Stress-strain curve/data

The mechanical piopeities of stmctuial foams and thek variation with polymer composition and density has been reviewed (103). The variation of stmctural foam mechanical properties with density as a function of polymer properties is extracted from stress—strain curves and, owkig to possible anisotropy of the foam, must be considered apparent data. These relations can provide valuable guidance toward arriving at an optimum stmctural foam, however. 

Strain and constant time can give respectively isometric stress-log time curves and isochronous stress-strain curves Figure 9.10). Whilst not providing any new information, such alternative presentations of the data may be preferred for certain purposes. 

Stress-strain curves at the conditions of product application. If applicable, this would usually indicate the toughness of material by sizing up the area under the curve (Chapter 2). It would also show the proportional limit, yield point, corresponding elongations, and other relevant data. 

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. 

Stress-strain-time data are usually presented as creep curves of strain versus log time. Sets of such curves, seen in Fig. 2-27, can be produced by smoothing and interpolating data on a computer. These data may also be presented in other ways, to facilitate the selection of information to meet specific design requirements. Sections may be taken t... 

The yield point is the first point on the stress-strain curve at which an increase in strain occurs without an increase in stress. The stress at which a material exhibits a special limiting deviation from the proportionality of stress-to-strain is the yield strength. A material whose stress-strain curve exhibits points of zero slope may be considered to have a yield point such as described in Fig. 2-11. The data sheets usually omit the yield strength when there is a zero slope point on the stress-strain curve in the yield region. In reinforced plastic materials, the values of the yield strength and the tensile strength are very close to each other. 

If product use conditions vary appreciably from those of the standard test, a stress-strain curve, derived using the procedure of anticipated requirement, should be requested and appropriate data developed. 

The test can provide compressive stress, compressive yield, and modulus. Many plastics do not show a true compressive modulus of elasticity. When loaded in compression, they display a deformation, but show almost no elastic portion on a stress-strain curve those types of materials should be compressed with light loads. The data are derived in the same manner as in the tensile test. Compression test specimen usually requires careful edge loading of the test specimens otherwise the edges tend to flour/spread out resulting in inacturate test result readings (2-19). 

Test results provides the hypothesis that syntactic foam is rate insensitive and that the static uniaxial strain stress-strain curve actually represents the general constitutive relation. Disagreement between the experimental data and the predicted behavior is greatest at low stresses (1 kbar) where experimental stresses are about double those predicted analytically. The discrepancy decreases at the higher stress levels and virtually disappears at and beyond 7 kbar. This range... 

Fig. 97.—Comparison between theoretical and experimental stress-strain curves for vulcanized rubber for elongations =0.40 to 2.0. Points are experimental data those for a <1 were obtained by inflating a rubber sheet. (Treloar. )...

Because of the previously mentioned inadequacy of the function a —l/a, a different value for the parameter %i is required for the set of points (Fig. 135) at each elongation a. These values are —0.90, — 0.73, and —0.56 for a = 1.4, 2.0, and 3.0, respectively. If the function a — l/a were replaced by an empirical representation of the shape of the stress-strain curve, a single value of xi would suffice to represent all of the data within experimental error. This limitation of Eq. (41) relates to an unexplained feature of the stress-strain curve and is... 

An Instron Tensile Tester Model TM was Interfaced to a micro-computer for data collection and transmission to a minicomputer. A FORTRAN program was developed to allow data analysis by the minicomputer. The program generates stress-strain curves from the raw data, calculates physical parameters, and produces reports and plots. 

A second method used to verify the validity of the results is visual inspection of the graphic data. After the tabular results are presented, the operator can call a subroutine which plots the stress-strain curves. Anomalous curves can usually be easily identified in this manner. 

Figure 10.1. USAXS observation during straining of an SBS block copolymer. Right monitor Intensity maxima on an ellipse. Raw-data coordinate system (x,y) and radial cuts for data analysis are indicated. Middle Videotaping of sample. Left Stress-strain curve. Control booth of beamline BW4, HASYLAB, Hamburg...

Figure 1. Stress-time data from stress-strain curves measured in simple tension at 30°C on the LHT-240 polyurethane elastomer at seven extension rates, A from 9.4 X t° 9.4 min 1. Key 0,9, stress as a function of time ( — 1)/X, at the indicated values of strain, ( — 1).

Gas compression in closed-cell polymer foams was analysed, and the effect on the uniaxial compression stress-strain curve predicted. Results were compared with experimental data for a foams with a range of cell sizes, and the heat transfer conditions inferred from the best fit with the simulations. The lateral expansion of the foam must be considered in the simulation, so in subsidiary experiments Poisson s ratio was measured at high compressive strains. 13 refs. 

As indicated in Fig 2, curve (a) is useful in correlating experimental data, curve (b) is essentially a stress-strain curve, although it has other interesting features which will be discussed later, and curve (c) is most useful in considering shock and rarefaction effects across boundaries of different media... 

Data can be obtained from tests in uniaxial tension, uniaxial compression, equibiaxial tension, pure shear and simple shear. Relevant test methods are described in subsequent sections. In principle, the coefficients for a model can be obtained from a single test, for example uniaxial tension. However, the coefficients are not fully independent and more than one set of values can be found to describe the tension stress strain curve. A difficulty will arise if these coefficients are applied to another mode of deformation, for example shear or compression, because the different sets of values may not be equivalent in these cases. To obtain more robust coefficients it is necessary to carry out tests using more than one geometry and to combine the data to optimize the coefficients. 

In practice, up to 90% of polyurethanes are used in compression, a few percent in torsion, and very little in tension. There is considerable data on the tensile stress against tensile strain (elongation) for polyurethanes. Most polyurethane specification sheets provide this data. Figure 7.3 and Figure 7.4 show typical stress-strain curves for both polyester and polyether polyurethanes. 

Calculations. The stress-strain curves for the silk fabric were plotted automatically from the data obtained with the Instron. The initial modulus was determined from a suitable straight line portion of the stress-strain curve. The strain-to-break was then calculated with an effective gauge length determined from extrapolation of the initial modulus. The energy-to-break was calculated from the integrated area under the corrected stress-strain curve to the break point. 

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