H. M. HASHEMIAN, Analysis and Measurement Services Corp., USA

DOI: 10.1533/9780857097453.2.284

Abstract: This chapter will address the ageing of nuclear power plant cables and test methods for these cables to manage ageing and verify reliability. The focus will be on instrumentation and control (I&C) cables, low-voltage cables and medium-voltage cables. Ageing due to long-term exposure to temperature, radiation, humidity, and other environments can cause the cable insulation material to deteriorate, allowing moisture into the cable. This can in turn cause cable failure and jeopardize plant safety. Various techniques are available to assess cable condition and health, including electrical and mechanical measurements, and chemical tests. Of these, electrical measurements are preferred as they allow in-situ cable testing in operating plants. Prognostic techniques estimate residual life of cables using data from periodic tests. To guard against ageing, nuclear power plants are implementing ageing management programs and regulators are writing new requirements for acceptable programs and techniques for cable ageing management.

Key words: insulation resistance, high-potential (Hi-Pot), partial discharge, quality factor, dissipation factor, AgeAlert™, LCR (inductance, capacitance, and resistance) tests, time domain reflectometry, frequency domain reflectometry, reverse time domain reflectometry.

6.1 Introduction

The thousands of miles of electrical cable and wire in light water reactors deliver the power and the signals enabling safety — and non-safety-related equipment to operate in normal and in post-accident conditions (U. S. NRC, 2010a; Hashemian, 2010; AMS Corp., 2011). All plant instrumentation and control (I&C) systems depend on reliable plant wiring (AMS Corp., 2010). They bring the necessary signals to the operators, control equipment, and safety systems, as well as delivering commands to activate relays, pumps, valves and motors. Reliable instrumentation signals are often essential to maintaining redundancy or containing an accident, and the loss of a cable can result in the loss of crucial performance and operational data. Similarly,

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In 2004, a failure occurred at Mihama 3, in the pipe of a loop condensate system between the fourth feedwater heater and the deaerator, on the sec­ondary side of the PWR.1 The accident resulted in five deaths among the workers preparing for periodic inspections at the time of the piping rupture. The rupture opening in the carbon steel pipe measured as follows: 51.5 cm (axial direction) by 93.0 cm (circumferential direction). At the time of the initial plant service, the nominal wall thickness of the pipe was 10 mm, with the thinnest section only 0.4 mm. Designed with a maximum service tem­perature of 195°C and a maximum service pressure of 1.27 MPa, the pipe ruptured when the temperature was only 140°C with a pressure of 0.93 MPa; the flow rate through the pipe was 1700 m3 h-1. There were no precursor indi­cators before the accident or special operations shown on the review of the plant parameters which could have caused the pipe to rupture. An investi­gation concluded that water quality had been maintained since the commis­sioning of the plant. A microscopic inspection was then conducted, which revealed that a fish-like pattern covered almost the entire inner surface of the ruptured pipe downstream of the orifice. The bottom of the pipe on the inside was also covered with a thick surface film. These findings are charac­teristic of FAC.

Intergranular SCC (IGSCC) and intergranular attack (IGA) are the most serious degradation processes affecting SG tubes, on the secondary side. This degradation commonly occurs in crevice regions at tube support plate and tube sheet locations or under sludge piles,8 9 although intergranu­lar SCC has also been observed in the free span of the tubes. The presence of lead in the secondary circuit was supposed to enhance IGSCC1011: Pb ions would influence passivity of the Alloy 600 surface, being incorporated into the Alloy 600 specimen surface and enhancing electronic conductance. Lead may cover a significant fraction of the Alloy and shift equilibria for the Ni oxide formation. IGA was observed at the secondary side, at the roll transition zone underneath crud deposits of SG tubes from McGuire Unit 1, for example. A wide variety of elements were present in the crud deposits, including Fe, Ni, Cr, Al, Si, Mg, Cu, Ti, Mn, Ca, K, and S. The copper was pre­sent in the deposit as metallic copper. The presence of metallic Cu indicates that the electrochemical potential was below the Cu/Cu oxide equilibrium. The SG unit had operated initially with Ni-Cu moisture separator reheaters. On the primary side, IGSCC occurs at locations of high stress, typically at regions where substantial plastic strain has occurred within the tube, during the SG manufacturing process and from in-service straining. Thus, IGSCC has been observed at the apex and at the transition from bent to straight portions of small radius U-bends.12 Examinations of SG tubes revealed the presence of axial cracks mainly at regions of transitions from expanded to non-expanded portions of the tube/tubesheet joint and circumferential cracks at the end of the transition.13

More recently, primary water SCC was found (2004) at the surface of the warm side of the divider plate of the SG #171 at Chinon Unit B4,1415 exposed to the primary environment at 325°C. Cracks initiated in a area which had been subject to grinding, on the hot side of the partition stub made of Alloy 600, close to the welds (Alloy 182), where a significant cold work was present and where a limited intergranular precipitation was observed. Examination showed intergranular and intragranular precipi­tates in the materials. The divider plate exhibited large non-recrystallized grains close to the surface. Cross-sections indicated the presence of IGSCC perpendicular to the surface. The maximal crack depth was 1.2 mm (<4% of the total thickness). After neutron diffraction examinations, the mean plastic strain present in the Alloy 600 stub was estimated as 5.3%, while the maximal strain in the heat affected zone reached 11%. In addition, the deformation was higher at the surface than in the bulk of the material. R&D studies1618 on representative hot rolled Alloy 600 have shown that no significant crack growth is expected as soon as the deformation is lower than 7-10%. Therefore, it was concluded that observed cracks could not significantly propagate in the bulk of the plate, where the deformation is low, even after 60 years.19

Materials used in the reactor undergo irradiation-assisted creep as well as thermal creep (which predominates if stress and temperature are high enough). The in-pile creep deformation of a material is the net contribu­tion by both of these processes and it is difficult to distinguished between them. Thermal creep rate of unirradiated material is different from that of

irradiated material and both are different from that for a material undergo­ing irradiation.

Zirconium base alloys, with slightly differing chemical compositions, are used for various components inside a reactor. The clad tubes in BWR and PWR are made of Zircaloy-2 or Zircaloy-4 for most of the operating reac­tors while new alloys are being proposed for the forthcoming reactors which have to withstand higher burnups (Table 3.2). The Zr-Nb alloy was intro­duced for spacer grids in place of stainless steel (from 1987 in the WWER-

Alloy Nominal chemical composition (wt.%) Component Type of reactor Sn Fe Cr Ni 0 Others Zr Zircaloy-2 1.5 0.15 0.1 0.05 0.1 Bal Fuel clad, channel, BWR (UNS grade R60802) calandria tube Zircaloy-4 1.5 0.2 0.1 0.1 Bal Guide tube, PWR (UNS grade R60804) instrument tube, calandria tube ZIRLO 1 0.1 0.1 1 Nb Bal Fuel clad, spacers PWR M5, E110 0.1 1 Nb Bal Fuel clad, spacers PWRWWER E635 1.2 0.35 0.1 1 Nb Bal Fuel clad WWER HANA 0.4 0.2 0.1 0.1 1.5 Nb Bal Fuel clad Zr-2.5wt.%Nb 0.1 2.5 Nb Bal Pressure tube (UNS Grade R60904) EXCEL alloy 3.5 0.8 Mo Bal 0.8 Nb

440 and the mid-1990s in the WWER-1000). With the recent developments in WWER fuels, Zr-1%Nb/Sn/Fe alloys, with higher resistance to irradiation induced growth, creep and corrosion, are being used for guide tubes and for fuel rod cladding with extended residence time (5-6 years).114

Fuel cladding is a key barrier in containing fission products and it is essen­tial that this barrier is strong and remains intact over a prolonged period — both in service and during repository storage. Fuel failure occurs when this barrier is degraded and breached. The fuel rod failure rate in LWRs has been significantly reduced since 1987. This achievement, besides design improvements, is due to the introduction of many improved variants of Zr base alloys over the years — the latter ones improved in properties over the earlier ones. The clad tubes in reactors undergo creep extension due to many service conditions. At low burnup, the pellet densifies and the external water pressure causes the clad tube to creep-down. On power ramp, the pellet expands and applies excess strain on the clad. This leads to the pellet touch­ing the clad thus leading to PCI failure or hydride related cracking (which are described in detail in later chapters). The sheath should have good creep rupture properties to withstand this additional strain. A non-symmetric axial growth or creep of the fuel assembly (and guide thimble) can lead to bowing of the assembly. There is another deformation which adds to the creep strain. An analysis performed at Ringhals revealed that the bowing of the rods in this reactor had been due to a large creep deformation caused by excessive compressive forces of the hold down spring on the fuel assemblies and a decrease in lateral stiffness. This problem, though, can be partly over­come by introducing advanced materials with a low growth rate and higher creep resistance (e. g. M5 or ZIRLO) for cladding and guide thimble which improves the dimensional stability of the assemblies albeit irradiation creep remains a matter of concern for these materials.

At the repository the Zircaloy clads of the fuel rods face a challenging environment. The clad temperature — a crucial parameter in influencing the cladding performance in the repository — is estimated to reach a tempera­ture of ~325°C, although the average temperature of the cladding is esti­mated to be less than 240°C.115 At this temperature and with a hoop stress of around 100 MPa due to fission gases the clad material can undergo thermal creep. The creep in clad tubes becomes all the more important with dry stor­age becoming common.116,117

• In PWRs it is found the Zircaloy-4 no longer meets corrosion and hydriding needs; therefore virtually all current PWR cladding use a zirconium alloy containing niobium. Table 4.11 lists materials currently being explored for use as cladding and structural materials, with the most widely used to date in the West, in addition to Zircaloy-4, being M5 and ZIRLO.

• For BWRs, Zircaloy-2 cladding, with various heat treatments to optimize the second phase precipitate size and distribution, remains the standard for BWR components. However, new channel materials are currently being explored to meet the challenges of channel bowing (described in the next chapter and in Garzarolli et al., 2011a). Table 4.12 lists some of those materials and heat treatments currently under development and early usage.

• Other trends and needs are given in the appropriate section of the next chapter.

The techniques outlined here are often applied individually to assess cable problems. However, none of these techniques can characterize the ageing condition of a cable with confidence, and most have never been evaluated comprehensively to determine if the changes they identify in a cable are correlated to cable age. Moreover, performing all these destructive/non — destructive mechanical, electrical, and chemical tests on the 9.1 million feet of cable and wiring in an LWR would be daunting and time consuming (AMS Corp., 2010). To more accurately determine or model the residual life in the cable network of a plant, a system and program is needed that combines and integrates these methods in such a way as to provide a more objective assessment of the health and ageing condition of low — and medium-voltage cables (AMS Corp., 2010 ).

Through their classic experiments on high purity aluminum (99.95%), Harper and Dorn22 came across a rate controlling mechanism that was seemingly independent of the grain size but still displayed characteristics

generally associated with Newtonian viscous creep. The creep experiments carried out at 0.99Tm provided stress exponent and activation energy values (n = 1 and Q = Ql) considered unique to N-H creep. However the grain size-independent behavior of the material combined with experimental strain rates around 1400 times larger than theoretical N-H creep predictions were suggestive of a new mechanism of creep. When the results obtained by Harper and Dorn were compared with theoretical N-H creep predictions, a large discrepancy was noted. In addition, by using markers Harper and Dorn22 found that the strains in the center of the grain are equal to the macroscopic strains noted in the creep experiments. The steady-state strain rate of deformation of this creep mechanism, now known as Harper-Dorn (H-D) creep mechanism, is given by

Studies over the years, on a host of other materials have led to a belief that

H-D creep is seen only in large grained materials (studies carried out by

Harper and Dorn were on Al with a grain size of 3.3 mm) and at very low

stresses and high temperatures. The primary characteristics of high temper­ature H-D creep are summarized below:5

• The stress exponent is equal to one.

• The creep rate is independent of grain size and similar creep rates are observed both in polycrystals and single crystals.

• The activation energy for creep is equal to that for lattice diffusion.

• The creep curves show a distinct primary stage which is followed by a steady-state stage.

• There is a random and reasonably uniform distribution of dislocations in specimens crept to the steady state.

• The dislocation density is low, of the order of 5 x 107 m-2, and is indepen­dent of stress.

• Very similar results are obtained in pure metals and solid solution alloys revealing that solute concentration has no effect on the creep behavior at these conditions.

While the initial studies were confined to very high temperatures (>0.95 TM), recent studies show that H-D creep can be rate controlling at inter­mediate temperatures as well. Creep studies in alpha titanium,23 beta cobalt,24 alpha iron25 and alpha zirconium26 have shown the presence of a H-D regime at homologous temperatures of around 0.35 to 0.6 for applied stresses around 9 x 10-5G (G is shear modulus) and grain sizes of around 500 pm.

Several models were proposed to understand the mechanism of H-D creep. The models of high temperature H-D creep were discussed in detail by Langdon and Yavari.27 Barrett et a/.28 proposed a model based on the creep strain resulting from dislocation glide with dislocation multiplication through climb. Murty29 suggested that H-D creep in Al-Mg solid solution arises from a modified viscous creep glide process (described later) with stress-independent dislocation density. More recently Kumar et a/.30 summarized the experimental results obtained on ceramic single crystals. Purity of crystals and a low initial dislocation density were cited as necessary conditions to unequivocally estab­lish the presence of H-D creep as a viable mechanism of deformation. A review of the viscous creep with n = 1 was recently made by Lingamurty et a/.31

We proceed with sections describing fundamental metallurgical properties and phenonema which ultimately affect core component behavior.

4.3.1 Basic irradiation damage

In structural materials like Zircaloy, the overwhelming majority of defects are caused by neutrons, and the most important type of defect is the dislo­cation loop. Two types of loops predominate: <a> and <c> loops. The <a> loop lies on a prism plane and has a Burgers vector in the <a> direction of the HCP lattice. Table 4.4 lists some important characteristics. Both vacancy and interstitial loops exist, but more than half have vacancy character. They are very small (100 nm ‘black spots’) and are difficult to analyze even with the transmission electron microscopy (TEM) (see Fig. 4.7).

Table 4.3 Commercial Zr base materials currently used for zirconium alloy fuel components in PWRs, BWRs, VVERs and RBMKs (Cox et a!., 2006) Alloy Sn % Nb % Fe % Cr % Ni % 0 % Fuel vendor BWRs Zircaloy-2 (SRAa/(RXAb) 1.2-1.7 — 0.07-0.2 0.05-0.15 0.03-0.08 0.1-0.14 All fuel vendors Zr-Linerb Sponge — — 0.015-0.06 — — 0.05-0.1 Only used in Japan and Russia ZrSn 0.25 — 0.03-0.06 — — 0.05-0.1 W ZrFe — — 0.4 — — 0.05-0.1 AREVA ZrFe — — 0.10 — — 0.05-0.1 GNFC PWRs Zircaloy-4 (SRA) 1.2-1.7 — 0.18-0.24 0.07-0.13 — 0.1-0.14 ZIRLO (SRA) 1 1 0.1 — — 0.12 W Optimized ZIRLO (SRA/pRXAd) 0.7 1 0.1 — — 0.12 W M5 (RXA) — 0.8-1.2 0.015-0.06 — — 0.09-0.12 AREVA HPA-49 (SRA/RXA) 0.6 — Fe+V — — 0.12 AREVA NDA’ (SRA) 1 0.1 0.3 0.2 0.12 N FI3 MDAh (SRA) 0.8 0.5 0.2 0.1 0.12 МНР VVER, RBMK E110 (RXA) — 0.9-1.1 0.014 <0.003 0.0035 0.05-0.07 Fuel cladding Alloy E125 (SRA) — 2.5 — — — 0.06 Structural components

aStress relieved annealed. bRecrystallized annealed. cGlobal nuclear fuel. d Partially recrystallized condition. eHigh performance alloy.

‘New developed alloy.

9 Nuclear fuel industries. h Mitsubishi developed alloy. ‘Mitsubishi heavy industries. Source: A. N.T International (2011).

These <a> loops form early in the irradiation and the number density reaches a saturation value at a fuel burnup below 5 GWd/MT (1 x 1021 n/ cm2, E > 1 MeV). The size of the loops increases with irradiation temper­ature, and the loops become unstable (start to disappear) at about 673K (400°C). As will be discussed later they have a strong effect on mechanical properties and dimensional stability.

The <c> type of loop lies on the basal plane and has its Burgers vector, or at least a strong component of it, in the c-direction of the HCP cell. As indi­cated in Table 4.5, and unlike the <a> loop, it is strictly a vacancy-type loop, is relatively large (100 nm) and does not form until considerable irradiation effects have occurred. In Zircaloy, <c> loops are first observed by TEM at a burnup of around 15 GWd/MT (~3 x 1025 n/m2, E > 1 MeV) and increase in density for the remainder of the fuel lifetime. They are thermally stable

to high temperature (>833K). It is thought that <c> loops strongly influ­ence irradiation growth and creep behaviour and probably do not affect mechanical properties. Figure 4.8 shows TEM images of a high density of <c> loops in highly irradiated Zircaloy. Such <c> loops, unlike <a> loops, do not appear to form in all zirconium alloys, particularly in those having additions of Nb, or Nb and Fe (Shishov et al., 2002), until high fluences are experienced.

As outlined in Tables 4.4 and 4.5, the formation kinetics of <a>- and <c>- type loops differ. The density of <a> type dislocation builds up quickly and saturates at a fluence less than 1 x 1025 n/m2, E > 1 MeV, as illustrated in Fig. 4.9. It appears that a fluence-incubation period exists before <c> type loops begin to form at about 3 x 1025 n/m2, E >1 MeV for typical reactor temperatures, as illustrated in Fig. 4.10 .

4.9 Variation of <a> type dislocation loops as a function of fluence in various reactors at 250-290°C (523-563K). (Source: Reprinted, with permission, from Davies et al. (1994), copyright ASTM International, 100 Barr Harbor Drive, West Conshohocken, PA 19428.) For a straightforward review of the relationship between irradiation — induced microstructure and Zircaloy properties, see Adamson (2000). More technical details and references can be found there.

The design basis RIA in a PWR is the control refection rod accident (REA) and in a BWR the control rod drop accident (RDA) (Strasser et al, 2010b). The REA is based on the assumption of a mechanical failure of the control rod drive mechanism located on the reactor vessel top, followed by the ejec­tion of the mechanism and the control rod by the internal reactor pressure. The resulting significant power surge is limited partly by Doppler feedback and finally terminated by the reactor trip. The BWR RDA is assumed to occur if a control rod is detached from its drive mechanism in the core bot­tom, stays stuck while inserted in the core and then, if loosened, drops out of the core by gravity, without involvement of a change in reactor pressure as in the REA. As a result the BWR power pulses are slower and the pulse widths wider than for a PWR. The pulse widths for PWRs are in the range of 10-30 ms and for BWRs in the range of 20-60 ms.

The reactivity transient during a RIA results in a rapid increase in fuel rod power leading to a nearly adiabatic heating of the fuel pellets (Strasser et al, 2010b). In a fresh fuel rod, the fissile material consists predominantly of U-235, which is usually uniformly distributed in the fuel pellets. Hence, both power and fission products are generated with a relatively small varia­tion along the fuel pellet radius. However, with increasing burnup, there is a non-uniform build-up of fissile plutonium isotopes through neutron capture by U-238 and formation of Pu-239 and heavier fissile isotopes of plutonium. Since the neutron capture takes place mainly at the pellet surface, the dis­tributions of fissile material, fission rate and fission products will develop marked peaks at the pellet surface as fuel burnup increases. The highest temperatures are occurring at the fuel pellet periphery.

The RIA-simulation experiments conducted in the 1960s and 1970s using zero or low burnup test rods showed that cladding failure occurred primar­ily by either (Strasser et al, 2010b):

• Post-DNB brittle fracture of the clad material occurring during the re-wetting phase of the overheated heavily oxidized (and thereby embrittled) clad due to the abrupt quenching resulting in large thermal clad stresses. This failure mode is imminent if the cladding is severely oxidized due to the RIA fuel clad temperature excursion.

• Cladding contact with molten fuel.

Contrary to low burnup rods, the failure mechanism for BWR/PWR high burnup rods not subjected to DNB is PCMI and potentially creep burst (for rods with a rod internal overpressure and subjected to DNB) (Strasser et al.,

2010b) while VVER high burnup rods only fail through creep burst (due to very low hydrogen contents in the fuel cladding).

PCMI — The change in failure mechanism is due to the decrease in pel­let-cladding gap and the embrittlement of the cladding (due to corrosion induced hydriding) with increased burnup (Fig. 5.10). The rapid increase in power leads to nearly adiabatic heating of the fuel pellets, which expand thermally and may cause fast straining of the surrounding cladding through PCMI. At this early heat-up stage of the RIA, the cladding material is still at a fairly low temperature (<650K), and the fast straining imposed by the expanding fuel pellets may cause a rapid and partially brittle mode of clad failure (Chung & Kassner, 1998). The survival of a high burnup fuel rod in a RIA is dependent on the ability of the cladding to resist PCMI, which depends primarily on the imposed stress and the cladding ductility. The duc­tility is dependent on the temperature to a large degree, which in turn is dependent on the pulse width and enthalpy increase of the transient. The condition of the cladding has a significant effect on the ductility, specifically the alloy composition, microstructure and texture. In addition, the cladding hydrogen content — most importantly the hydrogen distribution — has a sig­nificant impact on the PCMI response. More specifically, hydride rims/blisters and/or radial hydrides at the clad outer surface may result in a significant embrittlement effect. The degree of embrittlement due to precipitation of hydrides in the cladding is dependent on the amount of hydrogen in excess of the solubility limit, as well as on size, orientation and distribution of the hydrides. Hydride-induced embrittlement is a complex matter, and several mechanisms contribute to the loss of clad strength and ductility (Northwood & Kosasih,1983).

Hydride blisters can only be formed once the hydrogen content of the cladding has significantly exceeded the solubility limit and a certain temperature gradient is introduced by local oxide spallations (Strasser et al., 2010b). Thus the probability of significant hydride blisters forming depends on the average hydrogen content of the cladding, the thickness of the oxide pieces flaked off (and the difference in oxide layer thickness adjacent to the spalled region and at the position of oxide spallation) and on the heat flux.

Hydrides precipitate in the form of thin platelets on planes that depend on cladding microstructure, heat flux and stress (Strasser et al, 2010b). The orientation and continuity of these platelets with respect to residual or applied tensile stresses strongly influences the embrittlement. The orienta­tion of hydrides in clad tubes is affected by the thermo-mechanical treat­ment of the tubes under manufacturing, and by the stress state prevailing under precipitation. In the presence of a radial heat flux, hydride platelets are generally oriented with their surface normals preferentially aligned to the clad tube radial direction, and the width of the platelets along the tube axial direction is significantly larger than in the circumferential direction. These hydrides, usually termed ‘circumferential’ hydrides, have only a mod­erate embrittling effect, since there is no tensile stress in the clad tube radial direction, that is in the direction perpendicular to the hydride platelets (Northwood & Kosasih, 1983).

However, there are also hydride platelets oriented with their surface normals more or less aligned to the clad circumferential direction (Strasser et al, 2010b). These hydrides, which are usually termed ‘radial’ hydrides, are much more deleterious, since they are perpendicular to the dominating ten­sile stress in clad tubes of high-burnup fuel rods. The fraction of these det­rimental radial hydrides is larger in recrystallization annealed (RXA) clad materials than in SRA cladding (Northwood & Kosasih, 1983). The former heat treatment results in a larger fraction of grain boundaries in the radial direction, and since hydrides tend to precipitate along grain boundaries, this could to some extent explain the differences in hydride orientation between RXA and SRA materials. However, there are also other causes to these dif­ferences, such as difference in hydride size.

It is noteworthy that VVER fuel cladding will not fail due to PCMI because of the very low hydrogen clad contents in VVER fuel claddings (Strasser et al, 2010b). Instead VVER fuel rods with rod internal overpres­sures may fail due to creep burst.

If the cladding fails, fragmented fuel may disperse into the coolant (Lespiaux et al., 1997). This expulsion of hot fuel material into water has the potential to cause rapid steam generation and pressure pulses, which could damage nearby fuel assemblies and possibly also the reactor pres­sure vessel and internal components. Hence, ‘ Ihe potential consequences of fuel dispersal are of primary concern with respect to core and plant safety’ (Strasser et al, 2010b). The fuel dispersal tendency for high burnup fuel is very much dependant on the pulse width. For energy deposition with narrow pulse widths, heat conduction from the rim region is low and leads to higher local temperatures in the rim region due to the radial power peak­ing. Energy deposition with wider pulses allows for heat conduction from the pellet to the cladding, thus minimizing the temperature peaking in the pellet rim and maximising the fuel clad ductility. Lowering the pellet rim temperature decreases the potential for fuel particle dispersal.

The activation energy of deformation is dependent on the rate controlling mechanism of creep. As shown in Table 3.1, the activation energy changes with the underlying creep mechanism. For example, the activation energy of
creep is equal to that for grain boundary diffusion in the case of Coble creep and equal to lattice diffusion activation energy with N-H creep. Usually the activation energy of deformation is constant if a single thermally activated process is rate controlling. The Arrhenius plot — log of strain rate of defor­mation against reciprocal of temperature (in K) — is a straight line in such a case. However in certain cases more than one mechanism of creep, each with different activation energies, could be rate controlling. The Arrhenius plot in such a case is curved in the temperature range where the activity of the mechanisms is comparable. There are two cases which should be considered.

In case 1, the mechanisms of creep are independent of each other and hence occur simultaneously or in parallel. Each mechanism contributes a strain ei and the strain rates of deformation are additive. The total strain rate of deformation in such a scenario is given by

[3.38]

For example, for the case of two mechanisms occurring simultaneously, the temperature dependence of strain rate is given by

[3.39]

The Arrhenius plot for such a scenario is shown in Fig. 3.15a, and if Q1 > Q2, mechanism 1 makes the dominant contribution to the creep rate at high temperatures and mechanism 2 becomes dominant at low temperatures. In the temperature range where the activity of both mechanisms is compara­ble, the Arrhenius plot is curved. At any given temperature, the faster mech­anism is expected to control the rate of deformation.

In case 2, the mechanisms of creep occur sequentially and are known as series or sequential mechanisms. One mechanism cannot operate unless the other has taken place and vice versa, Here instead of the deformation strains, the time periods over which each mechanism has occurred are addi­tive. Thus the total strain rate of deformation, assuming each mechanism contributes to the total strain, is given by

[3.40]

For the case of two mechanisms occurring sequentially, the temperature dependence of the creep-rate is given by

3.15 Arrhenius plots for (a) parallel mechanisms and (b) sequential mechanisms of creep.

The Arrhenius plot for such a scenario is illustrated in Fig. 3.15b. Here, in any given temperature range, the slower process dominates the creep rate. However the amount of creep strain may not necessarily be controlled by the slower process. It could be possible that the slower mechanism contrib­utes little strain but allows the other mechanism with a greater strain contri­bution to operate. The dislocation glide-climb creep mechanism described earlier (Fig. 3.12) and Equations [3.30-3.34] is an example for this type of series mechanism while the simultaneous occurrence of N-H and Coble creep (Equations [3.17] and [3.18]) falls under parallel mechanisms.

Nodular corrosion has been shown to be very sensitive to the concentra­tion of Fe and Ni in the zirconium matrix. For a recent complete review see Franklin (2010). For unirradiated Zircaloy-2 annealing in the high alpha temperature range (<800°C, 1073K) causes a small increase in solute matrix concentration which is correlated to a sharp decrease in nodular corro­sion, without a significant change in size of the SPPs (Kruger et al, 1992) and without a significant change in the Fe/Cr ratio in the Zr(Fe, Cr)2 SPP, but with a significant decrease in the Ni/Fe ratio in the Zr2(Fe, Ni) SPP (Cheng et al, 1987). The mechanistic interpretation of these phenomena, as gleaned from Sections 4.2 and 4.3.1, is either that oxide conductivity is markedly increased by the solutes, or that the Galvanic potential between the SPPs and the matrix is decreased by increased solutes and chemistry changes in the SPPs. The importance of Ni in decreasing nodular corrosion by high alpha annealing is shown by the fact that such treatments for Zircaloy-4, with no alloying Ni, unlike those for Zircaloy-2 do not result in any decrease in nodular corrosion in the 520°C (793K) steam tests used in those studies.

Uniform corrosion appears not to be so sensitive to solute content, as even low fluence irradiation results in large changes in the chemistry of the SPPs and significant increases in solute matrix concentration without a significant change in oxide thickness. The experiments described above clearly indicate, however, that disappearance of the SPPs is correlated to oxide thickness increase.

The HPUF at high fluence appears to be correlated to both SPP disap­pearance and solute concentrations in the matrix. HPUF increases earlier in fluence compared to oxide thickness, indicating a connection to solutes, but there does not appear to be a clear correlation to Fe concentration in the matrix. When the SPPs do disappear (dissolved by irradiation effects, dispersing Fe and Ni in the matrix and leaving a local concentration of Cr) however, the HPUF sharply increases.

The role of Ni in HPUF issues is emphasized by the observations that HPUF in Zircaloy-4 does not increase at the high fluences reported thus far. A mechanism has been proposed (Garzarolli et al, 2011b) whereby Ni distribution in the growing Zircaloy-2 metal/oxide interface acts as an easy path for hydrogen ingress to the metal. This hypothesis and the data of Ishimoto et al. (2006) suggest a high value of the Fe/Ni ratio in Zircaloy-2 is desirable.