Uniaxial extension Subject

Elliott and co-workers performed a detailed SAXS investigation of the morphology of Nafion membranes that were subjected to uniaxial and biaxial deformation. For as-received membranes, manufactured by Du Pont using an extrusion process, the cluster reflection was shown to exhibit a limited degree of arching in the direction perpendicular to the machine direction. Upon uniaxial extension, this arching was observed to increase in a manner consistent with previous studies. This arching was rationalized on... 

Calculate the variation in entropy corresponding to a polydimethylsiloxane network of mass 6.89 g, with an average molecular weight between crosslinks Me = 8.3 X 10, subjected to a reversible uniaxial extension at 25°C until the length is double its initial length. 

From equation (1), It can be seen that If the bar at time x=0 is subjected to a single step in strain, p(t), then the stress necessary to keep the bar stretched at time t is equal to H(p(t), t), where H(l,t) 0. From data obtained from single step stress-relaxation experiments carried out at different levels of strain. It is evident that one can determine the stress response for any other strain history in uniaxial extension. However, since equation (1) is nonlinear, one cannot determine the strain as a function of the stress, as for example In a creep experiment. Equation (1) applies to the type of experiment where, knowing the strain history, one can determine the stress response and the calculated values can then be compared with experimentally determined quantities. 

In the field of rubber elasticity both experimentalists and theoreticians have mainly concentrated on the equilibrium stress-strain relation of these materials, i e on the stress as a function of strain at infinite time after the imposition of the strain > This approach is obviously impossible for polymer melts Another complication which has thwarted the comparison of stress-strain relations for networks and melts is that cross-linked networks can be stretched uniaxially more easily, because of their high elasticity, than polymer melts On the other hand, polymer melts can be subjected to large shear strains and networks cannot because of slippage at the shearing surface at relatively low strains These seem to be the main reasons why up to some time ago no experimental results were available to compare the nonlinear viscoelastic behaviour of these two types of material Yet, in the last decade, apparatuses have been built to measure the simple extension properties of polymer melts >. It has thus become possible to compare the stress-strain relation at large uniaxial extension of cross-linked rubbers and polymer melts ... 

Still another related effect can be observed when a quenched glassy polymer is subjected to varying mechanical history by successive stress relaxation experiments in uniaxial extension. The relaxation times of poly(methyl methacrylate) appear to increasp with this progressive stress history more rapidly than with the lapse of... 

A block of material subject to three different motions (a) uniaxial extension in the Xi direction, (b) simple shear in the X] direction, and (c) solid body rotation about the X3 axis with no change in Ax,. ... 

Fig. 4.20 Covalent and noncovalent contribution to the stress tu — /22 in a randomly oriented melt subject to a uniaxial extension of A = 2 as a function of density. (From Refs 182, 239).

Figure 10 Sketch of a sample subjected to (a) uniaxial extension and (b) simple shear...

For a component subjected to a uniaxial force, the engineering stress, a, in the material is the applied force (tensile or compressive) divided by the original cross-sectional area. The engineering strain, e, in the material is the extension (or reduction in length) divided by the original length. In a perfectly elastic (Hookean) material the stress, a, is directly proportional to be strain, e, and the relationship may be written, for uniaxial stress and strain, as... 

PP bead foams were subjected to oblique impacts (167), in which the material was compressed and sheared. This strain combination could occur when a cycle helmet hit a road surface. The results were compared with simple shear tests at low strain rates and to uniaxial compressive tests at impact strain rates. The observed shear hardening was greatest when there was no imposed density increase and practically zero when the angle of impact was less than 15 degrees. The shear hardening appeared to be a unique function of the main tensile extension ratio and was a polymer contribution, whereas the volumetric hardening was due to the isothermal compression of the cell gas. Eoam material models for FEA needed to be reformulated to consider the physics of the hardening mechanisms, so their... 

FIGURE 17.8 Fracture behavior of two cylindrical cheese samples subjected to uniaxial compression. Sample (1) concerns a hard and fairly brittle cheese, (2) a semihard green cheese that is quite extensible, (a) Stress a versus Hencky strain eH, resulting upon deformation at a strain rate W of 1CT2 s 1 the dotted lines indicate the strain at fracture fr. (b) Values of Sfr obtained at various W. (c) Fracture mode as seen in cross sections through the test pieces at the moment of maximum stress for (1) it is a vertical cross section, for (2) a horizontal one. 

Usually, sealants and adhesive materials for construction applications are evaluated by looking at the engineering side, butnotthe chemistry of the material. As a result, only tests that measure the mechanical properties are used. Most of the studies on the viscoelastic properties use traditional tests such as tensile testing to obtain data, which can be used in complicated mathematical equations to obtain information on the viscoelastic properties of a material. For example, Tock and co-workers studied the viscoelastic properties of stmctural silicone rubber sealants. According to the author, the behavior of silicone mbber materials subjected to uniaxial stress fields carmotbe predicted by classical mechanical theory which is based on linear stress-strain relationship. Nor do theories based on ideal elastomers concepts work well when extensions exceed... 

Fig. 5.13 Measured load plotted as a function of extension for the four sets of samples of the model linear polymer subjected to uniaxial tension increasing at a rate of 5 bar ps"f Data for each set are averaged over five samples, the four sets are based on polyethylene model PE I. The samples were prepared directly in the glassy state and sets A-D have different configurational properties (see Table 5.1) as a result of different preparation procedures.

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