Stress relaxation 634 INDEX

Mechanical properties of polyethylenes vary with density and melt index. Low-density polyethylenes are flexible and tough high-density products arc quite rigid and have creep resistance under load. Toughness is the primary mechanical property affected by melt index, with lower-melt-index polyethylenes having greater toughness. Under loads, polyethylene is subject to creep, stress relaxation, or a combination of both,... 

The number of unrelaxed modes per chain at time t is equal to the mode index p. Each unrelaxed mode contributes energy of order kT to the stress relaxation modulus. The stress relaxation modulus at time t is proportional to the thermal energy kT and the number density of sections with Njp monomers, 4>/(b N/p) ... 

The slope corresponding to the glass transition has been quantitatively treated by Aklonis and co-workers (61-63) for relaxation phenomena. Aklonis defined a steepness index (SI) as the maximum of the negative slope of a stress relaxation curve in the glass transition region. They found that while... 

The knowledge on the stress relaxation progression may be utilized for the prediction of a series of rheological properties of the blend. The plateau modulus, G°, an index of material rigidity, is obtained from (Eq. 14), at the onset of the terminal relaxation region ( = 0) ... 

Suppose we divide the flow segments into classes according to relaxation times and index the various states by the subscript i. Thus the relaxation time and the component of shear stress borne by the segments in class i are and Fj, respectively. The applied shear force is related to the Fj s through... 

Some fermentation broths are non-Newtonian due to the presence of microbial mycelia or fermentation products, such as polysaccharides. In some cases, a small amount of water-soluble polymer may be added to the broth to reduce stirrer power requirements, or to protect the microbes against excessive shear forces. These additives may develop non-Newtonian viscosity or even viscoelasticity of the broth, which in turn will affect the aeration characteristics of the fermentor. Viscoelastic liquids exhibit elasticity superimposed on viscosity. The elastic constant, an index of elasticity, is defined as the ratio of stress (Pa) to strain (—), while viscosity is shear stress divided by shear rate (Equation 2.4). The relaxation time (s) is viscosity (Pa s) divided by the elastic constant (Pa). 

Table 26.1 Cross model parameters is the zero shear viscosity, t critical shear stress, A relaxation time and n power exponent, where ES20 represents 20 wt% styrene ESI and MI denotes the melt index...

Although these simple considerations help to frame in a general logic the behavior of these bimetallic surface, there are at present no such simple models to explain the more complex mesoscopic reconstructions, such as the pyramids observed on Pt3Sn(100) or the hill and valley structure observed on PtsSnCl 10). These phenomena are obviously related to the tendency of the system to relax in-plane stress, in turn resulting from the different atomic radius of the elements involved in the presence of concentration gradients. This relaxation appears to take place on the (111) oriented plane simply by an outward relaxation of the tin atoms. On the other two low index surfaces, instead, it takes a more complex route leading to reconstruction phenomena (pyramids on the (100) and hill and valley on the (110)) which are so far unique to the Pt-Sn system. 

In chapter 7, several aspects of conductivity and dielectric relaxation were discussed. Various other properties such as shear modulus, viscosity, refractive index, volume, enthalpy etc. also exhibit relaxational behaviour particularly in the glass transition region. In this chapter, few further aspects of relaxation are discussed. Relaxation of generalized stress or perturbation whether electrical, mechanical or any other form is typically non-exponential in nature. The associated property is a function of time. A variety of empirical functions, (/) t), have been used to describe the relaxation. Some of them have already been discussed in chapters 6 and 7. The most widely used function is the Kohlraush-Williams-Watts (KWW) function (Kohlraush, 1847 Williams and Watts, 1970 Williams et al., 1971). It is more commonly referred to as the stretched exponential function. The decay or relaxation of the quantity is given by,... 

Relaxation time distribution breadth 2,4-dimethylpentad ienyl environmental stress crack resistance high-density polyethylene high-load melt index Janzen-Colby... 

The apparent diffiisivity for carbon dioxide of glassy poly(vinyl acetate) is shown as a function of aging time upon cooling from above Tg in Figure 7 (83). The decay of diffusion coefficient with aging time is similar to the relaxation-induced decay (or saturation growth) shown by properties such as yield stress, volume, enthalpy, and refractive index. 

It is appropriate to consider the multiphase systems as composed of a matrix and concentration-dependent dynamic clusters or aggregates characterized by specific strength, a, the aggregate relaxation time, Xy, and the cluster size polydispersity index, w w 0.2 — 1.0 [44]. Thus the apparent shear stress may he expressed as ... 

Here the index s (5 =1,2,3,...) indicates the viscoelastic strain spectrum constituent that corresponds to a certain relaxation time p is the average stress stands for highly elastic... 

The same authors studied the effects of application of collagen hydrolysates on the stress-strain characteristics of different hair 5 cm of virgin, bleached, and cold-wave-tteated hair were taken and stretched to 30% index in water at a rate extension of 0.25 cm/ min. After stretching, the fibers were allowed to relax overnight in water and restretched. Comparison of the stress applied (in kg/mm ) versus strain percent was made before and after treatments with collagen hydrolysate. It was found that when collagen hydrolysate is sorbed to the hair there is an increase in its tensile strength, markedly observable on cold-waved hair. 

The majority of results so far available in this Held have been derived from spectra recorded on dispersive instruments. In order to test tl validity of Eq. (1) several independent experiments have been performed in which a highly oriented polyethylene terephthalate film is subjected stepwise to increasingly higher stresses in the stretching machine illustrated in Fig. 1 and FTIR spectra are taken at the relaxed stress levels with unpolarized radiation. In Fig. 4 the wavenumber shifts of the v(0—CH2) absorption band are plotted as a fimctimi of the applied stress for different experiments. From these systematic investigations, however, no linear relationship between the wavenumber shift Av and the plied stress good index of determination (0.98) was obtained for the power function ... 

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