Stress extension

Another commercial development of the 1970s is the appHcation of superplasticity which is exhibited by a number of zinc alloys (135—138). Under the right conditions, the material becomes exceptionally soft and ductile and, under low stresses, extensions exceeding 1000% can be obtained without fracture. The grain size must be extremely small (about 1 micrometer) and stable. This grain size is less than one tenth that of common metals in the wrought condition. 

Fig. 8.94 Nominal stress-extension curves for mild steel in oil giving ductile failure, and in 4n NaN03 producing stress-corrosion failure, at the same test temperature (104°C)...

In any medium, cavities, voids, and density fluctuations exist. It is believed that these induce cavitation, leading to molecular rupture. In solid polymers, the microvoids present intrinsically are responsible for cavitation when they are subjected to a hydrostatic pressure in the manner of an impulse. One of the main causes of microvoid generation in polymer materials is the interatomic bond rupture when they are subjected to mechanical and thermal stresses. Extensive studies showing microvoid formation in stressed polymers have been carried out (Zhurkov et al., 1972). 

In a plot of (T, against A (Figure 53) yield will occur according to eqn 5.7 at point M that is to say the engineering stress-strain curve will show a maximum only if a tangent can be drawn from A => 0 to touch the true stress-extension ratio curve at a point such as M. 

Fig. 4. Strain-energy density is given by the area under a stress-extension ratio curve...

Symbols Amax, Mmax, ALmax, A( max maximum actuator force, torque, stroke, and angle respectively <7adm, Tadm, Sadm, 7adm admissible tensile stress, shear stress, extension, and shear respectively D SM wire diameter L SM wire length Dm -coil diameter if. number of turns b, h width and thickness of SM flat wires or bars. 

The fundamental experiment on weak mechanical perturbations can be presented as follows. Starting with a fluid at rest, we tpply at all times (t > 0) a small perturbative stress a- (the detailed specification of this stress—extension, or transverse shear—is not essential for our discussion). We now look at the strain e(t) induced by this step increase in stress. For small O , the strain is a linear function of the stress... 

Fig. 13.28. Stress-extension curve for a sample of natural rubber compared with the ideal rubber prediction [Eq. (35)] (Reprinted from Paul J. Flory, Principles of Polymer...

Fig. 14.4. Experimental stress-extension ratio curve for natural rubber along with a best fit of the predicted behavior for network described by the inverse Langevin function, and of Gaussian network [Eq. (28)] with the same network parameters (after Ref 7).

Fig. 8.1. Load (azz nominal tensile stress)-extension (A extension ratio) curve of a sample of PE (M = 3.6 10 , drawing velocity dX/dt = 2.4 lO s ). The changes in the shape of the sample are schematically indicated...

In order to understand better how this selection mechanism works we need a knowledge of elementary stress-extension curves, for example those which are measured for constant Hencky strain rates. If flow sets in locally and there the radius b of the sample begins to decrease, the extension A of the volume element at the centerline is given by... 

Fig. 8.7. Stress-extension curves measured for a sample of PE (M = 3.6 -10 ) at the indicated Hencky strain rates. Constant strain rates were realized by a registration of the strain at the location of a developing neck and a continuous readjustment of the applied tensile force, using an electronically controlled feedback circle. The broken line gives the cT22 (A)-curve measured for a poly(ethylene-co-vinylacetate)(27% vac-units, (j)c = 0.30). No strain rate dependence is observed for this rubbery material [85]...

Fig. 8.10. A-dependence of the retracting force f left, broken line) and the free energy right) of an elastic fiber with a sigmoidal stress-extension relation

Alftey includes a synopsis of the work of Hory on the formation of gels by polycondensation reactions [23]. He also recapitulates the discussion of Guth and James [24] on the explanation of the observed stress-extension curve. 

Between Aa and Ab, there exists a gap in the sequence of accessible states of deformation, which is a consequence of the non-linearity of the stress-extension curve. 

Figure 5 Typical stress-extension curve of a cross-linked rubber. Stress is defined as the force per unit cross-sectional area of the undeformed sample. Extension s is the ratio of the increase in length to the original length...

Figure 3. Stress-extension ratio curves (tensile behavior) for solution cast samples before and after annealing.

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