Nominal stress and strain

This equation is given in terms of true stress and true strain. As we said in Chapter 8, tensile data are usually given in terms of nominal stress and strain. From Chapter 8 ... 

Fig. 4.4. Axial stress and strain in the notched cross section for two different materials Linear-elastic (dashed line) and elastic-plastic (solid line). The figure shows the nominal stresses and strains (Tnss, nss) and the maximum values in the linear-elastic (o-max,el, Smax.el) and elastic-plastic case (Umax, Smax)...

Fig. 6.28 Deviations from Neuber s rule found by Huang in a plate with a central hole for various applied nominal stresses and strain hardening exponents n (modified from [39])...

Measurement of Residual Stress and Strain. The displacement of the 2 -value of a particular line in a diffraction pattern from its nominal, nonstressed position gives a measure of the amount of stress retained in the crystaUites during the crystallization process. Thus metals prepared in certain ways (eg, cold rolling) have stress in their polycrystalline form. Strain is a function of peak width, but the peak shape is different than that due to crystaUite size. Usually the two properties, crystaUite size and strain, are deterrnined together by a computer program. 

Chapter 8 Nominal and True Stress and Strain, Energy of Deformation... 

Detailed stress-optical measurements have been analyzed to yield further information [4]. In Fig. 10 the birefringence (order parameter) was plotted as a function of reduced temperature for several nominal stresses <7 . These results were combined with the predictions of the Landau model and static stress-strain curves and led to a number of interesting consequences. In Fig. 11 the shift in the phase transition temperature is plotted as a function of nominal stress and shifts of up to 7.5 K were found compared to maximum displacements by electric and magnetic fields of about 5 mK in low molecular weight materials. In Fig. 12 the birefringence An is shown as a function of strain X=L/Lq at constant nominal stress f7n = 2.11xlO Nmm. A strictly... 

Figure 10.19 Nominal stress-apparent strain curves after measurements at the bottom and top faces of SFRC elements subjected to bending. The curves correspond to ID and 2D fibre distributions and to various fibre volume content, after Babut (1983).

Fig. 2. Nominal stress versus strain curves for S-B-S triblock copolymer (Kraton 101) showing mechanical hysteresis (upper curve) and extension to break (lower curve) at 220°C and constant strain rate e = 0.444 min . ...

As expected, the analysis performed in ordinary conditions has shown that the tank is not subjected to excessive stresses and strains when everything operates normally both Von Mises stresses and displacements are smaller than the maximum allowable limit set by the designers. Moreover, the analysis has highlighted the weakness of the structure in correspondence of the conjunction between the wall and the dome of the inner vessel. This is due to the fact that the stresses concentrated in this portion of the structure are very high, as exemplified in Figure 1 which shows the stress level in the inner tank under external pressure, in nominal conditions. 

Fig. 3.6 Panel (a) Stress-strain curve of a homeotropic NE oriented by a surface treatment of the sample-bearing glass slides (Urayama et al. 2007). The data have been extracted from this reference. The stress is the nominal stress and the extension ratio 2 is defined by 2 = L/Lq, where L and Lq are the lengths of the NE for the stretched and un-stretched states. Panel (b) Stress-strain curve of the homeotropic NE oriented by an E-field (Rogez et al. 2011). For both samples, the solid lines for regimes II and III are not fitted curves but theoretical curves calculated from (3.6) to (3.8) derived from the neo-classical model, using the known values of parameters 2i and (see text). The excellent agreement between the experimental and the calculated curves shows that the elasticity of the network is Gaussian. Reprinted and adapted with kind permission of Springer Science + Business Media (Rogez and Martinoty 2011)...

Young s modulus E is the ratio of nominal stress to strain, as shown in equation (70). However, vulcanized rubbers do not obey Hooke s law (as is shown in Figure 5), so E is not a constant. The stress-strain relationship is generally assumed to be linear over small tensile or compressive strains, and Young s modulus is usually defined as the slope of the stress-strain curve in this range of deformation. " Hardness measurement is another way of determining values of this modulus. It is noteworthy that the slope of the stress-strain curve in the tensile and... 

The nominal stress at yielding. In many materials this is difficult to spot on the stress-strain curve and in such cases it is better to use a proof stress. 

Assuming that a diamond-pyramid hardness test creates a further nominal strain, on average, of 0.08, and that the hardness value is 3.0 times the true stress with this extra strain, construct the curve of nominal stress against nominal strain, and find ... 

Sketch curves of the nominal stress against nominal strain obtained from tensile tests on (a) a typical ductile material, (b) a typical non-ductile material. The following data were obtained in a tensile test on a specimen with 50 mm gauge length and a cross-sectional area of 160 mm. ... 

Figure 2 Nominal stress-strain curves calculated for three monodisperse polyethylenes of M = 1900 (a), M = 9,500 (b) and M = 250,000 (c).

It should be considered that in the case of plotting 1 = a/ X — X 2) against inverse extension ratio (X 1), the nominal stress a is defined as the force divided by the undeformed cross-sectional area of the sample and X is the extension ratio, defined as the ratio of deformed to the undeformed length of the sample stretched in the uniaxial direction (as shown in Fig. 3). For PTFE powder, the intrinsic strain is deduced from (2) by defining X - 1 ... 

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