Creep thermally activated

A well-known example of this time-temperature equivalence is the steady-state creep of a crystalline metal or ceramic, where it follows immediately from the kinetics of thermal activation (Chapter 6). At a constant stress o the creep rate varies with temperature as... 

It has been recognized that the behavior of atomic friction, such as stick-slip, creep, and velocity dependence, can be understood in terms of the energy structure of multistable states and noise activated motion. Noises like thermal activities may cause the atom to jump even before AUq becomes zero, but the time when the atom is activated depends on sliding velocity in such a way that for a given energy barrier, AI/q the probability of activation increases with decreasing velocity. It has been demonstrated [14] that the mechanism of noise activation leads to "the velocity... 

Creep-rupture represents, ultimately, the thermally activated breaking of bonds. Russian authors, in particular, have tried to describe it as a mechanically aided chemical process rather than a physical one. So far, however, there has been no widely used combined description of degradation by chemical and mechanical means. 

Figure 12 Ratio of flux creep rate S(T) to the magnetization at 1 second MQ(T) versus temperature. S and MQ are obtained by fitting data such as those in Figure 11 using Eq. (13). The slope of the dashed line corresponds to an effective flux pinning potential U = 83 meV according to a simple thermally activated flux creep model which yields Eq. (14).

Values from tables of friction coefficients always have to be used with caution, since the experimental results not only depend on the materials but also on surface preparation, which is often not well characterized. In the case of plastic deformation, the static coefficient of friction may depend on contact time. Creeping motion due to thermally activated processes leads to an increase in the true contact area and hence the friction coefficient with time. This can often be described by a logarithmic time dependence... 

The relation between the frequency v of local jumps, shear stress r, temperature T and macroscopic rate of creep e was well established by Eyring s reaction rate theory [41]. Let us consider that a number of vl0 thermally activated structural units attempt per unit time to cross a potential barrier Ur, the net flow v, of units that will succeed is then given by ... 

Another critical question is how the creep rate depends upon temperature. As hinted at in the title of this section, creep is in many instances mediated by the presence of mass transport. Part of the basis of this insight is the observed temperature dependence of the creep rate. In particular, it has been found that creep is thermally activated. Indeed, one can go further than this by noting the relation between the activation energy for diffusion and that of the creep process itself. A plot of this relation is shown in fig. 11.5. As a result, we see that the temperature dependence of the creep rate may be written in the form... 

The softening at high temperatures is related to thermally activated creep processes which are the subject of the next section. Deviations from stoichiometry produce constitutional defects which enhance diffusion and lead to softening at high temperatures, whereas at low temperatures these defects are immobile and act as strengthening deformation obstacles. These different effects of deviations from stoichiometry at low and high temperatures were studied in detail for binary NiAl (Vandervoort etal., 1966). 

Low-temperature creep was first studied by Meissner et al in 1930 [ ]. They found that above the yield stress there is appreciable creep even at liquid-helium temperatures. This result gave impetus to further studies at low temperatures. Characterizing creep in cadmium as athermic at 1.4 to 4.2 K, Glen [ assumed that creep proceeds bv dislocation tunneling through crystalline lattice barriers. Arko and Weertman [ revealed the sensitivity of creep to temperature at 4 K and inferred that it was the common thermally activated creep. Gindin etai assumed combined thermal activation and tunneling mechanisms. At the present time, there is not unanimous opinion on the nature of low-temperature creep. 

The temperature dependence of a was obtained in experiments on copper polycrystals [ ]. From Cu creep curves, values of a were determined in the temperature range 1.4 to 4.2 K for a constant r of 24 MPa. Figure 2 shows a plotted against temperature. From the logarithmic creep theory, based on the thermally activated creep assumption [ one expects the linear- and temperature-proportional behavior of the a factor to be... 

Certain important features of the a(T) curve are (1) there is a temperature dependence of a, a(T although weak and (2) the a(T) curve tends toward saturation in the very low temperature range and, if extrapolated to T = 0 K, ends in a finite nonzero value of ao- Contrary to the thermally activated creep theories, this suggests that there is a creep at 0 K. On the one hand, the temperature dependence of a is apparent on the other hand, its behavior differs from the predictions of the classical thermally activated creep laws. This leads one to assume that at 4 K, creep depends on two mechanisms, and as absolute zero is approached, the athermic component becomes more important [ ]. 

The second set of measurements studied the dependence of the creep rate ratio 82/81 on AT, obtained as a result of a temperature change of AT = T2—T1. It is readily seen that the classical thermally activated creep theory leads to the following relation between 82/81 and AT. 

When two metals come into contact under a given load, asperities are pressed against one another and undergo plastic flow and creep the area of contact increases with temperature and contact time, as in a hot hardness mutual indentation. Then, when the stress has dropped sufficiently the area of contact predominantly increases by surface or boundary diffusion as in sintering experiments. As these various mechanisms are thermally activated, the increase of area of contact with temperature can be written ... 

The rate dependencies of the ferroelectric material properties are also reflected in the dynamics after fatigue. Initially, most of the domain system will be switched almost instantaneously [235], and only a small amount of polarization will creep for longer time periods [194]. A highly retarded stretched exponential relaxation was observed after bipolar fatigue treatment [235], and these observations correlated well with the thermally activated domain dynamics. If the overall materials response was represented in a rate-dependent constitutive material law 236], however, then a growing defect cluster size would retard the domain dynamics considerably. Hard and soft material behaviors were also representable as different barrier heights to a thermally activated domain wall motion, as demonstrated by the theoretical studies of Belov and Kreher [236]. 

As expected from their amorphous structure, Si-C-N-0 and Si-C-N(O) fibers are prone to creep. For HPZ based fibers, the apparent energy for creep is -200 kJ/mol in the temperature range between 1150 and 1350°C, a value that is consistent with activation energies for thermally activated viscous flow of glasses at high temperatures [25]. 

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