Nominal cross-section stress

The term fracture toughness or toughness with a symbol, R or Gc, used throughout this chapter refers to the work dissipated in creating new fracture surfaces of a unit nominal cross-sectional area, or the critical potential energy release rate, of a composite specimen with a unit kJ/m. Fracture toughness is also often measured in terms of the critical stress intensity factor, with a unit MPay/m, based on linear elastic fracture mechanics (LEFM) principle. The various micro-failure mechanisms that make up the total specific work of fracture or fracture toughness are discussed in this section. 

The nominal or macroscopic stress on the section (here, uniaxial) is o = P/BW, where P is the load applied to the component, and B and W are shown in Fig. 7.98. In the limit of distances sufficiently removed from a notch or crack to no longer be influenced by it, a is the uniform cross-section stress in the material. However, in the vicinity of the... 

Fig. 45. Stress-strain relation for an amorphous Fe75Si oBis ribbon as shown in Figs, i 1 and 13. Nominal cross-section 16 p.m x 150 p.m. The arrow at 3.2 GPa and 2.5% strain indicates rupture.

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. ... 

The most convenient measure of the stress exhibited by an elongated elastomeric network is the nominal or engineering stress f = f/A, where f is the equilibrium value of the force and A is the cross-sectional area of the undeformed sample. 

Note The term engineering or nominal stress is often used in circumstances when the deformation of the body is not infinitesimal and its cross-sectional area changes. 

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 ... 

Nominal tensile stress, force/initial cross sectional area. 

It is usual in rubber testing to calculate tensile stresses, including that at break, on the initial cross-sectional area of the test piece. Strictly, the stress should be the force per unit area of the actual deformed section but this is rather more difficult to calculate and in any case, it is the force that a given piece of rubber will withstand which is of interest. The stress calculated on initial cross-section is sometimes called nominal stress. ... 

From the dynamic mechanical investigations we have derived a discontinuous jump of G and G" at the phase transformation isotropic to l.c. Additional information about the mechanical properties of the elastomers can be obtained by measurements of the retractive force of a strained sample. In Fig. 40 the retractive force divided by the cross-sectional area of the unstrained sample at the corresponding temperature, a° is measured at constant length of the sample as function of temperature. In the upper temperature range, T > T0 (Tc is indicated by the dashed line), the typical behavior of rubbers is observed, where the (nominal) stress depends linearly on temperature. Because of the small elongation of the sample, however, a decrease of ct° with increasing temperature is observed for X < 1.1. This indicates that the thermal expansion of the material predominates the retractive force due to entropy elasticity. Fork = 1.1 the nominal stress o° is independent on T, which is the so-called thermoelastic inversion point. In contrast to this normal behavior of the l.c. elastomer... 

After the strain-hardening phenomenon occurs. Usually the curves use nominal stress, cross section), and nominal strain, en = dL/L0. 

From Eq. (41) the nominal stress aR>[1 that relates the force F in spatial direction p to the initial cross section A0i(X is found by differentiation, For uniaxial extensions of unfilled rubbers (X=l) with X =X, X1=X-i=X 1/2 the following relation can be derived ... 

The true stress is the load divided by the instantaneous cross-sectional area of the sample, whereas engineers often use the nominal stress, which is the load divided by the initial (undeformed) cross-sectional area of the sample ... 

The distinction between elastomers, fibers, and plastics is most easily made in terms of the characteristics of tensile stress-strain curves of representative samples. The parameters of such curves are nominal stress (force on Ihe specimen divided by the original cross-sectional area), the corresponding nominal strain (increase in length divided by original length), and the modulus (slope of the stress-strain curve). We refer below to the initial modulus, which is this slope near zero strain. 

Figure 1-2 records some typical stress-strain curves for different polymer types. Some polymers exhibit a yield maximum in the nominal stress, as shown in part (c) of this figure. At stresses lower than the yield value, the sample deforms homogeneously. It begins to neck down at the yield stress, however, as sketched in Fig. 11-20. The necked region in some polymers stabilizes at a particular reduced diameter, and deformation continues at a more or less constant nominal stress until the neck has propagated across the whole gauge length. The cross-section of the necking portion of the specimen decreases with increasing extension, so the true stress may be increasing while the total force and the nominal stress...

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). 

The applied nominal stress, i.e. the load divided by the remote unnotched cross-section of 40 mm, is 0.65 - 7 MPa. Measurements are performed in air, demineralised water and phosphoric acid solution (pH=1.6). All tests are performed at... 

In terms of per-unit cross-sectional area of unswollen sample, unstretched sample, the nominal stress om is 20... 

The simplest model is the statistical theory of rubber-like elasticity, also called the affine model or neo-Hookean in the solids mechanics community. It predicts the nonlinear behavior at high strains of a rubber in uniaxial extension with Fq. (1), where ctn is the nominal stress defined as F/Aq, with F the tensile force and Aq the initial cross-section of the adhesive layer, A is the extension ratio, and G is the shear modulus. 

It is usual in rubber testing to calculate tensile stresses, including those at break, on the initial cross-sectional area of the test piece, and these stresses are sometimes called nominal stresses. 

For practical purposes, it is often adequate to ignore the continuous change in cross-sectional area that occurs when a force is applied. The stress so defined is called the engineering (or nominal) stress, a ... 

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