Tensile strains

Several functions are used to characterize tire response of a material to an applied strain or stress [4T]. The tensile relaxation modulus E(t) describes tire response to tire application of a constant tensile strain l/e -. 

Elastic behavior is commonly quantified by the Young s modulus E, the proportionality constant between the appHed tensile stress O, and the tensile strain (A length/original length). 

The parameter is a crack propagation velocity and n(e) is a crack activation law driven by the bulk tensile strain e and specified by the Weibull fracture theory... 

The kind of stress that we called a tensile stress induces a tensile strain. If the stressed cube of side /, shown in Fig. 3.3(a) extends by an amount u parallel to the tensile stress, the nominal tensile strain is... 

When it strains in this way, the cube usually gets thinner. The amount by which it shrinks inwards is described by Poisson s ratio, v, which is the negative of the ratio of the inward strain to the original tensile strain ... 

We can now define the elastic moduli. They are defined through Hooke s Law, which is merely a description of the experimental observation that, when strams are small, the strain is very nearly proportional to the stress that is, they are linear-elastic. The nominal tensile strain, for example, is proportional to the tensile stress for simple tension... 

One final point. We earlier defined Poisson s ratio as the negative of the lateral shrinkage strain to the tensile strain. This quantity, Poisson s ratio, is also an elastic constant, so we have four elastic constants E, G, K and v. In a moment when we give data for the elastic constants we list data only for . For many materials it is useful to know that... 

We now turn to the other end of the stress-strain curve and explain why, in tensile straining, materials eventually start to neck, a name for plastic instability. It means that flow becomes localised across one section of the specimen or component, as shown in Fig. 11.5, and (if straining continues) the material fractures there. Plasticine necks readily chewing gum is very resistant to necking. 

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. 

If, on the other hand, the channel section changes then tensile stresses will also be set up in the fluid and it is often necessary to determine the tensile viscosity, k, for use in flow calculations. If the tensile stress is a and the tensile strain rate is s then... 

To add to this picture it should be realised that so far only the viscous component of behaviour has been referred to. Since plastics are viscoelastic there will also be an elastic component which will influence the behaviour of the fluid. This means that there will be a shear modulus, G, and, if the channel section is not uniform, a tensile modulus, , to consider. If yr and er are the recoverable shear and tensile strains respectively then... 

Consider the annular element of fluid shown in Fig. 5.12. The true tensile strain Sr in this element is given by... 

That is, the total strain will be the sum of the tensile strain due to and the negative strain due to the Poisson s ratio effect caused by Oy. 

Thermal treatment and the nature of the casting solvent can also affect the deformation modes achieved in strained films of ionomers. For example, in films cast from polar dimethylformamide (DMF), the solvent interacts with ion-rich clusters and essentially destroys them, as is evident form absence of a second, higher temperature loss peak in such samples. As a result, even in a cast DMF sample of Na-SPS ionomer of high ion content (8.5 mol%), the only deformation mode observed in tensile straining is crazing. However, when these films are given an additional heat treatment (41 h at 210°C), shear... 

As one example, in thin films of Na or K salts of PS-based ionomers cast from a nonpolar solvent, THF, shear deformation is only present when the ion content is near to or above the critical ion content of about 6 mol% and the TEM scan of Fig. 3, for a sample of 8.2 mol% demonstrates this but, for a THF-cast sample of a divalent Ca-salt of an SPS ionomer, having only an ion content of 4.1 mol%, both shear deformation zones and crazes are developed upon tensile straining in contrast to only crazing for the monovalent K-salt. This is evident from the TEM scans of Fig. 5. For the Ca-salt, one sees both an unfibrillated shear deformation zone, and, within this zone, a typical fibrillated craze. The Ca-salt also develops a much more extended rubbery plateau region than Na or K salts in storage modulus versus temperature curves and this is another indication that a stronger and more stable ionic network is present when divalent ions replace monovalent ones. Still another indication that the presence of divalent counterions can enhance mechanical properties comes from... 

Fig. 4-2(k) Example of longitudinal tensile strain with harnessed elbows. 

The PGS obtained by Wang and coworkers was a kind of thermoset elastomer with the Young s modulus of 0.282 0.025 MPa, a tensile strain of at least 267 zE 59.4%, and a tensUe strength was at least 0.5 MPa. The mechanical properties of PGS were well consisted with that of some common soft tissues. Although PGS is a thermoset polymer, its prepolymer can be processed into various shapes by solving it in common organic solvents such as 1,3-dioxolane, tetrahydrofuran, isopropanol, ethanol, and iV,M-dimethylformamide. Porous scaffolds can be fabricated by salt leaching. 

Figure 18.1 is the typical stress-strain curves of the filled rubber (SBR filled with fine carbon black, HAF),

Pseudomorphic Pt monolayers on Ru(0001) interact very weakly with H pd, OHad, or Oad, because of electronic ligand (vertical ligand effects) and strain effects (tensile strain), in agreement with results obtained under UHV conditions and in DPT calculations. Therefore, base CVs on these surfaces do not show pronounced voltammettic features. 

The impact of settlement is a major concern in the design of the SWCR system. A number of facilities have settled 6 ft in a single year, and 40 ft or more over a period of years.5 The Meadowlands site in New Jersey, for example, was built at a height of 95 ft, settled to 40 ft, and then was rebuilt to 135 ft. Uniform settlement can actually be beneficial by compressing the length of the FMC and reducing tensile strains. However, if waste does not settle uniformly, it can be caused by interior berms that separate waste cells. 

Figure 6.2 Rectangular sample undergoing tensile strain... 

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