastic (time-independent) properties of single-phase polyurethane elastomers, including those prepared from a diisocyanate, a triol, and a diol, such as dihydroxy-terminated poly (propylene oxide) (1,2), and also from dihydroxy-terminated polymers and a triisocyanate (3,4,5). In this paper, equilibrium stress-strain data for three polyurethane elastomers, carefully prepared and studied some years ago (6), are presented along with their shear moduli. For two of these elastomers, primarily, consideration is given to the contributions to the modulus of elastically active chains and topological interactions between such chains. Toward this end, the concentration of active chains, vc, is calculated from the sol fraction and the initial formulation which consisted of a diisocyanate, a triol, a dihydroxy-terminated polyether, and a small amount of monohydroxy polyether. As all active junctions are trifunctional, their concentration always... 

Stress-Strain Data. Tensile tests were made with an Instron tester at some seven crosshead speeds from 0.02 to 20 inches per minute at five or six temperatures from 30° to —46°C. The tests were made on rings cut with a special rotary cutter from the circular sheets of the elastomers. The dimensions of each ring were determined from the weights of the ring and the disc from its center, the thickness of the ring, accurately measured, and the density of the rubber. Typically, the outside and inside diameters were 1.45 and 1.25 inches, respectively, and the thickness was about 0.085 inch. The test procedure used is described elsewhere (11), and the cubic equation, eq 4 in ref. j 2, was used to compute the average strain in a ring from the crosshead displacement. 

Stress-Strain Data. Figure 1 shows the tensile data obtained on the LHT-240 elastomer at 30°C and at seven crosshead speeds from 0.02 to 20 inches per minute. The nominal or engineering stress a is plotted against... 

A further test of the validity of ideal network theory can be obtained through studies of the equilibrium swelling of polymer networks (Eq. 11-22). The maximum amount of information can be extracted by inducing changes in the equilibrium swelling preferably combined with unidirectional stress-strain data (Eqs. III-21, 26 and 27). 

Fig. 28. Stress-strain data of a chemically crosslinked polyurethane rubber plotted according to Jackson, Shen and McQuarrie (95), see Eq. (IV-25). Data of Blok-...

The main interest in finite element analysis from a testing point of view is that it requires the input of test data. The rise in the use of finite element techniques in recent years is the reason for the greatly increased demand for stress strain data presented in terms of relationships such as the Mooney-Rivlin equation given in Section 1 above. 

Simple linear FEA programmes, as used for stress analysis of metals, take Young s modulus and Poisson s ratio as input but this is not satisfactory for rubbers because the strains involved cannot be considered as small and the Poisson s ratio is very close to 0.5. Non-linear FEA programmes for use with rubbers take data from a model such as the Mooney-Rivlin equation. More sophisticated programmes will allow a number of models to be used and may also allow direct input of the stress strain data. 

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