Creep is time-dependent, thermally activated plastic deformation process, as described in Chapter 5 where we entirely dealt with the conventional thermal creep

that generally occurs at elevated temperatures (>0.4Tm) under stress. Materials under stress could undergo creep effects (contributes to the dimensional instability of an irradiated material) under energetic particle flux (such as fast neutron expo­sure) even at much lower temperatures where thermal creep is essentially negligi­ble in the absence of neutron irradiation. The generation of point defects is at the heart of the irradiation creep process. One way to understand the process is from the point of vacancy production in materials from two sources — thermal vacancies (C*) and neutron-induced (C*). That is, the total vacancy concentration Cv = C* + C*. Thus, the total irradiation creep rate (eirr) can be expressed in two components:

eirr = e *+ eth (6.12)

where e* is affected by the radiation component and eth is affected by the thermal creep contribution. However, irradiation creep effect could be quite complex and research is ongoing to fully understand the effect in different material systems. Here, we lay out a general discussion on irradiation creep by categorizing it into two types: radiation-induced creep and radiation-enhanced creep. This is a rather simplistic way of describing irradiation creep, although it has substantial pedagogic advantages.

Radiation-induced creep occurs at lower homologous temperatures at which ther­mal creep is negligible (eth), that is, not thermally activated. At these lower tempera­ture regions, the vacancy concentration produced by atomic displacements due to irradiation (that are not in thermal equilibrium, but produced as a function of flu — ence) could be large enough to induce creep deformation under the application of

stress. A simple relation used for describing radiation-induced creep rate (eirr) is given by

eirr и e* = Bop, (6.13)

where B is a constant relatively insensitive to the test temperature, o is the applied stress, and p is the neutron flux. From the above relation, it is clear that the radia­tion-induced creep rate is directly proportional to the stress and the neutron flux. In essence, it means that with increasing stress and neutron flux, the creep effect would accelerate. If one integrates the above equation over time, it can be seen that the creep strain would vary with the neutron fluence (the product of flux and time). In 1967, Lewthwaite and coworkers in Scotland [30] demonstrated irradiation creep in several metals and alloys at 100 ° C and published their findings in Nature (a well — known journal). Later, the radiation-induced creep has been observed in a number of alloys, including ferritic-martensitic steels (HT9 and T91) and austenitic steels as well as zirconium-based alloys. One way to study the irradiation creep behavior has been to irradiate stressed specimens under neutron exposure and study the stress relaxation behavior. There have been several studies using this mode of testing [31]. Irradiated annealed 304-type austenitic stainless steel specimens at 30°C in a reactor under a neutron flux of 1013 ncm-2 s-1 for ~127 days to a total fluence of ~1.1 x 1019ncm-2. The specimens were subjected to torsional strain due to the application of ~30 MPa. It was found that the level of relaxation in the irradiated material was about a factor of 40 more compared to that in the unirradi­ated (control) material under comparable temperature and stress.

Radiation-enhanced creep, as the term suggests, is the creep process enhanced by irradiation. This occurs at homologous temperatures at which thermal creep can also operate. As we know, generation of defects like vacancies at higher tem­peratures increases the thermal vacancy concentration in the material. This translates into the increase of diffusivity. Thermal creep rate can be shown to be proportional to diffusivity (Section 5.1). Now the addition of more vacancies pro­duced through fast neutron irradiation can augment the vacancy concentration further, enhancing the overall creep rate. In this case, total radiation enhanced creep rate is given by

eirr = e * + eth = Bop + ADon, (6.14)

where eth = ADon. Here A is a constant, D is the diffusivity, o is the applied stress, and n is the stress exponent (n could be 5 or some other number depend­ing on the conditions) (see Eq. (5.40)). In Eq. (6.14), D is proportional to the vacancy concentration that comprises contributions from thermal vacancies (e-sf=lT) and atomic displacements due to radiation (/ dpa).

One example of radiation-enhanced creep is shown in Figure 6.39 from the work of J. R. Weir [32]. Weir determined in-reactor stress-rupture properties of hot — pressed beryllium. Figure 6.39 shows the stress versus rupture time for three beryl­lium materials under three conditions. The neutron flux was 9 x 1013 ncm-2 s-1. The results of the unirradiated material are compared with those of two types of irradiated materials. Some specimens were loaded after placing it in-reactor;

Rupture Time (h)

Figure 6.39 In-reactor stress-rupture properties of hot pressed beryllium at 600 °C.

however, a few specimens were loaded later after the specimens were irradiated for 800 h. The temperature was kept at ~600 °C (i. e., a homologous temperature of ~0.56). The stress-rupture life of the specimens got reduced when the specimen was loaded at once. But the specimen that was irradiated for 800 h accumulated more radiation damage leading to less rupture life. Similar reductions in stress — rupture life were found when stress-rupture tests were conducted on an irradiated 316-type austenitic stainless steel in the temperature range of 540, 600, 650, and 760 °C. Prior to stress-rupture tests, the steel specimens were irradiated up to a total neutron fluence of 1.2 x 1022 ncm~2 at an irradiation temperature of 440 °C.

Irradiation creep sometimes operates at the same time as swelling and radiation growth (if applicable). In such situations, it becomes important to distinguish the contribution of irradiation creep to the total strain. Toloczko and Garner [33] have analyzed irradiation creep data from HT-9 and used the concept of creep compliance (B0) to estimate the contribution of irradiation creep independent of swelling. Figure 6.40 shows the inclusion of an irradiation creep regime along with other thermal creep mechanisms on a deformation mechanism map of a 316-type stainless steel.

6.2.5