Activation energy of creep

One of the relations used to express creep-rupture time, t, as a function of the activation energy of creep, Qc, is ... 

A number of material properties (e.g., elastic modulus, Poisson s ratio, yield stress, activation energy of creep, etc.) are included as parameters within such an equation. The second task is to map the magnitude of fatigue deformation throughout the solder joint configuration. The latter requirement is accomplished by setting up finite element meshes of the various solder... 

A recent study considers SiOC materials consisting of two continuous (and interpenetrating) phases, i.e. silica and carbon. Thus, silica is considered to be continuous and embedded within a continuous carbon skin . This microstructure consideration was shown to be able to rationalize not only the creep rates of SiOC-based materials, but also the activation energies of creep, which were shown to be strongly affected by the nanodomain size of silica (i.e., the mesh size of the carbon network within the microstructure of SiOC) (lonescu, 2012d). 

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. 

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. 

Since both and Tg are inversely related to and the activation energies of the shift factors are independent of M, a common segmental motion must be involved in the creep behavior of all these specimens varying the crosslink density merely shifts the curves along the time axis. 

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

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-... 

Remember that the activation energy of firacture is equal to that of creep Therefore, the molecular mechanism causing both processes may well have the same origin. Indeed, a comparison between the kinetic parameters for the generation of excited bonds, Uod and and those of creep, Uo, and y > listed in Table 1 for perfectly drawn polymers, shows Uoa = Uqs and y = y, as well as Xod = feos. Therefore, the average time for the generation of excited bonds controls the kinetics of deformation and fracture. 

A detailed study of the strength and lifetime under constant stress of single PpPTA filaments using Weibull statistics and an exponentional kinetic breakdown model was carried out by Wu et al. [207], They found that filaments failed due to transverse crack propagation after very short creep times, but that after long creep times the failure mechanism was splitting and fibrillation. Activation energies of the failure process amounted to 340 kJ/mol, which seems to indicate rupture of the C — N bond in the chain backbone. 

Considering Eq. (6.4), the experimental value of the stress exponent, n, obtained for the Al204Mg single crystal is 3.9 with an activation energy of Q — 5.3 eV. The creep range of this single crystal is 0.65 T -0.71 T and it follows a dislocation mechanism of the creep law. More specifically, the values of... 

In Fig. 6.38, the strain-rate dependence on flow stress is shown for the indicated temperatures. The stress exponents at each temperature are also shown on the plots. A steady-state creep equation was used to define the dependence of strain rate on the flow stress, as given in Eq. (6.4), resulting in an activation energy of 628 24 kJ/mol for diffusion-controlled deformation. 

K using an activation energy of 590 kJ mol . The data are represented by a straight hne with a stress exponent of n 4. In this case, the deformation is attributed to dislocation-climb-controlled intragranular creep (Fig. 6.47). 

Vacancy diffusion needs not to occur through the bulk material in diffusion creep. Instead, vacancies may move directly along the grain boundaries (see figure 11.7). The activation energy of vacancy diffusion along a grain boundary is smaller than in the bulk because the lattice is distorted. 

---