Stored elastic energy

Melt Viscosity. The study of the viscosity of polymer melts (43—55) is important for the manufacturer who must supply suitable materials and for the fabrication engineer who must select polymers and fabrication methods. Thus melt viscosity as a function of temperature, pressure, rate of flow, and polymer molecular weight and stmcture is of considerable practical importance. Polymer melts exhibit elastic as well as viscous properties. This is evident in the swell of the polymer melt upon emergence from an extmsion die, a behavior that results from the recovery of stored elastic energy plus normal stress effects. 

The argument, at its simplest, is as follows. The primary function of a spring is that of storing elastic energy and - when required - releasing it again. The elastic energy stored per unit volume in a block of material stressed uniformly to a stress a is ... 

Fig. 4. Schematic of the JKR treatment of contact mechanics calculations. The point (, a, P) corresponds to the actual state under the action of interfacial forces and applied load P. P is the equivalent Hertzian load corresponding to contact radius a between the two surfaces, ( o, P) and (S], a, P ) are the Hertzian contact points. The net stored elastic energy and displacement S are calculated as the difference of steps 1 and 2.

The net stored elastic energy is given by stress distribution is given by... 

The JKR theory is essentially an equilibrium balance of energy released due to interfacial bond formation and the stored elastic energy. For simple elastic solids the deformation as a function of load, according to the JKR theory is given by... 

To evaluate the influx solution experimentally for an A/B cantilever beam configuration as shown in Fig. 1, we apply Griffith s theory at the critical moment of fracture, such that the incremental change in stored elastic energy U. with change in crack length a, is Just sufficient to overcome the fracture surface energy S... 

Figure 6 Variation of stored elastic energy (W) with the percent NBR content in NBR-CSPE blend.

Earlier studies [14,15] clearly reveal that there is a reaction between two polymers and that the extent of reaction depends on the blend ratio. As 50 50 ratio has been found to the optimum (from rheological and infrared studies) ratio for interchain crosslinking, the higher heat of reaction for the NBR-rich blend may be attributed to the cyclization of NBR at higher temperatures. There is an inflection point at 50 50 ratio where maximum interchain crosslinking is expected. Higher viscosity, relaxation time, and stored elastic energy are observed in the preheated blends. A maximum 50-60% of Hypalon in NBR is supposed to be an optimum ratio so far as processibility is concerned. 

Stored elastic energy (Fig. 12) also increases with shear rate both for preblends and preheated blends. Here again, we see that the W values increase sharply with NBR, attain a maximum at 50 50 level, and beyond 50% NBR the stored elastic energy decreases. 

Rheological parameters, such as relaxation time, shear modulus, and stored elastic energy, are determined from the extrudate swell and stress-strain data as previously described. Representative examples of the variation of these parameters with blend ratios for both blends are shown in Figs. 16-18. Figure 16 shows that relaxation time for both preblends without heating and... 

Stored elastic energy also increases up to 45-50% of Thiokol rubber and then decreases gradually until the end in the preheated blends (Fig. 18). A similar phenomenon is also noticed in the preblends without heating where the inflection point shifts toward the slightly higher level of Thiokol rubber. 

The plot of the rheological parameters (relaxation time, shear modulus, and stored elastic energy) are shown in Figs. 22-24. The relaxation time increases as the ACM content is increased to attain a maximum at 60 40 = ACM XNBR blend ratio for the preblends. For lower shear rate the rise is sharp and after 60 40 blend ratio, // remains almost constant, whereas for the higher shear rate region the rise is not sharp and after 60 40 blend ratio ty decreases as ACM percent increased in the blend. In the case of the preheated blends the /y increases up to 50 50 blend ratio and then decreases with the addition of ACM in the blend. The preheating increases the ty in both shear rate regions. 

The stored elastic energy, W (Fig. 24) increases with the increase of ACM content in the blend up to 50 50 blend ratio and then it decreased with the further... 

The plot of the rheological parameters (relaxation time, /r shear modulus, G and stored elastic energy, W ) are given in Figs. 28-30. The relaxation time of both preblends and preheated blends remains almost constant up to 50 50 blend ratio and then shoots up drastically at both shear rates. Up to 50 50 blend ratio it is observed that the relaxation time is more at lower shear rate. Preheating of blends lowers the values. 

The stored elastic energy, VV , decreases drastically with the addition of AU in the blends up to 50 50 blend ratio for both the preblends and preheated blends at both shear rates. After 50 50 blend ratio at both shear rates the W does not change for preheated blends. For preblends the W increase up to 60 40 AU-XNBR blend ratio for both the shear rates and then remain constant at lower shear rate, whereas at higher shear rates it decreased further with the addition of AU in the blend. At lower shear rates, the W gradually converge to the same value as the AU is added to the blend. 

Springs made from coils of wire are used to store elastic energy which is a form of potential energy. The most common type of spring is cylindrically shaped, with coils evenly spaced and of the same diameter. A ballpoint pen uses a coil spring to hold the point in place for writing and to return it to the case for protection. 

This behavior is similar to the cut growth and fatigue behavior of rubber compounds. The rate of the growth of a cut is a function of the tearing energy [38,39] which itself is proportional to the stored elastic energy density in the test piece. The exact value depends on the shape of the test piece. 

FIGURE 26.49 Calculated stored elastic energy and the horizontal stress component due to two line forces at an angle a to the plane of the rubber surface and a fixed distance x apart for different depths from the surface of a semi-infinite body. 

This is Mooney s equation for the stored elastic energy per unit volume. The constant Ci corresponds to the kTvel V of the statistical theory i.e., the first term in Eq. (49) is of the same form as the theoretical elastic free energy per unit volume AF =—TAiS/F where AaS is given by Eq. (41) with axayaz l. The second term in Eq. (49) contains the parameter whose significance from the point of view of the structure of the elastic body remains unknown at present. For simple extension, ax = a, ay — az—X/a, and the retractive force r per unit initial cross section, given by dW/da, is... 

Immediately upon fracture the fibre drops from a high-energy state equal to the stored elastic energy to its lowest energy, viz. the unloaded state. Hence, initiation of fracture in the domains in the tail of the orientation distribution p(0) does release most effectively the stored energy of a loaded polymer fibre. So, if there are no impurities and structural irregularities, fracture of the fibre is... 

The peak stress can be resolved into a component a0 cos S that is in place with the strain, related to the stored elastic energy and a component viscous loss of energy [1,3,9,10-13]. 

In non-polymeric materials the entropy change on deformation is minimal so that the intrinsic and stored elastic energies are the same at least for rapidly occurring events - but in polymers not only may the entropy contribution predominate but for large strains in rubbers the internal energy term is nearly negligible (but not at small strains where it may amount to 20% of the free energy). 

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