Category Archives: Materials’ ageing and degradation in. light water reactors

Sources of further information and advice

Major sources are many, including:

• ZIRAT Annual Reports and ZIRAT Special Topic Reports, A N T International, Molnlycke, Sweden (www. antinternational. com).

• The series of Zirconium in the Nuclear Industry, International Symposiums, ASTM International, West Conshohocken, PA, USA, held every 2-3 years.

• Zirconium Production and Technology: The Kroll Medal Papers 1985­2010, editor, R. B. Adamson, ASTM International RPS2, ASTM I, West Conshohocken, PA, USA, 2010.

• Proceedings of the LWR Fuel Performance Meeting/Top Fuel/WRFPM, held annually in the US, Europe or Asia.

• References given in Section 5.9.

• The previous chapter of this book, ‘Properties and Performance of Zirconium Alloy Components for Nuclear Power Light Water Reactors’, R. B. Adamson, Zircology Plus, Fremont, CA, USA and P. Rudling, ANT International, Molnlycke, Sweden.

5.4 Acknowledgements

The authors sincerely thank our colleagues in the expert network staff of ANT International: Alfred Strasser, Friedrich Garzarolli, Brian Cox and Charles Patterson. Their discussions, their expertise, their comments and their contributions to the ZIRAT programme reports have made Chapter 5 a possibility.

Major components experiencing corrosion

We continue the chapter by describing the major components within the reactor which are subject to corrosive damage.

1.2.2 Reactor pressure vessel (RPV)

Reactor vessel heads (RVH) can experience different types of corrosion. In 2002 boric acid crystal deposits and iron oxide were found to have flowed out from several openings in the lower service structure support skirt after removal of insulation from the Davis-Besse RVH, after an accumulated «16 effective full power years (EFPYs) of operation. A large corrosion cav­ity was found on the downhill side of the low-alloy steel RVH.1 Boric acid corrosion wastage occurred on the RPV head surface and lead to a total low-alloy steel loss of ~4.3 cm3. Boric acid corrosion was not the only mech­anism involved in the degradation: it was supposed that erosion-corrosion may have played a role in the initial cavity formation; galvanic corrosion between the low-alloy steel and the stainless steel occurred around the perimeter of the exposed cladding; and axial stress corrosion cracks were observed in five control rod drive mechanism (CRDM) nozzles adjacent to the J-groove weld.1 Both Alloy 600 and 182 weld metal failed by pri­mary water stress corrosion cracking (PWSCC). There was no conclusive evidence that hot cracking contributed to the J-groove weld cracking. The Davis-Besse event illustrates the severe consequence of in-service crack­ing of RVH-penetration components fabricated from Ni-base Alloy 600 and 182 weld metal in which PWR water leaking from the cracked nozzles severely corroded the RPV head low-alloy steel material down to the 308 stainless steel cladding material.2

In the vessel, internals are exposed to irradiation. Under neutron flux the microstructure of the material can evolve: segregation at the grain boundaries associated with dechromization and hardening induced by the recombination of point defects. The first cracked baffle-former bolts were observed in 1988 in Bugey Unit 2 (PWR, France), during ultrasonic testing (UT) controls. Several bolts were examined3-6 and the failure was attributed to a particular case of SCC: irradiation assisted stress corrosion cracking (IASCC). Periodic inspections and a replacement program were set up in the affected reactor types. The assessment of the damage affecting the bolts revealed that significant differences in cracking behaviors exist between the various reactors. For instance, taking into account the number of cracked bolts, Bugey Unit 2 (100 cracked bolts in 140 000 h) and Fessenheim Unit 2 (46 cracked bolts in 140 000 h) are the most affected reactors (the remaining reactors were mostly less than 30 cracked bolts). Additionally, their bolts were made from the same heat, suggesting the influence of initial composi­tion and microstructure.

4 Effect of a multi-axial state of stress

The final case study deals with understanding the effect of a multi-axial state of stress on creep life predictions. All models discussed inadvertently pre­dict the deformation rates under a uniaxial state of stress. However in real life situations, the engineering structures experience a multi-axial state of stress as well as variations of loading with time. Here we present an example of how a multi-axial state of stress would affect diffusion creep. For a more detailed account of the effects of multi-axial state of stress and loading his­tory, we refer the reader to Penny and Marriott.82

Raj109 proposed relationships to understand the strain rates of deforma­tion during diffusion creep under a multi-axial state of stress. Since strain rate in diffusion creep has a linear correlation with applied stress, Raj sug­gested that under a multi-axial state of stress the strain rates of deformation can be represented in terms of principal stresses and strain rates,

(a o-2 + a ^

. _k (а а+а^

,’£ 3- k3

( а + а2

1 1 2 ,

,l2 — k2 ^a2 2

3 2

к 2 /

[3.63 ]

These relationships are borrowed from equations of elasticity and Poisson’s ratio has been assumed to be 0.5 for constancy of volume. Here k1, k2 and k3 are creep constants that correspond to the appropriate diffusion creep mechanism. These strain rates of deformation will be identical for an iso­tropic or equiaxed microstructure but would be different for non-isotropic grain configuration. Also the diffusional creep should be independent of the hydrostatic state of stress which has an effect only on the diffusivity term.

Materials such as Zr and other hexagonal close packed metals and alloys exhibit distinct crystallographic textures leading to anisotropic mechanical and creep properties. Zr-alloys are commonly used as thin-walled tubes to clad radioactive fuel such as UO2 and tube reduction processes render them highly textured during the manufacturing of cladding tubes. Prediction of dimensional changes in-reactor of the cladding along both the diametral and axial directions requires consideration of multi-axial loading particularly with axial load superimposed with internal/external pressure. A modified

Hill formulation was shown to be convenient wherein the generalized stress, ag, is defined as the uniaxial stress along the tube axial direction,110

_2 _ R (( — ъ?)2+RP ( — ъ )2+P ( — ъ )2 [3.64]

g P(R +1) ‘

The parameters, R and P, are the mechanical anisotropy parameters. Using the Prandtl-Reuss energy balance in conjunction with the above yield crite­rion, the strain increments or strain rates along the three orthogonal direc­tions are related to the respective stresses

£ r

[(R+P)

-R

-P "

> г _

_ bg

P(R + 1 )Og

-R

-P

R(P + 1) — RP

-RP P(R +1)

°z _

where £g is the generalized strain rate corresponding to the generalized stress ag. These equations define the yield and flow loci, and the corre­sponding creep locus is referred to at a constant energy dissipation-rate, W (= atj etj = ag eg).111 It is clear from the above equations that the mechan­ical anisotropy parameters, R and P, are the transverse contractile strain (-rate) ratios in uniaxial tests. The contractile strain ratios (CSRs), R and P, define the resistance to wall thinning of an anisotropic material and thus control the formability which is of importance to the material manufac­turers, in tube reduction processes, sheet drawing and forming, etc.112 The mechanical anisotropy parameters are directly related to the preferred ori­entations of the grains. Thus obtained creep loci for cold-worked stress — relieved annealed and following complete recrystallization are shown in Fig. 3.28.113 Crystallite orientation distribution function (CODF) creep model predictions113 are shown as solid lines along with the experimental results.

These types of creep studies are not commonly found albeit materials in real engineering structures experience such complex multi-axial loadings. Additional complexity is encountered in attempting to predict transients in creep under such multi-axial loading.

Parameters

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_

Подпись: [4.3]

Подпись: 4.68 Strain vs time behaviour during creep under constant load, and the three stages of creep.

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

image235

Fast fluence фі (n/m2)

4.69 Effect of metallurgical condition and alloy composition on hoop creep strain vs fluence for SRA and RXA Zircaloy-4 and RXA M4 and M5. (Source: Reprinted, with permission, from Soniak et al. (2002), copyright ASTM International, 100 Barr Harbor Drive, West Conshohocken, PA 19428.)

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).

Chemical measurements

Chemical measurement techniques determine cable condition by measuring a chemical property of the cable insulation and then correlating the results with a known measure of electrical performance (U. S. NRC, 2001). In chem­ical cable testing, a small piece (a few milligrams) of cable insulation or jacket material is shaved off for chemical analysis in a laboratory using one of the following techniques:

• oxidation induction time/temperature (OIT/OITP) test;

• Fourier transform infrared (FTIR) spectroscopy;

• gel content or gel fraction tests;

• density tests.

Chemical tests are not considered in-situ since they require a small sam­ple, but the sample is so small that they are sometimes considered non-destructive.

The polymers used in cable insulation respond to radiation and thermal degradation through oxidation processes. The greater the radiation or ther­mal ageing conditions imposed on the cable insulation, the more antioxidants (manufactured into the insulation to slow degradation) in the polymer are consumed. Differential scanning calorimetry (DSC) instruments can be used to measure the rate of oxidation induction time (OIT) and oxidation induction temperature (OITP) in polymers. The OIT and OITP values correlate with the degree of cable insulation degradation. OIT — a measure of the remaining anti­oxidant in the insulation polymer — decreases with age (U. S. NRC, 2001).

The DSC instruments measure the difference in heat flow between a polymer sample oxidizing under heat and an identical empty sample pan (acting as a control) also being heated. The levels of antioxidant in the sam­ple will determine how long it takes for the heated polymer sample to begin oxidizing. The complete depletion of antioxidants would typically simulate polymer degradation after a 20-year operational life. A sample that takes a long time to begin oxidizing has substantial antioxidant levels, and therefore minimal degradation (U. S. NRC, 2001).

Fourier transform infrared (FTIR) spectroscopy, a laboratory technique for studying the molecular structure of materials,, can identify operating conditions where heat may cause cable insulation to become brittle or crack. FTIR involves applying infrared radiation to a small piece of cable insulation using a spectroscope. The spectroscope measures the ability of the material to absorb or transmit the radiation. When the chemical bonds in the sample absorb the radiation they begin to vibrate at specific wave­lengths. The FTIR technique compares the actual measured maximum vibrations of these chemical bonds to their known maximum vibrations to ascertain to what extent the bonds have already oxidized or degraded over time. The more the cable surface has been exposed to heat over time, the more likely the measured vibrations of the sample chemical bonds will dif­fer from the original values.

FTIR is extremely accurate — measuring to one tenth of a degree Fahrenheit — and enables relatively easy, trendable, non-destructive degra­dation monitoring. However, it requires expensive equipment and a small sample, which may be difficult to obtain from remote sections of a cable circuit (U. S. NRC, 2001; 2010a; 2010b).

N-H and Coble creep

The possibility of creep occurring by stress-assisted diffusional mass trans­port through the lattice was first considered by Nabarro18 in 1948 and Herring19 in 1950. A few years later, Coble20 proposed that grain boundaries could also provide an alternative path for stress-directed diffusional mass transport to take place. Figure 3.4 provides schematics of N-H and Coble creep mechanisms.

image011 image012

As Fig. 3.4 indicates, under the application of a stress, grain boundar­ies normal to the applied stress will develop a higher concentration of vacancies. On the other hand, grain boundaries parallel to the applied stress (lateral grain boundaries) will experience compressive stresses and will have a reduction in vacancy concentration. This causes a concentra­tion difference between the two boundaries leading to a flux of vacan­cies diffusing from the normal grain boundaries to the parallel or lateral grain boundaries (atoms diffuse in the opposite direction). The diffusion of vacancies can occur through the lattice (N-H) or via grain boundaries (Coble creep). The diffusion of vacancies or the motion of atoms from one grain boundary to another leads to a crystal strain which in turn contrib­utes to the deformation of the grains and consequently the material. The calculations of the steady-state flux of vacancies and the corresponding steady-state creep rate lead to the following relationships for N-H and Coble creep, respectively,

3.4 ( a) Schematic of N-H creep. Mass transport occurs through the lattice. (b) Schematic of Coble creep. Mass transport occurs along grain boundaries.

L

d 2kT

[3.17 ]

Db8boQ

d? kT ‘

[3.18 ]

£ = B

H

£ =

c

image013 Подпись: [3.19]

In Equation [3.17], BH is the N-H constant and has a value of about 12-15, Dl is the lattice diffusivity, Q is the atomic volume and к is the Boltzmann constant. In Equation [3.18], Bc is the Coble constant and has a value of 150, Db is the grain boundary diffusivity, and 8B is the grain boundary thickness. From the above relationships it is understood that the creep strain rate var­ies linearly with stress and is inversely proportional to the grain size. Usually with decreasing grain size, it is observed that Coble creep dominates N-H creep and vice versa. But when both the mechanisms operate in parallel the strain rate can be expressed by

Подпись: Deff = DL Подпись: d D Подпись: [3.20 ]

where Deff is the effective diffusion coefficient and is given by

From Equations [3.19] and [3.20], it is clear that the grain boundary diffu­sion will contribute more to the creep rate for larger Db/Dl ratios and for smaller grain sizes. In the derivation of the N-H and Coble creep equations, the following assumptions were made:

i. The grain boundaries are perfect sources and sinks of vacancies, and

ii. The initial dislocation density of the crystal is low.

This implies that the only sources and sinks for vacancies are the grain boundaries. Since their discovery, both N-H and Coble creep have been found to occur in a variety of materials and experimental results have agreed well with the proposed theory.21-26

Material used in fuel assemblies

The materials used for the FA components are Zr alloys, Inconel (precip­itation hardened Inconel X-750, Inconel 718 and solution treated Inconel 625) and stainless steel (SS 304L) (Cox et al., 2006). A low cobalt content is desired in the stainless steel and nickel base alloys to keep the activity trans­port by the coolant and the radiological exposure of the workers (man-rem) low. Since these alloys have high thermal neutron capture cross sections

Подпись: (b)
image120

(a)

4.6 (a) VVER-440 operating FA; (b) VVER-1000 FA (Cox et al., 2006).

that lead to reactivity losses, most of the FA components within the core are made of low cross section Zr alloys. These Zr-Sn based alloys are heat treated to reach optimum mechanical and corrosion resistance properties. Spring materials need to be made of materials with low stress relaxation rates, such as Inconel X-750 or Inconel 718. These Ni base alloys are gen­erally heat treated to reach an optimum precipitation hardening. Table 4.2 presents an overview of alloys used in LWR and their typical compositions.

Table 4.3 provides data for different Zr alloys used by different fuel vendors (Cox et al. , 2006). It is noteworthy that there are so many differ­ent Zr-alloys for PWR applications. Originally, Zircaloy-4 (Zr-4) was used in PWRs, but increased corrosion rates at extended burnups resulted in the

Table 4.2 Chemical compositions of various stainless steels and Ni base alloys

Material

Fe

(wt%)

Ni

(wt%)

Cr

(wt%)

Mn

(wt%)

Si

(wt%)

Mo

(wt%)

Ti

(wt%)

Nb

(wt%)

Al

(wt%)

AISI 304

Bal.

10

19

<2

<0.75

DIN 1.4541

Bal.

11

18

<2

<0.75

0.4

Inconel X-750

7

Bal.

15

<1

<1

2.6

1

0.7

Inconel 718

17

Bal.

19

0.5

0.75

3

0.7

5

0.6

Inconel 625

2.5

Bal.

22

0.3

0.1

8.8

0.3

3.9*

0.2

*(Nb + Ta) = 3.9 wt%.

Source: A. N.T. International (2011) and Cox et al. (2006).

need to develop more corrosion-resistant alloys. However for BWRs, whilst the material originally selected, namely Zircaloy-2 (Zry-2), appeared to have adequate corrosion performance, recent burnup experience has shown that alloys with better corrosion and hydriding resistance are needed. Improved versions of Zry-2 and advanced alloys are being developed. Initially pure Zr-sponge liner was used as a PCI remedy for BWR applications. It was later found that the pure Zr sponge material results in a tendency for secondary degradation of failed fuel and therefore all fuel vendors added some alloying elements to increase the resistance towards secondary degradation of failed rods. The most potent alloying element to obtain this increased resistance is Fe by improving corrosion resistance of the liner material. However, Fe also has a tendency to decrease PCI performance. In RBMK and VVER reactors, E110 has always been used as fuel cladding material while E125 is being used for some of the structural components in the fuel assemblies.

Embrittlement of the cladding

ECCS activation will stop the temperature rise and start to cool the core by injection from the bottom of the core in a PWR and from the top of the core in a BWR (Strasser et al, 2010b). The ‘cooling’ process as shown in Fig. 5.9 is relatively slow until the emergency coolant contacts the fuel that has been at the PCT. At that point, in the range of 400-800°C and identified as ‘quenching’ in Fig. 5.9 , the water from the ECCS will reduce the cladding temperature at a rapid rate (1-5°C/s) by re-wetting the cladding heat trans­fer surface. The process will collapse the vapour film on the cladding OD and cooling will be by nucleate boiling. Thermal shock due to the sudden change in heat transfer conditions can fracture the cladding at this stage and the ability of the cladding to withstand the thermal stresses will depend on the extent of oxidation and degree of cladding embrittlement that occurred during the LOCA transient.

The oxidation embrittlement process and final structure of the cladding after completion of the LOCA cycle is as follows (Strasser et al., 2010b):

• First, the increasing water and steam temperatures during heat-up increase the reaction rates with the cladding and increase the conver­sion of the cladding surface into thicker ZrO2 films.

• As the LOCA temperature passes the levels where a ^ в transforma­tions start and finish, the resulting structure consists of:

— The growing ZrO2 layer.

— A zirconium alloy layer with a very high oxygen content which sta­bilizes the a phase.

— The bulk cladding which is now in the в phase.

• The ECCS initiated quenching phase cools the cladding back down through the в^а transformation temperature and the bulk cladding is now re-transformed from the в into the a phase and referred to as the ‘prior or former в phase.’

Oxygen and hydrogen affect the formation of the structure as follows dur­ing the oxidation (Strasser et al, 2010b):

• Oxygen diffuses from the ZrO2 to the bulk cladding which is in the в phase at the high temperature (HT); however, the в phase has a low sol­ubility for oxygen.

• Increased hydrogen levels from the oxidation reactions prior to and dur­ing the LOCA increase the diffusion rate and solubility of oxygen in the в phase >1000°C.

• Wherever the solubility limit of oxygen in the в phase is exceeded, the excess oxygen stabilizes the a phase.

• The oxygen stabilized a phase forms next to the ZrO2 layer and grows, as does the ZrO2 layer, at the expense of the bulk cladding in the a phase and as a result after quenching in the ‘prior в phase.’

The final integrity of the cladding is based on the properties of the prior в phase, since the ZrO2 and oxygen stabilized a zones are too brittle to sus­tain a load (Strasser et al, 2010b). ‘Oxygen is the major source of cladding embrittlement as noted above and hydrogen is less likely to contribute to the embrittlement except to the extent that its presence increases the oxy­gen solubility’ (Strasser et al., 2010b ).

The n > 7 creep regime: power-law breakdown

Creep regimes with a stress exponent greater than 7 are sometimes described as the PLB regime. There are certain dispersion strengthened alloys that exhibit high stress exponents, but such a behavior is rationalized by invoking a threshold stress for the operation of the mechanism of five power-law creep. The PLB, also known as the exponential creep regime, is described by

image047

Подпись: 3.13 ( a) Subgrain formation in Ti-3Al-2.5V in a five power-law creep regime69 and (b) deformation microstructure in Ti-48Al showing the presence of jogged screw dislocations.65
image049

[3.37]

where A and B are material constants. The constant B is related to the acti­vation volume given by the area swept by dislocation and its Burgers vector (b). It has been observed that the PLB regime occurs at a > 10-3£. At such high stresses, the dislocation density increases more than that predicted by the Taylor equation (a2) and thus PLB could be controlled by the motion of dislocations. However the mechanism of steady-state creep deformation in the PLB regime is not clearly resolved.

The activation energy, Qc, for PLB has been found to be smaller than the activation energy for self diffusion, Qsd. In some cases, the activation energy was found to be equal to the activation energy for pipe diffusion suggesting that the mechanism of deformation could be dislocation climb but facilitated by short circuit diffusion of vacancies through the large

image050

3.14 Microstructure of NaCI corresponding to the power-law breakdown regime.72

number of dislocation cores generated at high applied stresses. Sherby and Burke16 suggest that vacancy diffusion due to vacancy supersaturation at high applied stresses can be associated with the rate controlling mechanism. Others have considered breaking down of subgrain walls70 and cross slip or cutting of forest dislocations71 instead of dislocation climb as the rate con­trolling mechanism. In any case PLB remains poorly understood and this is due to the relatively small number of studies that have been carried out in this regime.

Accelerated uniform corrosion

The observation that uniform corrosion of BWR materials may increase at high fluence (burnup) has been introduced. The main factor driving this increase is connected to the initial size distribution of the SPPs and their

(a) Zry-2 Channel, 43 MWd/kgU

image201

In shadow area 120 pm, 150 ppm H2

image202

Away from shadow area 20 pm, 300 ppm H2

4.46 Zirconium oxides (a) away from and (b) near a stainless steel control blade bundle (Adamson et al., 2000).

dissolution during irradiation. This was noted by Cheng and Adamson (1987) and then by Yang and Adamson (1989), in reference to thick uni­form oxide observed in welded regions of Zircaloy-4 having totally dis­solved SPPs. A clear correlation between SPP size and increased corrosion at high fluence was given by Garzarolli et al. (1994) (Fig. 4.47) where it was shown that ‘small SPP sizes’ resulted in relatively thick corrosion films after 3 or 4 cycles in-reactor but not after 1 or 2 cycles. Huang et al. (1996) showed that when SPPs virtually ‘disappeared’ (within the resolution of STEM at that time) corrosion increased, as did hydrogen pickup. Similar results were reported by Tagtstrom etal. (2002), Takagawa etal. (2004) and Ishimoto et al. (2006). It is clear that loss of SPPs affects corrosion performance, and even earlier in fluence, hydrogen pickup.

image203

Average precipitate size (pm)

4.47 Effect of SPP size on corrosion of Zircaloy-2 cladding. (Source: Reprinted, with permission, from Garzarolli et al. (1994), copyright ASTM International, 100 Barr Harbor Drive, West Conshohocken, PA 19428.)

Zircaloy-4, which does not contain alloying quantities of Ni, is also susceptible to increased corrosion when SPPs dissolve. An example is given in Fig. 4.42 for Zircaloy-4 with a relatively large SPP, about 0.2 pm average size determined by TEM (Garzarolli, et al., 2002). It is seen that when the volume fraction of SPPs gets very low, corrosion increases dramatically.

A compilation of data for Zircaloy-2 and -4 given by Garzarolli in Adamson et al. (2006) and Garzarolli et al. (2011b) illustrates that Zircaloy-4 generally has higher corrosion than Zircaloy-2 (see Fig. 4.49). However, the hydrogen pickup fraction (HPUF) for Zircaloy-4 appears to stay remark­ably low at high burnup, as indicated by the data of Miyashita et al. ( 2006 ) and the correlation given in Fig. 4.50.

In PWRs nodular corrosion in unlikely to occur due to high hydrogen and low oxygen in the water. Accelerated uniform corrosion does occur for Zircaloy-4 in PWRs as seen in Fig. 4.51 (and Fig. 4.48) and the HPUF is rel­atively low, as in BWRs (Fig. 4.52).Those figures also show that M5 (which is basically a ZrlNb alloy with 300-500 ppm Fe) does not undergo accelerated

4.48

image204

I nfluence by irradiation to very high fluences at 290°C (563K) on corrosion and SPP dissolution of Zircaloy-4 with large SPPs. (Source: Reprinted, with permission, from Garzarolli et al. (2002), copyright ASTM International, 100 Barr Harbor Drive, West Conshohocken, PA 19428.)

4.49 Oxide thickness of Zircaloy-2 and Zircaloy-4 under isothermal irradiation in different Japanese studies. Particularly important is the data of Miyashita et al. (2006); ZIRAT 11 compilation (Adamson et al., 2006).

uniform corrosion out to exposures equivalent to 70 GWd/mt at the PWR irradiation temperature of 315°C (587K). At that temperature, irradiation effects on SPPs are similar in BWRs and PWRs. Two types of SPPs exist for M5 — pNb and the Laves phase Zr(Fe, Nb)2. At high fluence all the Fe will

204 Materials’ ageing and degradation in light water reactors

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X be dissolved into the matrix, and SPPs of pNb will exist without apprecia­ble dissolution. Again it appears that it is the existence of the SPPs which is important.