Equilibrium tensile moduli

Values of stress and strain obtained from Figure 1 and from similar plots of data obtained on the other elastomers yield the plots of Xo vs. (X — 1) in Figure 2, where Xo is the true stress, i.e., the force per unit cross-sectional area of the deformed specimen. The data at strains up to 1.0 (100% elongation) give straight lines whose slopes equal the equilibrium tensile moduli, E values of 1 /3 are given in Table I. 

VI. To illustrate a lightly cross-linked amorphous polymer lightly vulcanized Hevea rubber, vulcanized with sulfur and an accelerator to an equilibrium tensile modulus Ee of about 7X10 dynes/cm. Dynamic data, in simple extension, of Cunningham and Ivey and Payne, together with creep data in simple extension of Martin, Roth, and Stiehler, were employed, all reduced to a reference temperature of 25 C. Certain minor adjustments in the data are described elsewhere. ... 

The equilibrium shear modulus of two similar polyurethane elastomers is shown to depend on both the concentration of elastically active chains, vc, and topological interactions between such chains (trapped entanglements). The elastomers were carefully prepared in different ways from the same amounts of toluene-2,4-diisocyanate, a polypropylene oxide) (PPO) triol, a dihydroxy-terminated PPO, and a monohydroxy PPO in small amount. Provided the network junctions do not fluctuate significantly, the modulus of both elastomers can be expressed as c( 1 + ve/vc)RT, the average value of vth>c being 0.61. The quantity vc equals TeG ax/RT, where TeG ax is the contribution of the topological interactions to the modulus. Both vc and Te were calculated from the sol fraction and the initial formulation. Discussed briefly is the dependence of the ultimate tensile properties on extension rate. 

Figure 22 is a plot of the initial tensile modulus of the epoxy matrix after equilibrium moisture exposure and dehydration. At both 20 °C and 70 °C, the effect of moisture absorption on the matrix is reversible as evidenced by the reattainment of dry properties. The exposure at 125 °C is not completely reversible as shown by the data. 

Fig. 3 Variation of equilibrium cluster diameter dQ i ith EH, cation form and water content, where EQ=275 joule-cm is the tensile modulus of a dry, 1200 EH sulfonate ionomer, A=0.667 is a constant and dQ is obtained from SAXS and water sorption data. The solid line is a least square fit of Eq. 1 to the EH and cation form data.

UHMW PE fibers grown by the surface growth technique above the thermodynamic equilibrium tenperature obtained a tensile modulus of 133 GPa and a breaking stress as high as 5.04 GPa at a breaking strain of 3.1 %, showing good physical properties. 

Special specimen preparation as with tensile testing. However, the extraction of intrinsic mechanical parameters from creep indentation data is analytically complex [3, 4]. Confined compression or unconfined compression tests require preparation of cylindrical cored specimens of tissue and underlying bone. With unconfined compression, the free draining tissue edges and low aspect ratio, layered nature of the test specimen may introduce error. Compression of a laterally confined specimen by a porous plunger produces uniaxial deformation and fluid flow. Confined compression creep data has been analyzed to yield an aggregate equilibrium compressive modulus and permeability coefficient [5] and uniaxial creep compliance [6]. 

Apart from the filler, the stiffening effect can also arise from the rubber network itself such as the crosslink concentration, as shown in Figure 3.9. The results shown here are based on compound formulations given in Table 3.4. The tensile modulus MlOO increased linearly with increasing crosslink concentration of the rubber network. The crosslink concentration was calculated by the Flory-Rehner equilibrium swelling equation ... 

Dufresne et al. (2000) reported a 350 % increase in tensile modulus of MFC/ starch nanocomposites at 50 wt% cellulose content compared to neat starch. However, at high humidity levels (75 % RH), the reinforcing effect was clearly diminished. This was attributed to the hydrophilic nature of both the starch and the cellulose, which resulted in the plasticization of starch and weakening of cellulose/ starch interfacial adhesion. On the other hand, the addition of cellulose to starch resulted in a decrease of both water uptake at equilibrium and the water diffusion coefficient. 

Figure 9.3 Tensile modulus of the resin tensile strength of GRP laminates as a function of water uptake after periods of immersion at various temperatures between 30°C and 100°C up to the onset of equilibrium absorption (Pritchard and Speake).

The indicated equilibrium compliance of 10 7 1 cm /djme corresponds to an equilibrium shear modulus of 12 x 10 dynes/cm, close to but considerably higher than that found. This may reflect an unexpected difficulty in preparing reproducible samples or it may reflect a different sample histoiy. The tensile specimens were tested shortly after preparation while the dynamic mechanical properties were measured some l8 months after preparation. 

Fig. 3. Stoichiometric DGEBA/DDS network M, versus prepolymer resin molecular weight. M . (M, calculated from equilibrium rubbery moduli at T = T, -h 45 K). O M, from equihbrium tensile experiments M, from 0.16 hz dynamic mechanical storage modulus measurements (After LeMay >)...

Storage modulus measurements. All measurements were taken at temperatures near 45 °C above the network Tg s. Representative network true stress versus strain curves from the tensile experiments are shown in Fig. 2. The ordinate axis, true stress, is normalized by 3eRT to account for the different test temperatures employed. The resultant curves are thereby directly comparable for structural differences, since the instantaneous slopes are proportional to l/M, after Eq. (2). The curves of all five networks are linear and reversible up to strains of around 10 percent. The reversibility suggests that the measurements were performed under near-equilibrium conditions and that the networks were stable at the high test temperatures employed. 

Early experiments with elastomers showed that the relaxation toward equilibrium was sharply dependent on crosslink density. It was found that tightly crosslinked networks relaxed very quickly, whereas networks with low crosslink density exhibited relaxation that covered an extremely broad time scale. These early experiments were correlated in terms of the expression for the tensile relaxation modulus E(t) ... 

Because of the time dependence of polymer properties, it is important that the time scale used in our standard tests corresponds exactly with that of the moment loading. That is, if the moment is to be a sustained load, then the tensile test should also be at very long loading, for example, in the equilibrium modulus region. 

PE/CSR 20°C Nr e-, 50-200 TGM-3 Tensile strength, elongation at break, equilibrium modulus, rigidity, density, gel fraction, degree of swelling, flexing resistance, aging 41... 

---