True stress plotted against

Figure 2. True stress plotted against strain. Data represent equilibrium behavior from Fig. 1 and similar plots of data on the other two polyurethane elastomers. Quantity A introduced for clarity.

Figure 11.16 Measured values of the compressive yield stress aj (true stress) plotted against applied tensile stress CT2 (nominal stress). The full circles denote ductile yield, the crosses denote brittle fracture and the combined points denote tests where ductile yielding occurred, followed immediately by brittle fracture. (Reproduced with permission from Bowden and Jukes, J. Mater. Set, 3,183 (1968))...

A plot of log o against log s should thus yield a straight line whose slope is n and which makes an intercept equal to log fej on the log o axis (at s = 1). Thus the constant kj represents the true stress at unit true strain and is termed the strength coefficient. The exponent n is known as the strain hardening exponent. 

Figure 5. True stress-at-break plotted on doubly logarithmic coordinates against the strain-at-break. Conditions 30°C extension rates from 9.4 X 103 to 9.4 min 1. Quantity A introduced for clarity.

One of the simplest criteria specific to the internal port cracking failure mode is based on the uniaxial strain capability in simple tension. Since the material properties are known to be strain rate- and temperature-dependent, tests are conducted under various conditions, and a failure strain boundary is generated. Strain at rupture is plotted against a variable such as reduced time, and any strain requirement which falls outside of the boundary will lead to rupture, and any condition inside will be considered safe. Ad hoc criteria have been proposed, such as that of Landel (55) in which the failure strain eL is defined as the ratio of the maximum true stress to the initial modulus, where the true stress is defined as the product of the extension ratio and the engineering stress —i.e., breaks down at low strain rates and higher temperatures. Milloway and Wiegand (68) suggested that motor strain should be less than half of the uniaxial tensile strain at failure at 0.74 min.-1. This criterion was based on 41 small motor tests. 

The plots show that under cold shock and for all values of Bi, the maximum tensile stress is achieved at the surfaces while the maximum compressive stress is achieved at the centre of the plate. The opposite is true for hot shock conditions. The maximum tensile stress, cr, achieved at the surface during cold shock and at the centre during hot shock, is then plotted against IIBi, as shown in Fig. 15.3. 

This equation shows that the ratio of the birefringence to the true stress should be independent of stress. The expression on the RHS of equation (11.13) is known as the stress-optical coefficient. A test of equation (11.13) can be made by plotting An against cr, when a straight line should be obtained. Such plots for a vulcanised natural rubber at various temperatures are shown in fig. 11.5. The hysteresis shown in the curves for the lower temperatures is interpreted as being due to stress crystallisation, with the crystallites produced being oriented in the stretching direction and... 

In a plot of (T, against A (Figure 53) yield will occur according to eqn 5.7 at point M that is to say the engineering stress-strain curve will show a maximum only if a tangent can be drawn from A => 0 to touch the true stress-extension ratio curve at a point such as M. 

To return linear viscoelasticity, it is required that g(e) approaches unity for small strain. The stress-strain data for Smith s SBR vulcanisate rubber material are plotted in Figure 11.3(a). Log stress against log time plots were obtained for fixed strains and, as shown in Figure 11.3(b), form parallel linear relationships. This suggests via Equation (11.7) that the quantity g(e)/e is independent of time. It was found that for extension ratios up to 2, g(e) = 1 provided that a is understood to denote the true stress. At higher strains, the empirical function... 

When the results of a tensile test are plotted on a graph of true stress against linear strain, show that the point at which necking starts is the point of contact of the tangent to the curve that passes through the point on the strain axis where the strain equals —1. This is the construction of Considere. 

Figure 12.41 Plots of tensile stress at a range of levels of true strain against log strain rate. (Reproduced with permission from Sweeney, ]., Naz, S. and Coates, P. D. (2011) Modeling the tensile behavior of ultra-high-molecular-weight polyethylene with a novel flow rule. /. Appl. Polym. Sci., 121, 2936. Copyright (2011) John Wiley Sons, Inc.)...

Figure 3 shows plots of true strain against time for the zirconia - spinel samples tested at 1623 and 1673 K and at constant stresses of 7.5 and 9.0 MPa. It is apparent that for the samples tested at 7.5 MPa the steady-state condition is reached within the durations of the experiments. However, it is not clear that a true steady-state condition was attained for the sample tested at a constant stress of 9.0 MPa. 

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