Nominal stress Subject

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). 

Ultimate strength n. The maximum nominal stress a material can withstand when subjected to an applied tensile, compressive, or shear load. If the mode of loading is not specified, it is assumed to be tensile. In materials that exhibit a definite yield strength, ultimate strength will usually mean the nominal stress at break, which can be less than the maximum. Shah V (1998) Handbook of plastics testing technology. John Wiley and Sons, New York. 

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).

In what follows, nominal stress is defined as the load on the sample, registered in tension, divided by the initial cross-sectional area of the sample. True stress is the load divided by the actual cross-section of the sample as it narrows under extension. When a sample is subjected to a tensile force or load at a constant rate of strain, the stress measured as a function of strain can show certain unusual features (Figure 9.1). 

The nominal stress, denoted by Sy, carries the same information provided by the Cauehy stress in terms of current equilibrium but taking area elements of the undeformed configuration. To clarify the concept, let us consider a rubber band pulled uniaxially (Fig. 1). The current cross-section has the area a b and is subjected to the uniform stress whereas in the natural configuration fire cross-section area is ao bo- The only nonvanishing component of fire nominal stress is such that Uq... 

For a single circular opening in a flat plate with infinite boundaries in two directions (not ffirough the thickness) that is subjected to applied forces and stresses along opposite edges of the plate, stresses are increased above the nominal applied stress in the unperforated plate. The stresses decrease away from the opening until the nominal stress in the plate is obtained. The ratio of the stress at the examined point divided by the nominal stress is the stress intensity factor. 

Vertical in-line pumps that are supported only by the attached piping may be subjected to component piping loads that are more than double the values shown in Table 2. lA (2. IB) if these loads do not cause a principal stress greater than 41 MPa (5950 psi) in either nozzle. For calculation purposes, the section properties of the pump nozzles shall be based on Schedule 40 pipe whose nominal size is equal to that of the appropriate pump nozzle. Equations F-6A (F-6B), F-7A (F-7B), and F-8A (F-8B) can be used to evaluate principal stress, longitudinal stress, and shear stress, respectively, in the nozzles. 

Apply the calculated force to give the desired nominal surface stress. Allow the force to act for 5 min to compensate partially for the creep exhibited at room temperature when subjected to the specified nominal simface stress. Set the reading of the deflection measuring instrument to zero. Apply the desired load to obtain the desired maximum fiber stress of0.455 or 1.82 MPa to the specimen. Five minutes after applying load, adjust the deflection measming device to zero/starting position. 

Stress-strain responses of UV and UC conditioned GFRP samples are shown in Fig. 21.14 and Tables 21.4 and 21.5. 2 wt% samples subjected to UV and UC conditioning for 15 days showed similar results, with increases for UV of 10% in strength and 10% in modulus, and for UC of 19.8% in strength and 6.25% in modulus, over their neat counterparts similarly conditioned (Table 21.4). However, 1 wt% samples showed a nominal increase in these properties in comparison to neat samples similarly conditioned. 

When an instantaneous strain is applied to an ideal elastic solid a frnite and constant stress will be recorded. For a linear viscoelastic solid subjected to a nominally instantaneous strain the initial stress will be proportional to the applied strain and will decrease with time (Figure 4.4), at a rate characterized by the relaxation time r. This behaviour is called stress relaxation. For amorphous linear polymers at high temperatures the stress may eventually decay to zero. In the following discussion we shall ignore transient behaviour. 

Because the specimen is loaded by the inertia bar, the specimen is subjected to tensile as well as torsional stresses, which perturb the nominally firee vibrations. For more precise work the specimen can be mounted as in Figure 5.7, with the inertia bar clamped at its upper end. The assembly is then suspended by an elastic wire or ribbon, which has a negligible effect on damping. 

The formation of a through-the-thickness crack in a film subjected to a residual or applied tensile stress relieves that stress in the film material at points adjacent to the crack path. At points in the film at some distance from the crack path, the stress remains unrelaxed due to the constraint of the substrate. Consequently, a long crack that is parallel to the first formed crack can also form. Indeed, an array of parallel cracks over the entire film surface is likely, and the point of the discussion in this section is to provide an estimate of the dependence of the spacing between cracks in such an array on the film thickness hf and the mismatch stress a. The discussion is limited to the case when the equi-biaxial mismatch stress is uniform throughout the film, the elastic properties of the film and substrate are nominally the same, and hg/hf is sufficiently large so that the behavior is insensitive to the substrate thickness hg. Furthermore, it is assumed that the cracks grow through the thickness of the film to the depth hj, but that they do not penetrate into the substrate. There is no fundamental barrier to relaxation of these limitations, but the relatively simple system is sufficiently rich in physical detail to reveal the principal features of behavior. 

An isotropic elastic solid with a nominally flat, traction-free surface is subjected to an initial equilibrium stress field. Suppose that the shape of the free surface S in the undeformed reference configuration of the material is not actually a plane, but that it is slightly wavy. The nominally flat surface coincides with the plane y = 0 and the position of the actual surface varies with respect to y = 0 in the x—direction. At time t, the position of the surface at coordinate x is given hy y = h x,t). For the discussion in this section, it is assumed that the slope of the surface is small everywhere, that is, h,x boundary condition which must be enforced on the wavy surface is that the traction is zero. 

---