·Table of Contents ·Nuclear Industry | Determination of Acceptance Criteria for V VER Steam Generator Tubes Based on Application of Advanced Eddy Current TechniquesDamir Stanic, M.Sc.M.E.INETEC - Institute for Nuclear Technology Koturaska 51, Zagreb 10000, CROATIA tel: 385 - 1 - 6171 - 355, 385 - 1 - 6171 - 325 e-mail: damir.stanic@inetec.hr Contact |
Fig 1: Definition of Acceptance Criteria |
Fig 2a: IGA/SCC on VVER SG tube | Fig 2b: Pitting on VVER SG tube |
Depending of nature of degradation mechanisms, different shapes of damages appear on steam generator tubes. Considering morphology, the defect may be classified as: cracks (IGA/SCC), volumetric loss of material (wear, thinning) or hole-like damage (pitting). This classification is important from the analytical point of view, because depending of type of the defect, the most suitable method for evaluation of tube structural integrity have to be used.
Fig 3a: measurement of depth and volume |
Fig 3b: measurement of shape, length and width |
Fig 3: Bobbin probe signal (a) and rotating probe signal (b) |
4.1 Analytical methods
These methods are usually aplicable only for simpler flaw morphology. For some type of flaws, determination of proper analytical expression is very complex and time consuming because of flaw geometry and high material ductility. In accordance with applicable regulative [1] for pipes in VVER type of NPP's the following criteria have to be satisfied:
s _{eq} < [s] , where s _{eq} - _{ }equivalent stress according to maximum shear stress criterion;
Application of safety factors [
1]
(n_{m}=2.6; and n_{0.2}=1.5.) leads to the allowable stress intensities as follows:
4.2 Experimental Methods
The most common experimental method for tube integrity evaluation considers performance of burst pressure test. Beside confirmation of analytical solutions, experimental results may provide definition of empirical formula or determination of some unknown coefficients in formula. Test results give the values of burst pressure for different damage parameters (depth, length, shape or any other). Allowable operating pressure is then obtained by dividing obtained value by safety factors. According to US regulative, safety factors are 3 for operating conditions and Ö2 for accidental conditions.
4.3 Numerical methods
Various flaw types and different operating conditions may be very effectively evaluated by numerical methods, such as finite element method (FEM). It provides relatively simple and fast modeling of real circumstances, as well as good ability of visual presentation of results.
5.1 VVER-440 Steam Generator Data
VVER-440 SG consists of 5536 tubes where outer radius is 8mm and thickness is 1.4mm. Tubes are made of austenitic steel 08X18H10T (GOST standard) which material characteristics [
1]
, are given in Table 5.1 for 50^{o}
C and 300^{o}
C (near operating temperature). It should be noted that specified values are minimal values for this material. Tensile tests performed on real tubes showed much larger values than those given in Table. In spite of greater values obtained by testing, the calculations were made assuming minimal values of material characteristics. Further investigations have to confirm that all tubes in particular SG have characteristics as those which were tested. Since tube material exhibits property of extensive yielding, material behavior in plastic area is presented by bilinear diagram.
Temperature[^{o}C] | E[MPa] | n | R_{p0,2}[MPa] | R_{m}[MPa] |
50 | 202000 | 0.3 | 206 | 471 |
300 | 180000 | 0.3 | 177 | 412 |
Table 5.2: Tube Material Characteristics |
Three types of loading [2] has been taken in consideration: operating conditions (OC), upset conditions (UC) and hydro test (HT). Values of internal and outer pressure for specified conditions are given in Table 5.2. In addition to these pressures, SG tubes are exposed to bending stresses due to flow, vibrations, and influence of residual stresses (on the location of tube bending and expansion). All those influences are neglected in this analysis. Normal operating conditions considers temperature difference between coolant and feedwater temperature which influence on stress level through the tube thickness may be neglected. It may be assumed that tube is exposed to operating temperature of ~ 300^{o}C, so all material characteristics correspond to that value.
p_{i}[MPa] | p_{o}[MPa] | D_{p}[MPa] | |
Operating condition | 12.5 | 4.32 | 8.18 |
Hydro test | 17.2 | 0.0981 | 12.4 |
Upset condition | 14.7 | 4.32 | 10.38 |
Table 5.3 Loadings of VVER-440 steam generator tubes |
5.2 Uniform Thinning
From analytical point of view it is the easiest type of problem for evaluation and it may be evaluated by analytical methods. Calculations are made for all loading combination defined in Table 5.3 and the results are given in Figure 4. Allowable thinning for particular condition is defined by intersection with corresponding value of allowable stress intensity.
Fig 4: Value of s _{eq} for tube wall thinning |
Structural integrity for this damage type may be assessed by the burst pressure tests, also. It has been shown that the most suitable formula for uniform thinning is Svenson formula:
where value of burst pressure is given in relation to flow stress (s
_{f}), tube radius (r) and actual tube thickness (t). Because of lack of appropriate data for VVER tube material, factor k has been assumed as 0.5, although experiments showed that it is usually greater (3). Values obtained by Svenson are the values of critical pressure which cause tube burst, so they should be divided by safety factor in order to get allowable internal pressure (or pressure difference where internal pressure is larger than outer). In order to compare burst pressure value per two different approaches, recalculation has been made for analytical approach where pressure had been expressed as pressure difference acting only on inner tube surface. Comparison of results is presented in Figure 5. As may be seen, for operating conditions results match very well. Critical tube thinning per different criteria is defined by crossing the appropriate curve with the values of pressure difference for corresponding operating conditions (P_{OC} - pressure difference for normal OC, P_{HT} - pressure difference for hydro test, P_{UC} - pressure difference for UC).
Fig 5: Allowable pressures per different approach |
5.3 Pitting
Fig 6: FEM model with hole-like flaw simulating pitting damage |
Fig 7: s _{eq} for tube with hole-like flaw of 60%, tube with thinning of 60% and undefected tube |
Comparison of stress levels for thinning and pitting damages reveals that stresses are greater for pitting damages what lead to more conservative criteria. However, despite of earlier forming of plastic zone in vicinity of flaw, the tube with pitting damage may withstand greater pressure. This is confirmed by testing of different flaw types where burst pressures were greater than those obtained for uniform thinning. It can be concluded that local plastic zone formed around flaw, does not increase the burst pressure. As have been presented, FEM calculations may be used to asses critical pressures for different flaw parameters. Additional confirmation by burst test results would provide determination of appropriate criteria for damages formed because of pitting.
5.4 IGA/SCC
Damages formed due to action of intergranular attack stress/corrosion cracking have a form of a crack. Usual approach for this flaw type is based on pipe theory which assumes that existence of crack on tube will cause local increase of stress level defined by, so-called, "bulging factor". There are several approximations for this factor (Folias, Erdogen, Pruitt, ...), but it may be calculated by finite element method, too. Burst pressure for tube having axial crack is defined by assuming plastic collapse as failure criterion because of high material ductility. For 100% cracks (through-wall cracks), value of critical pressure in relation of flaw length may be derived from the following formula:
where | m = f(c,r,t) - bulging factor | 2c flaw length |
t wall thickness | s_{j} circumferential stress | |
s_{y} yield stress | s_{u} ultimate strength | |
p internal pressure | k material coefficient |
As may be seen in Figure 8, burst pressure values calculated per different approximations match very well.
Fig 8: Comparison of burst pressure values calculated per different approximations |
Beside the length, another interesting parameter of crack is its depth. The influence of crack depth on critical pressure for different flaw lengths is presented in Figure 9. As expected, the longer cracks are more influenced by flaw depth than shorter cracks.
Fig 9: Burst pressure for different crack length |
The formula for structural integrity evaluation of tubes having axial crack which takes in account flaw length and depth is the one proposed by Kurtz:
Comparison of experimental results with the Kurtz formula and FEM based calculation, are given in Figure 10.
Fig 10: Burst pressure for corrosion flaws in comparison with FEM and Kurtz results |
It may be concluded that both evaluations satisfactorily match with experimental data. The importance of this conclusion is that FEM based evaluation may be effectively applied for structural integrity analysis of tubes having cracks. The benefit of using FEM is the possibility of simple modeling and evaluation of various effects such as: influences of tube support, tubesheet, elbows and others.
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