Relaxation of stresses

The relaxation time Tstress depends on B and differs from 7strain. In first approximation we can calculate a reduction of the stress due to reversible molecular displacements. According to Hooke we have A a = Go y where Ay is given by z/z0. Thus we find 

If there are irreversible flow processes at a given constant deformation To with A kT, we get 

This implies ym = o0IG0. The total deformation becomes viscous. As in (63) the denominator is greater than in the equation for r-m 

The stress decreases to zero. After these dislocations the flowing processes will come to an end. The total strain To remains constant. In Fig. 25 the course of the strain 

Distribution of purely elastic, viscoelastic and viscous deformations correlated to a decrease of stress at a constant deformation rate 70, with all deformation processes coupled, (a) 7(f). (b) ° ) 

---

Another aspect of plasticity is the time dependent progressive deformation under constant load, known as creep. This process occurs when a fiber is loaded above the yield value and continues over several logarithmic decades of time. The extension under fixed load, or creep, is analogous to the relaxation of stress under fixed extension. Stress relaxation is the process whereby the stress that is generated as a result of a deformation is dissipated as a function of time. Both of these time dependent processes are reflections of plastic flow resulting from various molecular motions in the fiber. As a direct consequence of creep and stress relaxation, the shape of a stress—strain curve is in many cases strongly dependent on the rate of deformation, as is illustrated in Figure 6. 

Changes in polarization may be caused by either the input stress profile or a relaxation of stress in the piezoelectric material. The mechanical relaxation is obviously inelastic but the present model should serve as an approximation to the inelastic behavior. Internal conduction is not treated in the theory nevertheless, if electrical relaxations in current due to conduction are not large, an approximate solution is obtained. The analysis is particularly useful for determining the signs and magnitudes of the electric fields so that threshold conditions for conduction can be established. 

Figure 2 The lamellar substructure of a fibril. (a) Reciprocal positions of crystalline lamellae as a result of fiber annealing. (b) The situation after relaxation of stress affecting TTM. ai.2 - average angle of orientation of TTM CL - crystalline lamellae CB - crystalline blocks (crystallites) mF -border of microfibrils and F - fibril. In order to simplify it was assumed that (1) there are the taut tie molecules (TTM) only in the separating layers, (2) the axis of the fibril is parallel to the fiber axis.

Thus a strong bond is not always desirable. We can see this from Table 7 and 8. The authors of [100] interpreted their experimental data as follows the rigidity of specimens increases with increasing PVC-filler interaction as a result the rate of relaxation of stresses arising at interphases in the course of deformation decreases. The overstressed states at the interphases may, in the authors opinion, promote separation of the polymer from the filler surface. That is, it is more desirable that the matrix-filler bond is not rigid but labile. 

The most desirable annealing temperatures for amorphous plastics, certain blends, and block copolymers is just above their glass transition temperature (Tg) where the relaxation of stress and orientation is the most rapid. However, the required temperatures may cause excessive distortion and warping. 

Studies have been made of the stresses produced in several non-steady flow histories. These include the buildup to steady state of a and pu — p22 at the onset of steady shearing flow (355-35 ) relaxation of stresses from their steady state values when the flow is suddenly stopped (356-360) stress relaxation after suddenly imposed large deformations (361) recoil behavior when the shear stress is suddenly removed after a steady state in the non-linear region has been reached (362) and parallel or transverse oscillations superimposed on steady shearing flow (363-367). Experimental problems caused by the inertia and compliance of the experimental apparatus are much more severe than in steady state measurements (368,369). Quantitative interpretations must therefore still be somewhat tentative. Nevertheless, the pattern of behavior emerging is suggestive with respect to possible molecular flow mechanisms. 

We find differences between the relaxation of stress and strain12. ... 

The existence of the functional dependency of Eq. (8) provides a possibility411 to assume that relaxation processes develop in time similarly after different homogeneous extensions (and even after a preliminary partial relaxation of stresses), if the accumulated elastic strain a and irreversible strain velocity ep in the medium are similar at the moment of start of relaxation. According to the above, we can take, for example, instead of parameters (a, e ) parameters (cr, a). If the processes of stress relaxation coincide in time, the processes of retardation occur automatically similarly under the same initial conditions of (at, e ). 

Paradoxically, such a mechanical fatigue apparently acts as a treatment for relaxation of stress and allows flaws, located at the stress areas to be partly dissipated. Also, mechanical fatigue treatments can eliminate effects of a previous thermal treatment. Two samples that were initially different became more similar with regard to their crystallinity after 50 x 103 cycles. They had a medium level of crystallinity characterized by disorder parameter values that are particularly low. 

Figure 8.1. Diagram showing Maxwell mechanical model of viscoelastic behavior of connective tissues. In this model an elastic element (spring) with a stiffness Em is in series with a viscous element (dashpot) with viscosity T m. This model is used to represent time dependent relaxation of stress in a specimen bold of fixed length.

Hutzenlaub s equation7 may be used to calculate the quantity of air entrained in a roll in practice there always is a lot of air—usually enough to compensate for variations in thickness. After winding, the relaxation of stresses in the film will cause shrinkage, tension in the material will rise, giving an increase of... 

For the moment, assume that the VE picture is correct and inertial solvent motion causes negligible dephasing. Diffusive motion must be the primary cause of coherence decay. In the VE theory, the diffusive motion is the relaxation of stress fluctuations in the solvent by viscous flow. The VE theory calculates both the magnitude Am and lifetime z0J of the resulting vibrational frequency perturbations. A Kubo-like treatment then predicts the coherence decay as a function of the viscosity of the solvent. Figure 19 shows results for typical solvent parameters. At low viscosity, the modulation is in the fast limit, so the decay is slow and nearly exponential. Under these conditions, the dephasing time is inversely proportional to the viscosity, as in previous theories [Equation (19)]. As the viscosity increases, the modulation rate slows. The decay becomes faster and approaches a... 

Upon hardening of the composition the plastometer will record the process of relaxation of the stresses with the working bar being idle. Stresses arising in the material with the progress of time fall off to an equilibrium value Tq. Figure 5 shows the hardening process of the aminoplasts at temperatures 140 and 1 and 160 °C under a continuous deformation and the relaxation of stresses which attains the maximum value Tq. 

For these first experiments, a temperature relatively close to Tg, T=123°C, was chosen with the intention of minimizing the relaxation of stress and chain orientation during the quenching the weight-average relaxation time of sample SI at 123°C is calculated from that at 140°C and the thermal shift factor between 123°C and 140°C Xw(123°C) 380s. On the other hand the cooling time of the stretched specimens can be estimated to a few seconds [19], which is very small compared to the polymer relaxation time at the temperature of the experiments. 

Doi was the first to point out that the decrease of tube length due to these fluctuations leads to partial relaxation of stress. The stress relaxation modulus G(t) is not quite constant in the rubbery plateau, but decreases -slightly with time. The weak time dependence of the stress relaxation... 

Thus, a finite fraction of the stress relaxes by constraint release at time scales of the order of the constraint lifetime in the Rouse model of constraint release. This is also the time scale at which the stress relaxes by reptation in monodisperse entangled solutions and melts. Both processes simultaneously contribute to the relaxation of stress. Therefore, constraint release has to be taken into account for a quantitative description of stress relaxation even in monodisperse systems. The contribution of constraint -release to stress relaxation in pefydispcrse solutions and melts is even more important as will be discussed below. 

Twinning facilitates relaxation of stress by plastic deformation but interaction of twin bands with grain boundaries may initiate cracks. Plasticity of Crl8Re and Cr35Re alloys is sufficient to impeach the formation of such cracks even after 71% deformation at room temperature. 

New tube materials allow the design for much higher exit temperatures and heat fluxes, in particular when applying a side wall fired reformer furnace to ensure better control of the maximum tube wall temperature and optimum use of the high alloy material. Thinner tube walls made possible by the use of the new materials reduce the risk for creep due to faster relaxation of stresses at start and stop of the reformer (14). 

---