Irradiation creep of austenitic steels can be envisaged as having four stages. These are the transient regime, the creep regime in the absence of swelling, swelling — enhanced creep, and creep disappearance. The first three contributions have traditionally been described using the following equation.1

2 = A[1 — exp(—dpa/t)] + B0 + DS.

a

The equivalent strain per unit equivalent stress, sometimes called the creep modulus B, is the sum of a transient contribution that saturates usually at a dpa or less, the creep compliance B0 in the absence of swelling, and stress-enhanced creep where the enhanced creep rate is proportional to the void swelling rate. Bubble swelling also accelerates irradi­ation creep, but the influence is expressed primarily in the early stages of creep.167

The coefficients A and t are empirical, experimen­tally determined constants that are very material- specific (composition, thermal-mechanical treatment and texture) and sometimes stress-state dependent. For many high-exposure applications, the transient can be ignored. Even more importantly, the transient term can be obscured if significant precipitation — related strains are developing concurrently. In gen­eral, the magnitude of the transient-induced strain increases with increasing stress, but the duration in time or dpa usually does not increase with stress.

The creep transient involves both the dose needed to establish equilibrium densities of point defects, but most importantly, it involves the dose required for establishment of the quasi-equilibrium dislocation density. The transient is most pronounced for cold — worked steels that start at higher dislocation density. As recombination-annihilation mechanisms reduce the dislocation density the instantaneous creep rate drops until the quasi-equilibrium dislocation density is reached and the steady-state creep rate B0 is estab­lished. For any austenitic steel it can be safely assumed that B0 is ~1 x 10—6 (MPa dpa)—1 and is effectively a ‘crystal constant’ similar to the 1% per dpa swelling rate of austenitic steels.

The creep compliance B0 is not only independent of composition but also starting state, dpa rate, and temperature over the range of reactor-relevant condi­tions. There appears to be one exception, however, in that the creep rate at temperatures somewhere below ^100 °C can increase significantly above B0, as shown at 60 °C by Grossbeck and Mansur for various austenitic steels.168,169 At very low temperatures, vacancies are relatively immobile and cannot cancel the climb of dislocations produced by more mobile interstitials. Examples of such behavior have been seen in other studies.170,171 A good example of acceler­ated creep at low temperatures is shown in Figure 66.

The swelling-creep coupling coefficient D was originally assumed also to be a crystal constant at ^0.6 x 10—2MPa,—1 but as discussed later, it was found that D declines with increasing swelling to approximately one-third of this value or even to zero, depending on the stress state, stress history, and swelling history. This decline is an expression of the fourth stage of irradiation creep, variously designated as creep cessation, creep disappearance, or creep damping.

One feature of irradiation creep that distinguishes it as different from thermal creep is that it varies with stress to power 1.0 rather than a higher power typical of thermal creep. This linearity is shown in Figure 67. The creep equation presented above also predicts

that the creep rate is proportional to dpa both before and after swelling begins.

As discussed later, some important characteristics of creep have been redefined in the past two decades, especially for the creep compliance. B0 is known to be generally independent of alloy composition, thermal-mechanical treatment, irradiation tempera­ture, and dpa rate, but swelling is known to be very sensitive to all of these variables. This means that the irradiation creep modulus B quickly assumes all of the parametric sensitivities of void swelling. When the swelling rate reaches only 0.017% per dpa the swelling-enhanced contribution equals the B0 contri­bution, effectively doubling the creep rate.

There are a number of consequences of the cou­pling between swelling, creep, and precipitation — related strains.

1. The onset of swelling can be detected by a jump in creep modulus B long before measurable swelling — induced changes in dimension can be detected, and often before microscopy confirms the pres­ence of voids.

2. Attempts to measure B0 in the presence of low and sometimes undetectable levels of voids or bubbles will lead to misleading values, usually higher than ~1 x 10-6 (MPa dpa)-1.

3. Any local stress gradient generated by a swelling gradient will be reduced to a very low level by a local gradient of creep exactly matched to that of swelling.

4. Attempts to measure B0 in the presence of precipitate-related strains will lead to mislead­ingly different values, either too large, too small, and even negative values.

5. Whenever the stress state is generated solely by swelling, the coupling between creep and swelling guarantees that the system cannot operate at a stress level higher than D-1 or 160 MPa.1,16