Activation creep

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. 

Activators. Activators are chemicals that increase the rate of vulcanization by reacting first with the accelerators to form mbber soluble complexes. These complexes then react with the sulfur to achieve vulcanization. The most common activators are combinations of zinc oxide and stearic acid. Other metal oxides have been used for specific purposes, ie, lead, cadmium, etc, and other fatty acids used include lauric, oleic, and propionic acids. Soluble zinc salts of fatty acid such as zinc 2-ethyIhexanoate are also used, and these mbber-soluble activators are effective in natural mbber to produce low set, low creep compounds used in load-bearing appHcations. Weak amines and amino alcohols have also been used as activators in combination with the metal oxides. 

Here R is the Universal Gas Constant (8.31 Jmol K ) and Q is called the Activation Energy for Creep - it has units of Jmol . Note that the creep rate increases exponentially with temperature (Fig. 17.6, inset). An increase in temperature of 20 C can double the creep rate. 

This method of writing D emphasises its exponential dependence on temperature, and gives a conveniently sized activation energy (expressed per mole of diffusing atoms rather than per atom). Thinking again of creep, the thing about eqn. (18.12) is that the exponential dependence of D on temperature has exactly the same form as the dependence of on temperature that we seek to explain. 

Here o is the stress, A and n are creep constants and Q is the activation energy for creep. Most engineering design against creep is based on this equation. Finally, the creep rate accelerates again into tertiary creep and fracture. 

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... 

The effect of carbon on the corrosion of stainless steels in liquid sodium depends upon the test conditions and the composition of the steels . Stabilised stainless steels tend to pick up carbon from sodium, leading to a degree of carburisation which corresponds to the carbon activity in the liquid metal. Conversely, unstabilised stainless steels suffer slight decarburisation when exposed to very pure sodium. The decarburisation may promote corrosion in the surface region of the material and, under creep rupture conditions, can lead to cavity formation at the grain boundaries and decreased strength. 

The same situation, as stated in papers of G. V. Vinogradov s school in the 1950s, takes place during creep of plastic dispersion systems, i.e. low-molecular-weight liquids with netforming (active) fillers. 

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... 

The use of soluble zinc soap activators such as zinc 2-ethyl hexanoate instead of conventional stearic acid gives efficiency of vulcanisation and ensures that stress relaxation and creep properties are optimised. Zinc soaps, including the new high efficiency activating types, do not bloom from the compound, either during processing or subsequently during service. 

In a further development of the continuous chain model it has been shown that the viscoelastic and plastic behaviour, as manifested by the yielding phenomenon, creep and stress relaxation, can be satisfactorily described by the Eyring reduced time (ERT) model [10]. Creep in polymer fibres is brought about by the time-dependent shear deformation, resulting in a mutual displacement of adjacent chains [7-10]. As will be shown in Sect. 4, this process can be described by activated shear transitions with a distribution of activation energies. The ERT model will be used to derive the relationship that describes the strength of a polymer fibre as a function of the time and the temperature. 

In cellulose II with a chain modulus of 88 GPa the likely shear planes are the 110 and 020 lattice planes, both with a spacing of dc=0.41 nm [26]. The periodic spacing of the force centres in the shear direction along the chain axis is the distance between the interchain hydrogen bonds p=c/2=0.51 nm (c chain axis). There are four monomers in the unit cell with a volume Vcen=68-10-30 m3. The activation energy for creep of rayon yarns has been determined by Halsey et al. [37]. They found at a relative humidity (RH) of 57% that Wa=86.6 kj mole-1, at an RH of 4% Wa =97.5 kj mole 1 and at an RH of <0.5% Wa= 102.5 kj mole-1. Extrapolation to an RH of 65% gives Wa=86 kj mole-1 (the molar volume of cellulose taken by Halsey in his model for creep is equal to the volume of the unit cell instead of one fourth thereof). 

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