Step elongational strain

Step-strain stress-relaxation measurements have been frequently used to determine Sr(X) for polymer melts > . Equation (6) shows that if separability of time and strain effects is possible for the melt under consideration, the stress after a step elongational strain can be factored into a time-dependent function, the linear shear relaxation modulus G(t), and a strain-dependent function, the nonlinear strain measure Sr(X). Also other types of experiment may be oerformed to obtain Sr(X), such as constant-strain-rate experiments "", creep under constant stress and constant-stretching-rate experiments but these methods require more involved analytical and/or numerical calculations. 

Figure E7.2 compares a stepwise increase in interfacial area in simple shear flow with optimal initial orientation, and simple shear flow where, at the beginning of each step, the interfacial area element is placed 45° to the direction of shear. The figure shows that, whereas in the former case the area ratio after four shear units is 4.1, in the latter case the ratio is 6.1, with a theoretical value of 7.3 when the 45° between the plane and direction of shear is maintained at all times. We note, however, that it is quite difficult to generate steady extensional flows for times sufficiently long to attain the required total elongational strain. This is why a mixing protocol of stepwise stretching and folding (bakers transformation) is so efficient. Not only does it impose elongational stretching, but it also distributes the surface area elements over the volume.

The mathematical form of the function can be derived simply from a fit of the experimental h(y) as obtained in step shear strain for example. However, the problem is further complicated if one now takes into account flows where the two invariants differ from each other as, for example, in uniaxial elongational flows where ... 

This equation indicates that the interfacial area growth function in a material undergoing large shear proceeds linearly with shear strain. Numerical integration of the above equation over all possible orientations following the steps described for elongational strain yields... 

Monte Carlo computer simulations were also carried out on filled networks [50,61-63] in an attempt to obtain a better molecular interpretation of how such dispersed fillers reinforce elastomeric materials. The approach taken enabled estimation of the effect of the excluded volume of the filler particles on the network chains and on the elastic properties of the networks. In the first step, distribution functions for the end-to-end vectors of the chains were obtained by applying Monte Carlo methods to rotational isomeric state representations of the chains [64], Conformations of chains that overlapped with any filler particle during the simulation were rejected. The resulting perturbed distributions were then used in the three-chain elasticity model [16] to obtain the desired stress-strain isotherms in elongation. 

Since no strain-related kinetic data are available, it would be premature to discuss nucleophilic additions in terms of strain release during the addition step. However, the elongation of the carbon-carbon double bond in the computed transition state for addition of hydride to ethylene appears to be small (265). 

Effects of Biaxial Stretching LDPE films were biaxially stretched, in one step, then clamped in frames (to maintain the elongation) and put in the weatherometer. Their photooxldatlon as a function of engineering strain (e = = 62 = engineering... 

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