Activation energy creep

Fig. 6.7 a Creep curve at a temperature T = 1412 °C and under a resolved shear stress <7 = 5 kg/mm. b Creep rate (logarithmic scale) versus 1/kT, for the constant resolved shear stress <7 = 5 kg/mm. The slope gives the creep activation energy [45]. With kind permission, Permissions Dept., EDP Sciences by Dr. Corinne Griffon and Professor Escaig... 

The subscripts and superscripts 1 and 2 refer to cross-slip and climb, respectively. Dislocation motion must overcome significant structural barriers or must cross-slip or climb past obstructions. At the lower temperatures, dislocation crossslip and climb both occur. At the higher temperatures, dislocation climb becomes a rate-controlling mechanism and classic values of the stress exponent (n = 4.5) are obtained. The creep-activation energy is that of cation diffusion. 

Cold rolling led also to an increase in the creep strain and secondary creep strain-rate. The creep activation energy was found to increase with increasing rolling reduction. Within the secondary creep stage, the creep process in polypropylene is mainly due to the a-relaxation process and most of the creep strain was recoverable. 

Peschanskaya, N. N., Bershtein, V. A., Stepanov, V. A. (1978). The Connection of Glassy Polymers Creep Activation Energy with Cohesion Energy. Fizika Tverdogo Tela, 20(11), 3371-3374. 

The creep behavior of stoichiometric UO2 can be split up into two regions (69, 70) (i) low stress (up to about 30MN/m ) where the creep activation energy is about 0.4 MJ/mol (90-100 kcal/mol) and the creep rate is linear with stress and approximately inversely proportional to the square of the grain size, and (ii) high stress (above 40 MN/m ) where the activation energy is higher, approximately 0.6 MJ/mol (140 kcal/mol), and the creep rate proportional to stress to the power 4.5. 

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. 

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). 

You have developed a new semicrystalline polymer, which has a typical activation energy for relaxation of Erei = 120 kJ/mol. You wish to know the creep compliance for 10 years at 27°C. You know that, in principle, you can obtain the same information in a much shorter period of time by conducting your compliance tests at a temperature above 27°C. 

An alloy is evalnated for potential creep deformation in a short-term laboratory experiment. The creep rate is fonnd to be 1% per honr at 880°C and 5.5 x 10 % per honr at 700°C. (a) Calculate the activation energy for creep in this temperatnre range, (b) Estimate the creep rate to be expected at a service temperatnre of 500°C. (c) What important assnmption nnderlies the validity of yonr answer to part b ... 

The activation energy for polystyrene creep as given by Figure 9 is approximately 8 kcal. This relatively low activation energy probably indicates that the flow units—e.g., chain segments—whose mobility causes the creep are relatively short. 

The data points in the upper part of Figure 9 represent the creep rate during irradiation. Although there is some scatter in these data, a definite trend is evident, and the activation energy appears to be of... 

The increase in polystyrene creep rate owing to the radiation is directly proportional to the applied stress for a constant radiation intensity. The activation energy at constant radiation intensity for creep of polystyrene during irradiation at different temperatures is similar to the activation energy for creep without radiation. 

The mechanical properties of Shell Kraton 102 were determined in tensile creep and stress relaxation. Below 15°C the temperature dependence is described by a WLF equation. Here the polystyrene domains act as inert filler. Above 15°C the temperature dependence reflects added contributions from the polystyrene domains. The shift factors, after the WLF contribution, obeyed Arrhenius equations (AHa = 35 and 39 kcal/mole). From plots of the creep data shifted according to the WLF equation, the added compliance could be obtained and its temperature dependence determined independently. It obeyed an Arrhenius equation ( AHa = 37 kcal/mole). Plots of the compliances derived from the relaxation measurements after conversion to creep data gave the same activation energy. Thus, the compliances are additive in determining the mechanical behavior. 

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