Creep experiments in a neutron irradiation environment have been con­ducted since the early 1960s and continue today. Since creep without irra­diation tends to have a relatively high initial rate, and since irradiation damage builds up with time, the creep curve (strain vs time or fluence) is usually divided into primary and secondary stages, as shown in Fig. 4.68 . Whether or not a true ‘steady state’ creep rate is obtained in-reactor is problematic to prove, but in any case it is assumed for the analysis of the
important parameters influencing creep strains and rates. A tertiary stage is not reached except in very rare, localized high stress cases.

In-reactor creep of any component or specimen consists of three parts: (1) thermal creep (which in most practical cases is small, and in all cases is different from thermal creep of unirradiated material), (2) true irradiation creep and (3) irradiation growth. The most common practice is to assume that the three parts are independent and additive, although from a mecha­nistic view this is questionable. In data analyses, only in-reactor creep has been analysed typically, without any separation of thermal and irradiation creep components; if possible, any irradiation growth should be subtracted from the experimental creep measurements.

The steady state creep rate, є, is most often expressed as a function of variables:

d£ ~Q

є = — r = f(Ф, A, e RT, f, G,p, A) [4.2]

dt

and in-reactor strain, e, is often expressed for a specific alloy and alloy con­dition as:

_ Q_

є = А(ф)т Ae RT

where p, n and m are constants and ф is the neutron flux, n/m2/s or dpa/s a is the applied stress, MPa t is the time, s

Q is the activation energy, cal/mole

Q/R is the activation temperature, K

R is the universal gas constant, 1.98 cal/K/mole

T is the temperature, K

f is a texture parameter

G is the grain size

p is a parameter related to the dislocation density and degree of CW A is a metallurgical factor for a specific alloy.

Recent extensive reviews of creep data have been given by Holt (2008) and Adamson et al. (2009, noted below as AGP, 2009).

Using large amounts of data, it was determined (AGP, 2009) that in the temperature range 275-390°C (548-663K), with flux in the range 0.50-50 x 1013 n/cm2/s, E > 1 MeV and independent of the direction of creep, material composition and material condition, the flux dependency, p, is 0.85. Purely irradiation creep mechanisms would predict p = 1, but the inevitable con­tributions of thermal creep tend to reduce the value below unity. For the very low neutron fluxes that occur at fuel bundle extremities, lower values of p would be expected. For the value of m, giving the fluence dependency, Soniak et al. (2002) obtained ‘m’ near 0.5.

Continued analyses conclude that the stress dependency of in-reactor creep is linear, n = 1, in the most relevant stress range of <10-200 MPa. This applies for temperatures in the range of 275-390°C (548-663K), inde­pendent of the direction of creep, flux, material composition and material condition. Mechanistic analyses, described briefly above, predict a range of n-values from 1 to higher than 2. SIPA and elastodiffusion predict a linear stress dependency, but the favoured climb and glide mechanisms predict higher values of n.

The temperature dependence of in-reactor creep also has components based on thermal and irradiation processes. It is generally assumed that pure irradiation creep has only a small temperature dependence (often the process is called ‘athermal’), but thermal processes play an increasingly large role at temperatures above about 300°C (573K). At temperatures above about 350°C (623K) thermally produced vacancies and annealing of small vacancy clusters compete with irradiation-produced PDs, and thermal processes dominate in-reactor creep by 400°C (673K). In all cases increas­ing the temperature increases the creep rate. Analysis of a large amount of normalized data by Garzarolli (in AGP, 2009) indicates that temperature dependency in the most interesting range of 270-400°C varies and depends on several important variables include cold work, Sn content, alloy content and fabrication history. The lowest temperature dependency is ascribed to heavily cold-worked Zircaloy-2 and -4, while the highest is for Zr-2.5Nb CANDU pressure tubes. (It should be noted that the operating temperature of CANDU pressure tubes is generally below 310°C, 583K.)

Several metallurgical factors influence creep. Disturbances in the regular­ity of the lattice such as those caused by under — or over-sized atoms interfere with dislocation motion and act as sinks for irradiation-produced vacancies and SIAs. Of particular importance are the elements disturbing the regular­ity of the lattice and having appreciable solubility in Zr: Sn, Nb and O, all of which increase the creep strength (Seibold & Garzarolli, 2002). On the other hand, an element having low solubility, S, has been proposed to increase the creep strength of Zr-1Nb alloys (Soniak et al, 2002; Mardon and Bordy, 2004; Rebeyrolle et al, 2004). The mechanism is not yet well defined, but is proposed to be a dislocation interaction effect.

Cold working affects three metallurgical parameters: dislocation den­sity, grain shape and texture (anisotropy), all of which can affect creep rate. The general observation is that cold worked or cold worked/stress relieved (CWSRA) zirconium alloys have higher creep rates than RXA alloys. An example is shown in Fig. 4.69 (Soniak, et al, 2002). Mechanistic analyses are, once again, not firm on a quantitative effect of dislocation density, but most, including varieties of the SIPA mechanism, predict higher in-reactor creep rates with higher dislocation density, p. Stress relaxation experiments

suggest a moderate dependency (p02), whereas for irradiation growth it is about p0 8, summarized by Holt (2008).

Since the HCP crystal structure is anisotropic, many properties are expected to be anisotropic, and so it proves to be. The often-preferred slip (glide) direction is <a> (prism slip), as is the preferred diffusion direction of SIAs, both occurring parallel to the basal plane. The prevalence of basal slip increases in irradiated material, but even so prism slip predominates at low stress, so the climb and glide mechanism predicts higher creep strain in the <a> direction (in Zircaloy components this is called the longitudinal direc­tion), as do conventional and modified SIPA mechanisms. Although texture (as defined by basal pole figures) is nearly the same for RXA and SRA materials, the anisotropy as expressed by anisotropy coefficients are differ­ent for the two. Forfuel rods, for example, creep in the rod results in a rod length decrease for SRA material and an increase for RXA material (AGP, 2009). Analyses confirm that for uniaxial stress conditions, creep of Zircaloy components in the longitudinal direction is greater than in the transverse direction (Fidleris, 1988). Zr-2.5Nb pressure tubes have a different texture to most Zircaloy components, so the anisotropy is different to that for typical Zircaloy components, but the basic principles are the same (Holt, 2008).