Activation energy for creep

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. 

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 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). 

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 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. 

Fig. 11.5. Plot of activation energies for creep and bulk diffusion (adapted from Courtney (1990)).

Using the strain rate data shown in Fig. 12, the activation energy for creep in monoclinic zirconia has been found to be Qc 330-360kJ mol"1 [48, 49], The measured stress exponent, n, from equation ... 

The slope of a plot of n Tde/dt) versus /kT should yield the activation energy for creep. If creep occurs by lattice diffusion, that value should be the same as that measured in a diffusion experiment. This is often found to be the case. 

In view of the discussed composition dependence of the creep resistance, it is concluded that the effective diffusion coefficient is of primary importance for controlling the creep resistance (Sauthoff, 1993 b). This of course does not mean that the other parameters in Eq. (2) can be neglected. This is demonstrated by the temperature dependence of the creep of B2 (Ni,Fe)Al, as was discussed earlier (Sauthoff, 1991 a). In view of Eqs. (2) and (3), the apparent activation energy for creep is expected to correspond to that for diffusion since the other parameters depend less sensitively on temperature, and indeed this has been confirmed repeatedly in the case of conventional disordered alloys. However, in the case of B2 (Ni,Fe) Al, the apparent activation energy for creep only corresponds to that for diffusion at temperatures up to 900 °C, whereas at higher temperatures the apparent activation energy for creep is much higher. Acti-... 

It was suggested by the dislocation-climb model that the activation energy for creep in many materials at high temperatures is equal to their activation energy for self-diffusion. According to both models, the activation energy for high-temperature... 

Here, Qc is the activation energy for creep and n is the stress exponent. A similar expression may be given for climb-controlled creep ... 

Hardness independent of loading time at 45°C but slow softening at 400°C activation energy for creep 527 KJ moP ... 

During a creep test carried out at constant stress, the creep rate was exactly doubled by a sudden increase in the test temperature from 230 C (603 K) to 240 C (513 K). Calculate the activation energy for creep. 

Several theoretical mechanisms have been proposed to explain the creep behavior for various materials these mechanisms involve stress-induced vacancy diffusion, grain boundary diffusion, dislocation motion, and grain boimdary sliding. Each leads to a different value of the stress exponent n in Equations 8.24 and 8.25. It has been possible to elucidate the creep mechanism for a particular material by comparing its experimental n value with values predicted for the various mechanisms. In addition, correlations have been made between the activation energy for creep (Qc) and the activation energy for diffusion (g Equation 5.8). 

Here R is the gas constant (8.314 J mol K ) and Q the activation energy for creep. For T < -10°C, Q = 60 kJ/mol, wUch implies that the deformation rate for a given stress at -10°C is about five times that at -2S C. The Arrhenius relation breaks down at temperatures above -10°C because water at grain boundaries introduces additional deformation mechanisms. Current practice is to retain Eq. 5 but increase the value of Q. Experiments show that the value of Ao depends on crystal fabric and impurity content, but not on hydrostatic pressure provided that T is measured relative to the appropriate melting temperature. 

Creep tests were conducted on Sn-Ag and Sn-Zn eutectic solders at 25 °C and 80 °C over the stress range from 10 to 22 MPa and the creep data of log steady state strain rate vs. log stress were fit to straight hnes as shown in Fig. 5. The resulting activation energies were 82 and 68 kJ/mol, respectively [7]. These values are lower than the activation energy for creep of Sn. The exponents n were determined to be 11 and 6, respectively. The value 11 is high and may indicate threshold-stress-type behavior. The creep rates in the alloys are lower than that observed in pure Sn. This is mainly attributed to changes in the preexponential term. A, which is a function of microstructure. The theory for this is not well in hand. 

Where is the creq) strain rate(l/5), A and B are the creep constants of material, cr is the appUed stress, n is the stress exponent, Q is activation energy for creep deformation process,. R(=8.617DlO-5eF/A ) is Boltzmann s constant, and T is the absolute temperature. Moreovo-, the Norton power law creep equation can be also used to model the steady-state creep rate as a function of temperature and has the form in Equation (6). 

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