There are several models that have been proposed to describe the rate con­trolling mechanism in the five power-law creep regime. The general con­sensus is that the five power-law creep regime is diffusion-controlled. This is evident from the equivalence between the activation energy for creep and that for self diffusion. In addition, factors affecting self-diffusion such as phase transformation, superimposed hydrostatic pressure, etc., simi­larly influence creep-rates thereby rendering support to the fact that the creep-rate is proportional to self-diffusivity (DL). Thus, all models that have been proposed to explain the five power-law creep regime are built around the concept of a dislocation climb-controlled creep mechanism.

The earliest model to describe creep by dislocation climb was proposed by Weertman5663 who considered the creep processes to be a result of the glide and climb of dislocations, with climb being the rate controlling process. The glide motion of dislocations is impeded by long range stresses due to dislocation interactions and the stresses are relieved by dislocation climb and subsequent annihilation. The rate of dislocation climb is determined by the concentration gradient existing between the equilibrium vacancy concentration and the concentration in the region surrounding the climb­ing dislocation. Creep strain, however, arises mainly through the glide of dislocations. In the glide-climb model (Fig. 3.12) a dislocation produced by the Frank-Read source glides a distance L’ until a barrier of height ‘h’ is

encountered which it has to climb so that another dislocation can be gener­ated by the source.

A rather simple way of deriving the relation between the strain rate and the applied stress and temperature is given by referring to Fig. 3.12: thus the total strain is given by,

Ay = strain during glide-climb event = Ayg + Ay. « Ayg = p b L

h

t = time of glide-climb event = tg + tc ~tc = ,vc = climb velocity

vc

■ = Ay=pbbL

t h / vc

where vc <x ACv e-Em/kT, Em = activation energy for vacancy migration Y = 9bvc, where ACV = C+ — C — = C0 e lkT = C0 2sinh ^ ^ j

sothate = apbLv = apbLC0e~EmlkT 2sinh| |

H h c H h v { kT)

At low stresses, sinh (oV/kT) ~ oV/kT

e = A1pb(L/h)C0e~EmlkT (V/kT)

є = AipbLDL ~ A2pcrLDl. [3.31]

h kT h

Assuming that the dislocation density (p) varies as stress is raised to the power 2 (a2), we find that

£ = Aa’DL. [3.32]

This is known as ‘natural creep law’ and Weertman showed that L/h in Equation [3.31] varied as o15 so that

e = ADLo45.

This equation with n = 4.5 and D = DL agreed closely with the experimental results on pure aluminum. Subsequently, this has been generalized with n close to 5 and is referred to as the five power-law creep.

At high stresses, Equation [3.30] predicts an exponential stress dependence:

sinh | 0V1« exp I 0V j so that є = A1pbLDLeoV/kT УkT) УkT) h

and є = A о2 DLe°VlkT ~ A’DLe°V/kT,

as is commonly noted in the PLB regime. Both the power-law and exponen­tial stress regimes can be combined into a single equation as proposed by Garofalo6

є = ADl (sinhBo)n, [3.35]

which describes both the power-law creep regime at low stresses and expo­nential stress dependence at high stresses.

Another model that considered the non-conservative motion of disloca­tions was proposed by Barrett and Nix.64 This model came to be known as the ‘jogged screw dislocation’ model. The rate controlling mechanism is the motion of screw dislocations containing edge jogs. The edge jogs impede the motion of the screw dislocations and the non-conservative motion of the edge jogs becomes the rate controlling mechanism. This model is sim­ilar to the Weertman model in the sense that the rate of climb of the edge jogs is dependent on the concentration gradient established by the climb­ing jogs. In the original model Barrett and Nix assumed the jogs to be of atomic height, but recently Viswanathan et al.65 have shown that these jogs could be several times larger than atomic dimensions. The modified jogged screw model proposed by Viswanathan et al. has been used to satisfactorily explain the creep behavior of titanium aluminides65 and some titanium and zirconium alloys.66,67

Ivanov and Yanushkevich68 were the first to identify subgrain boundaries as important rate controlling features. The subgrain walls were suggested as obstacles to the motion of dislocations emitted within the subgrain. Subsequent plastic deformation could occur only when the dislocations
were annihilated at the subgrain boundaries. This annihilation process is climb controlled.

There are a few other network and recovery based models that appear attractive. These models consider the dislocation networks (Frank net­works) present inside the subgrains to explain the hardening and recovery during creep.