On the failure of fast reactor fuel pins

Nuclear Engineering and Design 101 (1987) 281-303 North-Holland, Amsterdam

281

ON THE FAILURE OF FAST REACTOR FUEL PINS J.R. M A T T H E W S UK Atomic Energy Authority, Theoretical Physics Division, AERE Harwell, Oxfordshire 0X11 ORA, UK

and T. P R E U S S E R Institut fff~r Reaktortechnik, Technische Hochschule, Darmstadt, Fed. Rep. Germany

The prediction of the timing and position of fuel pin failures is an important task in the modelling of fast reactor fuel behaviour. The range of processes that can provoke failure of fast reactor fuel pins in normal operating conditions and during hypothetical accidents is reviewed. Some of the mechanisms of failure are examined in more detail and the effect of hot spots and local stress concentrations is discussed. A review of failure criteria used in fast reactor fuel pin codes is given elsewhere, but the difficulties in applying various types of criteria are examined. Some discussion is also given on probabilistic approaches. Recommendations are given for a future approach to the problem of failure prediction, resolving the dilemma between inadequate empirical criteria and over-complexphysically based approaches.

I. Introduction

Of all the tasks in fuel rod behaviour analysis the prediction of fuel rod failure is the most difficult. It is made more difficult in the case of fast reactor fuel pins, because of their robust construction and the lack of a large data-base of failure observations during normal operating conditions. The situation is easier for accident assessment because of the information gathered in experiments in the CABRI [1], TREAT [2] and other safety facilities. This paper looks at the present state of our understanding of fast reactor fuel pin failure and confronts the present dilemma of modellers in choosing empirical failure criteria, that have inherent inconsistencies and over simplifications, or trying to develop physically based models of failure, which are time consuming and complex to formulate and to use. We will not review failure criteria for hypothetical accident conditions as this has already been done recently by one of the authors [3,4]. Some discussion is, however, given on the relative merits of different approaches, The subject of failure prediction during normal operation is less well developed for reasons already stated and an attempt is made at laying the foundations of an approach to the problem, that could lead to improved fuel designs.

In normal operation fuel pin failure is of interest for two reasons. The first is the release of radioactive fission products into the reactor primary circuit, which increases operator doses and makes more difficult the decontamination of components such as pumps, heat exchangers and refuelling mechanisms. The second reason is perhaps even more important and that is that the mixed oxide fuel is not completely compatible with the sodium coolant. The formation of sodium compounds tends to develop the failure and cause secondary failures. This process is found in practice to be slow and failed fuel pins can be easily detected and removed before there is significant release of fuel fragments. The necessity to remove failed fuel is a constraint on reactor operations that it is desirable to avoid and hence, there is an economic advantage in reducing failure rates in normal operation to negligible levels. In hypothetical accident conditions the timing and position of fuel pin failure to a large extent controls the course of the accident through reactivity changes from associated fuel movements and by the formation of blockages in the coolant channels. The reliable prediction of fuel pin failure is thus a key part of the fuel modelling.

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282

J.R. Matthews, T. Preu.~ser / t'?~ilut'e o[]ast rea(tor /uel pm.s

2. Loadings and paths to failure 2.1. Steady-state conditions

During normal operation a number of changes occur in the fuel and its cladding which may in some circumstances lead to failure and affect the response of the fuel in any subsequent transient. These may be loosely classed into: restructuring, which covers a wide range of fuel structural changes; fuel swelling; redistribution of fission products and associated chemical effects; and radiation effects on the cladding. Let us first look at restructuring, which tends to be more important in fast reactor fuels than in thermal reactor oxide fuels because of a tendency to use lower linear rating and hence lower temperatures. We will restrict ourselves to oxide fuels. The main processes are: (i) Fuel densification resulting from radiation induced sintering of fine fabrication porosity at low temperatures (1200°C) and thermal sintering of fuel above the fabrication sintering temperature (>_ 1600°C). The amount of densification which takes place predominantly early in the fuel irradiation is determined bY the initial pellet density and the size and morphology of the fabricated pores. This to a large extent is controllable through the fabrication process. The densification increases the fuel conductivity which tends to reduce the fuel temperature, but if excessive can cause the fuel-clad gap to open and produce a high fuel surface temperature. An instability of this sort was seen in vibro-compacted fuels irradiated in DFR and PFR [5] and is thought to have triggered failure by a corrosion process. (ii) Pore migration and columnar grain formation driven by the fuel thermal gradient. These processes require fuel temperatures above 1600 to 1700°C or a fuel linear rating in excess of 35 kW m 1. Fabrication pores and pores originating from cracks move up the temperature gradient by a vapour-transport mechanism [6]. The pore volume transferred is added to that of the fuel central void. This reduces the fuel centre temperature and may be critical in governing the behaviour of the fuel in over-power transients. Recent observations on the high temperature response of oxide fuels in compression at HEDL indicate'that hot pressing of fabrication pores is much less than would be anticipated from the creep strength [7]. This may explain the superior performance of annular pellet fuels in transients. (iii) Grain growth which is observed predominantly between 1200°C and 1600°C above which columnar grains dominate. Increased grain size is important through its indirect effect of increasing the creep strength of the fuel and reducing fission gas release.

(iv) Thermal expansion which in turn leads to the generation of internal stresses and cracking. Thermal expansion produces shape changes in the pellet (" hour glassing") which are relieved by cracking. The effect of cracking and pellet distortions are dealt with in section 3.3. Cracking also allows more of the pellet expansion to be released, reducing the fuel~ cladding gap and hence fuel temperatures. Movement of the pellet fragments, termed relocation, can also be important in reducing fuel temperatures where there is a large initial gap. Fuel swelling is a complex process which is produced by three main mechanisms. The first is by the direct and essentially inexorable expansion of the fuel by fission products. Taking all the fission products and placing them in the fuel crystal lattice produces a volume expansion of between 1 and 1.4% per % burn-up. Some of the fission products remain dissolved in fuel, some form inclusions which alter the swelling very little, but the alkali metals and the noble gases which form 25 to 30% of the fission products (or 0.5 to 0.6 atoms for each fuel atom fissioned) have more profound effects. Caesium and rubidium migrate from the hotter fuel regions (1300°C) and move to the fuel-cladding gap, the cooler fuel ends or the blanket pellets, if sufficient oxygen is available in the fuel the formation of compounds with the fuel or cladding components gives rise to enhanced swelling. The noble gases Kr and Xe are essentially insoluble in the fuel and precipitate into the bubbles. A description of the interaction is given elsewhere [8] but swelling from bubbles within the fuel grains in oxide fuels is only of marginal significance. However, during fission gas release, gas collects on the grain boundaries until an interconnected system of pores is generated. This porosity can generate between 6 and 20% volume change which is to some extent compressible. Fuel swelling effects are more important in fast reactor fuels than thermal reactor fuels as a pellet-clad mechanical interaction (PCMI) mechanism, because of the higher target burn-ups (> 10% heavy atoms). Relatively low density fuel is used to accommodate the large swelling, the fuel void volume being distributed between the fuel-clad gap, the fabrication porosity and in some cases pellet dishes or fabricated central voids (annular fuel). The relatively high strength of fast reactor fuel pin cladding means that PCMI does not produce significant strains until a critical burn-up is reached when fuel swelling can no longer be accommodated by taking up the fuel void volume. An example of this is shown in fig. 1 [9]. The critical burn-up is dependent on the available fuel void volume, the amount of clad swelling (see below) and details of the design. It is hypothesised

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that each fuel design has a limiting fuel burn-up after which failure is likely, due to the rapid build-up of PCMI damage. The release of fission gas is usually 50% or more in fast reactor fuels and the design of fuel pins must take account of this. Fission gas release is essentially complete for fuel above 1600°C, is extensive above 1200°C and significant at high burn-up at lower temperatures. The released fission gas is an important driving force for cladding rupture, both in normal operating conditions and in transients, particularly for reduced coolant flow. Irradiation effects on fast reactor cladding are complex and a satisfactory means of predicting behaviour for fuel codes has yet to be developed. It would not be possible in this paper to adequately describe all the effects and their consequences. Bullough has recently reviewed the microstructural behaviour [10] and there is also a recent paper on how these effects interact with the fuel pin and sub-assembly behaviour [11]. The following points, however, are worth noting. The most important radiation effect on materials subjected to a fast neutron flux is swelling. The amount of swelling is very sensitive to the details of the metallurgical state of the material. In general pure metals and alloys in an annealed state swell more than multicomponent materials and materials with a high dislocation density. The austenitic stainless steels often used for fast reactor cladding can swell at rates of up to 1% per dpa, where displacements per atom (dpa) is a measure of the fast neutron damage typically reaching 100 dpa for the fuel life in a large fast reactor. High nickel alloys have been found to swell significantly slower and martensitic/ferritic alloys are befieved to be essentially swelling re-

283

sistant. Swelling starts after an incubation dose of a few tens of dpa. The incubation dose can be raised by prior cold working and the addition of carbide forming elements such as Ti and Nb. Swelling can affect failure both directly and indirectly. When cladding swelling starts any PCMI steady state loadings are reduced and for alloys with a high swelling rate a gap can open between the fuel and clad [9]. This leads to a rise in fuel temperatures with as yet undetermined effects on fission product redistribution and corrosion. High swelling rates can also produce cladding internal stresses, as the swelling is a sensitive function of temperature. To date most experience on cladding swelling as a driving force to failure has been derived from observations of pin bundle distortions, arising from differences between the swelling of the cladding, any wrapping wires and the sub-assembly duct. If the cladding swells more than the wire wrap, the pins can distort in a corkscrew fashion [13]. In the worst cases ovalisation of pins driven against the duct can occur [14]. Interactions of this type and related effects in gridded fuel bundles can lead to local cladding temperature rises and the possibility of early failure [11]. The presence of a PCMI or fission gas loading on the pin cladding promotes creep deformation. In steady-state conditions these loadings are well below the cladding yield strength. For all except the highest temperatures the cladding deformation is dominated by irradiation creep. This is probably not a single process, but irradiation creep is characterised by a low stress sensitivity (the creep rate is usually linear with stress), linear dependence on displacement dose rate and relative insensitivity to temperature. Irradiation creep is considered to be a benign process as it does not lead to plastic instability or strain concentrations [15]. At temperatures of 600°C or more thermal creep donfinates over irradiation creep. Thermal creep is much more stress sensitive, with a typical dependence of creep rate on stress to the power six. This leads to a redistribution of stress within the cladding wall. Elastic calculations indicate a slight stress concentration on the cladding inner surface, but non-linear creep moves this stress peak to the outer surface. Thermal creep is also very temperature sensitive and this further enhances the internal stress redistribution, see fig. 2. Internal stresses from thermal expansion are comparable to those from creep, but are not important in steady-state conditions as they are relaxed by the creep processes. The internal stresses from swelling inhomogeneities, however, are not so easily dismissed as their relaxation requires strains comparable with the swelling strains and these can

284

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lower power operation is followed by a power increase. In such conditions the fuel-clad gap closes and the differential expansion strain is manifested in full on the power increase. The cladding strain increment produced by this mechanism is limited to between 0.05 and 0A% and unless the cladding is severely embrittled several such cycles would be required to provoke failure. There is one recorded example of a failure by such an up-ramp [18].

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amount to several %. The internal stress from swelling can peak at either the inner or outer clad surfaces depending on the part of the temperature relationship the cladding temperature difference covers. Corrosion of the cladding of fast reactor fuel pins is not usually a direct cause of failure although the progressive, but slow, attack from the fission products and the coolant reduce the clad effective thickness. There is, however, evidence that highly rated oxide fuel can exhibit severe corrosion leading to failure [16]. This can occur quite early in life and probably results from a combination of a high local oxygen potential from the hot fuel and an enhanced distillation of volatile fission products, notably Te and Cs, to the fuel-clad gap.

Use of fuel codes shows that the loads and cladding response to power changes is strongly affected by the fuel configuration and the rate of power rise. Some examples of TRAFIC [19] calculations are shown in fig. 3 and 4. High smear density fuel has significantly higher interaction stresses compared with low smear density fuel and annular fuel is significantly weaker than solid pellet fuel. Fuel with a fabricated central hole still tends to have a lower interaction stress than solid pellet fuel of the same smear density, despite restructuring forming a central void. This is because fuel pores in the cooler outer fuel regions cannot hot-press at a significant rate. The size of the clad loading is also reduced if slower power ramps are used. Burn-up also has an effect on the

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As part of the normal operating history of the reactor fast reactor fuel will be subjected to power changes. The main difference from steady operation is the role of differential thermal expansion between the fuel and the cladding. An increase in fuel power will cause the fuel to expand against the cladding and produce an interactive load. Simply reducing power and then immediately returning to the same power level does not produce an interaction except where pellet fragment relocation has occurred. Similarly load following or diurnal power cycling has been shown to be harmless, both by irradiation experiment and by the use of fuel codes [17]. Problems are more likely to occur when a long period of

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285

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interaction stress which tends to saturate when the fuel structure has fully developed. The loading levels on power changes increase with increasing ramp rate and for high smear density fuels the clad can go into yield. Mild over power transients if rapid enough have been calculated to give incremental cladding damage that can eventually lead to failure [20]. These conclusions are at present being tested in an experimental programme in EBR-II.

Comparison of codes have been made recently and these highlight the differences between models [21,22]. This, in particular, is valid for the simple fuel codes often applied to whole core analysis or for the description of special experiments. The authors of this paper feel that only a consistent physically based fuel pin analysis may be used as a basis for developing techniques for failure prediction. We have already discussed many of the processes that control the transient response of the fuel pin in section 2.1, however, the changes in cladding properties with irradiation is of special importance. Five basic phenomena have been identified [23,24]: thermal annealing, irradiation hardening, helium embrittlement, chemical embrittlement and corrosion. Thermal annealing of cladding cold work is a consequence of typical cladding steady-state temperatures (500-600 °C). Irradiation hardening occurs at lower temperatures (300-500°C) as a consequence of radiation damage processes. The competition between the two effects can be seen clearly in fig. 5. For high fast neutron doses the yield stress can be raised above the unirradiated values for even heavily cold worked steel. At temperatures higher than 600 ° C there is the possibility of recrystallisation of cold worked steel, which produces a sharp drop in yield strength down to fully annealed values [25,26]. Fast neutron irradiation and the presence of a load on the cladding from PCMI or fission gas pressure is likely to accelerate recrystallisation. Helium embrittlement will be discussed in more detail in section 3, but it is an essentially high temperature phenomenon ( > 650°C). Helium produced by (n, a) reactions can weaken the material when it collects at grain boundaries; creep ductilities can be sharply reduced. Chemical embrittlement will also be discussed in

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The characterisation of pretransient conditions for accident analysis still remains a challenge to fuel element structural analysis, although much progress has been made over the past years. There is still disagreement in the prediction of the state of the fuel pin after irradiation, particularly at high burn-up, when comparing different codes. "This disagreement reflects, in an integral sense, the difference in models that comprise each code. It also reflects the lack of experimental data necessary to determine which models are correct" [21].

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J.R. Matthew& T Prem'ser / Failure of fast reactor /uel pm~'

286

section 3. This is identified with a reduction in cladding strength and ductility when irradiated in contact with fuel - the "fuel adjacency effect" [27,28] (fig. 6). This effect has now been almost conclusively associated with the presence of the fission products caesium and tellurium on the cladding inner surface [29]. The effective decrease in cladding thickness due to such phenomena as pellet-cladding chemical interaction (PCCI), cladding coolant interaction and cladding-spacer wire wear will influence failure rates in transients by decreasing the load bearing area in the cladding [23,24] wall. The most important effect comes from PCCI. The migration of oxygen and the fission products Te and Cs down the fuel thermal gradient to the clad inner surface, forms an oxidising environment with preferential chemical attack on the Cr content of stainless steels. This results in the creation of an inner corroded layer of cladding, which is incapable of sustaining a tensile hoop stress. The depth of this attack depends on cladding temperature, fuel temperature (i.e. linear rating), burn-up, irradiation time and the fuel stoichiometry. Correlation of all the effects has not yet been possible but for normal linear ratings ( - 4 0 kW m 1) the depth of attack will not exceed 15/~m per 70 burn-up. A lower oxygen to metal ratio in the fuel is thought to reduce cladding corrosion by reducing the amount of free oxygen available, but this has not yet been demonstrated conclusively. A similar corrosion takes place on the outer cladding surface, because of the solubility of some cladding components, notably Cr, leaving a ferritic layer [23]. The corrosion rate is very sensitive to the oxygen content of the coolant, but in practice this should not exceed 5 #m per year [30].

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2.4. Transient mechanical loadinR During a transient, the cladding is loaded by a variety of mechanisms. One of these is thermal stress, arising from the temperature differences between cladding inner and outer surface. The temperature gradient in the cladding is a function of the heat flux from the fuel into the coolant and the thermal properties of the cladding material. Consequently, both the temperature difference and the thermal stresses will rise with increasing cladding wall thickness The same is the case with increasing heat flux. However. during a transient such an increase in temperature difference will not only increase the thermal stresses, but also lead to significant differences in the material behaviour between inner and outer surface, because of the strong temperature dependence of the mechanical properties. A "cold" outer surface may have considerably higher load bearing capabilities compared with a "hot" (near melting point) inner surface. In this way the cladding load is c o n centrated onto the clad outer zone in a way even more marked than that shown in fig. 2. The second transient loading of the cladding arises from the internal gas pressure. With increasing fission gas content in the available gas volume plenum, central void and gap, the pressure load of the cladding is consequently increased. As long as the gap is open, the integral cladding load is formed by combination of the thermo-elastic stresses, the internal (fission gas) pressure, and the external (coolant) pressure. However, during the transient, the gas pressures within the pin may not be in equilibrium and this may produce a very high local pressure build-up. In particular this will happen if the internal connections between the various gas volumes within the pin are interrupted, e.g. if a closed melt cavity forms. Similar non-equilibrium conditions may occur after failure initiation, because of restrictions on the gas-flow from the plenum to the failure site. If the gap is closed or closes during a transient, the additional pellet cladding mechanical interaction (PCMI) increases the loading of the cladding• This may be caused by thermal differential strains, fuel swelling, fuel volume increase due to melting, or other effects like cracking, relocation, etc. The thermal expansion loadings are essentially the same as those for operational power changes. However, the strain rates will be much higher, and only little time is available for stress relaxation by cladding or fuel creep. Axial thermal (and swelling) differential expansion contributes significantly to the loading of the cladding, if the gap is closed. Again the cladding restrains the fuel expansion, leading to axial friction forces which induce axial stresses in

J.R. Matthews, T. Preusser / Failure of fast reactor fuel pins

both fuel and cladding. Stress relaxation occurs due to plastic deformation and creep, leading to cladding length increases which are often measured. On the other hand, fuel elongation is hindered, which is of importance when discussing reactivity feedback effects. As with the radial interaction, transient accident events with high strain rates and no time for relaxation will lead to a considerably higher axial loading than for operational events. Fig. 7 shows as an example of the development of cladding mid-wall hoop stress versus transient time for 5 $ s 1 reactivity ramp at an axial position where failure is expected to occur. Calculated results of different computer codes are compared; a detailed analysis of the complicated behaviour is given in refs. [21] and [31]. The most distinctive feature of the curves in this figure is that they all show several maxima in cladding stress. The first increase comes from the different thermal expansion of fuel and cladding which increases the hoop stress to a point where the cladding begins to yield. The hoop stress then decreases as both fuel and cladding soften and deform plastically. Fuel expansion on melting and additional fission gas release then again increase the stresses if the transient goes on. A second decrease is to be expected if cladding temperatures reach high values and the cladding becomes very soft; failure is likely to intervene before this stage. 2.5. Transient failure initiation

Before discussing the actual failure processes in section 3, we will discuss the relationship between the main driving forces to failure for the three classes of hypothetical accident: Transient Overpower (TOP); Lossof-Flow (LOF); Loss-of-Flow driven Transient Over Power (LOFTOP). The range of conditions of interest is

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287

very wide, for TOP the reactivity insertion rates range from a few ¢ s -1 up to several $ s 1, leading to accident sequences going from tens of seconds down to milliseconds [23,24]. Over these timescales an increase in fuel enthalpy is produced leading to central fuel melting, transient fission gas release, pressure build-up, thermal expansion strains and ultimately build-up of fuel vapour pressure. All these events are potential mechanisms for cladding burst failure. The LOF sequence consists of decreasing coolant flow, sodium boiling, cooling voiding of the sub-channels and eventually clad surface dry-out and melting. This voiding may lead to a power excursion via the positive void coefficient of reactivity. In this LOFTOP sequence the fuel is subjected to a TOP with the coolant channel filled with sodium, void or on the verge of clad melting, depending on the position in the core. In TOP accidents, and to a lesser extent in LOF conditions prior to a LOFTOP, transient fission gas release, fuel swelling and volatile fission product redistribution will occur prior to cladding failure. Prior to cladding failure the response of the fuel to the above transients, particularly if molten fuel is produced, has a strong influence on the further accident development. The axial position of the failure will determine, by the route taken by fuel expelled into the coolant channel, whether a positive or negative reactivity feedback is expected. To better characterise the events related with TOP, LOF and LOFTOP accidents, seven different failure mechanisms have been identified [3,4]: (1) Coolant boiling at the cladding surface. (2) Melting of the clad due to contact between molten fuel and cladding inner surface. (3) Failure due to fuel vapour pressure build-up. (4) Differential thermal expansion of fuel and cladding. (5) Fission gas release on fuel melting. (6) Fission gas release prior to fuel melting. (7) Transient fuel swelling. In general fuel failure will be caused by a combination of several of these processes, but it is convenient to identify a dominant mechanism for a particular set of conditions. Before commenting on each mechanism it is worth looking at the relative conditions that will produce fuel melting and coolant boiling. In fig. 8 loci are shown for first fuel melting and coolant boiling for various combinations of reactor power and flow. The curves labelled with r values represent power ramp rates with a power doubling time given by r. It can be seen that in TOP conditions fuel melting always precedes coolant boiling except for very slow transients at the ends of the pins where the power is reduced. In

J.R. Matthews, T. Pre~ser / Failure o/'fast reactor /uel pins

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LOF conditions coolant boiling always precedes fuel melting, but melting will occur very quickly on the initiation of a LOFTOP. For fast transients fuel melting is almost independent of the coolant interactions. Failure mechanism 1. Coolant boiling at the cladding surface mainly occurs during LOF-transients. In TOPtransients it is only a possibility, if the integrity of the cladding is maintained long after accident initiation.

This may happen with fresh fuel in slow TOP because of the absence of fission gas, and because of the large initial gap size and high cladding ductility. Coolant pressure and temperature during the pretransient phase play a significant part in this mechanism. Once dry-out occurs the cladding temperature is likely to rise at rates typically 100°C s-1 and failure by clad melting follows within a few seconds.

J.R. Matthews, T. Preusser / Failure of fast reactor fuel pins Failure mechanism 2. Melting of the cladding due to contact between molten fuel and cladding inner surface is to be expected with very high melt fractions (80-90%). The pressurised melt may destroy locally the solid, outer fuel ring and come into contact with the cladding. If the melt penetrates through cracks, the mechanism is unlikely to operate due to immediate freezing. A very high cladding (and coolant) temperature is necessary for this mechanism, see section 3.3. Failure mechanism 3. It is not very likely that this mechanism, failure in consequence of a pressure buildup due to fuel vapour, will occur in an accident. It is only possible for very high power insertion rates, and if, at the same time, all other mechanisms are delayed. This can be the case for fresh fuel without fission gas and with a large gap. Failure mechanism 4. Thermal differential expansion of fuel and cladding will always occur during a TOPtransient. The fuel temperatures rise much faster than the cladding temperatures. Thus, the gap between fuel and cladding will be closed (if not yet closed at the beginning of the transient), and a significant mechanical loading on the cladding takes place. The amount of damage is clearly dependent on the pretransient gap-size, on the fuel density, the porosity distribution, and rate of power rise. Differential thermal straining occurs in nearly every TOP-transient and is therefore always a potential mechanism or in combination with other mechanisms. Failure mechanism 5. Fission gas release due to fuel melting occurs immediately the melt front reaches a radial zone of the fuel with large amounts of stored fission gas (equiaxed region and unrestructured region). A significant pressure increase results in the molten fuel which gives additional mechanical loading on the cladding (via the non-molten fuel). The influence of this mechanism during a transient depends on the linear rating and on the burn-up. With increasing power the gas retaining regions are moved outwards to the pellet surface. This means that the necessary melt fraction to initiate this mechanism increases with the pre-transient power level. The pressure increase is directly related with the amount of gas available, which is a function of burn-up. In rapid transients the full pressure of the gas in the molten fuel may be delayed as the gas is restricted by the surface tension of small bubbles. The bubbles have to coalesce before the effect of surface tension is reduced [32]. In very slow transients most of the gas may have been released before melting [33]. Failure mechanism 6. Transient pre-melting fission gas release is not completely understood. Several HEDL-tests clearly showed that significant fractions of

289

the stored gas will be released during temperature increases above 2000°C [34]. As a consequence of the temperature increase, the steady-state equilibrium between intragranular gas production, bubble formation, and bubble movement is disturbed. There is some controversy over the mechanism of release, but there is good evidence for bubble migration in the fuel temperature gradient [8]. The mechanism leads to a pressure build-up. Whether this is sufficient to provoke failure depends on available paths for the released gas to escape from the fuel column into the fission gas plenum. Annular fuel designs are thus virtually immune to this mechanism. Failure mechanism 7. Transient swelling is directly related with transient fission gas release. The volume of the gas bubbles will increase with temperature due to the pressure increase and due to the precipitation and coalescence of small bubbles, which leads to larger bubbles requiring a greater volume for equilibrium with the gas pressure. Swelling can also arise from gas on the grain boundaries. However, if this porosity is interconnected the gas will be released. This release may be hindered by cladding restraint or hydrostatic pressure in the fuel matrix. Fuel in the unrestructured region without interconnected porosity may permit significant additional transient swelling. The fission gas induced swelling augments the mechanical loading of the cladding. However, the volume increase from bubble coalescence and grain boundary porosity growth is not a sudden process but needs timescales of the order of seconds. Thus, this mechanism is more relevant for slow TOP and possibly LOF accidents. An example is shown in fig. 9 of how a clad loading can be produced in a slow TOP. For failure to occur the cladding temperature must also be high.

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Fig. 9. Variation of clad hoop stress in the pin mid-plane during an over power transient with a doubling time of 8 s, as calculated by T R A F I C (85% smear density solid pellet fuel at 4% burn-up).

J.R. Matthews, T. Pre~s'ser/ £bilure q[/ast reactor.fi~elpros

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Fig. 10. Failure maps for CABRI experiments.

An example of how this set of failure mechanisms can be applied is given in fig. 10. This shows schematically how failures in the CABRI TOP (A series) and LOFTOP (B series) experiments can be classified [35]. The strong effect of pre-irradiation, even to a comparatively low burn-up, can profoundly affect the operating failure mechanisms through the generation of fission gases, weakening of the cladding and the closure of the fuel-clad gap. The CABRI series uses a relatively rapid power rise rate (power doubling times of the order 100 ms). The conditions over which a particular failure mechanism dominates is sensitive to the power rise rate and the fuel form. Low density annular fuel resists Mechanisms 4 to 6 and much higher enthalpies are required to provide a sufficient clad load to induce failure. There is also some evidence from TREAT tests that the melt fraction required to initiate Mechanism 2 is decreased with increasing fuel smear density.

3. Failure processes

In this section we turn from the examination of the driving forces for failure to the actual processes that control the breach of the cladding. The bulk of experimental work has been done on cold worked 316 stainless steel, so our discussion will be aimed mainly at this alloy.

3.1. Clad rupture rnechanisrr£s Since the last review of this topic [15] many new experimental observations have become available on the effect of irradiation on the rupture of stainless steels. The failure of irradiated austenitic stainless steels can be classified by six characteristic processes: (1) Channel fracture. (2) Transgranular failure. (3) Grain boundary ductile failure. (4) Intergranular creep fracture. (5) Ductile creep rupture. (6) Grain boundary cavity growth. Fig. 11 shows schematically how these processes dominate under various temperature and loading conditions, based on the most recent published experimental data and modified from the version given in ref. [15]. We will examine each of the mechanisms and in particular identify the controlling stress component. Type 1 channel fracture. This is a low temperature process that leads to a marked reduction of ductility in materials subjected to severe irradiation damage [36]. It is characterised by a mosaic of flat plate-like areas on the fracture surface that could be mistaken for transgranular cleavage. This type of failure is caused by the production of a fine dispersion of dislocation obstacles produced by irradiation; i.e. point defect loops, small voids, helium bubbles and precipitates. Severe radiation hardening is produced and when plastic flow occurs it is

J.R. Matthews, T. Preusser / Failure of fast reactor fuel pins

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confined locally to areas where slip has cleared a path of the obstacles. This type of failure is often seen in combination with transgranular failure type 2. The mechanism is dependent on a critical applied shear stress and this would provide a suitable failure criterion. Type 2 transgranular failure. Another type of common intragranular failure seen after irradiation, particularly when a test is done at low temperatures, is by plastic instability between voids or semi-coherent precipitates. This is characterised by a dimpled appearance of the fracture surface [36,37]. The conditions for this type of failure are very sensitive to the composition of the steel and the irradiation history. For a particular volume fraction of voids or precipitates there will be a critical shear strain to initiate the plastic instability. If the voids or precipitates are on a finer scale than the local dislocation structure they will form obstacles for dislocation movement adding to the irradiation strengthening or when the concentration is high enough initiating channel fracture. Type 3 grain boundary ductile failure. This is characterised by the linkage of a large number of grain boundary cracks, nucleated by sliding or stress concentrations at boundary precipitates [38]. As the material is able to relieve its strain and irradiation hardening at these temperatures the coalescence of the boundary cracks is by a ductile tearing process. The strain to

failure is rather greater than in the related mechanism type 4. The relevant stress component is the maximum resolved shear stress. Type 4 intergranular creep fracture. This mechanism differs from type 3 by the unstable propagation of the grain boundary cracks when they reach a critical length. This type of propagation is permitted because of irradiation hardening at the lower end of the temperature range and the apparent marked decrease in the effective surface energy of the material in the presence of helium [39]. The cracks can nucleate by a grain boundary sliding process concentrating the strain at grain junctions or at large precipitates. The nucleation phase is controlled by the maximum resolved shear stress and the propagation phase by the normal stress on the boundaries bearing the crack nuclei. In practice the final failure will be by the propagation of a crack through the cladding section, absorbing grain boundary cracks nucleated ahead of the tip. Mechanisms types 3 and 4 are both sensitive to the grain size and grain boundary precipitate structure. Type 5 ductile creep rupture. This is not really a failure mechanism as such but a separate domain where creep strains are sufficient to significantly modify the stress state in the section bearing the load. The time to failure is thus controlled by the beginnings of a creepplastic stability. The final failure and hence the failure

J.R. Matthews, T. Premser / Failure of.fast reactor fuel pins

292

strain is controlled by one of the other mechanisms type 3, 4 or 6. The time to failure is given by the Hoff law and is inversely proportional to the initial strain rate in the specimen (for constant applied load) [40]. There are two types of conditions where this mechanism dominates. For high stresses and high temperatures there is often a significant creep deformation before intergranular fracture or cavity growth can operate, because creep has a greater stress sensitivity and a high activation energy. Creep ductility can also be large for very low stresses, which are below the critical stress necessary to trigger cavity growth. Type 6 grain boundary cavity growth. Cavities can be nucleated on grain boundaries either by vacancy condensation on helium bubbles or precipitates or by grain boundary sliding at precipitates. Fast neutron irradiation greatly enhances the potential for nucleation because of helium generation and the coarsening of the grain boundary precipitate structure. Growth of the cavity can occur when the H y a m - S u m n e r criterion is satisfied [41], i.e. a critical normal stress to the grain boundary is exceeded for a particular cavity radius or gas content: 3 I' 32~y3 ]1/2 o,=5t9#~/

m i n i m u m in the rupture ductility I45], corresponding to a vertical section through fig. 11. A sharp increase in ductility in irradiated stainless steel is often seen for tensile tests on going to high temperatures [46], corresponding to a move from processes type 1 and 2 te 3 and 5. The Fuel Cladding Transient Test (FCTT) style of test, which notes the failure temperature for clad specimens subjected to a range of pressures and a constant temperature ramp rate, gives results that make a curving path on fig. 11, crossing from processes 1 and 2, to 3 and 5 and finishing in process 6. The expected maximum in ductility with respect to the applied stress or observed failure temperature range is seen [47]. However, the analysis of failure mechanisms is even more important in identifying and emphasising the sensitivity of failure criteria to the details of the metallurgical state of the cladding. An example is helium embrittlement. Fig. 12 shows the effect of helium produced by thermal irradiation on the creep rupture behaviour of 316 stainless steel [39]. Similar materials, but 10

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where y is the surface energy, n is the n u m b e r of gas atoms, k is Boltzmann's constant, T the absolute temperature. This critical stress is sensitive to the density of cavity nuclei on the boundary and the form of the criterion is altered if the cavities are nucleated on gas bubbles associated with precipitates. Once nucleated the rate of cavity growth may be by vacancy flow from the grain boundary or by creep deformation, but these processes will be constrained by the rate of surface diffusion, geometric creep constraints and the limitations placed on vacancy production on the boundaries because of the presence of precipitates [42]. For austenitic stainless steels below the "solution" temperature vacancy production appears to be the limiting process and this reduces the cavity growth rate by several orders of magnitude over the value expected from unrestricted grain boundary diffusion [43,44]. The growth of grain boundary cavities is controlled by the normal stress on the grain b o u n d a r y and hence failure will be related to the maximum principle stress. The analysis of failure in terms of the characteristic processes is very valuable in interpreting the observed variations in failure strain for various types of mechanical test. For example the creep rupture tests, which scan a range of loads for a given temperature often show a

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J,R. Matthews, T. Preusser / Failure of fast reactor fuel pins with different grain sizes and different degrees of segregation of boron to the grain boundaries, the main source of helium, gave very different responses to the helium. Helium generated directly at the boundary is immediately available for embrittlement. Helium generated in the interior grains has to diffuse to the boundaries and may be trapped in intragranular bubbles or cavities. In fast neutron irradiation, the effects are even more complicated as helium is also generated by fast neutron interactions with Ni and other constituents of the steel [48]. With materials as complicated as austenitic stainless steels the range of precipitation, segregation and microstructural effects is enormous. Establishing the failure characteristics from first principles is thus impossible, for fast reactor cladding subjected to a wide range of possible temperature, loading and irradiation histories. Some other approach must be sought.

3.2. Fuel adjacency effect The Fuel Adjacency Effect (FAE) (see section 2.3) is so potentially important that it deserves separate attention. The term was first used by Hunter and Johnson to explain reduced strength and ductility in cladding irradiated in contact with fuel [27]. As already stated the presence of Cs and Te on the cladding inner surface has been identified as responsible [29]. Earlier interpretations has suggested that a stress corrosion mechanism, fission damage or enhanced He production in cladding in contact with the fuel was responsible [15,28]. It is now generally accepted that "Liquid Metal Embrittlement" (LME) is responsible [11,49]. LME covers a wide range of observations of the loss of ductility of metals and alloys in contact with liquid metals [50,51]. The effect is most marked close to the melting point of the liquid metal, at higher temperatures the test material often recovers all or part of its ductility. One explanation of this is that the liquid metal coats the surface of cracks and reduces the effective surface energy of the material. If the effect is sufficiently large the material becomes truly brittle and crack propagation can take place with little associated plasticity. At higher temperatures the dislocation flow stress is reduced and the material again becomes ductile. Such classic LME behaviour has been observed when stainless steel is mechanically tested in the presence of mixtures Cs and Te [52,53]. The effect is seen for temperatures above 550 ° C when the compound Te-Cs 2 melts. In the case of cold-worked 316 stainless steel the ductility essentially disappears and failure occurs at around 2/3 of the yield stress. For solution annealed

293

316 steel there is some ductility until the strain hardening increases the yield stress and failure occurs. This implies that a critical stress could be used as a failure criterion. Adamson and his co-workers have found that Cs or Te by themselves do not cause embrittlement, but mixtures with a C s : T e ratio below 2 show the effect most strongly. It is suggested that Cs acts as a getter for oxygen exposing a clean metal surface to the effects of Te or a compound of Cs and Te. Similar work at Harwell has shown that Te can cause a loss of ductility in a low oxygen potential environment [54]. Creep rupture observations of 316 stainless steel in the presence of Cs alone show that although there is some intergranular corrosion there is no loss of ductility [53]. The LME from Cs and Te is found to affect a wide range of austenitic stainless steels but is not thought to be important for ferritic steels. Cs is produced during fission at a rate at least seven times higher than Te. At such a high ratio LME would not be expected. The observations of FAE in FCTT and creep rupture tests show a very large scatter and recent work using cladding irradiated in PFR rather than EBR-II have failed to show the effect, see figure 13. The PFR fuel was a full length driver fuel, with an 80% smear density in annular pelleted form, and with blanket pellets at each end. The EBR-II fuel was shorter, with 85-90% smear density solid pellets, no blanket pellets and with a large proportion of the fissions in 235U. The differences are not yet fully understood but one hypothesis is that a higher surface oxygen potential in the EBR-II fuel tied up most of the Cs in the form of uranates and chromates leaving a lower Cs : Te ratio to cause LME.

3.3. Local effects In nearly every case there will be some significant effect on the timing and position of failure from local perturbations in temperature, configuration and loading distributions. Such local variations require two or three dimensional treatments of the cladding behaviour and cannot be directly handled in a "1½ dimensional" fuel code. Much can be done, however, in providing add-on models to fuel codes to cope with specific cases. The problem can be split into two distinct categories: fission gas driven rupture effects and stress concentrations associated with PCMI. Strain localisation during fission gas driven creep of the cladding arises either because of a local temperature increase or a local clad wall thickness decrease arising from a fabrication defect or by some form of damage. Provided the variation in temperature or thickness is

294

J.R. Matthews, T. Preusser / Fadure of /U,st reactor.h~el pm.s 500r

PFR irrad~aled adjacent 'to fue[

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Fig. 13. Thc effect of irradiation on the transient rupture characteristics of 20% cold-worked 316 steel subjected to a temperature rise rate of 5.6 K s 1. Irradiated specimens were with doses between 20 and 40 dpa.

small, the local disturbance may be treated by a perturbation technique [57,58]. This is appropriate for fast reactor fuel pin calculations because of the small strains to failure. The cladding tube tends to be weak with respect to bending in the r-O plane, compared with diametral expansion, and for this reason the tube section tends to remain circular. Many temperature perturbations from bundle interactions and cladding thickness variations from loading scratches or wire-wrap fretting interactions, are long compared to the pin diameter. In these cases an even simpler approximation may be adopted, where the pin radius, diametral strain and hoop stress is calculated for the average condition, and the strain and stress in the perturbed region is calculated by applying the load over the minimum reduced section or at maximum temperature. The failure criterion is applied to the perturbed zone. In the case of axially localised perturbations bending of the tube in the r - z plane is difficult and the local temperature

fluctuation or wall damage must be much more severe to be significant. This was the case in many failures in experimental clusters in D F R because of adherent gas bubbles, caused by the low flow velocity [59,60]. In these cases a small area of the cladding was subjected to a temperature increase of more than I(X)°C for long periods. For such very. localised conditions a treatment of the patch deformation, with edges constrained to the more normal surrounding conditions, is more appropriate [61]. The study of stress concentration associated with pellet hour-glassing and cracking has been considered important in thermal reactor fuel studies for many years. However, this aspect has not received much attention by fast reactor fuel pin modellers as PCMI is not so important in normal operation and because the stress concentrations were considered less severe with the fast reactor fuel cladding having a relatively large thickness to diameter ratio. Such stress concentrations are worth some attention as thcy provide a means of initiating failure during power up-ramps through PCMI when the average strain increments are lower than those expected to provoke failure. The usual method of calculating the strain concentrations over pellet cracks assumes that the pellet fragments move rigidly and a thin shell model is used to describe the cladding deformation around its circumference [62]. This approach has recently received some criticism for a number of reasons [63]. The thin shell model when properly formulated can predict the mean cladding strain concentration through the cladding wall, but severely underpredicts the concentration close to the clad inner surface adjacent to the crack [64]. The size of the concentration is sensitive to the friction coefficient between the cladding and the fuel, which is not well known and likely to be a function of burn-up and local oxygen potential, etc. The fuel fragments are also not completely rigid and the crack opening will be offset to some extent by deformation at the crack root, where the fuel temperature is higher and the fuel more plastic. The problem may be investigated using two dimensional finite element analyses using realistic fuel crack distributions, but the question of interracial friction remains unresolved. This is an important area for future research. 3.4. Melt-through

It is relatively straightforward to establish the conditions for melt-through of the cladding by contact with molten fuel from the point of view of heat transfer but establishing sequence of events is more difficult. In

J.R. Matthews, 7", Preusser / Failure of fast reactor fuel pins

order to trigger melting the cladding temperature has to be above 900°C at the time of contact and if the contact is over a limited clad area the clad temperature needs to be even hotter [65]. A good general guide is that the coolant should be boiling or absent before melt-through can proceed. The melting front takes some 30 ms to penetrate the cladding and in TOP conditions some other failure process may intervene during that time. These conclusions are consistent with experimental observations on fresh fuel. Molten fuel penetrating the clad and contacting a relatively cold cladding in SCARABEE tests showed no signs of melting or other damage [67]. However, molten fuel contacting the cladding under similar circumstances, but with the cladding at 1000°C, showed the start of melting in a HFR experiment [67]. Penetration of fuel cracks by molten fuel is not commonly seen in irradiated fuel for a number of reasons: the fuel-clad gap being closed at nominal power will prevent crack formation and opening during the power ramp by generating compressive fuel stresses; and the presence of fission gas bubbles will reduce the fuel density making freezing during crack penetration more likely. There are circumstances when melt-through might be important in irradiated fuel during a TOP or a LOF accident. In a slow TOP the generation of pressure in the central molten cavity may cause the fuel column to separate and a part of it to move axially. Molten fuel can then flood into the resulting gap and contact the clad. Sufficient axial clearance is required for the fuel column. The separation is most likely to occur towards the top of the fuel column where cladding temperatures are higher and PCMI pressures are less, or in a LOF when the gap is open. Such behaviour is only possible in high smear density solid pellet fuel for large melt fractions. Axial movement of the molten fuel is relatively easy in annular pellet designs. Failure by melt-through will always be an uncertain process and the use of melt fraction criteria unreliable.

4.

Difficulties

in

applying

failure

criteria

Pin failure models may be divided in the following way: (A) Empirical correlations. (B) Correlations based on mechanical descriptions: (B1) strain based criteria; (B2) stress based criteria. (C) Microphysical models. Let us first of all examine models of type A and B. Typical examples are:

295

- Melt Fraction Criteria [681; - Failure Potential or Enthalpy Criteria [69]; - Melt-Through Criteria [65,70]; Integrated Strain Rate Method [70]; - Strain Failure Limit Correlations [71]; Conservative Strain Critria [3]; - Transient Failure Strain Criterion [3]; - Life Fraction Rules, Dorn & Larson-Miller Parameters [72,73]. They are widely discussed in literature, including recent applications, comparisons, and evaluations [3,4]. Besides practical experience with these models, theoretical evaluation already shows how difficult and uncertain the applications will be. All correlations suffer from: small and uncertain data basis; - non-prototypic in-pile test conditions (geometry and irradiation); non-prototypic out-of-pile tests; uncertainties of the fuel element codes applied when fitting the models to experimental evidence; - no or only small basis for extrapolations; the fact that material dynamics is not yet adequately understood; applicability limits either not defined or too narrow; - sensitivity of failure process to variations in material composition and history. There are a lot of difficulties due to these constraints. Missing applicability fimits present perhaps the most severe problem because the user will be induced to apply the models to arbitrary conditions beyond the original data-base. In the few cases where applicability limits have been set they are too restrictive, e.g. the Failure Potential Criterion has such a narrow application range that it will be quite hard to find a relevant accident sequence: - burn-up 30000 to 50000 M W d / t - steady-state power 17 to 38 k W / m - fluence 2.4 X 1026 to 6 × 1026 n / m 2 reactivity rate 0.5 to 3 $ / s Similar problems occur with the Life Fraction Rule, which should be used between temperature rates of 2 to 115 K s I. Thus, slow transients ( < 5 ¢ s 1) are too slow, but fast transients (> 5 $ s 1) are too fast. Well aware of these problems some users tend to neglect the limitations, making the situation not better but worse. However, what else should be done if a limit is only exceeded during 10 time-steps out of 500 of the transient course? A comparison as discussed [4] would not be possible without contravening some limitations. The result of such a style of programming is that the models contain more IF-statements than physical equations.

296

J.R. Matthews, 7: Preusser / Failure of jast reuctor [uel pm.s

Then, engineering judgement is required for model result interpretation. There are other difficulties arising from restrictions of the models to one or few failure paths only. As pointed out previously, the most likely case for a complex transient event is that different failure models contribute to the cladding damage. For example, during an accident sequence, first damage could occur due to thermal differential straining. Later, strong fission gas release due to temperature evaluation then leads to other effects governing the damage. Eventually, meltthrough conditions could be reached. Most of the empirical failure criteria are not able to consider these changing conditions. As a result, many codes apply different criteria in parallel, defining failure just at the moment when the first model reaches failure conditions. Because of the different bases of the models and their quite differing reliability, such an approach requires additional engineering interpretation. Another problem is that most criteria require a clear definition of the start of the transient. This, however, is a most difficult question. Even in simple TREAT-TOP tests with well defined power history, a short "operational" transient (to reach steady-state conditions) always precedes the "accident" transient (see fig. 14) [74]. Test calculations prove that failure models sometimes predict completely different failure times when applied from time zero or from time 5.0 s. Real transients, with several power maxima due to reactivity feedbacks are even more difficult to treat. In particular for LOF-TOP cases, where "nothing" happens during the first seconds before a sharp reactivity increase is triggered, the definition of appropriate starting times is a complicated matter, often controlled

150

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by the user's personal experience only. The uncertainties of the fuel element codes themselves are widely known, as shown by various code evaluation projects and blind calculations. Even codes with the best reputations have difficulties in predicting the cladding loading history during a complicated transient. The fuel and cladding constitutive relations for high temperatures and high bum-ups are not well defined. The problems related with the formation of melt cavities are well known and contribute a lot to the uncertainties of the calculated loading history: at what time will the plenum be isolated? Does a "sealed-bottle" phenomenon take place? Will the gas pressure crack the outer fuel ring, thus leading to a pressure drop in the cavity? What are the consequences of axial liquid fuel movement? At present, these and other questions cannot be answered with the accuracy needed for failure predictions. When applying life fraction rules obtained from out-of-pile cladding tests, care should be taken to use an appropriate measure of the load on the clad. The correlation may be made in terms of either the pressure applied to the cladding inner surface or the hoop stress derived from the internal pressure using the initial cladding geometry. Depending on the sophistication of the fuel model the effects of the change in cladding section with deformation may be ignored or accounted for. When cladding strains are low ( > 2%) there is not much effect from the change in geometry and the life fraction rule may be applied directly. When the strains are higher or the clad is subjected to significant volume swelling, the geometrical changes will be important. In a complete description of the cladding mechanics, i.e. not making a thin shell approximation, variations in cladding stress will be calculated from thermal expansion gradients and stress redistributions from the constitutive relations, see fig. 2. A decision has also to be made, whether to apply the failure criteria at a number of positions in the cladding wall, at some representative point, or using some weighted average. A combination of an uncertain code with an uncertain failure model will lead to unreliable results. It is necessary to validate the failure criteria and the codes that use them against a wide range of experimental evidences as possible. However, the data bases themselves are quite limited. Much of the out-of-pile data on irradiated cladding behaviour comes from the HEDL FCTT tests [75] and are well documented in literature [76,77] under the name "Thermal Transient Tests". The test is carried out in three steps: pre-pressurisation of the argon-filled cladding tube at room temperature up to 80% of the test pressure;

J.R. Matthews, T. Preusser / Failure of fast reactor fuel pins

- inductive heating of the specimen up to 371° C, 100% test pressure; further heating with temperature rates of 5.56 ° C s 1 or 111.1° C s 1 and constant pressure until failure. As a result, failure temperature and failure strain are obtained for particular test conditions. The failure stress can be derived from pressure and temperature. However, some restrictions have to be taken into consideration when evaluating FCTT-results: A constant test pressure does not correspond to any realistic transient. - The geometry of the specimen is different from a typical LMFBR cladding. - The specimen is loaded with an axial uniform temperature (non-prototypic). No fuel is inside the cladding; thus, the transient fuel adjacency effect is not taken into consideration (although in some tests fission products and some fuel fragments remain in contact with the cladding during the test). - Temperature measurement is possible only at the outer cladding surface. Simulation of stress concentrations associated with fuel-cladding mechanical interaction (e.g. ridging) is not possible. A wide range of other out-of-pile tests have been used, although the amount of data on irradiated cladding tubes is often not so extensive. There is a lot of data available on stress-rupture tests where the tube is held at constant pressure load and temperature, and in some cases creep strains are also monitored. Another style of test uses a temperature ramp and then a period at constant high temperature, with constant pressure load to simulate LOF conditions [78]. More complicated tests can be constructed with changes in temperature ramp rate and pressure loading to simulate LOFTOP conditions [79]. Altematively the cladding tube may be loaded with a pressure ramp at constant temperature [29] and with modern computer control the pressure can be adjusted to maintain a constant strain rate in the tube [79]. These different styles of test enable failure criteria to be established for a wider range of conditions and to test that they are not sensitive to loading history. It is even possible using a nickel membrane surrounded with a layer of fuel to simulate PCMI, and the effect of the presence of fuel and fission products in creep rupture tests can be accommodated by pressure testing on complete fuel pins [80]. This style of test also permits the release of fission products to be monitored after failure. Even the most sophisticated mechanical tests are not capable of reproducing the internal stress distributions -

-

-

-

297

in the cladding wall that are produced in in-pile. Confidence in failure criteria can only be established after comparison with reactor experiments. The most extensive range of failure observations come from the TREAT reactor with experiments largely in NaK filled capsules sponsored by HEDL [81] and more complex experiments in recirculating sodium loops sponsored by ANL [82,83]. These tests have provided a great deal of information that has proved invaluable in validating failure models. However, they may be criticised because of various aspects which are un-prototypic: short pins; low ratio of clad dose to fuel burn-up (because of pre-irradiation in EBR-II at high fuel enrichment); - thermal neutron spectrum in TREAT with associated radial power depression; - relatively flat axial power profile: - non-typical coolant conditions. Some of these objections have been overcome in the CABRI [1] and PFR-TREAT [2] experiments, with full length fuel pins irradiated in PFR and Phenix. There remain, however, the difficulties of getting the information out of in-pile experiments. Failure time, and to some extent failure position, may be obtained by inference from microphones, flow detectors, thermocouples and neutron imaging devices, but direct visualisation or strain measurements are not possible. Also microstmcture is often lost after failure as the reactor cannot always be tripped before extensive damage to the cladding done by molten fuel etc. Let us now turn to the problems associated with microphysical models. In section 3 some of these models were examined and it was generally found that they are sensitive to the details of the microstructure of the cladding. Often sufficient characterisation of cladding alloys is not available in terms of grain size, precipitate types and distributions, segregation and dislocation density. Complete characterisation of complex alloys such as 316 stainless steel is not possible and the alloy specification is not precise and encompasses a range of compositions giving mechanical behaviour that is similar but variable. Complete microphysical modelling is not achievable and there will always be some uncertainty in failure behaviour. Even more of a problem is that basic materials properties required to construct microphysical models are not well known. Quantities such as diffusion rates and interfacial energies have to be estimated from a very limited data-base. Some models with assumptions that would be attractive to implement, are intractable or too expensive in their demands on computer capacity or running time. Despite this microphysical modelling remains an important alterna-

298

J.R. Matthew& 71 Preusser / Failure (~[fit,~t reactor/uel pins'

tive to more empirical approaches. Microphysical modelling can identify when failure mechanisms change in importance under different conditions. It can give guidance on the manner in which complicated loading and temperature histories can be dealt with and what stress and strain components should be used in complex stress states. Microphysical modelling can also be useful in anticipating effects that are outside the scope of empirical criteria, such as the recovery of cladding damage during periods of low load. This is particularly important when assessing the consequence of repeated transients or the life-reduction of a fuel pin after a terminated transient.

5. Probabilistic approaches The failure of fast reactor fuel pins is intrinsically stochastic. In normal operation the incidence of failure by all causes is variable and to date the data for failure can only indicate the edge of any probabilistic distribution. Failure, therefore, occurs in exceptional pins with adverse combinations of variations in fabrication details and local environmental conditions. On the other hand for unterminated transients failure is inevitable and it should be possible to build up a distribution of failure times if sufficient experiments were carried out. However, the results would almost certainly reflect more the variation in the experimental conditions than those characteristic of the pin and its environment in the real case. The question of variability of failure is very important from the point of view of whole core accident calculations as the "incoherence" provided by a statistical distribution of failures can ameliorate the effects of the transient and reduce reactivity rise rates. A number of techniques are available for probabihstic analysis of fuel behaviour. The most direct is the use of parametric variations, which is efficient when the number of parameters that are uncertain are small, but impractical for most problems. The most widely used technique is Monte-Carlo analysis which builds up a response distribution with many calculations with randomly varied parameters about predetermined distributions. This method has been widely used in fuel behaviour assessment although it is expensive in computing time especially with sophisticated codes [84,85]. Alternatively the variations in parameters may be selected systematically and a response surface constructed, with a decrease in computing costs, but an increase in complexity [86]. A novel approach has been taken by Lassmann recently in which numerical noise, with the characteristics of the uncertainty distributions

of the parameters, is applied to a sirlglc calculation i87j. This enables the variation in response to be obtained extremely cheaply. This has proved successful in the calculation of temperature variations, but the soundness of the technique for mechanical response and failure has yet to be established. To demonstrate the sensitivity of failure in acccidem conditions the Monte-Carlo technique has been applied with a range of empirical failure models. The statistical version [85] of the URANUS code [88] was used with the FAILRE subcode containing the failure criteria [89], The materials data and the power history are considered to be stochastic variables with normal distributions. A probability density function is obtained for all the relevant output data items. The same 3 TOP transients, covering 5 ¢ s i 50 ¢ s t and 5 $ s ~ transients, are used as in earlier work and the basic input data-sets arc given in refs. [4,21,89]. Standard deviations of o = 0.038 are applied to the power history, the Young's modulus, thermal expansion, thermal conductivity, creep rate and yield strength for both the fuel and its cladding. This standard deviation corresponds to 99% of the values lying in the range + 10% about the nominal conditions. Although random combinations at the limits of the range will occur they will only occur infrequently in the distribution. The technique is a useful way to evaluate the sensitivity of the criteria to uncertainty in properties and conditions, or the range of conditions found within a sub-assembly, but on the other hand it is expensive. Fifty calculations have been run for each of the transients, always based on the identical pre-irradiation history (which therefore does not contribute to the statistical distributions), Ten different failure criteria are applied in parallel, namely the Failure Potential Criterion (FPC), 2 Melt-Fraction Criteria (MFCI, MFC-II), the Melt-Through Criterion (MTC), 2 Life Fraction Rules with Dorn and Larson-Miller Parameters, respectively (LFR-DP, LFR-LMP), the Integrated Strain Rate Method (ISRM), the Conservative Strain Criterion (CSC), the Strain Failure Limit Correlation (SFLC), and the Transient Failure Strain Criterion (TFSC). Detailed description of these criteria is presented in ref. [3], deterministic results are analysed m ref. [89] (further literature references see section 4). In spite of the narrow range of input standard deviations quite remarkable changes in predicted failure times resulted in some cases; failure locations are not so much affected. The maximum deviations in failure times are different for each criterion and and data case (cf. table 1). There are two main results worthy of mention. First, that the differences in predicted failure times significantly increase with decreasing reactivity rise

J.R. Matthews, 7". Preusser / Failure of fast reaetor fuel pins rates. This is due to the comparatively longer times available for the slow cases permitting stress relaxations, transient swelling and other effects which do not occur during rapid transients, making the slow cases more complicated to analyse. Secondly, it has to be stated that an increasing number of input variables into a single criterion results in a broader scatter of the results. Thus, e.g., Life Fraction Rule criteria are much more sensitive to the Monte-Carlo analysis than simple Melt Fraction correlations. However, one should not conclude from this that, e.g., M F C are better because of their "stability" - on the contrary: the small sensitivity

f

lO

Oetermfnistic

ResuLt

I

FPC

Jl

MFC-I

lO

i

0

MFC-II

j

299

confirms the previously made statement that over-simplification will lead to unsatisfactory results. Figs. 15 and 16 show the probability density functions for the 5 $ s-1 and the 5 ¢ s-~ cases. There is no need to discuss the different failure locations obtained with different criteria; as pointed out previously (sections 3 and 4) there are still quite a number of objections against most of the empirical correlations which, in an integral sense, are reflected in the different results achieved. More relevant are the variabilities of failure because of their influence on the transient course via reactivity feedback effects. In particular, one should always keep in mind that, e.g., for the Life Fraction Rules only probability functions for LF = 1 are discussed; but not the probability that failure indeed would occur at this value. Fig. 17 [91] shows clearly that LF = 1 itself represents the most likely failure value from a probability distribution given by the experimental results. As far as the present knowledge allows we have to accept that uncertainties still remain when applying failure criteria; and that one has to be extremely cautious when analysing whole core accident scenarios based on the prediction of fuel pin failure times and locations gained from above models.

18

0

: t

MTC

FPC

1o !

i

~ 0eterministic ResuLt

t

lill

_

o

10 LFR-OP 1o o lO

LFR-LMP

I L

,m MTC

II

o____. L'-ff.- L

ISRM "

0

MFC-II

5

CSC

I;"

L F R - L M P

~

"

ISRM

10 0

100

200

100

/.00

SOIl

6110 ms 700

Fig. 15. Probability density functions for 1.0 failure criteria applied to 5 $ s 1 transient. URANUS Monte-Carlo analysis, 50 runs. Dashed fields: unexpected failure location.

0

20

~.0

60

s

80

Fig. 16. Probability density functions for 10 failure criteria applied to a 5 ¢ s 1 transient. URANUS Monte-Carlo analysis, 50 runs. Dashed fields: unexpected failure location.

J.R. Matthews, T. Preusser / Failure of fast reactor fuel pins

300

Table 1 Deterministic fialure time predictions and statistical deviations obtained from 3 ×50 URANUS Monte-Carlo runs for different transient cases Criterion

5 $/s Time (ms)

FPC

590

MFC-I

576

MFC-II

532

LFR-LMP

563

LFR-DP

678

ISRM

700 a)

SFLC

×

MTC

602

CSC

546

TFSC

270

~')

50 ¢ / s Variation (ms) 18 + 18 22 + 14 25 15 69 +134 - 34 > +22 23 > + 0 a) × 28 + 14 49 + 33 10 + 74

5 ¢/s

Time (s)

Variation (s)

Time (s)

Variation ~s)

4,49

0.18 ~ 0.46 0.37 +0.30 -0.35 +0.31 - 0.78 + 1.52 0.33 +0.31 - 0.52 +0.70 -0.12 +0.61 -- 0.32 +/).34 - 0.40 +052 0.12 ~ 0.61

57.0

2.4 10.6 6.1 ~8l ~ &3 > ~.4.0 14.5 ~ 18.5 ~:

4.84 4.35 3,97 4.48 5.36 1.46 4.84 4,28 L,46

64.0 ~ 76.0 48.0 × 71.3 15.0 ;4 80.0 13.0

9.9 4 7.5 0.0 ~ 54.9 :~ -

- 13.8 > ;(1 4.0 + 12.0

100% relative height.

Life Fraction 0.1 1.0 10 100 ~,6o 'i if i] i I i 50-Non Conserv~servative a,O0.01

2O

'0

0

-2

-1 0 1 Lo01o ILife Fraction)

Fig. L7. Distribution of calculated Life Fraction values correlated with transient test data (from ref. [91]).

6. Discussion and conclusions It h a s b e e n d e m o n s t r a t e d in this p a p e r that failure p r e d i c t i o n for fast r e a c t o r fuel p i n s is a c o m p l i c a t e d a n d difficult subject. U n d e r l y i n g the d i s c u s s i o n is the ass u m p t i o n that t h e t h e r m a l a n d m e c h a n i c a l state o f the

fuel a n d the c l a d d i n g c a n b e m o d e l l e d accurately a n d in detail. This r e q u i r e s a s o p h i s t i c a t e d fuel c o d e that is able to calculate a s p e c t s o f fuel b e h a v i o u r such as: - stress r e d i s t r i b u t i o n t h r o u g h c l a d d i n g wall; finite d e f o r m a t i o n analysis; fuel restructuring; - fission gas d i s t r i b u t i o n s ; - fuel creep. N o t all fuel c o d e s treat the fuel in such detail, a n d in p a r t i c u l a r the fuel m o d e l s used in w h o l e - c o r e a c c i d e n t c o d e s are f r e q u e n t l y very s i m p l e [90]. T h e r e is a t r e n d to d e v e l o p c o m p l e x s u b - r o u t i n e s , b u t the c o n s t r a i n t s o f r u n n i n g time will m e a n that effective s i m p l e r m o d e l s will b e r e q u i r e d as well as the m o r e d e t a i l e d i n t e r p r e t i v e c o d e s such as T R A F I C [19] a n d U R A N U S [88]. T h e m o s t effective w a y o f using c o d e s y s t e m s is to d e v e l o p b o t h d e t a i l e d a n d s i m p l e models. T h e d e t a i l e d c o d e s s h o u l d b e extensively v a l i d a t e d a n d e n d o r s e d against a wide range of experimental observations. A mechanistic u n d e r s t a n d i n g o f the p r o c e s s e s g o v e r n i n g the b e h a v i o u r s h o u l d b e o b t a i n e d . O n l y t h e n s h o u l d gross simplifying assumptions be introduced and they should be based on

J.R. Matthews, T. Preusser / Failure of fast reactor fuel pins the mechanistic understanding. The simple models developed in this way should be compared with the same experimental data-base as the complex codes, and in addition comparisons between the complex and simple codes, should be made for extreme conditions that are not accessible to experimentation, because of cost or practical difficulties. Such a progression will give confidence to the appliclation of simple codes for design or accident calculations and reduce the variability between models. We have established in this paper that a full microphysical description of failure is not achievable. However, microphysical modelling is still important in the development of empirical failure criteria, by helping to establish their bounds and indicating features that should be included. In another study some failure models have been shown to be more soundly based than others [3]. For many applications an "Integrated Strain Rate Criterion" or the "Life Fraction Rule using the D o r n Parameter" is sufficient, supplemented by " C l a d ding Melting and Melt-Through" criteria. Care has to be taken that no conflicts are introduced in their application. Study of failure processes indicates that a simple stress limit may in some cases be appropriate or applied additionally to other criteria. For the future new criteria should be based on microphysical models. The problems of incomplete characterisation of the cladding and lack of certain basic properties data can be overcome by using "semi-empirical" models. These use the microphysical descriptions to give the basic framework for the model, but simplifying assumptions are made and unknown quantities are used as fitting constants. In this way the number of variables used in the fitting are reduced and the mathematical form of the model is pre-determined. Models for cavity growth on grain boundaries and the propagation of creep cracks should eventually be used to determine failure and take account of local stress distribution. The effect of fission products on cladding embrittlement needs further attention and future fuel behaviour codes will contain comprehensive descriptions of fission product redistributions and chemical interactions. In particular a reliable technique for calculating the oxygen potential at the fuel-cladding gap as a function of burn-up is required. More attention should also be given to investigating local temperature and stress effects in fuel behaviour codes and this will depend on a deeper understanding being obtained from two- and three-dimensional fuel models. Finally the stochastic nature of failure must be recognised and there is scope for the development of cheap and efficient techniques for determining failure probability distributions.

301

References [1] J. Dadillon et al., CABRI project recent progress and present status, Proc. LMFBR Safety Topical meeting, Lyon-Ecully, 1982, p. II-177. [2] C.B. Cowking et al., The PFR/TREAT programme: objective, progress and future work, ibid., p. 11-103. [31 T. Preusser, State-of-the-art review of physical and mathematical models for theoretical analysis of the transient mechanical fuel pin loading and for the determination of fuel pin failure thresholds for HCDA analysis of LMFBRs', Technical University of Darmstadt Report, RTDA-98-83 (1983). [4] T, Preusser and H.P. Schiffer, Application and evaluation of different fuel element failure criteria to FBR hypothetical accidents, 8th Internat. Conf. on Structural Mechanics in Reactor Technology, Brussels, 1985, paper C2/8. [5] D. Wilmore and J,R. Matthews, FRUMP - a physically based fuel model, Proc. Conf. on Fast Breeder Reactor Fuel, Monterey, CA, 1979, p. 665. [61 C. Ronchi and C. Sari, J. Nucl. Mater. 50 (1974) 91-97. [7] O.D. Slagle et al., Nucl. Engrg. Des. 79 (1984) 301-307. [8] J.R. Matthews and M.H. Wood, Eur. Appl. Res. Rept. Nucl. Sci. Technol. 5 (1984) 1685. [9] K. Uematsu et al., Irradiation performance of mixed oxide fuel pins - Japanese experience, Proc. Conf. on Fast Breeder Reactor Fuel, Monterey CA, 1979, p. 16. [10] R. Bullough, Dislocations and radiation damage, Proc. Conf. on Dislocations and the Properties of Real Materials, Royal Society, London (Metals Soc., 1984) p. 283. [11] J.R. Matthews and M.H. Wood, Radiation effects on safety aspects of fuel assembly design, Proc. Internat. Topical Meeting on Fast Reactor Safety, Knoxville, TN, 1985. [12] M.R. Hayns, J. Nucl. Mater. 65 (1977) 16. [13] J. Rousseau et al., Deformation des aiguilles avec ills espaceur en presence de gonflement et de fluage d'irradiation, Proc. Conf. on Irradiation Behaviour of Components, Ajaccio, 1979, CEA p. 291. [14] J.M. Dupouy, Rapsodie and phenix the materials story, ASTM STP 782 (1982) p. 1179. [15] J.R. Matthews, Deformation and rupture processes in fuel cladding under steady state and transient reactor conditions, Proc. Conf. on Irradiation Behaviour of metallic materials for Fast Reactor Core Components, Corsica, 1979, p. 273. [16] J.F.W. Bishop, Nucl. Energy 20 (1981) 31 48. [17] J.R. Matthews and H. Hughes, Fast reactor fuel modelling in the UK, IAEA Specialists Meeting on Theoretical Modelling of LMFBR Fuel Pin Behaviour, Fontenayaux-Rose, 1979, IWGFR/31, p. 112. [18] M. Patel and R.E. Murata, Preliminary analysis of the cause of failures of experimental mixed oxide fuel rods in EBRII, General Electric Report, GEAP-14057 (1975). [19] J.R. Matthews, M.H. Wood and R. Thetford, The application of the TRAFIC fuel performance code to steady and transient conditions, Proc. Conf. on Nuclear Fuel Performance, BNES, Stratford-upon-Avon, 1985, p. 52.

302

J.R. Matthews, T. Preusser / failure o[jm't reactor tuel pros

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