Stepwise deformation

In stress relaxation a sample is stepwise deformed to a tensile deformation sQ or to a shear deformation yQ and the decreasing stress is measured as a function of time proportionality factors between stress and deformation are the Young modulus E(t) and the shear modulus G(f)... 

Having seen the eharaeteristic features of the linear viscoelasticity, we shall now study the nonlinear viscoelasticity. Before studying the general situation, we shall first consider a simple case, the stress relaxation after stepwise deformation. " Suppose that at time r = 0, a polymeric liquid is suddenly deformed homogeneously. The deformation creates a stress which gradually relaxes with time. Our problem is to find how this relaxation takes place. 

Neutron scattering. In a series of experiments, Bou6 et al. have studied by neutron scattering the conformational relaxation of the labelled chain after the stepwise deformation. In the short time-scale, the observed relaxation is well described by the Rouse dynamics. In the long time-scale (near t/ ), no clear indication has been found so far for the contraction of the contour length. Various reasons for this behaviour are conceivable such as the limited range of the scattering wave vector or polydi rsity of the sample. On the other hand the results may indicate the importance of the tube deformation in the nonequilibrium state. ... 

To assess the accuracy of the lA approximation, let us consider the stepwise deformation E imposed at f = 0. In this case the orientational distribution before the deformation is... 

On the other hand the correct value of S pis, +0) is Qap( given by eqn (7.115). Thus in the case of stepwise deformation, the lA approximation amounts to a decoupling approximation... 

This section treats the time evolution of the stress after a sudden deformation is given to an equilibrium state of the network. The deformation, being followed by a constant strain, creates a stress which gradually relaxes with time. The long-term behavior of stress relaxation following a large stepwise deformation is frequently measured in rheological experiments. It is known as the nonlinear stress relaxation. 

As an aside, it should be noted that a large intrinsic ET barrier does not necessarily imply an increase of the bond length upon radical anion formation. A substantial angle deformation also may contribute to the internal intrinsic barrier, AGqj. This was shown in the case of the stepwise dissociative oxidation of oxalate ( O2C-CO2 — 02C-C02 4-e—CO2-F CO2 ), where the data suggest that the oxalate undergoes a substantial increase of... 

Figure 13.3.10 shows the typical spheroidal deformation of stainless steel particles with treatment time. As compared with the result of copper particles, the rate of spheroidal deformation was lower. Thus, the stainless steel particles were easier for stepwise adjustment of the shape index with treatment time. 

In summary, my view is that the fundamental cause for superplasticity is electronic in origin which has to do with the probability curves for the formation of compounds. This in turn creates the instability of the compounds and results in the ultra small grain size. Then, on the application of tensile stress, the plastic deformation is purely mechanical and has nothing to do with electrons. This is completely different from that observed in the normal plasticity as described above. The cause and mechanism for super-plasticity and normal plasticity are therefore fundamentally different. The phenomenon of superplasticity therefore can be viewed stepwise as follows ... 

The magnetostrictive measurements were made on the same Ni plate. In the external magnetic fields more than 100 mT the change of deformations were not essential. However, the GMR effect appeared as usual in such fields. There was not any correlation between the magnetostrictive deformation and the stepwise change of current of the Ni-polymer-Cu structure. 

From the microhardness behaviour during the strain-induced polymorphic transition of PBT, differences were found for the three above described systems. The common characteristic feature among PBT (Section 6.2.1), its copolymer PEE (Section 6.2.2) and the PBT/PEE blend (Section 6.2.3) is the relatively sharp (within 2-4% of deformation) stepwise decrease in H (typically by 20-30% of starting H value). This drop appears at different deformation intervals for PBT the sharp decrease occurs between 5-8% (Fig. 6.2), for PEE it appears between 25-30% (Fig. 6.5), while for the blends one observes two sharp decreases with increasing strain (Fig. 6.8). The first 20% decrease in the starting H value coincides with the deformation interval... 

On stepwise heating of the acid with sorbed methanol the PAS FTIR spectra show the development of two sharp bands, one at 1453 cm 1 attributed to the CH 3 symmetric deformation in the CH3O groups and the second at 1022 cm 1, identified as that due to the C-0 stretch in WOCH3 (Fig. 12). 

The stepwise reactivity of cyanuric chloride can be readily interpreted on the basis of the electron structure. The nitrogen atoms of the triazine ring possess a larger nuclear charge than the carbon atoms and thus deform the n-electron system of the ring and a distorted cycle, in a direction opposite to that of the carbon atoms, is formed ... 

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