Stress remaining

This is demonstrated graphieally in Figure 4.27 whieh shows the loading stress remains less than some given value of allowable strength (Haugen, 1968 Rao, 1992). The probability of a strength in an interval dSi is ... 

The shear stress, t, due to the assembly torque diminishes to zero with time, the preload, F, remaining constant, and so the stress on the solenoid section is only the direct stress,. v, as given in equation 4.75 (see Figure 4.41(b)) (Edwards and McKee, 1991). A second reliability can then be determined by considering the requirement that the pre-load stress remains above a minimum level to avoid loosening in service (0.5 S/)min from experiment) (Marbacher, 1999). The reliability, R, can then be determined from the probabilistic requirement, P, to avoid loosening ... 

Example 2.15 In the previous Example, what would be the strain after 125 seconds if (a) the stress remained constant at 10 MN/m after 100 seconds and (b) the stress was reduced to zero after 100 seconds. 

The implications of a significant role for strain rate are wider than the obvious one that stress corrosion should only occur over a restricted range of strain rates. Thus, in constant load tests, since cracks will continue to propagate only if their rate of advancement is sufficient to maintain the crack-tip strain rate above the minimum rate for cracking, it is to be expected that cracks will sometimes stop propagating, particularly below the threshold stress. Such non-propagating cracks are indeed observed below the thres-hold . Moreover, in constant-load or constant-strain tests, the strain rate diminishes with time after loading, by creep exhaustion if the stress remains sensibly constant, and it is found that the stress-corrosion results are sensitive to the relative times at which the stress and electrochemical... 

In essence, it follows from Fig. 7 that the viscosity of a dispersion medium does not affect yield stress, since with the variation in temperature (as in Fig. 7), the viscosity of a polymer melt changes by a hundred times, while yield stress remains unchanged. 

MPa. At the stress maximum or in the region where the stresses remain nearly constant a strong delamination occurred, which probably reduces the interlaminar shear strength dramatically. Therefore the high strain-values cannot really be used for design. 

The strength and extensibility of a noncrystallizable elastomer depend on its viscoelastic properties (28,29), even when the stress remains in equilibrium with the strain until macroscopic fracture occurs. In theory, such elastomers have a time- or rate-independent strength and ultimate elongation, but such threshold quantities apparently have not been measured, though rough estimates have been made (28,30). 

Data are presented which illustrate that the tensile strength and elongation-at-break depend significantly on the extension rate even when the stress remains in equilibrium with the strain prior to fracture. A crude estimate was made of the threshold (lowest possible) values of the true stress-at-break and the elongation-at-break for the TIPA elastomer. The estimated quantities are about 26% less than those found at an extension rate of about 0.01 min-1 at 30°C. 

Experiment III. The sample was stressed (2300 p.s.i.g.) and allowed to creep for 10 minutes, at which time the beam was turned on for 5.5 minutes. The beam was then turned off while the stress remained on. Deflection measurements continued for 2 minutes after the beam was turned off. This run was a typical creep measurement before, during, and after irradiation (Figure 6, III). 

With the aid of the two-color Laser-Doppler-Anemometry (LDA), Bewersdorff was able to measure the axial and the radial turbulence intensities simultaneously and also the Reynolds shear stresses. The injection of polymer results in a damping of both intensities in the region of their maxima. In his Reynolds shear stress measurements he showed that the polymer injection results in a drastic damping, and the stress maximum is shifted towards the center of the pipe. In a homogeneous polymer solution the maximum of the Reynolds shear stress remains in the same position-as for water. Only in the region of the buffer zone are the shear stresses reduced. 

When a typical elastic solid is stressed, it immediately deforms by an amount proportional to the applied stress and maintains a constant deformation as long as the stress remains constant - i.e. it obeys Hooke s law. On removal of the stress, the elastic energy stored in the solid is released and the solid immediately recovers its original shape. Newtonian liquids, on the other hand, deform at a rate proportional to the applied stress and show no recovery when the stress is removed, the energy involved having been dissipated as heat in overcoming the internal frictional resistance. 

When a stress is applied to a cross-linked rabber it reaches a state of equilibrium almost immediately with the stress remaining constant for an indefinite time in a sample maintained at constant strain. Once at equilibrium the properties of the rubber can be described by thermodynamics. The elastomeric force, /, the force developed on stretching an elastomeric material, has two components, an entropic component f, and an internal energy component,/, with... 

This ability of solid foams to undergo considerable deformation while the stress remains low makes them ideal for cushioning sensitive items to protect them against mechanical damage. The presence of air bubbles also makes them excellent thermal insulators. This characteristic also influences the processing of cellular foods where heat transfer plays an important role. 

The threshold is even more visible on this representation, as when the strong slip starts, the shear rate experienced by the polymer is no longer proportional to Vt. In fact, at the onset of strong slip, the shear stress remains locked, while the velocity at the wall strongly increases. 

In the stratified-flow regime, the shear stress remains constant, equal to the value (Tmax> in both zones. Thus, the shear stress measured in such a flow should be independent of... 

Stress relaxation between manufacture and testing. Between manufacturing and testing, relaxation of the residual stress will occur as a result of the viscoelastic properties of the matrix, which controls the behaviour of the 90° layer. Measurements to determine the relaxation of the ply-to-ply residual stress of the carbon-polyetherimide lay-up, with the highest level of residual stresses of the laminates tested ([904c/04c]s), have been presented previously [5]. It shows that the level of residual stress follows a power law with time. For the purpose of this study, it was chosen to perform the bending experiments 240 hours after fabrication, as the level of residual stress remains more or less constant. The level of residual stress as calculated in (1) is then altered by a reduction factor,/,. The relaxed residual stress. 

Thus, the fraction of stress remaining at the end of the equilibration period (t is (from Eq. 96) ... 

Equation [2.3.2] describes the momentum balance in such a liquid. Under the imposed restriction all terms in [2.3.1] except the diagonal ones vanish, i.e. only the normal stresses remain. Hence, what is left is... 

Consider imposing a step strain of magnitude 7 at time t = 0 (see Fig. 7.20). If the material between the plates is a perfectly elastic solid, the stress will jump up to its equilibrium value Gj given by Hooke s law [Eq. (7.98)] and stay there as long as the strain is applied. On the other hand, if the material is a Newtonian liquid, the transient stress response from the jump in strain will be a spike that instantaneously decays to zero. For viscoelastic materials, the stress after such a step strain can have some general time dependence a(t). The stress relaxation modulus G(t) is defined as the ratio of the stress remaining at time t (after a step strain was applied at time t = 0) and the magnitude of this step strain 7 ... 

This equation simply states that, for linear response, the stress resulting from each step is independent of all the other steps. The system remembers the deformations that were imposed on it earlier, and continues to relax from each earlier deformation as new ones are applied. The stress relaxation modulus tells how much stress remains at time t from each past deformation 7, through the elapsed time t — ti that has passed since that deformation was applied at time t,-. 

---