Ultrasonic testing (UT) is being used to detect leaking BWR and PWR fuel rods. The testing method makes use of differences in scattering by water and gas of ultrasonic (pressure) waves as they are reflected between the inner and outer surfaces of fuel cladding. The UT process makes use of two probes, which move laterally across a FA. The probes are arranged in a “pitch-catch” configuration in which one probe transmits a signal, which is picked up by the cladding, reflected between the inner and outer surfaces and ultimately received by a second probe. The scattering by water at the inner surface of a failed rod is greater than the scattering by gas at the inner surface of a sound rod. Such differences are used to identify the specific rod or rods that are leaking.

Nuclear power plants provide around 20% of the total electrical supply in the United States and roughly around the same level across the world, help­ing to reduce harmful greenhouse gases (GHG). Many commercial nuclear reactors operating worldwide are of the Generation-II category and the majority of this generation is light water type; Generation-III type reac­tors are at an advanced stage of commercialization and deployment. The main reasons for downtime of the light water reactors (LWRs) currently operating are materials-related issues primarily due to material ageing and degradation. Degradation of materials is caused by the very aggres­sive environments to which the LWR structures are exposed including high neutron fluences, high temperatures along with aggressive environmental factors such as water and steam. A major objective of this book is to bring forth issues confronting the nuclear industry in terms of materials ageing and degrading with particular emphasis on mechanisms and management. This book is a compilation of chapters written by experts in the field. The book is divided into three different parts: Part I on ‘Fundamental ageing issues and degradation mechanisms’, Part II on ‘Materials ageing and deg­radation in particular light water reactor (LWR) components’ and Part III on ‘Materials management strategies for light water reactors (LWRs)’. Each of these three parts contains three chapters.

In Chapter 1, Murty and Ramaswamy present an overview of various materials issues with discussions on fundamental aspects along with per­tinent references to various materials of different LWR structures. The chapter covers briefly all the seven components (fuel, structure, moderator/ reflector, control, coolant, shields and safety systems) comprising an LWR with references that deal with more details. Corrosion and stress corrosion cracking (SCC) are the most commonly limiting factors and damaging phe­nomena that are covered in Chapter 2 by Couvant. This is an important chapter that summarizes the corrosion phenomena encountered in LWRs. Murty et al, discuss in detail the time-dependent permanent deformation known as creep in Chapter 3 , Any structure that is exposed to high tem­peratures and loads experiences creep deformation, and both the creep mechanisms and creep-life prediction methodologies are important aspects

covered here, referencing their applications to LWR structural materials such as Zr-based alloys, stainless steels and Ni-based superalloys.

Part II on Materials ageing and degradation of specific light water reac­tor components comprises three chapters commencing with Chapter 4 by Adamson and Rudling on the zirconium-based alloys that are commonly used as thin-walled tubing to clad radioactive UO2 fuel. This chapter starts with the basic crystallography of Zr leading to many degradation phenom­ena often noted in operating reactors of both PWR and BWR type such as PCI (pellet-cladding interaction), oxidation and hydriding, crud forma­tion, radiation growth and creep, grid-to-rod-fretting (GTRF), fuel rod and assembly bow. Rudling and Adamson continue the issues of Zircaloy cladding in Chapter 5 with emphasis on performance and inspection of fuel bundle components. Issues of possible degradation and ageing of various electrical cables are dealt by Hashemian in Chapter 6; it is to be noted that the various aspects covered in this chapter are usually found only in special­ized treatises.

Part III covers Materials management strategies wherein Chapter 7 by Jeong and Hwang deals with PWR management in Korea while Katona describes similar aspects for Russian VVERs in Chapter 8 . In the final chapter, Ray and Lahoda cover materials problems facing operating LWR vendors following which the needs of nuclear technology and industry are pointed out.

The uniqueness of the book lies in the fact that, while fundamental materials aspects/phenomena are dealt with initially, other content is not easily found in the technical journals on nuclear materials, especially the management strategies of LWR vendors covered in Part III. The various materials science aspects described in these articles for predicting the life of nuclear structures echo the comment made by Placid Rodriguez during his Presidential address delivered at the Golden Jubilee Celebration of the Indian Institute of Metals in 1966: To be able to predict the life of an engineer­ing component accurately, … [one needs to] take into account the synergistic effects of and interactions between a variety of damaging processes like creep, fatigue, dynamic strain ageing, environmental effect and microstructural deg­radation. The importance and significance of knowledge and background in nuclear materials are nicely summed up by Norman Hilberry, the former director of Argonne National Laboratory, who made the following state­ment way back in the 1950s: We physicists can dream up and work out all the details of power reactors based on dozens of combinations of the essentials, but it’s only a paper reactor until the metallurgist tells us whether it can be built and from what. Then only, one can figure whether there is any hope that they can produce power.

Acknowledgements are due to the efforts and continued persistence of Messrs. Steven Mathews, Sarah Hughes and Rachel Cox of Woodhead

Publishing in arranging for various authors to contribute their chapters in an appropriate time frame and in making this publication a reality.

K. Linga (KL) Murty Professor and Director of Graduate Programs Department of Nuclear Engineering North Carolina State University

In the previous sections, we discussed the different mechanisms of creep that have been observed in various materials. The stress, temperature and microstructural dependence of each mechanism was described and the steady-state strain rate of deformation of each mechanism was correlated to these parameters. We also outlined the different regions, through defor­mation mechanism maps, where a given mechanism would be dominant over others. In all these sections, more emphasis was laid on the second­ary creep region and the mechanism maps were also constructed taking into account these steady-state creep-rates. However, such a methodology would be based on the premise that the secondary creep stage accounts for a significant fraction of the useful creep life. While such a method is not entirely wrong, it is unsuitable for several materials which tend to have larger primary or tertiary creep regimes. For example, Ni-based superalloys have been found to exhibit primary creep strains of the order of 1% or more.81 These alloys are used as materials for fan and compressor blades of aero-engines. The dimensional tolerance for these components is very small and plastic strains in the order of 1% are sufficient to wreck the stability of the engine. Hence under such conditions, modeling by considering only the steady-state creep rates will grossly overestimate the useful creep life of the material. Furthermore some of the mechanisms of creep, for example in
the power-law creep regime, have been proposed following microstructural studies on the crept specimens. For instance observation of subgrains in the crept microstructure is considered evidence for creep controlled by climb of edge dislocations. Similarly observation of jogged screw dislocations is believed to indicate deformation controlled by the Barrett-Nix model or its recent modification proposed by Mills and co-workers.

In most cases the deformation microstructures are investigated through TEM studies. Hence the sample studied, due to its very small volume, may not be a real representation of the condition of the material. Thus there is some uncertainty associated with the rate controlling mechanism. While the physically based mechanisms discussed in the previous sections are impor­tant for understanding and predicting deformation rates, an equally large number of studies has been carried out to predict creep life using math­ematical models and empirical correlations. The Larson-Miller parameter (LMP), Monkman-Grant constant, в-projection concept and a host of other graphical and mathematical methods have been utilized to predict the creep life of various engineering materials.

Generally engineering components are designed for a stress level below which there is no danger of rupture or excess deformation during the ser­vice life of the component. The stress level is decided by one of the follow­ing two criteria: (a) stress level at which rupture/failure would be caused in 100 000 or 200 000 h, whichever period is appropriate and (b) stress level which produces a nominal strain of 0.1%, 0.2% or 0.5% in a certain period, say 100 000 h.82 However there are not many tests carried out till 100 000 h even for established materials and hence it is necessary to extrapolate data from much shorter tests, say 103-104 h. This is especially important for new materials where it is necessary to understand their long term behavior within a short span of time. Hence the extrapolation techniques become important and in this section we discuss some of the existing extrapolation techniques for predicting long term creep behaviors. Penny and Marriott82 provide an excellent review of the various extrapolation methods and also the advantages and disadvantages associated with each method. They divide the extrapolation techniques into three main groups:

1 Parametric methods

2 Graphical methods

3 Algebraic methods.

Equations correlating time-temperature or stress-time fall under the para­metric method. Functional relationships between time, temperature and stress are established and it is believed that when stress is plotted against a function of time and temperature, a single master curve will be obtained. This master curve can be constructed by performing short term tests at

higher temperatures. It is then assumed to be equally valid for longer times and lower temperatures thus allowing for extrapolation. The Larson-Miller method83 is based on this logic. The original Larson-Miller equation is given by the following:

LMP = T (C + logic tr), [3.49]

where LMP is the Larson-Miller parameter and C is a constant which was assumed to be equal to 20 and was found to be reasonably accurate for many materials. Plots of applied stress versus the LMP would then allow extrapolation of short term data for long term predictions. Figure 3.19 shows a LMP obtained from short term tests for a variety of materials. It is interesting to note the change in slope as lower stresses are approached. Some of the other parameters which fall under the category of paramet­ric methods are by Dorn and Shepherd,84 Manson and Haferd,85 Murry,86 etc. However, LMP is quite commonly used in creep life predictions and extrapolations.

Under graphical methods, there are procedures which seek to extrapo­late rupture curves by direct manipulation of the plotted data. Grant and Bucklin,87 Glen,88 Mendelsohn and Manson89 and others proposed methods

that fall under this category. Here we provide a brief description of the Grant — Bucklin method. Grant and Bucklin considered the fact that creep rupture would be influenced by several time — and temperature-dependent effects and hence mode of failure might not be uniform over the whole range of time and temperature. They identified distinct segments of the rupture curve where one mode of failure might be dominant. These segments were later described by linear relations (Fig. 3.20). By plotting the slopes of like seg­ments against temperature, it is possible to extrapolate to temperatures out­side the experimental range. Secondly the positions of the transition points may be plotted on axes of temperature versus tr for extrapolation. However Penny and Marriott87 indicate that such extensions are subjective and sensi­tive to the ability or judgment of the analyst, albeit Grant and Bucklin imply that reliable extrapolations of the rupture curves are not critically dependent on the accurate determination of either slopes or transition points.

The algebraic methods are similar in a way to the parametric methods. The difference lies in finding functions which can combine the effects of stress, temperature and time into a single relation such as

f (c, tr, T )c = constant. [3.50]

Any function f (a, t„ T)c which can be separated into two functions such as

f(a, tr, T )c = f (a) f2 (tr, T) = constant [3.51]

is similar to the time-temperature method of parametric types. In addition to these methods, there are several other methods which have been proposed and found to provide reasonable predictions. Monkman and Grant90 pro­posed a relationship between the steady-state strain rate and rupture time:

estr = к, [3.52]

where к is a material constant known as the Monkman-Grant constant. Figure 3.21 depicts such a plot for internally pressurized cp-Ti tubing.91

Other methods of extrapolation include the в-projection method advo­cated by Wilshire and co-workers9293 where the total creep curve is described by a series of в parameters. Wilshire92 suggests that for most materials the secondary creep region is only an inflection that appears to be a constant over a limited strain range. Hence it was emphasized that creep life mod­eling should take into account the total creep curve including the tertiary creep regime rather than just focusing on the secondary creep rates. On this premise, Wilshire and co-workers advocated the в — projection concept where the total creep curve would be described as

е=вг(1 — exp (-вгі))+ 0з(ехр(04О -1), [3.53]

where 61 scales the primary creep regime, в2 is a rate parameter govern­ing the curvature of the primary stage, в3 scales the tertiary creep regime and в4 is a rate parameter quantifying the shape of the tertiary curve. These parameters are found to change with stress and temperature conditions and accordingly influence a change in the shape of the creep curve. A determina­tion of the stress and temperature dependencies of the в parameters would allow the prediction of long term creep properties. Furthermore Wilshire counters the widely accepted view of transitions in creep mechanisms with changing stress and temperature conditions. The creep characteristics of a 0.5Cr-0.5Mo-0.25V ferritic steel could thus be described by the в-projection over a wide range of stress values based on a single dislocation-based mech­anism. However, as shown in Fig. 3.22 , there are definite changes in stress exponent values with changing stress. Wilshire argues that if different mech­anisms operate in different stress and temperature regimes, data collected in one mechanism regime should not be able to predict the creep behav­ior in a different mechanism regime. Furthermore Wilshire contends that the в-projection approach can be utilized to quantify material behavior in complex, non-steady stress-temperature conditions encountered in service conditions.

In addition to these methods, creep life predictions are also guided by damage mechanics. The irreversible material damage caused by mechan­ical loading and environmental features during creep eventually leads to very high strain rates of deformation and failure. Damage could be due to cavity formation, microcracks and gross deformation such as strain — or ageing-induced. A materials scientist viewpoint on micromechanical causes of damage is given by Le May.94 In addition to creep damage, other mechanisms of damage such as fatigue, surface oxidation and internal cor­rosion are also important. Although some of these phenomena are not temperature dependent, their interactions with creep, such as creep-fatigue interaction, can have significant effects on high temperature damage accu­mulation. The different damage processes constitute ductile creep rupture, intergranular cavitation during creep, continuum creep rupture, continuum fatigue damage, environmental damage and age — and strain-induced hard­ening and softening. In contrast to creep life predictions based on mecha­nistic models, continuum damage mechanics (CDM) attempts to provide a holistic view of the damage process and accordingly models the useful creep life of a material. By accepting the fact that damage is a result of the complex interactions between different mechanisms, CDM provides greater accuracy in creep life estimation in comparison to models based on a single mechanism of creep, namely grain boundary sliding or dislo­cation creep. While there have been many continuum damage mechanics models advocated over the years, a unique model is the one proposed by Kachanov,95 later elaborated by Rabotnov96 and commonly referred to as the Kachanov-Rabotnov model. A brief review of the Kachanov-Rabotnov model is presented below.

Irradiation growth occurs simultaneously with irradiation creep if there is an applied stress. The two processes are considered to be independent and additive, even though they compete for the same irradiation-produced defects mechanistically. Earlier ZIRAT reviews providing more detail can be found in the ZIRAT7 STR (Adamson & Rudling, 2002) and the Fuel Material Technology Report, Vol. 2 (Rudling et al., 2007).

Irradiation growth is a change in the dimensions of a zirconium alloy reactor component even though the applied stress is nominally zero. It is an approximately constant volume process, so if there is, for example, an increase in the length of a component, the width and/or thickness must decrease to maintain constant volume. Understanding of the detailed mechanism is still evolving; however a clear correlation of growth to microstructure evolu­tion exists, and many empirical observations have revealed key mechanistic aspects. The inherent anisotropy of the Zr crystallographic structure plays a strong role in the mechanism, as materials with isotropic crystallographic structure (like stainless steel, copper, Inconel, etc.) do not undergo irradia­tion growth. It should not be confused with irradiation swelling, which does not conserve volume and does not occur in zirconium alloys under normal reactor operating conditions.

Irradiation growth is strongly affected by fluence, CW, texture, irradiation temperature and material chemistry (alloying and impurity elements).

Cable components such as the conductor wires, insulation, shielding, and jacket material can all be tested to reveal signs of degradation. By applying the right testing method or combination of methods effectively faults that typically occur at cable connections can be confirmed; these include termi­nations, penetrations, and/or splices that have been exposed to mechani­cal stress, oxidation, or corrosion. Other faults include end-device failure such as motor windings, sensors, transmitters, and detectors that may also be detected using appropriate testing methods (AMS Corp., 2010).

Cable analysis and assessment methods require observing, measuring, and trending indicators of cable condition that correlate to the physical condition of the cable or its functional performance (U. S. NRC, 2010b). According to the NRC, an ‘ideal’ condition monitoring technique should have the following desired attributes: ‘nondestructive and nonintrusive, capable of measuring property changes or indicators that are trendable and can be consistently correlated to functional performance during normal service, applicable to cable types and materials commonly used in nuclear power plants, provides reproducible results that are not affected by the test environment or, if they are so affected, the results can be corrected for those effects, able to identify the location of any defects in the cable, allows the establishment of a well-defined end condition, and provides suf­ficient time before incipient failure to allow corrective actions’ (U. S. NRC, 2010b). However, because the nuclear industry relies primarily on manufac­turer qualification data, it does insufficient testing to confirm that cables can operate dependably in the long term (IAEA, 2011).

Cable testing methods can be characterized in multiple ways (see Table 6.1). In the broadest terms, two cable ageing methods are avail­able: laboratory tests (involving microsampling, e. g. conducted in non­operational conditions in a lab) and in-situ tests (conducted on cables as installed in a plant) (U. S. NRC, 2010a; IAEA, 2011). However, another way of categorizing cable ageing methods is life testing versus electrical testing. Life-testing techniques involve testing — visually, physically, or chemically — the physical properties (e. g. hardness) of spare cable samples of the same cables actually installed and in operation at the plant. When such ‘real-time’ testing is not possible or desirable, accelerated life testing can compress the time required to test the ageing processes by ‘pre-ageing’ cable samples and monitoring their performance when installed in the same environment as actual in-service cables.

Electrical testing of cables involves the testing of electrical properties such as insulation resistance/polarization index, voltage withstand, dielec­tric loss/dissipation factor, time and/or frequency domain reflectometry, and partial discharge. These electrical testing methods can be further catego­rized according to whether the inspection or test is performed in-situ on electric cables in the plant or whether it is a laboratory-type test performed on representative material specimens in a controlled laboratory setting.

Which of these testing techniques is used will depend on the type of insu­lation material in the cable and type of environmental stressors to which the cable is subjected (Hashemian, 2010). For example, historically, visual and tactile inspection techniques have been the most commonly used meth­ods for cables that are accessible. Some, such as the gel content and other

Cable testing technique

Visual/tactile (visual screening test)

Ні-Pot test (high voltage test may damage insulation)

AgeAlert™ (wireless sensors attached to cables)

TDR (time domain reflectometry)

RTDR (reverseTDR for coaxial shielded cables)

Impedance measurements (inductance, capacitance, and AC resistance)

Partial discharge

Insulation resistance (dielectric absorption ratio, polarization index) (sustained higher DC voltage resistance)

Dissipation factor (Tan Delta)

AC voltage withstand (low frequency, high voltage)

DC step voltage

chemical and mechanical tests like the cable indenter, were developed spe­cifically for evaluating the condition of the protective jacket or insulation on a cable (AMS Corp., 2010).

On the basis of his studies, Andrade1 proposed that the creep curve could be described by an equation of the form

Є = £0 (1 + , [3.1]

where e is the strain, t is the time and в and к are constants. The transient creep, that is the primary creep stage, is described by в; the constant к rep­resenting the secondary stage describes an extension per unit length that proceeds at a constant rate. Elsewhere, the dependence of creep rate on time was described by a power series5 where ё is the creep rate, a, and n, are functions of both temperature and stress. The primary stage of a normal creep curve, namely curve A, can be described by Equation [3.2] when n attains a value of 2/3. In such a case, the time dependence of creep strain (є) is described by

є- Є0 + Д1/3, [3.3]

where є0 is the instantaneous strain, в isa constant and t is time. Equation [3.3] is in accordance with the time law of creep proposed by Andrade,1 known as Andrade’s в-flow.

For steady-state creep, n = 0. The creep curve is then described by

є — £0 + £st, [3.4]

where es is the steady-state creep rate. The total creep curve consisting of the primary, secondary and tertiary region can be then described by

є — є0 + вШ + est + Yt3, [3.5]

where yt3 describes the tertiary component of the creep curve. There were several other time-creep law equations proposed to describe creep data. A major objection to the Andrade’s P-flow equation is that it predicts infinite creep-rate at the instant of loading (i. e. as t approaches 0) which is consid­ered to be unrealistic.4 Garofalo6 proposed the following equation:

є — єо + є (l- e~rt)+ ёst, [3.6]

where e, is the limit for transient creep and r is the rate of exhaustion of the transient creep that is a function of the ratio of initial creep strain rate (et^0).4 An extension of the Garofalo equation that further includes the tertiary creep regime, would be7:

є — єо + є (l — e~rt) + Gt + єьер{‘(-°,), [3.7]

where eL is a constant equal to the smallest strain deviation from steady state at the onset of tertiary creep, p is a constant and tot is the time for onset of tertiary creep.

In comparison to the normal creep equation, the logarithmic creep behav­ior is usually described by

£ = £0 + aln (+ y), [3.8]

where a and у are constants. This equation indicates that over a long period of time, the strain rate of deformation tends to become zero. Such an equa­tion, as discussed in the previous section, would be useful for describing exhaustion creep.

While Andrade’s equation is an empirical correlation borne out of his experimental observations, a number of researchers have derived similar relations on the basis of physically based mechanisms. For example, the Garofalo equation has been derived by considering sub-structural changes during deformation and by modeling the whole phenomenon as a first order reaction. Webster et at.8 and Amin et at.9 have correlated the stress and tem­perature dependence of eT, r and £s to the rate controlling mechanisms of high temperature creep using first order reaction rate concepts. They found that the Garofalo equation can be derived by assuming that the transient creep follows a first order kinetic reaction rate theory with a rate constant 1/t = K£s that depends on stress and temperature. Here 1/t is the relaxa­tion frequency which is similar to r in Equation [3.6] and т is the relaxation time for rearrangement of dislocations during transient creep controlled by dislocation climb. The physical mechanisms, for example, dislocation climb, that have been suggested to control or govern creep will be discussed in a subsequent section.

During their analyses of the creep results on Zr-based alloys, Murty10 found the following equation better describes the primary creep compared to the Garofalo equation:

Ak-t. £j 1

£ = — , A = L and B =

1 + AB £ st £ s £tr

where A is the ratio of the initial strain rate to steady-state value and B is the inverse of the extent of the primary creep. A was found to be around 10 as reported earlier by Dorn and co-workers49 for many materials that behave like pure metals and class-M alloys.

A distinctly different approach was used by incorporating anelastic11 strain in the description of the primary creep regime and especially in predicting the transients in creep strain due to sudden stress changes. i 2 Accordingly, the total strain at any given time is given by

£ = £e + £a + £ p, [310]

where the subscripts E, a and p correspond to the elastic, anelastic and plastic strains; the plastic strain (ep) is given by Equation [3.9]. The anelas­tic strain (ea) is time dependent, completely recoverable strain in contrast to the permanent plastic strain which is not recoverable and elastic strain which is recoverable but instantaneous (time-independent). The anelastic strain at the loading is given by

[3.11]

In the above equation, v ~ 7 and a* (~2.5 x 1022) are material constants in Hart’s equation of state and p is the anelastic modulus.

In the following section we discuss the importance of the different param­eters, namely stress temperature and microstructure. The strain rate of deformation, є can be expressed as

є = f (a, T, microstructure), [3.12]

where a is the applied stress and T is the test temperature.

All the load bearing components in the core of the reactor, namely clad tubes, guide tubes (GT), GT assemblies and BWR channels undergo irra­diation creep, albeit at different rates. The clad tube is a crucial boundary which has to withstand steep temperature and pressure gradient across its thickness. Steady-state creep dominates the service life of the clad and only in very rare cases the material may enter tertiary creep range. The creep rate of clad material under an irradiation environment is many times higher (depending on the material chemistry and the flux) than that under out-of­pile conditions. Further, the dimensional changes in clad tube (an aniso­tropic material) happen in a preferential direction which gives rise to other unwanted problems. The irradiation creep is not just the thermal creep imposed with high defect density. In the former the interstitial and vacancy loops that form during irradiation play a major role in the creep mechanism; in the latter the creep rate increases with temperature. The irradiation creep is weakly dependent on irradiation temperature (‘athermal’) and in-reactor thermal creep controls the deformation above ~400°C.

Two mechanisms are proposed to explain the irradiation creep phenom­enon: (a) stress-induced preferential absorption (SIPA), where extra planes of atoms accumulate on crystal planes so as to produce creep strain in the direction of the applied stress and (b) stress-induced preferential nucle — ation (SIPN), which assumes that nucleation of loops is preferred on planes with a high resolved normal stress. Both of these mechanisms assume that the growth or formation of loops occur at a favorable orientation with respect to applied stress and causes macroscopic strain. Neutron irradia­tion produces large quantities of point defects — vacancies and self intersti­tial atoms (SIAs). These defects migrate to different sinks like dislocations and grain boundaries, in a preferential manner due to the anisotropy of the zirconium crystal lattice, in order to reduce the energy of the system. Because of the diffusional anisotropy, interstitial atoms tend to migrate to dislocations lying on prism planes and to grain boundaries oriented paral­lel to prism planes, while vacancies drift preferentially to dislocations lying on basal planes and to boundaries parallel to basal planes. This gives rise to elongation in one direction and contraction in the other.136 The creep rate is controlled by dislocation glide and this in turn can be controlled by suitable alloying elements and by choosing an appropriate texture of zir­conium matrix.

The total strain measured in an irradiation creep consists of the strain due to thermal creep (eth), irradiation creep (eirr) and irradiation growth (eg) and is assumed to be additive:

£ = % + £irr + £ [366]

The creep rate ((e)) is given by the empirical relation

£ = f (<pmone-Q/RT, f,d, p, a) [3.67]

where A is a constant, 9 the flux, a the stress, f the texture parameter, d the grain size, m (~0.4-0.7) and n (~0.8-2) are constants, and the others have their usual meaning.

As the dislocation density in a CWSR material is high and, as glide but not climb is the rate controlling mechanism under reactor conditions, the creep rate of CWSR is higher than that of recrystallized material as shown in the figures. The creep rate (a) increases with increase in the flux, (b) increases with increase in temperature (contribution by thermal creep predominates above 400°C), (c) is higher along the rolling direction than the transverse direction, (d) decreases with fluence (as radiation hardening sets in) and (e) depends upon the type of alloy (Nb and Sn content increases creep resistance). The irradiation creep rates of cold-worked Zr-2.5wt.%Nb alloy are about one-third of those of cold-worked Zircaloy-2137 at comparable temperature, stress and fast neutron flux while the creep down of HANA (High Performance Alloy for Nuclear Applications) alloy (after a dose of 12 MWd/Kg U) is half that for Zircaloy-4.138

If the rod internal pressure becomes larger than the reactor system pres­sure, the fuel cladding may start to creep outwards (Fig. 5.5) (Strasser

et al., 2010a). If the fuel cladding outward creep rate exceeds the fuel swelling rate (due to fission product production during irradiation), the pellet-cladding gap may increase. This phenomenon is denoted cladding liftoff. Since this gap constitutes a significant heat flux barrier, such a gap increase may result in increased fuel pellet temperature. This higher tem­perature will in turn increase the gaseous fission product release rate, fur­ther increasing the fuel rod overpressure and leading to an even higher outward cladding creep rate. Such a thermal feedback condition may lead to fuel failure.

A larger fuel rod free volume, lower FGR rate and increased clad creep strength increases the margins towards liftoff (i. e. a larger rod internal pres­sure can be accepted without getting liftoff) (Strasser et al, 2010a). Free volume refers to the void volume bounded by the inner surfaces of the clad­ding and end plugs and the outer pellet surface minus the volume of ple­num springs and other internal hardware. Note that closed pellet porosity is within the pellet volume, while open porosity, dishes, chips and other surface irregularities with finite, open volume are in the free volume.

The earliest model to explain GBS accommodated by dislocation movement was proposed by Ball and Hutchison.4 8 Later modifications to this model were brought about by Langdon,49 Mukherjee50 and Arieli and Mukherjee.51 The Ball-Hutchison model is well illustrated by Fig. 3.8.52 As shown in the figure, when the grains tend to slide under the application of a shear stress, strain incompatibilities and stress concentrations are developed at triple points53 and grain boundary ledges.54 Dislocation emission from these ledges and triple points is a natural consequence of the stress concentration. The emitted dislocations traverse the grain diameter until they encounter the opposite grain boundary at which point the dislocations start piling up and generate a back stress that prevents the further emission of dislocations. To enable further deformation, the lead dislocation at the pile-up climbs into

3.8 I llustration of the Ball-Hutchison model of GBS accommodated by dislocation movement.58

or along the grain boundary resulting in the rate controlling step being the climb of dislocations at the grain boundary.

Gifkins56 presented a similar but slightly different model to explain the mechanism of GBS known as the ‘core and mantle’ model and considered the grain as the core and the regions adjacent to the grain boundary as the mantle. All deformation was assumed to occur only in the mantle region of the grain. This model and the rest of the models predicted strain rates which had an n = 2 dependence of the applied stress. According to this model

wherep = 2or3 and D = DLorDB — depending on whether the motion of the dislocations is along the lattice or along the grain boundary respectively. Superplasticity — the ability of a material to exhibit high tensile elongations before failing — is primarily attributed to GBS. The mechanism of defor­mation in superplastic materials is supposed to be in accordance with the mechanisms discussed in this section.

In order for significant strain to occur, dislocations must overcome the obstacles to their motion — the irradiation-induced <a> loops. At low stresses this may happen by the process of dislocation climb, which means irradiation-induced point defects (PDs) diffuse to the dislocation and allow it to move around the obstacle. This is an important creep process, to be covered further in Section 4.6. At high stress or high strain rates, as in a power excursion, or at all practical strain rates out-of-reactor, the disloca­tions can actually interact with the <a> loop defects and remove them from the microstructure. In effect this creates a localized soft area, where addi­tional deformation tends to concentrate: this process is called dislocation channelling. The physical process is illustrated in Fig. 4.21. The long straight

white bands are dislocation channels in which irradiation damage (black areas and black spots) is removed. In zirconium alloys the channels are in the order of 0.01-0.30 pm wide depending on fluence and irradiation tem­perature, and each channel can accommodate large (50-300%) local strains. The channels intersect the surface to cause large protrusions or slip steps there (Adamson, 1968; Sharp, 1972).

In Zircaloy, the dislocation channels tend to form in a very a localized area called a deformation band. For a simple uniaxial tensile test specimen the sequence of formation is illustrated in Fig. 4.22. At point (A) the defor­mation band begins to form and is fully formed at (B). At point (B) a second deformation band forms perpendicular to the first, and the specimen frac­tures at point (D). Because virtually all the strain forms in the deformation band, there is little or no deformation in the rest of the specimen gauge length. A plot of measured strain along the length of a typical specimen is given in Fig. 4.23 . Since little plastic strain occurred outside deformation bands, the true gauge length of the specimen is much shorter than the nomi­nal specimen gauge length. Therefore, specimen geometry greatly influences reported strain values. The effect of test specimen geometry on failure strain is illustrated in Fig. 4.24 where the conventional value of uniform elongation (UE) is plotted against gauge length for different specimen geometries of

482 414 345 276 207 138 69

0.04

4.22 Engineering stress-strain curve for Zircaloy-2 sheet that had been irradiated at 280°C to a neutron fluence of 5 x 1020 n/cm2 and subsequently tested at 300°C. (Source: Reprinted, with permission, from Bement et al. (1965), copyright ASTM International, 100 Barr Harbor Drive, West Conshohocken, PA 19428.)

basically the same material. These data show that strain values developed for use as failure criteria or strain limits are not real material properties, but are strongly influenced by the specimen design used to obtain the data.

For burst tests of irradiated materials at 350°C (623K) (Onimus et al, 2004) careful laser imaging measurements indicate that tubing deformed

homogeneously throughout the gauge section until strain concentrates in the burst region. However, this strain (i. e. the number of channels) is small compared to the burst strain.

A main reason that anisotropic deformation is decreased relative to unir­radiated material (Mahmood et al, 2000) is that the high stresses needed to reach the yield point activate alternate slip systems in irradiated Zircaloy. The primary slip plane in unirradiated Zircaloy is the prism plane, the so-called <1120>(1010) system. As the applied stress becomes high, both the pyramidal and basal planes can become active. Observations of prism plane dislocation channels have been well documented (Adamson et al., 1986; Bell, 1974; Adamson & Bell, 1986; Bourdiliau et al, 2010), but obser­vation of pyramidal and basal channels have also been reported (Bell, 1974; Fregonese et al, 2000; Regnard et al, 2001; Onimus et al, 2004, 2005; Bourdiliau et al., 2010). In fact the CEA group show with considerable data and justification that, for 350°C (623K) testing temperature, basal slip pre­dominates, but that may yet prove to be a function of irradiation and test­ing temperature, testing mode and impurity level (Bourdiliau et al, 2010). Dislocation channelling phenomena themselves and details about which channelling planes predominate are important when modelling crack prop­agation and material response to actual in-reactor loading patterns. Onimus et al. (2005) have made good progress in modelling the phenomena for the CEA conditions. The data is summarized in a ZIRAT 15 Annual Report (Adamson et al, 2010).

Specimen design plays a dual role, influencing ductility through both geometry and stress state. The type of plane stress specimens shown in Fig. 4.22 result in a ‘classical’ deformation band formation. The disloca­tion channels can freely extend from surface to surface. In the plane strain specimens of Fig. 4.25, the channels run into specimen regions where the stress is significantly lower before a free surface is reached, therefore pre­venting formation of a well-developed deformation band. The latter case, constrained plane strain, more realistically represents deformation in most reactor component situations.