True tensile stress

F(FG = normal (shear) component of force A = area u(w) = normal (shear) component of displacement o-(e ) = true tensile stress (nominal tensile strain) t(7) = true shear stress (true engineering shear strain) p(A) = external pressure (dilatation) v = Poisson s ratio = Young s modulus G = shear modulus K = bulk modulus. 

Fig. 12.26 True tensile stress-Hencky strain curves for resins C and E at Hencky strain rate of 20 s-1 and temperature of 170°C. [Reprinted by permission from E. G. Muliawan, S. G. Hatzikiriakos, and M. Sentmanat, Melt Fracture of Linear Polyethylene, Int. Polym. Process., 20, 60 (2005).]...

In the equations above a is the true tensile stress, i.e. F/A. In practice in general use is made of engineering stress, which is equal to F/Aa, where F is the tensile load and A and A0 are the cross-sectional surface areas of the sample in the deformed and non-deformed state, respectively. Because the Poisson constant Vi for rubbers A = A0/A, so that the equations for the tensile stress become ... 

In these experiments, the tensile force is measured as a function of time, so that at a constant rate of deformation e it is possible to calculate the true tensile stress and the extensional viscosity r/c elastic properties of the deformation can be determined by measuring the elastic strain e. 

True Tensile Stress-Strain. As indicated above, analysis of high speed motion pictures of material deformation during tensile testing provides a measure of maximum strain change in cross-sectional area and... 

When a material is subjected to small deformations, the cross-sectional area of the unstrained sample, Aq, coincides with the cross-sectional area of the strained sample, A. However, in the case of elastomers, in which the deformations can be extremely high, account has to be taken of the change in the cross section of the sample. Consequently, the value of the stress a, calculated by using Eq. (3,33) and called nominal stress, does not coincide with the true tensile stress (A (Fig. 3.10). 

If an elastomer sample in the form of a unit cube is deformed by pure shear, then the three principal extension ratios are A, = X, = 1, X = MX. [Compare with the case of simple extension where X = X = 1 NX.] Following the arguments of Section B, derive an expression relating aE and A, where [Pg.208]

Let the true tensile stress on a sample of initial cross-sectional area and initial length /q be a. If the length and area are / and A, respectively, when the strain is e, then for constant volume... 

The velocity gradient dt /dz may be identified with the true strain rate deydt (eqn 7.8), which in turn may be found fix>m the elongational viscosity A and the true tensile stress (Ti acting on the melt The stress is given by... 

It is instructive to plot the true tensile stress at any elongation rather than the nominal stress This is given by a = P/A, where A is the actual cross-section at any time. We now assume, as is usual for plastic deformation, that the deformation takes place at constant volume. Then Al = A lo, and if we put // /o = A, where X is the extension ratio. 

Figure 4. Conversion of load strain data to the true tensile stress strain curves to failure for PSZT four point bend specimens at 23, 75, 86, 100 and 120°C.

Figure 5. True tensile stress strain curves to failure of two different strain gauged PSZT four point bend specimens at (a) 23, (b) 75, (c) 86, (d) 100 and (e) 120°C.

Figure 7. True tensile stress strain behavior (strain gauge technique) of unpoled and poled depoled PSZT at room temperature.

FIG. 19 True tensile stress-strain curves for HDPE at various pressures, kg cm curve 1,1 curve 2, 1000 curve 3, 2000. (From Ref. 34.)... 

Figure 3.13 True tensile stress—strain curves for HDPE (solid lines) and LDPE (dashed lines) at various pressures. 1 1 kg/cm 2 1000 kg/cm 3 2000 kg/cm [23]...

Plastic flow in crystals occurs by dislocations moving on slip planes that slide over one another. Most experiments with single crystals to determine the CRSS are performed with tensile specimens. The shear stress on the active slip plane is computed by resolving the tensile stress onto the active slip plane. With polycrystalline tensile specimens, plastic flow still occurs on slip planes in the individual grains and these are grouped into wide shear bands that traverse the specimen at 45° from the tensile axis. The shear stress is usually calculated approximately for the whole specimen by dividing the tensile stress in half. Failure of a ductile tensile specimen usually occurs by initiation of a shear crack that is followed by a mode I crack that is normal to the tensile axis. Sudden flnal failure occurs when the true tensile stress exceeds the mode I fracture stress. 

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