The prediction problems of VVER fuel element cladding failure theory

https://doi.org/10.1016/j.nucengdes.2016.04.005Get rights and content

Highlights

  • Fuel cladding failure forecasting is based on the fuel load history and the damage distribution.

  • The limit damage parameter is exceeded, though limit stresses are not reached.

  • The damage parameter plays a significant role in predicting the cladding failure.

  • The proposed failure probability criterion can be used to control the cladding tightness.

Abstract

A method for forecasting of VVER fuel element (FE) cladding failure due to accumulation of deformation damage parameter, taking into account the fuel assembly (FA) loading history and the damage parameter distribution among FEs included in the FA, has been developed. Using the concept of conservative FE groups, it is shown that the safety limit for damage parameter is exceeded for some FA rearrangement, though the limits for circumferential and equivalent stresses are not reached. This new result contradicts the wide-spread idea that the damage parameter value plays a minor role when estimating the limiting state of cladding. The necessary condition of rearrangement algorithm admissibility and the criterion for minimization of the probability of cladding failure due to damage parameter accumulation have been derived, for using in automated systems controlling the cladding tightness.

Introduction

Development of methods for forecasting of VVER fuel element cladding integrity is imperative for Ukraine due to the great nuclear share (near 50%) of electricity generation. In order to insure a high quality of electricity, the nuclear power plants should have the ability to follow load on a regular basis, including daily variations of the power demand.

Though no integrated data on cladding failure frequency during the last 5–10 years has been found in open publications, the following information concerning the period 1994–2006 is available:

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    only 40% of Ukrainian VVER-1000 reactors are operated with zero cladding failure frequency;

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    in the whole world, in 2006 near 1% of discharged VVER-1000 fuel assemblies had depressurized claddings, while in the most unsuccessful 2001 year – near 7%;

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    in Ukraine, the main suspected cause of cladding failure for VVER-1000 fuel is debris fretting, the share of failures with unknown causes is undetermined;

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    in Russia, the main suspected causes of cladding failure for VVER-1000 fuel are: debris fretting and fretting wear on fuel element plugs in the bottom support grids – 20% of all cases, and unknown causes – 80% (2002–2006);

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    in the whole world, the main suspected causes of cladding failure for PWR fuel are: grid-to-rod fretting – 55% of all cases, debris fretting – 11%, fabrication-related failures – 5%, crud/corrosion-related failures – 4%, and unknown causes – 25% (IAEA, 2010).

The presently available VVER-1000 technological system controlling the hermeticity of fuel element cladding by a casual radiochemical analysis of water probes taken from the primary coolant circuit, does not allow to make the root cause analysis for cladding failures (Оvchinnikov and Semenov, 1988).

As a rule, the cause of cladding failure in VVER is not known reliably, hence, in order to guarantee the fuel operation safety and reliability, complex methods for controlling the cladding failure probability must be developed, considering different physical mechanisms leading to cladding failure, including damage accumulation (Pelykh, 2013).

Taking into account the physical mechanism of cladding damage parameter ω(t) accumulation in VVER variable loading modes, let's consider the prediction problems of cladding failure theory, since the present fuel operation practice excluding a statistical service procedure for localization of untight cladding areas, fundamentally contradicts the current normative document demanding the control of cladding failures (SECNRS, 2008).

In order to understand the differences between different strength criteria discussed hereafter, let's look at the group of normative strength criteria for VVER-1000 fuel element сladding (Novikov et al., 2005) including the criteria SC1…SC5, each of them is used with the appointed normative safety coefficient KSC (Table 1).

It can be seen that, omitting the SC3 and SC5 criteria, the strength of cladding under normal operation conditions is described by the SC1, SC2 and SC4 criteria only.

When a fuel element is operated in nonstationary regimes, quasi-static damage and fatigue damage are simultaneously accumulated in the cladding, therefore it is generally accepted, that the quasi-static cladding damage parameter ωq-s originated from long slowly changing stresses and the fatigue cladding damage parameter ωfat originated from cyclic inelastic deformations, are distinguished. Thus, when the damage accumulates, the limiting state is determined by summing up (Popov, 2000):ω=ωq-s+ωfat.

Generally speaking, the cladding material damage parameter can be considered as a structure parameter describing the material state (ω = 0, for an intact material and ω = 1, for a damaged material). The second possible approach is considering ω(τ) as a characteristic of discontinuity flaw. That is when ω = 0, there are no submicrocracks in the cladding material. But if ω = 1, it is supposed that the submicrocracks have integrated into a macrocrack situated in some cross-section of the cladding.

The approach shown by Eq. (1) is used in the normative strength criterion SC4 (OECD, 2012):ω(t)=0tdttlim+ininilim<1KSC4,

where t is time; tlim is the creep-rupture life under steady-state operation conditions; ni is the number and nilim is the limiting number of i-type power-cycles; KSC4 is the normative safety coefficient, KSC4 = 10 (Alexeyev, 2008).

When calculating ω(t) using Eq. (2), after 4 years of VVER-1000 load according to 100–80–100% Nnom and 100–50–100% Nnom daily power-cycles (Novikov et al., 2005):ωq-sωfat5(SC4).

Оn the contrary, according to the experimental data obtained by two independent research groups (Sosnin et al., 1986) and (Kim et al., 2007), when a thin cylinder cladding is loaded at frequencies ν <<1Hz, creep is the main physical process of deformation damage accumulation:ωq-s>>ωfat(Sosnin,1986andKim,2007).

Hence, the SC4 criterion is not adequate. This inadequacy was pre-determined by the common practice of load acceleration used in experiments conducted in 60−70 years of the last century. But this acceleration of cyclic loading changed the main physical mechanism of cladding deformation failure depending on frequency ν (Pelykh and Maksimov, 2011):ifν1Hz,thenfatigueisdominantandcreepisneglected;ifν<<1Hz,thencreepisdominantandfatigueisneglected.

The calculation model of ω(τ) based on SC4 is uncertain due to:

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    model incompleteness caused by eliminating, when determining the limiting components nilim and tlim for each fuel assembly, its real loading history as well as the real sequence of sets of its operating parameters. The following factors influencing the cladding creep strain rate are ignored specifically: fuel assembly rearrangement order, cladding corrosion rate, neutron fluence and spectrum, gas pressure in the inner fuel element volume, varying axial profiles of the coolant temperature and ω(t), disposition and movement of control elements of the reactor control system, parameters of reactor loading cycle, etc.;

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    model inadequacy caused by neglecting the main physical mechanism of ω(τ) accumulation at ν <<1 Hz (creep), in particular, by setting the equal coefficient for ωq-s and ωfat in Eq. (1).

Considering this uncertainty, the SC4 criterion cannot be used for forecasting of cladding failure due to increase of ω(t) under variable loading. So the opinion that the value of ω(t) does not really limit the fuel element durability under maneuvering regimes is widely spread, and cladding depressurization by the mechanism of damage accumulation is considered to be prevented when the following two conditions are satisfied:

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    Circumferential stresses σθ(t) are not exceeding some established limiting value, e.g. according to the normative strength criterion SC1 (see Table 1):σθ(t)<250KSC1P

    where KSC1 is the normative safety coefficient, KSC1 = 1.2.

  • 2.

    Equivalent stresses σe(t) are not exceeding the yield stress σ0, e.g. according to the normative strength criterion SC2 (Table 1):σe(t)<σ0(t)KSC2=σ0(t)P

    where KSC2 is the normative safety coefficient for SC2, KSC2 = 1.

Though using conditions similar to Eq. (5) for cladding durability justification is a common practice (Suzuki, 2010), the calculated value of cladding axial segment volume-averaged σθ(t) does not take into account the mixed (intragranular and intergranular) nature of creep which is described by equivalent stress σe(t) best of all (Popov, 2000).

So, in order to take into account the leading role of creep in the process of cladding damage parameter ω(t) accumulation at loading frequencies ν <<1 Hz, it is reasonable to use the CET-method based on the experimentally proved creep energy theory (Sosnin et al., 1986), where ω(t) is found for the innermost cladding radial element having the maximum temperature as the integral function of σe(t) (Pа) multiplied by the rate of equivalent creep strain p˙e(t) (s-1), and the CET-criterion is written as (Pelykh et al., 2013a, Pelykh et al., 2013b):ω(t)=A(t)A0<1KSC4;A(t)=0tσep˙edt;A(t)[0;A0],

where A0 is specific dispersion energy A(t) at the moment t0 of cladding failure, МJ/m3; the limiting component A0 does not depend on the fuel element loading history, A0 is determined by the cladding material properties only, and, for Zircaloy-4 alloy, the calculated value of A0 is 55 МJ/m3 (Pelykh et al., 2013a, Pelykh et al., 2013b).

Comparing Eqs. (6) and (2), the CET-criterion has such advantages as:

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    in contrast with SС4, the limiting component is constant for all sequences of sets of fuel operating parameters influencing ω(t):A0=const;

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    for any cladding material, having a verified software tool designed for analyzing the dynamic behavior of the corresponding nuclear fuel, the value of A0 is easily found according to the limiting condition (Pelykh et al., 2013a, Pelykh et al., 2013b):lim(dA/dt)10whentt0.

The physical sense of Eq. (8) is that, according to the known experiments (Sosnin et al., 1986), the specific dispersion energy A(t) comes equal to A0 in the end of the rapid creep stage (third characteristic creep stage), at the moment when the A(t) curve becomes vertical (Pelykh, 2013).

Section snippets

The proposed method for forecasting of cladding failure due to damage accumulation

Considering VVER-1000 fuel elements, the method for forecasting of cladding failure due to damage accumulation is described by the following algorithm:

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    Initialization of the calculation model by setting all the parameters describing:

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    fuel element, fuel assembly and reactor core design;

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    core power control algorithm including the layout of control elements used during the power maneuvering and core power control program defining the curves for reactor power, axial position of control elements, core

Results and discussion

Having calculated cladding damage parameter ω(t) in axial segment 6 for all 14 rearrangements, the obtained spread of ω(t) for algorithms A and B was:

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    one-group model, [2.2…4.82%] and [2.25…3,74%], respectively;

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    four-group model, [0.72…10,8%] and [0,75…6,16%], respectively.

Hence, when using the four-group model, the maximum cladding damage parameter ωmax for algorithms A and B, in comparison with the one-group model, has increased 2.2 and 1.6 times, respectively.

For example, the values of ω(1460 

Conclusions

The presented methodology is intended to estimate the failure probability due to cladding deformation damage including the damage originated from pellet to cladding interaction. There are plenty of well-known and widely used methods for elimination of fuel element cladding failures due to grid/rod fretting, debris fretting, manufacturing flaws, etc. in VVERs, and there is still a great uncertainty in knowing the true cause of cladding failure, while the generally accepted goal of achieving a

References (22)

  • S.N. Pelykh

    Grounds of VVER Fuel Element Behavior Control

    (2013)
  • Cited by (0)

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