Thermally Activated Slip

The formation of a new glide layer due to the motion of the internal boundary edge under stress may occur for o o in a thermally activated way. In [6.29] the expression has been derived for the boundary-edge velocity, vs  

The expressions for the velocity of a homogeneous, thermally activated slip in the layer under applied stress which is less than o are somewhat cumbersome [6.29]. However, if the relative area of the glide layer occupied by coincident sites is equal to wc, and the critical stresses in noncoincident sites are distributed nearly uniformly within the range [trc0, rcm], then the slip velocity is given by 

It follows from this expression that the activation volume of a homogeneous slip may be as large as 2-3t)a. The activation volume of the slip-layer edge motion, as 

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The number of parameters to be identified is small energy and activation volume of the viscoplastic flow law based on Arrhenius s law (stress-assisted thermally activated slip). The experimental curves used during parameter adjustment are tensile curves, obtained at different rates. Unlike the Taylor or Sachs models, the previous mean-field homogenization models naturally predict a limited number of systems activated at low amplitude and a large number at high amplitude. Even at equal cumulated... 

A change of temperature will affect the rate of radical production in three ways. Firstly the number N of highly extended chains will decrease if thermally activated slip becomes possible. Secondly the activation energy U(T) decreases with increasing temperature. Thirdly the sample modulus E and the crystalUne modulus are affected by temperature. 

The dependence of friction on sliding velocity is more complicated. Apparent stick-slip motions between SAM covered mica surfaces were observed at the low velocity region, which would disappear when the sliding velocity excesses a certain threshold [35]. In AFM experiments when the tip scanned over the monolayers at low speeds, friction force was reported to increase with the logarithm of the velocity, which is similar to that observed when the tip scans on smooth substrates. This is interpreted in terms of thermal activation that results in depinning of interfacial atoms in case that the potential barrier becomes small [36]. 

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... 

At elevated temperatures, the thermal recovery processes described in Section 5.1.2.3 can occur concurrently with deformation, and both strength and strain hardening are consequently reduced. The latter effect results in decreasing the difference between yield and tensile strengths until at sufficiently high temperatures, they are essentially equal. At lower temperatures, temperature has a marked influence on deformation in crystalline materials. Temperature can affect the number of active slip systems in some... 

The validity of Coulomb s law has been verified also on the nanoscale Zworner et al. [484] showed that, for different carbon compound surfaces, friction does not depend on sliding velocity in the range between 0.1 /xm/s and up to 24 /xm/s. At low speeds, a weak (logarithmic) dependence of friction on speed was observed by Gnecco et al. [485] on a NaCl(lOO) surface and by Bennewitz et al. [486] on a Cu (111) surface. This can be modeled when taking into account thermal activation of the irreversible jumps in atomic stick-slip [487],... 

Since it is presumed that the process of cross slip is thermally activated, to the extent that we are trying to explicate the unit processes that make up plasticity it is of great interest to come up with an estimate for the activation energy for cross slip. In broad terms, what this implies is a comparison of the energies between the unconstricted and constricted states. The simplest continuum estimate... 

A dislocation is normally dissociated in its slip plane, and therefore cross slip requires some kind of constriction which means that cross slip is, generally speaking, a thermally activated process, e.g. [2], This does not exclude that the activation energy may be zero for certain conditions. 

The nanotheory implies that cyclic saturation is a thermally activated process of PSB plasticity by repeated avalanches of slip producing intense surface fatigue damage at the nanoscale. The relevant activation energy for recovery... 

Brown s statistical theory [30] of annihilation of screw dislocation dipoles by thermally activated jog migration determines the PSB nanostructure and the saturation stress. The statistical theory is compatible with the nanotheory and the required activation energies are available for both cross-slip and jog motion in copper, as described in 2.2 and 2.3. What remains is to combine and quantify the above theories of thermally activated fatigue hardening, PSB nucleation, cyclic saturation and PSB surface damage to test their quantitative predictions against experimental data. 

Further below, time-dependent deformation (creep) iiutiated by climb will be extensively discussed. In this section, an example of dislocation climb is illustrated. Figure 3.70 shows dislocation climb in an AI2O3-YAG specimen. Here, climb was assisted by thermal activation. Such a dislocation network, resulting from the reaction of dislocations from the basal and pyramidal slip systems, involves dislocation climb. It is a diffusion-controlled deformation mode characterizing creep deformation and, in this particular case, the activation energy determined is Q = 670 kJ/mol. 

Bulk-diflRision-assisted creep occurs in the processes listed above, namely in (b) climb (c) climb-assisted glide and (d) thermally-activated glide via cross-slip. All these are obviously associated with dislocation motion. High stress, below yield stress, causes creep by conservative dislocation motion, namely by dislocation glide within its slip plane. This readily occurs at high temperatures above 0.3 Tm for pure metals and at about 0.4 Tm for alloys, where the dependence on strain rate becomes quite strong. For ceramics, T > 0.4—0.5 T (K). A formulation used for such creep is ... 

If we consider the Peierls force from section 6.2.9 as obstacle, it can also be overcome by thermal activation. This is especially relevant if the Peierls force is large i. e., when slip is along planes that are not close-packed, for example in body-centred cubic lattices. For this reason, the yield strength of body-centred cubic lattices is strongly dependent on the temperature, different from face-centred cubic metals (figure 6.29). The Peierls stress can reach values of up to several hundred megapascal. 

As we have seen, the strain rate dependence does suggest that yield behaviour often indicates the presence of two thermally activated processes, as discussed above. In some cases, notably polyethylene, a double yield point is observed. Ward and co-workers [64], Seguala and Darras [65] and Gupta and Rose [66] concur that these two deformation processes are essentially interlamellar shear and intra lamellar shear (or c-slip). They are akin to the dynamic mechanical relaxation processes identified in Chapter 10.7.1 for the specially oriented PE sheets, and Seguala and Darras have related them to the a and o 2 transitions reported by Takayanagi [67]. This establishes a direct link between yield and viscoelastic behaviour. 

The sinh law equation has been derived from first principles. Underlying mechanisms are based upon thermally activated diffusion processes, ranging from theories of point defect motion (vacancies and interstitials) and dislocation cross slip at the low stresses, to dislocation glide... 

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