Strain rate Strength” parameter

Both % El and % RA are frequendy used as a measure of workabifity. Workabifity information also is obtained from parameters such as strain hardening, yield strength, ultimate tensile strength, area under the stress—strain diagram, and strain-rate sensitivity. 

For a fixed strain rate, a comparison of Eq. (74) and experimental data [51, 52] of miscible blends is shown in Fig. 32. Curves 1 and 2 represent, respectively, the PPO/PS blends in compression, and the PPO/PS-pCIS blends in tension.Table 2 lists the three parameters fjf2, CK, and A/f2 used in curves 1 and 2. The unique feature here is the presence of a maximum yield (or strength) for 0 <

nonequilibrium interaction (A < 0). Such phenomenon does not occur in incompatible blends or composite systems. Table 2 also reveals that the frozen-in free volume fractions which are equal to 0.0243 and 0.0211 for polystyrene and for PPO, respectively. These are reasonable values for polymers in the glassy state. In the search for strong blends, we prefer to have —A/f2 > 1, and a larger difference between the yield stresses of blending polymers. 

Materials can show linear and nonlinear viscoelastic behavior. If the response of the sample (e.g., shear strain rate) is proportional to the strength of the defined signal (e.g., shear stress), i.e., if the superposition principle applies, then the measurements were undertaken in the linear viscoelastic range. For example, the increase in shear stress by a factor of two will double the shear strain rate. All differential equations (for example, Eq. (13)) are linear. The constants in these equations, such as viscosity or modulus of rigidity, will not change when the experimental parameters are varied. As a consequence, the range in which the experimental variables can be modified is usually quite small. It is important that the experimenter checks that the test variables indeed lie in the linear viscoelastic region. If this is achieved, the quality control of materials on the basis of viscoelastic properties is much more reproducible than the use of simple viscosity measurements. Non-linear viscoelasticity experiments are more difficult to model and hence rarely used compared to linear viscoelasticity models. 

Tensile tests at room temperature have shown that HPT-processed titanium demonstrates yield stress higher that 800 MPa, ultimate strength of 980 MPa and elongation to fracture of 12% (Fig. 5). A strain-rate jump test of this material has revealed an increased strain rate sensitivity value of 0.12-0.15, which is visibly higher than that for conventional coarse-grained Ti where this parameter is less than 0.05. 

Each type of propellant has specific mechanical characteristics, but the influence of test parameters (temperature, strain rate, and pressure) is the same for all propellants (11). Tensile tests are widely used to analyze propellant behavior as well as examine the manufacturing controls of the propellants. Because their behavior is not linear-elastic, it is necessary to define several parameters that allow a better representation of the experimental tensile curve. The stylistic experimental stress-strain response at a constant strain rate from a uniaxial tensile test is shown in Figure 7, where E is the elastic modulus (initial slope), Sr P is the tensile strength (used later for a failure criterion), and eXj> is the strain at tensile strength. 

In practice, large deformation properties are far more useful, and determination of the full relation between stress and strain gives the best information. Materials vary widely in their linear region, i.e., the strain range over which stress and strain remain proportional. Deforming it much farther, the material may eventually break. Relevant parameters then are fracture stress or strength, fracture strain or shortness, and work of fracture or toughness. The correlation between fracture parameters and the modulus is often poor. Since many soft solids exhibit viscoelastic behavior, the values of these parameters can depend, often markedly, on the strain rate. 

Some of the important fracture parameters that are determined from the stress-strain curves are also illustrated in Figure 6, and include the initial modulus, proportional limit stress, ultimate strength and strain to failure. It is often very difficult to determine unambiguously the stress at which the first matrix crack occurs, so the proportional limit stress, i.e. the stress at which the strain deviates by 0.005% from linear loading, is more commonly used to characterize this important stress level. All of the in-plane fracture data reported here was measured at initial strain rates (prior to matrix cracking) between 3 x 10 and 10 " s unless otherwise noted. 

Based on the evidence so far, it seems probable that impact strength in rubber-modified plastics depends on the relative importance of crazing and shear yielding induced by the rubber particles,f as weU as on other parameters such as the rubber characteristics (below). As mentioned above, however, extrapolation from low-strain-rate to high-strain-rate tests cannot be made quantitatively. Research into the deformation mechanisms at high strain rates should be fruitful, though difficult to accomplish. 

The first technique, dynamic loading or dynamic fatigue, can be used to obtain the slow crack growth parameter n as a function of strain rate and tenrperature. The dynamic loading technique requires a large number of tests for each strain rate. If the strength distributions in two series of specimens are the same, then at equivalent failure probabilities (Evans, 1974) ... 

During the test, a two-pen X-Y plotter recorded strain gage output as a function offload. Our procedure was to load cycle the specimen (strain rate, e = 3 x 10 s ) to 25 to 35% of its ultimate strength four times with high sensitivity settings on the plotter these data yielded the elastic parameters. We decreased the plotter sensitivity on the final loading cycle to record the fracture parameters. 

Consider a tensile specimen of an isotropic metal with elastic parameters E = 210 000 MPa and v = 0.3, and a yield strength (Tf = 210 MPa. The material hardens linearly and isotropically according to equation (3.50), with hardening parameter H = 10 000 MPa. The tensile specimen is elongated, starting with an unloaded state, at a constant strain rate of n = 0.001 s . We want to determine the time-dependence of stresses and strains. 

Loading of the material at high strain rates, for example in the notched bar impact bending test, or at low temperature. This is due to the fact that the yield strength always depends on these two parameters (see section 6.3.2), whereas the cleavage strength is almost constant. This is particularly the... 

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