Reduced 300% tensile stress function

The evolution of PUs postcure processes was compared by us by introducing and following a reduced 300% tensile stress function (a) which we calculated according to eq. (4.21) as follows ... 

When phosphorus is added to Si02, in addition to gettering mobile alkali ions, it tends to reduce the intrinsic tensile stress in such films, thereby reducing their tendency to crack. Both functions are important when the film is used as a final passivation film for integrated circuits encapsulated in plastic. Phosphorus additions of 7 weight percent seem to be optimum in order to produce the above desirable film characteristics. 

From the tensile tests presented, it appeared that the nanocomposites made by alkyl silane-functionalized sepiolite give the best mechanical performances, in particular for what concerns the yield stress. In fact, the sepiolite surface fimctionalization by silane is a reactive treatment, which decreases the interparticle aggregation (improved dispersion) and, at the same time, increases the matrix-filler interactions. The addition of fimc-tionalized polymers is, instead, a nonreactive surface treatment. It leads to a decrease of the particle-particle interaction but can also reduce the matrix-particle interaction, which leads to lower yield stress and ultimate tensile stress. 

Strain-Induced Dilatation. An alternative view of yield in polymers comes from the fact that a tensile strain induces a hydrostatic tension in the material and a corresponding increase in the sample volume. This in turn translates to an increase in the free volume, which increases the polymer mobility and effectively lowers the glass-transition temperature (Tg) of the polymer (alternatively it can be looked upon as increasing the free volume to the value it would have at the normal measured Tg). The increased mobility results in a lowering of the yield stress. Rnauss and Emri (35) used an integral representation of nonlinear viscoelasticity with a state-dependent variable related to free volume to model the yield behavior, with the free volume a function of temperature, time, and stress history. This model uses the concept of reduced time (see VISCOELASTICITY), where application of a tensile stress causes a volume dilatation and consequently causes the material time scale to change by a shift factor related to the magnitude of the applied stress. Yield occurs because the free-volume shift factor causes the molecular mobility to increase in such a way that yield can occur. 

Figure 9.11. Tensile stress divided by SXGye as a function of reduced time for a single mode of a Maxwell fluid. Reprinted with permission from Denn and Marrucci, AIChE /., 17,101 (1971). Copyright American Institute of Chemical Engineers.

Figure 9.12. Tensile stress divided by ye as a function of reduced time for a two-mode Maxwell fluid, rj is the viscosity and X is the mean relaxation time. Reprinted from Denn, in R. S. Rivlin, ed.. The Mechanics of Viscoelastic Fluids, AMD Vol. 22, ASME, New York, 1977, p. 101.

Fig. 7.18. Steady state extensional viscosities r) as a function of the applied tensile stress, as observed for various samples of PE. Data are given in reduced form, with reference to the respective zero shear rate viscosities tjq. Prom Miinstedt and Laun [79]...

The two-parameter and three-parameter approaches are frequently used to describe the tensile stress/strain behavior. The two-parameter approach is the exponential series development proposed by Schoche [14]. This so-called "prony-series" is in the form of a relaxation function and is distinguished by the characteristic variables asi and Sxi. Reducing the exponential series to the first term leads to the so-called two-parameter formulation as per the following equation (1). 

Acetate and triacetate exhibit moderate changes in mechanical properties as a function of temperature. As the temperature is raised, the tensile modulus of acetate and triacetate fibers is reduced, and the fibers extend more readily under stress (see Fig. 4). Acetate and triacetate are weakened by prolonged exposure to elevated temperatures in ah (see Fig. 5). 

The classical means for following vulcanization by physical methods is to vulcanize a series of sheets for increasing time intervals and then measure the stress strain properties of each and plot the results as a function of vulcanization time. A modification of this test generally called a rapid modulus test is widely used in the industry as a production control test. A single sample taken from a production batch of compounded rubber is vulcanized at a high temperature and its tensile modulus is measured. Temperatures as high as 380°F are used to reduce the vulcanization test time to only a few minutes. Any modulus value deviating from a predetermined acceptance limit indicates that the batch is defective and is to be rejected. 

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