The activation energy of deformation is dependent on the rate controlling mechanism of creep. As shown in Table 3.1, the activation energy changes with the underlying creep mechanism. For example, the activation energy of
creep is equal to that for grain boundary diffusion in the case of Coble creep and equal to lattice diffusion activation energy with N-H creep. Usually the activation energy of deformation is constant if a single thermally activated process is rate controlling. The Arrhenius plot — log of strain rate of defor­mation against reciprocal of temperature (in K) — is a straight line in such a case. However in certain cases more than one mechanism of creep, each with different activation energies, could be rate controlling. The Arrhenius plot in such a case is curved in the temperature range where the activity of the mechanisms is comparable. There are two cases which should be considered.

In case 1, the mechanisms of creep are independent of each other and hence occur simultaneously or in parallel. Each mechanism contributes a strain ei and the strain rates of deformation are additive. The total strain rate of deformation in such a scenario is given by

[3.38]

For example, for the case of two mechanisms occurring simultaneously, the temperature dependence of strain rate is given by

[3.39]

The Arrhenius plot for such a scenario is shown in Fig. 3.15a, and if Q1 > Q2, mechanism 1 makes the dominant contribution to the creep rate at high temperatures and mechanism 2 becomes dominant at low temperatures. In the temperature range where the activity of both mechanisms is compara­ble, the Arrhenius plot is curved. At any given temperature, the faster mech­anism is expected to control the rate of deformation.

In case 2, the mechanisms of creep occur sequentially and are known as series or sequential mechanisms. One mechanism cannot operate unless the other has taken place and vice versa, Here instead of the deformation strains, the time periods over which each mechanism has occurred are addi­tive. Thus the total strain rate of deformation, assuming each mechanism contributes to the total strain, is given by

[3.40]

For the case of two mechanisms occurring sequentially, the temperature dependence of the creep-rate is given by

3.15 Arrhenius plots for (a) parallel mechanisms and (b) sequential mechanisms of creep.

The Arrhenius plot for such a scenario is illustrated in Fig. 3.15b. Here, in any given temperature range, the slower process dominates the creep rate. However the amount of creep strain may not necessarily be controlled by the slower process. It could be possible that the slower mechanism contrib­utes little strain but allows the other mechanism with a greater strain contri­bution to operate. The dislocation glide-climb creep mechanism described earlier (Fig. 3.12) and Equations [3.30-3.34] is an example for this type of series mechanism while the simultaneous occurrence of N-H and Coble creep (Equations [3.17] and [3.18]) falls under parallel mechanisms.