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Pretest fracture assessment of the NESC-1 spinning cylinder under a PTS transient
International Journal of Pressure Vessels and Piping 75 (1998) 203–212
Pretest fracture assessment of the NESC-1 spinning cylinder under a PTS transient Iradj Sattari-Far, Lars Dahlberg SAQ Kontroll Ltd, Box 49306, S-10029 Stockholm, Sweden Received 28 December 1997; accepted 8 January 1998
Abstract This report presents pretest fracture assessments of the NESC-1 spinning cylinder. The clad cylinder has an internal diameter of 1045 mm, a wall thickness of 175 mm and a length of 1296 mm. An internal surface breaking crack with a depth of 73 mm and a length of 205 mm subjected to a thermal shock is studied. Three-dimensional elastic-plastic finite element calculations, considering the crack-tip constraint, are employed in the assessments. Also performed are sensitivity studies to demonstrate how different affecting factors, especially the cladding residual stresses, impact the crack driving force. It is found that the crack front conditions in the cladding and at the deepest point of the crack are far from critical, but cleavage fracture events can be expected in the cladding HAZ. The results show substantial loss of crack-tip constraint in the cladding HAZ compared with the SSY solutions. From the sensitivity studies, it is observed that uncertainties due to different assumptions in the analysis influence the assessment results less than uncertainties in the fracture toughness data of the materials. 䉷 1998 Elsevier Science Ltd. All rights reserved Keywords: pretest fracture assessment; NESC-1 spinning cylinder; PTS
1. Introduction It is recognized that pressurized water reactors can experience a class of incidents termed pressurized thermal shock (PTS), when the reactor is subjected to emergency cooling following a loss of coolant accident. The significance of such transients to the integrity of a embrittled operating reactor vessel is that failure might result if the critical conditions are present at the time of the transient. The combination of; existence of flaws, brittle materials (due to high irradiation) and severe cooling of the vessel may lead to crack propagation. Due to severe cooling on the internal surface of the vessel, high thermal stresses are developed in the wall of the vessel near to the internal surface. The cooling also decreases the fracture toughness of the actual materials which may lead to a critical situation for cleavage fracture. In recent years, several international collaborative projects have been initiated to investigate the capabilities of the specific disciplines which are used in integrity assessments of pressure vessels. The Network for Evaluation of Steel Components (NESC) is set up to arrange collaborative projects in investigating the whole process of structural integrity assessment. The first NESC project, termed as NESC-1 Spinning Cylinder Project, is a major international 0308-0161/98/$19.00 䉷 1998 Elsevier Science Ltd. All rights reserved PII: S0 30 8 -0 1 61 ( 98 ) 00 0 04 - 0
project with participation and contribution from many countries. Participation in the project is arranged by the European Commission’s Joint Research Centre (JRC). The NESC-1 project addresses the integrity issues affecting embrittled reactor pressure vessels (due to irradiation) under PTS conditions. In particular, the project is intended to address the issues of inspection, material characterizations and fracture mechanics in assessment of the behavior of cracks in simulated end of life RPV material, exposed to a PTS transient. The project is based on the testing of a clad cylinder of A508 class 3 forging material containing a range of defects. This report presents defect assessment results from a final pretest analysis of the spinning cylinder based on the NDE defect definitions and the prescribed loading conditions. The results presented here are fracture assessments of a surface breaking crack. Three-dimensional elastic-plastic finite element analyses, considering the crack-tip constraint, are employed in the assessments. Also performed are sensitivity studies to demonstrate how different affecting parameters impact the crack driving force. In the sensitivity studies, a more comprehensive study is performed on effects of the cladding residual stresses on the crack driving force of 2D surface cracks in a PWR pressure vessel under a LOCA transient. Detailed results of this study can be found in a report presented by Sattari-Far [1].
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Table 1 Material properties used in the analysis of the spinning cylinder, T is in ⬚C Material property
Base (A508 forging)
HAZ (under cladding)
Cladding (stainless steel)
Thermal conductivity [W/m⬚C]
40.26 (25⬚C) 40.93 (150⬚C) 39.68 (250⬚C) 37.24 (350⬚C) 4.1·10 ¹4·T þ 0.432 7800 (20⬚C) 7750 (290⬚C) 12.7·10 ¹6 (T ¼ 75⬚C) 14.1·10 ¹6 (T ¼ 115⬚C) 15.6·10 ¹6 (T ¼ 275⬚C) 211.7–0.0682·T 0.28 584.03–0.3716·T 740.76–0.5689·T
40.26 (25⬚C) 40.93 (150⬚C) 39.68 (250⬚C) 37.24 (350⬚C) 4.1·10 ¹4·T þ 0.432 7800 (20⬚C) 7750 (290⬚C) 12.7·10 ¹6 (T ¼ 75⬚C) 14.1·10 ¹6 (T ¼ 115⬚C) 15.6·10 ¹6 (T ¼ 275⬚C) 211.7–0.0682·T 0.28 665.85–0.2616·T 758.72–0.0739·T
13.34 (25⬚C) 15.90 (150⬚C) 18.15 (250⬚C) 20.10 (350⬚C) 4.1·10 ¹4·T þ 0.432 7800 (20⬚C) 7750 (290⬚C) 16.7·10 ¹6 (T ¼ 100⬚C) 17.3·10 ¹6 (T ¼ 200⬚C) 10.5·10 ¹6 (T ¼ 300⬚C) 150.2–0.0682·T 0.32 451.87·T ¹0.1326 813.84·T ¹0.1265 Not available
30. þ 70.e 0.019(T¹68) 35. þ 102.e 0.019(T¹68) J 0.2 ¼ 95. þ 0.24·T J ¼ 207.26 (Da) 0.3357
30. þ 70.e 0.019(T¹16) 35. þ 102.e 0.019(T¹16) J 0.2 ¼ 115.4 þ 0.076·T J ¼ 222.64 (Da) 0.4051
Specific heat, [kJ/kg⬚C] Density, [kg/m 3] Coefficient of thermal expansion, [1/⬚C]
Elastic modulus, [GPa] Poisson ratio Yield strength, [MPa] Tensile strength, [MPa] Cleavage K Jc, MPa冑m 50% probability 95% probability Ductile fracture initiation toughness, kN/m Ductile fracture (for T ¼ 150⬚C)
2. Theoretical aspects The crack tip stress field for a given material in a cylindrical coordinate system (r, v) centred at the crack tip can in general be given by jij r J , v, k, ¼ fij ; geometry (1) j0 (J=j0 ) Lj0 Here, the stress components j ij are normalized with j 0 (usually equal to the yield strength), and the distance from the crack tip is normalized by the value J/j 0. The crack tip constraint is denoted by k which depends on the remote load and crack geometry. L is a characteristic length of the finite geometry and J the applied J-integral, defined by Rice [2]. Asymptotic expansions of eqn (1) denoting the Mode I stress components around a crack tip in a power law hardening material have been developed in the following form, see for instance Sharma and Aravas [3], rj q 0 þ Qj0 jˆ (1) jij ¼ jHRR ij ij (v, n) þ higher order terms J (2) The first term in eqn (2) is the asymptotic HRR solution, after Hutchinson [4] and Rice and Rosengren. [5] If the HRR term in eqn (2) can be considered to dominate over a significant region that encompasses the fracture process zone, J uniquely and autonomously characterizes the local stresses and strains ahead of a stationary crack. However, observations from large-scale yielding experiments indicate that the relationship between the single characterizing parameter J and the near-tip fields loses the one-to-one correspondence when the plastic zone size ahead of the crack tip is significant compared to the characteristic dimensions of the cracked body. This loss of uniqueness, often termed as loss of constraint, results in different fracture toughness
J 0.2 ¼ 679.1T ¹0.2147 J ¼ 364.92 (Da) 0.4585
properties in different types of specimen of a given material. In recent years, a number of researchers have attempted to extend the limit of fracture mechanics by introducing a second parameter to characterize the crack-tip constraint. Accordingly, in such an approach, toughness properties of the structure are described by a J-k locus. In this report, two constraint parameters which have received most attention in the literature are used. O’Dowd and Shih [6,7] have suggested that the crack-tip stress field within the annulus J/j 0 ⱕ r ⱕ 5J/j 0 ahead of the crack tip in a cracked body can be approximated by jij ⬇ jRef ij þ Qj 0 dij
(3)
is a reference field with high stress triaxiality, Here, jRef ij which can be the HRR or the SSY solution assuming plane strain conditions. Q is used as a constraint parameter and can be defined as Q¼
jvv ¹ jSYY r v ¼2 at v ¼ 0 and j0 (J=j0 )
(4)
where, j vv is the opening stress taken from the analysis of the actual geometry and jSYY the opening stress from the vv SSY analysis (with zero T-stress). J-Q theory in combination with a micromechanical model has been successfully applied in description of cleavage fracture in different geometries, Ref. [8–13]. The second constraint parameter is defined as the cracktip stress triaxiality termed by h, which for a three-dimensional crack problem has the form h(r, v, z) ¼
1 jh (r, v, z) 3j kk ¼ q je (r, v, z) 3 2Sij Sij
(5)
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Here, j e is the von Mises effective stress and j h the hydrostatic stress. Several authors have used h or its reciprocal as an appropriate crack-tip constraint measure for ductile crack growth, Ref. [14–19]. Here, to be consistent with the definition of Q in eqn (4), the following definition is used. SSY jh jh r ¼2 ¼ h ¹ hSSY at v ¼ 0 and H¼ ¹ (J=j0 ) je je (6) where h SYY is the ratio of the hydrostatic stress to the effective stress obtained from the SSY analysis (with zero T-stress).
3. Geometry, materials and loads The spinning cylinder for the NESC-1 experiment has an inner diameter of 1045 mm, a wall thickness of 175 mm (including 4 mm cladding and 10 mm cladding HAZ) and a length of 1296 mm. The base material of the cylinder is A508 class 3 forging steel. The cylinder is fabricated by welding together the halves of two cylinders from two previous tested spinning cylinders which were known to have poor toughness properties, suitable for the NESC-1 project. The cladding procedure involved depositing of two layers stainless steel cladding and afterward reducing the cladding thickness to 4 mm. The cladded cylinder experienced two post-weld heat-treatments; six hours at 550⬚C before machining of the cladding and six hours at 550⬚C after machining. The cladding procedure resulted in a cladding HAZ thickness of about 10 mm. The material properties used in the analyses are given in Table 1, Rintamaa [20]. It should be noted that the cladding HAZ material is actually inhomogeneous which causes large scatters in tensile properties obtained from specimens taken from different locations in the HAZ.
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The results presented here are obtained from the analysis of an internal axial surface breaking crack with depth of 73 mm and length of 205 mm in the spinning cylinder. The corresponding results obtained from the analysis of a subclad crack with depth of 78 mm and length of 264 mm are presented in Ref. [1]. The loading conditions for the cylinder consisted of: uniformly heating up to 290⬚C, spinning, quenching and accelerating. The main features of the thermal transient scenario applied to the FE model are as follows: Initial temperature:
290⬚C
Quenching temperature:
5⬚C
Initial spinning speed:
2100 rpm
Final spinning speed:
2280 rpm
Acceleration time:
5 minutes
Total test time:
12 minutes
Heat transfer coefficient:
10 000 W/m 2⬚C
Stress free temperature:
290⬚C
4. Finite element modeling The general purpose FEM program ABAQUS [21] was used for the computations reported in this study. ABAQUS uses the domain integral method to evaluate the J-integral around a crack tip. The pre-processor of the FEM program ANSYS [22] was used for development of the three-dimensional FE models. The materials (base, HAZ and cladding) were assumed to be elastic-plastic with a piece-wise linear approximation of the hardening behavior taken from the uniaxial test results. It was assumed that the materials
Fig. 1. The finite element model used in the analysis of the spinning cylinder.
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Fig. 2. Distribution of temperature and the corresponding elastic-plastic hoop stress in the wall of the spinning cylinder under the thermal transient.
obeyed the von Mises flow criterion with its associated flow rule and isotropic hardening behavior. Typical FE model used for the 3D analyses is shown in Fig. 1. Due to symmetry in geometry and load, only one fourth of the cylinder needed to be modeled. The cladding thickness of 4 mm and the cladding HAZ of 10 mm were specifically modeled. The mesh consisted of 2317 twentynoded solid elements. The mesh around the crack tip was
Fig. 3. Variation of the crack driving forces J at three different positions along the surface crack front during the transient.
Fig. 4. Comparison of the crack driving force J and the material toughness at three different positions along the surface crack front during the transient.
fine enough to resolve the crack-tip fields at the load level of interest. The SSY solution is chosen in this study as a reference field representing a high level of stress triaxiality. The solution is obtained by imposing a K-field on the remote boundary of a standard boundary-layer model (a semicracked annulus). The FE model used for evaluation of the SSY solution consisted of 640 eight-noded elements comprised in 40 rings focused toward the crack tip. A comparison of some results obtained from small respectively large strain formulation showed that the most effects of large strain formulation were within the zone r ⱕ J/j 0 ahead of the crack tip, Sattari-Far. [19] Thus, the actual crack-tip constraint parameters can be evaluated at the distance r ¼ 2J/j 0, where the differences between the two theories are small. The results presented in this report are
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Fig. 5. Comparison of the crack driving force K J and the material toughness during the transient at the crack front in the middle of the cladding HAZ.
based on small strain formulation. In converting the crack driving forces J and K, the following plane-strain equation has been employed 0·5 (7) KI ¼ JE=(1 ¹ n2 )
5. Numerical results The distributions of temperature and stress in the wall of the cylinder were obtained by performing uncoupled heat transfer analyses of the 3D FE model. The transient scenario, described in Section 3, was applied to the model. The crack surfaces were assumed to be insulated in the thermal analysis. The temperature profiles and stress distribution in the wall of the cylinder at different times into the transient are shown in Fig. 2. Here, the stresses are hoop stresses, which are obtained from elastic-plastic analysis of the uncracked cylinder. It is observed that the transient results in yielding in the cladding material. The results
Fig. 6. Variation of the constraint parameters Q and H along the crack front, evaluated at the distance r/(J/s Y) ¼ 2 ahead of the crack tip.
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presented in Fig. 2 indicate that the peak stresses in the studied crack geometry due to the transient would be at a time of about four minutes into the transient. Variation of the crack driving forces J during the transient at three different positions along the crack front are shown in Fig. 3. These positions are at the middle of clad layer (2 mm from the internal surface), at the middle of the cladding HAZ (9 mm from the internal surface) and at the deepest point of the crack (73 mm from the internal surface). It is observed that the peak of the crack driving forces occurs in the cladding HAZ. Comparisons of the crack driving force J and the cleavage and ductile toughness of the materials as a function of the temperature during the transient are shown in Fig. 4 for these three positions. Note that for the cladding material, due to the lack of cleavage toughness data, only ductile fracture initiation data are used. It is observed that the situations in the cladding and at the deepest point of the crack front are far from critical, but ductile and cleavage fracture events can be expected in the cladding HAZ. By using the peak J-value in the cladding HAZ and the ductile fracture resistance data of the material, one obtains about 2·5 mm ductile crack growth in the cladding HAZ. However, due to loss of crack-tip constraint in the cladding HAZ, which will be discussed later, the amount of the actual ductile crack growth is expected to be less than 2·5 mm. Fig. 5 shows the crack driving force K J compared with the material fracture toughness in the middle of the cladding HAZ for the studied crack geometry during the transient. The estimated cleavage fracture toughness of the cladding HAZ are based on 50% probability respectively 95% probability of cleavage fracture. It is observed that for an evaluation based on 95% fracture probability, no cleavage fracture event can be expected for the studied crack geometry. However, considering 50% fracture probability, one can expect that a cleavage fracture event can be achieved. Providing that constraint effects do not influence the time of the cleavages events, Fig. 5 indicates that a cleavage event in the surface crack can occur at a time around 200 s into the transient. Variation of the constraint parameters Q and H, evaluated according to eqns (4) and (6), along the crack front at the time of 240 s into the transient are shown in Fig. 6. As can be observed, the parameters Q and H give different constraint values along the crack front, but both of them indicate substantially loss of constraint in the cladding and the cladding HAZ. It is also observed that the constraint variation are very large in the cladding HAZ. In practice, it is very difficult to correctly consider the constraint effects for this relative small zone with such a high constraint variation. It should be mentioned that thermal transients cause multiaxial stress states in the wall of pressure vessels. Thus, cracks in such a vessel are subjected to far-field stresses both in the direction normal to the crack surface (in-plane) and in the direction parallel with it (out-of-plane) under a PTS transient. The out-of-plane
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study the influence of the cladding residual stresses on the crack driving force.
Fig. 7. Comparison of the crack driving force K J at the middle of the cladding HAZ obtained from different analyses. Case 0 is the reference case.
A comparison of the results obtained from all analyzed cases in the sensitivity study is shown in Fig. 7. As the potential point for a cleavage fracture event can be expected to be in the cladding HAZ, only the crack driving forces at the middle point of that are presented here. Also shown in Fig. 7 are fracture toughness data of the cladding HAZ corresponding to 50% and 95% fracture probability. The K J-values are obtained by converting the elastic-plastic Jvalues according to eqn (7). In the following, the variations of the crack driving force and the crack tip temperature at the middle position of the cladding HAZ and at the deepest point during the imposed thermal transient are compared with those of the reference case (Case 0).
components of these stresses have no equivalence in the laboratory experiments used in the evaluation of fracture toughness properties. A comparison of uniaxial and biaxial loading effects in a pressure vessel containing a surface crack has shown that, for a similar J-value in the two cases of loading, the biaxial loading substantially increases the level of the stresses ahead of the crack tip, Sattari-Far [23].
6.1. Influence of specific modeling of the cladding HAZ
6. Sensitivity studies
6.2. Influence of pure elastic analysis
To demonstrate how different factors influence the crack driving force and the time of eventual cleavage event, the following cases are studied.
It is observed that the elastic analysis leads to slight underestimation of the crack driving force at the deepest point. In the cladding HAZ, the elastic J is somewhat higher than the elastic-plastic one during the first four minutes of the transient. Thus, because the differences in the J-values obtained from the elastic and the elastic-plastic analyses are relatively small for the studied case, one can use elastic analysis for engineering fracture assessment of similar cases, providing that J alone characterize the crack-tip field.
Case 0: This is used as the reference case in the sensitivity analysis. The input data for this case are as those presented in Section 3. Case 1: Input data as in Case 0 except that no specific modeling of the cladding HAZ is used in the analysis, i.e. the HAZ is assumed to have the same properties as the base material. Case 2: Input data as in Case 0 except that the analysis is elastic. Case 3: Input data as in Case 0 except that the heat transfer coeff. is 5 kW/m 2⬚C. Case 4: Input data as in Case 0 except that the stress free temperature is 20⬚C. Case 5: Input data as in Case 0 except the crack depth is 80 mm. Case 6: Input data as in Case 0 except that the spinning acceleration rate is twice as high as in Case 0, i.e. from 2100 rpm to 2280 rpm within 2·5 minutes. Case 7: Input data as in Case 0 except that T 0 is 20⬚C and a prescribed cladding residual stress distribution is imposed in the model. Case 8: Analysis of some 2D shallow and deep crack geometries in a reactor pressure vessel geometry to
It is observed that specific modeling of the cladding HAZ can significantly influence the resulting crack driving force in the cladding HAZ, but has little effect at the deepest point. During the transient, the J-values in the cladding HAZ of Case 1 are lower than those in Case 0, mainly due to the fact that the yield strength of the cladding HAZ material is higher than that of the base material.
6.3. Influence of the heat transfer coefficient It is observed that using a lower value of heat transfer coefficient leads to slightly lower J-values along the crack front. These results indicate that the variation of the heat transfer coefficient within the used values cannot significantly influence the crack driving force and the crack tip temperature during the transient. 6.4. Influence of the stress free temperature In Case 4, it is assumed that the cylinder is stress free at 20⬚C. The cylinder is uniformly heated up to 290⬚C, before the thermal transient is imposed. It is observed that the Jvalues are lower for Case 4 than for Case 0 during the first four minutes of the transient. This is due to the fact that, in
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The crack depth in Case 5 is 10% bigger than that in Case 0, having the same crack length. It is observed that the deeper crack causes higher J in the cladding HAZ but lower J at the deepest point of the crack front. The fact that a larger part of the crack front in Case 5 is under compressive thermal stresses than that in Case 0 during the transient, see Fig. 2, can explain the differences between these two cases. According to this analysis, a 10% increase in the crack depth results in about 5% increase in the J-value in the cladding HAZ. This implies that, for the actual case, the crack driving forces are not very sensitive to the crack depth size.
and the base material, new stresses are induced in the cladding and adjacent base material during cooling down to the ambient temperature. A large scatter can be observed in measured cladding induced stresses reported in the literature, Sattari-Far [24]. In general, it can be stated that the cladding residual stresses are tensile in the cladding and compressive in the base metal. The magnitude of the tensile stresses in the cladding depends on temperature, and at the ambient temperature it is about the yield strength of the cladding material. The measurement of the cladding residual stresses in the NESC-1 spinning cylinder is performed by Kockelman using the ring-core technique and the results are reported by the NESC TG4 [25]. The measured results are presented in Fig. 8. In Case 7, it is assumed that the vessel is stress free at 20⬚C and a cladding residual stress profile similar to the TG4 results is prescribed as initial stresses to the FEM model. It should be noted that the cladding mechanical properties used in the FE analyses cannot lead to an initial stress profile which has a peak as high as in the TG4 results. This explains deviations between the TG4 results and prescribed FEM stresses in Fig. 8. The cylinder is then uniformly heated up to 290⬚C before the thermal transient is imposed. Comparison of the crack driving forces during the transient for Case 0 and Case 7 are shown in Fig. 7. It is observed that, during the first minutes of the transient, the Jvalues are somewhat lower in Case 7 than those in Case 0. This is due to the fact that, in Case 7, heating up of the cylinder to 290⬚C has not only completely released the tensile initial stresses but also caused some compressive stresses in the cladding. Since the prescribed residual stresses act as primary stresses, J increases during the whole time interval in Case 7. Thus, the peaks of J for the two cases occur at different times. However, considering the time interval with maximum J in Case 0, one can conclude that, for the actual case, modeling of the cladding residual stresses has small effect on J in the cladding HAZ.
6.6. Influence of the spinning acceleration rate
6.8. Study of some 2D crack geometries
The acceleration rate in Case 6 is assumed to be twice as high as in Case 0, i.e. the initial spinning speed before imposing the quenching is 1920 rpm which reaches 2280 rpm within 5 minutes. It is observed that the variation of the acceleration rate has negligible effects and both cases show similar maximum J-values at the time of interest into the transient.
To better understand the effects of uncertainties in the cladding residual stresses, some 2D surface crack geometries are studied in a real PWR pressure vessel geometry. The vessel has an inner radius of 2000 mm and a wall thickness of 174 mm (including 4 mm cladding). The material properties presented in Table 1 are used in this analysis. Both axial and circumferential surface cracks are studied. Two different crack depths; a 10 mm shallow one and a 50 mm deep one, are studied. The cladding HAZ is not specifically modeled in the analysis. The FE models used for the analysis have 870 eight-noded elements. The operation pressure and temperature of the vessel are 320⬚C respectively 16 MPa. The vessel is subjected to a LOCA transient, in which the pressure falls to 8 MPa within 5 s and then to 4 MPa within 60 s. The coolant temperature falls from 320⬚C to 50⬚C within 5 s into the transient. The
Fig. 8. Results of the measurements and calculations of the cladding residual stresses at T ¼ 20⬚C. The FEM results are obtained from analysis of an axisymmetric model.
Case 4, heating up of the cylinder causes compressive stresses in cladding. During the transient, some part of the thermal stresses is used to overcome these compressive stresses, and consequently resulting in a lower crack driving force compared to Case 0. 6.5. Influence of the crack depth
6.7. Influence of the cladding residual stresses In a common practice of reactor pressure vessel manufacturing, a clad vessel experiences a final PWHT above 600⬚C for about 20 h. This can effectively release the cladding welding residual stresses at the PWHT temperature. However, due to significant differences in thermal expansion coefficient and mechanical properties of the cladding
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Table 2 Elastic-plastic K J-values [MPa冑m] of 2D cracks in a PWR pressure vessel under different loading scenarios. (t ¼ 174 mm, including 4 mm cladding, R i ¼ 2000 mm)
Axial cracks Case A11 Case A12 Case A13 Case A21 Case A22 Case A23 Circum. cracks Case C11 Case C12 Case C13 Case C21 Case C22 Case C23 *
Crack depth [mm]
Only CRS at T ¼ 20⬚C
CRS þ P 0* at T ¼ 50⬚C
LOCA (time into LOCA, s)
Remarks
10 10 10 50 50 50
12.231 9.381 26.657 6.957 5.348 13.015
48.02 43.62 57.83 121.14 119.86 126.47
145.02 (126) 140.16 (126) 145.33 (126) 274.18 (242) 273.09 (242) 284.65 (242)
T0 T0 T0 T0 T0 T0
¼ ¼ ¼ ¼ ¼ ¼
620⬚C 320⬚C 20⬚C and CRS 620⬚C 320⬚C 20⬚C and CRS
10 10 10 50 50 50
20.765 14.304 26.616 8.775 6.797 10.488
31.01 28.53 41.85 55.14 54.70 59.07
124.98 (136) 124.10 (130) 132.42 (136) 222.58 (276) 222.24 (276) 224.41 (276)
T0 T0 T0 T0 T0 T0
¼ ¼ ¼ ¼ ¼ ¼
620⬚C 320⬚C 20⬚C and CRS 620⬚C 320⬚C 20⬚C and CRS
CRS stands for cladding residual stresses and P 0 for the internal pressure MPa.
heat transfer coefficient is assumed to be 10 kW/m 2⬚C during the transient. The cladding residual stresses are introduced to the FE model in three different ways. First, it is assumed that the vessel is stress free at 620⬚C (the PWHT temperature), following a cooling to the ambient temperature. Second, it is assumed that the vessel is stress free at its operation temperature (320⬚C). Finally, it is assumed that the vessel is stress free at the ambient temperature, and a cladding residual stress profile similar to TG4 results are introduced to the model as initial prescribed stresses. Fig. 8 shows the cladding residual stresses at the ambient temperature obtained through these three ways compared with two reported measured data, TG4 and Rybicki [26]. The crack driving force K J, at the deepest point of the crack obtained from the analysis of the different cases are presented in Table 2. For each combination of crack geometry and cladding residual stresses, three different load cases are analyzed. In the third column of Table 2, only contribution of the cladding residual stresses (CRS) at the ambient temperature is given. The contribution of the cladding residual stresses and the internal pressure at 50⬚C (for instance during a cold pressurizing scenario) is presented in column four. The maximum crack driving force and its time of occurrence during the studied LOCA transient are given in column five for different cases.
7. Discussions The evaluated results presented in the previous sections indicate that, for the studied crack geometry, local cleavage fracture events can be expected in the cladding HAZ. The crack driving force K J compared with the material fracture toughness in the middle of the cladding HAZ during the transient are presented in Fig. 5. Providing that crack-tip constraint effects are small, a cleavage event can be
expected for the studied case at a time around 200 s into the transient. However, the results of the evaluation of the crack-tip constraint presented in Fig. 6 indicate substantial loss of constraint in the cladding HAZ compared with the SSY solutions. To make a more exact evaluation on the possibility and the occurrence time of a cleavage fracture event one needs to have access to cleavage fracture toughness data of the cladding HAZ material corresponding to the actual constraint conditions. One can expect that the loss of crack-tip constraint in the cladding HAZ may decrease the probability of any cleavage event or delay its occurrence time for the studied crack geometry. There are some sources of uncertainty which potentially can influence eventual cleavage fracture events in the studied case. These sources are the following. 1. Presented material data of the cladding HAZ show large scatter. The cladding HAZ is actually an inhomogeneous zone with varying material properties. This affects the crack driving forces and toughness properties estimated for the cladding HAZ. 2. The FE results indicate substantial loss of crack-tip constraint in the cladding HAZ compared with the SSY solutions. The constraint variations are very large in the cladding HAZ. This together with (1) cause practical difficulties to provide relevant fracture material data for the cladding HAZ. 3. The eventual intervention of warm prestressing may also make a cleavage fracture initiation difficult to achieve in the experiment. While the consideration of crack-tip constraint conditions and warm prestressing phenomena indicate difficulties in occurrence of a cleavage fracture event, there is a potential to promote the initiation of a cleavage fracture event. Investigation by Sattari-Far [19] shows that a thin hard layer (of about 100 mm) is formed at the cladding/base interface due
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to cladding. This relatively small hard zone has very low toughness properties and, therefore, can be a potential site for initiation of a brittle fracture event. Considering the effects of the cladding residual stresses presented in Table 2 and Fig. 7, it is observed that the cladding residual stresses have negligible contributions to critical situations of the studied crack geometries under a LOCA type transient. The critical crack driving forces are practically insensitive to the way the cladding residual stresses are introduced in the model, especially for deep cracks. However, the contribution of the cladding residual stresses can be considerable under other conditions, like hydro testing and cold pressurizing. For shallow cracks, the results are dependent on the way the cladding residual stresses are modeled. This is of importance when acceptance assessments are performed. For such cases, it is reasonable to assume that tensile residual stresses of the magnitude of the yield strength of the cladding material prevail in the cladding at ambient temperature. It is observed that, for the studied crack geometry, the critical situation occurs in a location (the cladding HAZ) where interactions of the material properties and the constraint effects are very complex. The performed sensitivity studies of influencing parameters indicate that the fracture toughness properties of the cladding HAZ are the strongest sources of uncertainty. Therefore, to perform a more accurate evaluation, relevant cleavage fracture toughness data of the cladding HAZ material are needed. These data should to some extent cover the constraint conditions prevailing in the cladding HAZ of the actual crack cases. It is worthy to note that the different constraint parameters used in this study give different degrees of loss of constraint in the studied cases. More studies are, therefore, needed to find the best measure to quantify the constraint effects. A post-test analysis on the spinning cylinder experiment will hopefully give more information to verify the utility of the J-integral concept for crack cases of this kind.
8. Conclusions Based on pretest fracture assessments of a surface breaking crack in the NESC-1 spinning cylinder, the following conclusions can be made. 1. For deep cracks under thermal transient of this kind, the critical situation does not occur at the deepest point of the crack front, but in or near the cladding HAZ, where the crack driving force can exceed the actual fracture toughness properties of the material. 2. Some limited ductile crack growth is expected to occur along the crack front in the cladding HAZ and adjacent base material in the studied crack geometry. 3. Consideration of the crack tip triaxiality indicates substantial loss of the crack-tip constraint in the cladding HAZ compared with the SSY solutions. In addition, the
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constraint variations in this zone are very large in the studied cases. 4. Providing that the constraint and warm prestressing effects do not substantially affect the situations in the studied cases, one can expect cleavage fracture to occur in the cladding HAZ at time around 200 s into the transient, using cleavage fracture data with 50% fracture probability. 5. Specific modelling of the cladding HAZ can significantly influence the calculated crack driving force in the cladding HAZ, but not at the deepest point of the crack. 6. The cladding residual stresses give negligible contribution in critical situations of the studied crack geometries under a LOCA type transient, but their contributions can be considerable under other conditions such as; fatigue, IGSCC and cold pressurizing. It is reasonable to assume that tensile residual stresses of the magnitude of the yield strength of the cladding material prevail in the cladding at the ambient temperature.
Acknowledgements Funding of this study was provided by the Swedish Nuclear Power Inspection (SKI). This support is greatly appreciated. The authors are also grateful to valuable discussions with Dr. Bjo¨rn Brickstad (SAQ).
References [1] Sattari-Far I. Pretest analysis of the NESC-1 spinning cylinder experiment. SAQ/FoU-Report 97/03, Stockholm: SAQ Kontroll AB, 1997. [2] Rice JR A path independent integral and the approximate analysis of strain concentration by notches and cracks. J. App. Mech., 1968;35:379–386. [3] Sharma SM, Aravas N Determination of higher-order terms in asymptotic elastoplastic crack tip solutions. J. Mech. Phys. Solids, 1991;39:1043–1072. [4] Hutchinson JW Singular behavior at the end of a tensile crack in a hardening material. J. Mech. Phys. Solids, 1968;16:13–31. [5] Rice JR, Rosengren GF Plane strain deformation near a crack tip in a power law hardening material. J. Mech. Phys. Solids, 1968;16:1–12. [6] O’Dowd NP, Shih CF Family of crack-tip fields characterized by a triaxiality parameter-I. Structure of fields. J. Mech. Phys. Solids, 1991;39:989–1015. [7] O’Dowd NP, Shih CF Family of crack-tip fields characterized by a triaxiality parameter-II. Fracture applications. J. Mech. Phys. Solids, 1992;40:939–963. [8] Sumpter JDG, Forbes AT. Constraint based analysis of shallow cracks in mild steels. In Proc. Int. Con. Shallow Crack Fracture Mechanics Tests and Applications. Cambridge, UK: TWI, 1992. [9] Dodds RH, Shih CF, Anderson TL Continuum and micromechanics treatment of constraint in fracture. Int. J. Fract., 1993;64:101–133. [10] Dodds RH, Tang M, Anderson TL. Effects of prior ductile tearing on cleavage fracture toughness in the transition region. Structural Research, Series No. 583, University of Illinois at Urbana-Champaign, IL, 1993. [11] Shih CF, O’Dowd NP, Kirk MT. A framework for quantifying crack tip constraint. In Constraint effects in fracture, ASTM STP 1171.
212
[12]
[13]
[14] [15]
[16] [17]
[18]
I. Sattari-Far, L. Dahlberg/International Journal of Pressure Vessels and Piping 75 (1998) 203–212 Philadelphia, PA: American Society for Testing and Materials, 1993:2–20. Kirk MT, Koppenhoefer KC, Shih CF. Effect of Constraint on specimen dimensions needed to obtain structurally relevant toughness measures. In Constraint effects in fracture, ASTM STP 1171. Philadelphia,PA: American Society for Testing and Materials, 1993:79–103. Faleskog J. Effects of local constraints along three dimensional crack fronts-A numerical and experimental investigation. J. Mech. Phys. Solids, 1996. Aurich D, Sommer E The effect of constraint on elastic-plastic fracture. Steel Research, 1988;59:358–367. Brocks W, Knecke G, Noak HD, Veith H On the transferability of fracture mechanics parameters to structures using FEM. Nucl. Eng. Design., 1989;112:1–14. Kordisch H, Sommer E, Schmitt W The influence of triaxiality on stable crack growth. Nucl. Eng. Des., 1989;112:27–35. Brocks W, Knecke G. On the influence of triaxiality of the stress state on ductile tearing resistance. In Elements of defect assessment. ESIS/ EGF Publication 9. London: Mechanical Engineering Publishers, 1991:189–201. Brocks W, Schmitt W. Quantitative assessment of the role of crack tip constraint on ductile tearing. In Constraint effects in fracture, ASTM
[19]
[20] [21] [22] [23]
[24]
[25]
[26]
STP 1171. Philadelphia, PA: American Society for Testing and Materials, 1993:64–78. Sattari-Far I Constraint effects on ductile crack growth in cladded components subjected to unaxial loading. Int. J. Fatigue Fract., 1995;18:1051–1069. Rintamaa R. NESC1 Spinning Cylinder Project: summary of material property data. Material Task Group, 1996. ABAQUS, User’s manual. Version 5.3. Hibbit, Karlsson and Sorenson, 1995. ANSYS, Users manual. Version 5.0. Swanson Analysis System, 1993. Sattari-Far I Constraint effects on behavior of surface cracks in cladded reactor pressure vessels subjected to PTS transients. Int. J. Pres. Ves. and Piping, 1996;67:185–197. Sattari-Far I, The significant of cladding material on the integrity of nuclear pressure vessels with cracks. SA/FoU-Report 89/03. Stockholm: SAQ Kontroll AB, 1989. Kockelman H. Residual stress measurement on cladding and adjacent base metal on NESC-1 spinning cylinder. Report No. NESCDOCTG3(97)03 TG4 Residual Stress Report, NESC TG4. Rybicki EF, Shadley JR, Sandhu AS. Experimental evaluation residual stresses in a weld clad plate and clad test specimens. US Nuclear Regulatory Commission Report NUREG/CR-4646, 1986.
Pretest fracture assessment of the NESC-1 spinning cylinder under a PTS transient Iradj Sattari-Far, Lars Dahlberg SAQ Kontroll Ltd, Box 49306, S-10029 Stockholm, Sweden Received 28 December 1997; accepted 8 January 1998
Abstract This report presents pretest fracture assessments of the NESC-1 spinning cylinder. The clad cylinder has an internal diameter of 1045 mm, a wall thickness of 175 mm and a length of 1296 mm. An internal surface breaking crack with a depth of 73 mm and a length of 205 mm subjected to a thermal shock is studied. Three-dimensional elastic-plastic finite element calculations, considering the crack-tip constraint, are employed in the assessments. Also performed are sensitivity studies to demonstrate how different affecting factors, especially the cladding residual stresses, impact the crack driving force. It is found that the crack front conditions in the cladding and at the deepest point of the crack are far from critical, but cleavage fracture events can be expected in the cladding HAZ. The results show substantial loss of crack-tip constraint in the cladding HAZ compared with the SSY solutions. From the sensitivity studies, it is observed that uncertainties due to different assumptions in the analysis influence the assessment results less than uncertainties in the fracture toughness data of the materials. 䉷 1998 Elsevier Science Ltd. All rights reserved Keywords: pretest fracture assessment; NESC-1 spinning cylinder; PTS
1. Introduction It is recognized that pressurized water reactors can experience a class of incidents termed pressurized thermal shock (PTS), when the reactor is subjected to emergency cooling following a loss of coolant accident. The significance of such transients to the integrity of a embrittled operating reactor vessel is that failure might result if the critical conditions are present at the time of the transient. The combination of; existence of flaws, brittle materials (due to high irradiation) and severe cooling of the vessel may lead to crack propagation. Due to severe cooling on the internal surface of the vessel, high thermal stresses are developed in the wall of the vessel near to the internal surface. The cooling also decreases the fracture toughness of the actual materials which may lead to a critical situation for cleavage fracture. In recent years, several international collaborative projects have been initiated to investigate the capabilities of the specific disciplines which are used in integrity assessments of pressure vessels. The Network for Evaluation of Steel Components (NESC) is set up to arrange collaborative projects in investigating the whole process of structural integrity assessment. The first NESC project, termed as NESC-1 Spinning Cylinder Project, is a major international 0308-0161/98/$19.00 䉷 1998 Elsevier Science Ltd. All rights reserved PII: S0 30 8 -0 1 61 ( 98 ) 00 0 04 - 0
project with participation and contribution from many countries. Participation in the project is arranged by the European Commission’s Joint Research Centre (JRC). The NESC-1 project addresses the integrity issues affecting embrittled reactor pressure vessels (due to irradiation) under PTS conditions. In particular, the project is intended to address the issues of inspection, material characterizations and fracture mechanics in assessment of the behavior of cracks in simulated end of life RPV material, exposed to a PTS transient. The project is based on the testing of a clad cylinder of A508 class 3 forging material containing a range of defects. This report presents defect assessment results from a final pretest analysis of the spinning cylinder based on the NDE defect definitions and the prescribed loading conditions. The results presented here are fracture assessments of a surface breaking crack. Three-dimensional elastic-plastic finite element analyses, considering the crack-tip constraint, are employed in the assessments. Also performed are sensitivity studies to demonstrate how different affecting parameters impact the crack driving force. In the sensitivity studies, a more comprehensive study is performed on effects of the cladding residual stresses on the crack driving force of 2D surface cracks in a PWR pressure vessel under a LOCA transient. Detailed results of this study can be found in a report presented by Sattari-Far [1].
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Table 1 Material properties used in the analysis of the spinning cylinder, T is in ⬚C Material property
Base (A508 forging)
HAZ (under cladding)
Cladding (stainless steel)
Thermal conductivity [W/m⬚C]
40.26 (25⬚C) 40.93 (150⬚C) 39.68 (250⬚C) 37.24 (350⬚C) 4.1·10 ¹4·T þ 0.432 7800 (20⬚C) 7750 (290⬚C) 12.7·10 ¹6 (T ¼ 75⬚C) 14.1·10 ¹6 (T ¼ 115⬚C) 15.6·10 ¹6 (T ¼ 275⬚C) 211.7–0.0682·T 0.28 584.03–0.3716·T 740.76–0.5689·T
40.26 (25⬚C) 40.93 (150⬚C) 39.68 (250⬚C) 37.24 (350⬚C) 4.1·10 ¹4·T þ 0.432 7800 (20⬚C) 7750 (290⬚C) 12.7·10 ¹6 (T ¼ 75⬚C) 14.1·10 ¹6 (T ¼ 115⬚C) 15.6·10 ¹6 (T ¼ 275⬚C) 211.7–0.0682·T 0.28 665.85–0.2616·T 758.72–0.0739·T
13.34 (25⬚C) 15.90 (150⬚C) 18.15 (250⬚C) 20.10 (350⬚C) 4.1·10 ¹4·T þ 0.432 7800 (20⬚C) 7750 (290⬚C) 16.7·10 ¹6 (T ¼ 100⬚C) 17.3·10 ¹6 (T ¼ 200⬚C) 10.5·10 ¹6 (T ¼ 300⬚C) 150.2–0.0682·T 0.32 451.87·T ¹0.1326 813.84·T ¹0.1265 Not available
30. þ 70.e 0.019(T¹68) 35. þ 102.e 0.019(T¹68) J 0.2 ¼ 95. þ 0.24·T J ¼ 207.26 (Da) 0.3357
30. þ 70.e 0.019(T¹16) 35. þ 102.e 0.019(T¹16) J 0.2 ¼ 115.4 þ 0.076·T J ¼ 222.64 (Da) 0.4051
Specific heat, [kJ/kg⬚C] Density, [kg/m 3] Coefficient of thermal expansion, [1/⬚C]
Elastic modulus, [GPa] Poisson ratio Yield strength, [MPa] Tensile strength, [MPa] Cleavage K Jc, MPa冑m 50% probability 95% probability Ductile fracture initiation toughness, kN/m Ductile fracture (for T ¼ 150⬚C)
2. Theoretical aspects The crack tip stress field for a given material in a cylindrical coordinate system (r, v) centred at the crack tip can in general be given by jij r J , v, k, ¼ fij ; geometry (1) j0 (J=j0 ) Lj0 Here, the stress components j ij are normalized with j 0 (usually equal to the yield strength), and the distance from the crack tip is normalized by the value J/j 0. The crack tip constraint is denoted by k which depends on the remote load and crack geometry. L is a characteristic length of the finite geometry and J the applied J-integral, defined by Rice [2]. Asymptotic expansions of eqn (1) denoting the Mode I stress components around a crack tip in a power law hardening material have been developed in the following form, see for instance Sharma and Aravas [3], rj q 0 þ Qj0 jˆ (1) jij ¼ jHRR ij ij (v, n) þ higher order terms J (2) The first term in eqn (2) is the asymptotic HRR solution, after Hutchinson [4] and Rice and Rosengren. [5] If the HRR term in eqn (2) can be considered to dominate over a significant region that encompasses the fracture process zone, J uniquely and autonomously characterizes the local stresses and strains ahead of a stationary crack. However, observations from large-scale yielding experiments indicate that the relationship between the single characterizing parameter J and the near-tip fields loses the one-to-one correspondence when the plastic zone size ahead of the crack tip is significant compared to the characteristic dimensions of the cracked body. This loss of uniqueness, often termed as loss of constraint, results in different fracture toughness
J 0.2 ¼ 679.1T ¹0.2147 J ¼ 364.92 (Da) 0.4585
properties in different types of specimen of a given material. In recent years, a number of researchers have attempted to extend the limit of fracture mechanics by introducing a second parameter to characterize the crack-tip constraint. Accordingly, in such an approach, toughness properties of the structure are described by a J-k locus. In this report, two constraint parameters which have received most attention in the literature are used. O’Dowd and Shih [6,7] have suggested that the crack-tip stress field within the annulus J/j 0 ⱕ r ⱕ 5J/j 0 ahead of the crack tip in a cracked body can be approximated by jij ⬇ jRef ij þ Qj 0 dij
(3)
is a reference field with high stress triaxiality, Here, jRef ij which can be the HRR or the SSY solution assuming plane strain conditions. Q is used as a constraint parameter and can be defined as Q¼
jvv ¹ jSYY r v ¼2 at v ¼ 0 and j0 (J=j0 )
(4)
where, j vv is the opening stress taken from the analysis of the actual geometry and jSYY the opening stress from the vv SSY analysis (with zero T-stress). J-Q theory in combination with a micromechanical model has been successfully applied in description of cleavage fracture in different geometries, Ref. [8–13]. The second constraint parameter is defined as the cracktip stress triaxiality termed by h, which for a three-dimensional crack problem has the form h(r, v, z) ¼
1 jh (r, v, z) 3j kk ¼ q je (r, v, z) 3 2Sij Sij
(5)
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Here, j e is the von Mises effective stress and j h the hydrostatic stress. Several authors have used h or its reciprocal as an appropriate crack-tip constraint measure for ductile crack growth, Ref. [14–19]. Here, to be consistent with the definition of Q in eqn (4), the following definition is used. SSY jh jh r ¼2 ¼ h ¹ hSSY at v ¼ 0 and H¼ ¹ (J=j0 ) je je (6) where h SYY is the ratio of the hydrostatic stress to the effective stress obtained from the SSY analysis (with zero T-stress).
3. Geometry, materials and loads The spinning cylinder for the NESC-1 experiment has an inner diameter of 1045 mm, a wall thickness of 175 mm (including 4 mm cladding and 10 mm cladding HAZ) and a length of 1296 mm. The base material of the cylinder is A508 class 3 forging steel. The cylinder is fabricated by welding together the halves of two cylinders from two previous tested spinning cylinders which were known to have poor toughness properties, suitable for the NESC-1 project. The cladding procedure involved depositing of two layers stainless steel cladding and afterward reducing the cladding thickness to 4 mm. The cladded cylinder experienced two post-weld heat-treatments; six hours at 550⬚C before machining of the cladding and six hours at 550⬚C after machining. The cladding procedure resulted in a cladding HAZ thickness of about 10 mm. The material properties used in the analyses are given in Table 1, Rintamaa [20]. It should be noted that the cladding HAZ material is actually inhomogeneous which causes large scatters in tensile properties obtained from specimens taken from different locations in the HAZ.
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The results presented here are obtained from the analysis of an internal axial surface breaking crack with depth of 73 mm and length of 205 mm in the spinning cylinder. The corresponding results obtained from the analysis of a subclad crack with depth of 78 mm and length of 264 mm are presented in Ref. [1]. The loading conditions for the cylinder consisted of: uniformly heating up to 290⬚C, spinning, quenching and accelerating. The main features of the thermal transient scenario applied to the FE model are as follows: Initial temperature:
290⬚C
Quenching temperature:
5⬚C
Initial spinning speed:
2100 rpm
Final spinning speed:
2280 rpm
Acceleration time:
5 minutes
Total test time:
12 minutes
Heat transfer coefficient:
10 000 W/m 2⬚C
Stress free temperature:
290⬚C
4. Finite element modeling The general purpose FEM program ABAQUS [21] was used for the computations reported in this study. ABAQUS uses the domain integral method to evaluate the J-integral around a crack tip. The pre-processor of the FEM program ANSYS [22] was used for development of the three-dimensional FE models. The materials (base, HAZ and cladding) were assumed to be elastic-plastic with a piece-wise linear approximation of the hardening behavior taken from the uniaxial test results. It was assumed that the materials
Fig. 1. The finite element model used in the analysis of the spinning cylinder.
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Fig. 2. Distribution of temperature and the corresponding elastic-plastic hoop stress in the wall of the spinning cylinder under the thermal transient.
obeyed the von Mises flow criterion with its associated flow rule and isotropic hardening behavior. Typical FE model used for the 3D analyses is shown in Fig. 1. Due to symmetry in geometry and load, only one fourth of the cylinder needed to be modeled. The cladding thickness of 4 mm and the cladding HAZ of 10 mm were specifically modeled. The mesh consisted of 2317 twentynoded solid elements. The mesh around the crack tip was
Fig. 3. Variation of the crack driving forces J at three different positions along the surface crack front during the transient.
Fig. 4. Comparison of the crack driving force J and the material toughness at three different positions along the surface crack front during the transient.
fine enough to resolve the crack-tip fields at the load level of interest. The SSY solution is chosen in this study as a reference field representing a high level of stress triaxiality. The solution is obtained by imposing a K-field on the remote boundary of a standard boundary-layer model (a semicracked annulus). The FE model used for evaluation of the SSY solution consisted of 640 eight-noded elements comprised in 40 rings focused toward the crack tip. A comparison of some results obtained from small respectively large strain formulation showed that the most effects of large strain formulation were within the zone r ⱕ J/j 0 ahead of the crack tip, Sattari-Far. [19] Thus, the actual crack-tip constraint parameters can be evaluated at the distance r ¼ 2J/j 0, where the differences between the two theories are small. The results presented in this report are
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Fig. 5. Comparison of the crack driving force K J and the material toughness during the transient at the crack front in the middle of the cladding HAZ.
based on small strain formulation. In converting the crack driving forces J and K, the following plane-strain equation has been employed 0·5 (7) KI ¼ JE=(1 ¹ n2 )
5. Numerical results The distributions of temperature and stress in the wall of the cylinder were obtained by performing uncoupled heat transfer analyses of the 3D FE model. The transient scenario, described in Section 3, was applied to the model. The crack surfaces were assumed to be insulated in the thermal analysis. The temperature profiles and stress distribution in the wall of the cylinder at different times into the transient are shown in Fig. 2. Here, the stresses are hoop stresses, which are obtained from elastic-plastic analysis of the uncracked cylinder. It is observed that the transient results in yielding in the cladding material. The results
Fig. 6. Variation of the constraint parameters Q and H along the crack front, evaluated at the distance r/(J/s Y) ¼ 2 ahead of the crack tip.
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presented in Fig. 2 indicate that the peak stresses in the studied crack geometry due to the transient would be at a time of about four minutes into the transient. Variation of the crack driving forces J during the transient at three different positions along the crack front are shown in Fig. 3. These positions are at the middle of clad layer (2 mm from the internal surface), at the middle of the cladding HAZ (9 mm from the internal surface) and at the deepest point of the crack (73 mm from the internal surface). It is observed that the peak of the crack driving forces occurs in the cladding HAZ. Comparisons of the crack driving force J and the cleavage and ductile toughness of the materials as a function of the temperature during the transient are shown in Fig. 4 for these three positions. Note that for the cladding material, due to the lack of cleavage toughness data, only ductile fracture initiation data are used. It is observed that the situations in the cladding and at the deepest point of the crack front are far from critical, but ductile and cleavage fracture events can be expected in the cladding HAZ. By using the peak J-value in the cladding HAZ and the ductile fracture resistance data of the material, one obtains about 2·5 mm ductile crack growth in the cladding HAZ. However, due to loss of crack-tip constraint in the cladding HAZ, which will be discussed later, the amount of the actual ductile crack growth is expected to be less than 2·5 mm. Fig. 5 shows the crack driving force K J compared with the material fracture toughness in the middle of the cladding HAZ for the studied crack geometry during the transient. The estimated cleavage fracture toughness of the cladding HAZ are based on 50% probability respectively 95% probability of cleavage fracture. It is observed that for an evaluation based on 95% fracture probability, no cleavage fracture event can be expected for the studied crack geometry. However, considering 50% fracture probability, one can expect that a cleavage fracture event can be achieved. Providing that constraint effects do not influence the time of the cleavages events, Fig. 5 indicates that a cleavage event in the surface crack can occur at a time around 200 s into the transient. Variation of the constraint parameters Q and H, evaluated according to eqns (4) and (6), along the crack front at the time of 240 s into the transient are shown in Fig. 6. As can be observed, the parameters Q and H give different constraint values along the crack front, but both of them indicate substantially loss of constraint in the cladding and the cladding HAZ. It is also observed that the constraint variation are very large in the cladding HAZ. In practice, it is very difficult to correctly consider the constraint effects for this relative small zone with such a high constraint variation. It should be mentioned that thermal transients cause multiaxial stress states in the wall of pressure vessels. Thus, cracks in such a vessel are subjected to far-field stresses both in the direction normal to the crack surface (in-plane) and in the direction parallel with it (out-of-plane) under a PTS transient. The out-of-plane
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study the influence of the cladding residual stresses on the crack driving force.
Fig. 7. Comparison of the crack driving force K J at the middle of the cladding HAZ obtained from different analyses. Case 0 is the reference case.
A comparison of the results obtained from all analyzed cases in the sensitivity study is shown in Fig. 7. As the potential point for a cleavage fracture event can be expected to be in the cladding HAZ, only the crack driving forces at the middle point of that are presented here. Also shown in Fig. 7 are fracture toughness data of the cladding HAZ corresponding to 50% and 95% fracture probability. The K J-values are obtained by converting the elastic-plastic Jvalues according to eqn (7). In the following, the variations of the crack driving force and the crack tip temperature at the middle position of the cladding HAZ and at the deepest point during the imposed thermal transient are compared with those of the reference case (Case 0).
components of these stresses have no equivalence in the laboratory experiments used in the evaluation of fracture toughness properties. A comparison of uniaxial and biaxial loading effects in a pressure vessel containing a surface crack has shown that, for a similar J-value in the two cases of loading, the biaxial loading substantially increases the level of the stresses ahead of the crack tip, Sattari-Far [23].
6.1. Influence of specific modeling of the cladding HAZ
6. Sensitivity studies
6.2. Influence of pure elastic analysis
To demonstrate how different factors influence the crack driving force and the time of eventual cleavage event, the following cases are studied.
It is observed that the elastic analysis leads to slight underestimation of the crack driving force at the deepest point. In the cladding HAZ, the elastic J is somewhat higher than the elastic-plastic one during the first four minutes of the transient. Thus, because the differences in the J-values obtained from the elastic and the elastic-plastic analyses are relatively small for the studied case, one can use elastic analysis for engineering fracture assessment of similar cases, providing that J alone characterize the crack-tip field.
Case 0: This is used as the reference case in the sensitivity analysis. The input data for this case are as those presented in Section 3. Case 1: Input data as in Case 0 except that no specific modeling of the cladding HAZ is used in the analysis, i.e. the HAZ is assumed to have the same properties as the base material. Case 2: Input data as in Case 0 except that the analysis is elastic. Case 3: Input data as in Case 0 except that the heat transfer coeff. is 5 kW/m 2⬚C. Case 4: Input data as in Case 0 except that the stress free temperature is 20⬚C. Case 5: Input data as in Case 0 except the crack depth is 80 mm. Case 6: Input data as in Case 0 except that the spinning acceleration rate is twice as high as in Case 0, i.e. from 2100 rpm to 2280 rpm within 2·5 minutes. Case 7: Input data as in Case 0 except that T 0 is 20⬚C and a prescribed cladding residual stress distribution is imposed in the model. Case 8: Analysis of some 2D shallow and deep crack geometries in a reactor pressure vessel geometry to
It is observed that specific modeling of the cladding HAZ can significantly influence the resulting crack driving force in the cladding HAZ, but has little effect at the deepest point. During the transient, the J-values in the cladding HAZ of Case 1 are lower than those in Case 0, mainly due to the fact that the yield strength of the cladding HAZ material is higher than that of the base material.
6.3. Influence of the heat transfer coefficient It is observed that using a lower value of heat transfer coefficient leads to slightly lower J-values along the crack front. These results indicate that the variation of the heat transfer coefficient within the used values cannot significantly influence the crack driving force and the crack tip temperature during the transient. 6.4. Influence of the stress free temperature In Case 4, it is assumed that the cylinder is stress free at 20⬚C. The cylinder is uniformly heated up to 290⬚C, before the thermal transient is imposed. It is observed that the Jvalues are lower for Case 4 than for Case 0 during the first four minutes of the transient. This is due to the fact that, in
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The crack depth in Case 5 is 10% bigger than that in Case 0, having the same crack length. It is observed that the deeper crack causes higher J in the cladding HAZ but lower J at the deepest point of the crack front. The fact that a larger part of the crack front in Case 5 is under compressive thermal stresses than that in Case 0 during the transient, see Fig. 2, can explain the differences between these two cases. According to this analysis, a 10% increase in the crack depth results in about 5% increase in the J-value in the cladding HAZ. This implies that, for the actual case, the crack driving forces are not very sensitive to the crack depth size.
and the base material, new stresses are induced in the cladding and adjacent base material during cooling down to the ambient temperature. A large scatter can be observed in measured cladding induced stresses reported in the literature, Sattari-Far [24]. In general, it can be stated that the cladding residual stresses are tensile in the cladding and compressive in the base metal. The magnitude of the tensile stresses in the cladding depends on temperature, and at the ambient temperature it is about the yield strength of the cladding material. The measurement of the cladding residual stresses in the NESC-1 spinning cylinder is performed by Kockelman using the ring-core technique and the results are reported by the NESC TG4 [25]. The measured results are presented in Fig. 8. In Case 7, it is assumed that the vessel is stress free at 20⬚C and a cladding residual stress profile similar to the TG4 results is prescribed as initial stresses to the FEM model. It should be noted that the cladding mechanical properties used in the FE analyses cannot lead to an initial stress profile which has a peak as high as in the TG4 results. This explains deviations between the TG4 results and prescribed FEM stresses in Fig. 8. The cylinder is then uniformly heated up to 290⬚C before the thermal transient is imposed. Comparison of the crack driving forces during the transient for Case 0 and Case 7 are shown in Fig. 7. It is observed that, during the first minutes of the transient, the Jvalues are somewhat lower in Case 7 than those in Case 0. This is due to the fact that, in Case 7, heating up of the cylinder to 290⬚C has not only completely released the tensile initial stresses but also caused some compressive stresses in the cladding. Since the prescribed residual stresses act as primary stresses, J increases during the whole time interval in Case 7. Thus, the peaks of J for the two cases occur at different times. However, considering the time interval with maximum J in Case 0, one can conclude that, for the actual case, modeling of the cladding residual stresses has small effect on J in the cladding HAZ.
6.6. Influence of the spinning acceleration rate
6.8. Study of some 2D crack geometries
The acceleration rate in Case 6 is assumed to be twice as high as in Case 0, i.e. the initial spinning speed before imposing the quenching is 1920 rpm which reaches 2280 rpm within 5 minutes. It is observed that the variation of the acceleration rate has negligible effects and both cases show similar maximum J-values at the time of interest into the transient.
To better understand the effects of uncertainties in the cladding residual stresses, some 2D surface crack geometries are studied in a real PWR pressure vessel geometry. The vessel has an inner radius of 2000 mm and a wall thickness of 174 mm (including 4 mm cladding). The material properties presented in Table 1 are used in this analysis. Both axial and circumferential surface cracks are studied. Two different crack depths; a 10 mm shallow one and a 50 mm deep one, are studied. The cladding HAZ is not specifically modeled in the analysis. The FE models used for the analysis have 870 eight-noded elements. The operation pressure and temperature of the vessel are 320⬚C respectively 16 MPa. The vessel is subjected to a LOCA transient, in which the pressure falls to 8 MPa within 5 s and then to 4 MPa within 60 s. The coolant temperature falls from 320⬚C to 50⬚C within 5 s into the transient. The
Fig. 8. Results of the measurements and calculations of the cladding residual stresses at T ¼ 20⬚C. The FEM results are obtained from analysis of an axisymmetric model.
Case 4, heating up of the cylinder causes compressive stresses in cladding. During the transient, some part of the thermal stresses is used to overcome these compressive stresses, and consequently resulting in a lower crack driving force compared to Case 0. 6.5. Influence of the crack depth
6.7. Influence of the cladding residual stresses In a common practice of reactor pressure vessel manufacturing, a clad vessel experiences a final PWHT above 600⬚C for about 20 h. This can effectively release the cladding welding residual stresses at the PWHT temperature. However, due to significant differences in thermal expansion coefficient and mechanical properties of the cladding
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Table 2 Elastic-plastic K J-values [MPa冑m] of 2D cracks in a PWR pressure vessel under different loading scenarios. (t ¼ 174 mm, including 4 mm cladding, R i ¼ 2000 mm)
Axial cracks Case A11 Case A12 Case A13 Case A21 Case A22 Case A23 Circum. cracks Case C11 Case C12 Case C13 Case C21 Case C22 Case C23 *
Crack depth [mm]
Only CRS at T ¼ 20⬚C
CRS þ P 0* at T ¼ 50⬚C
LOCA (time into LOCA, s)
Remarks
10 10 10 50 50 50
12.231 9.381 26.657 6.957 5.348 13.015
48.02 43.62 57.83 121.14 119.86 126.47
145.02 (126) 140.16 (126) 145.33 (126) 274.18 (242) 273.09 (242) 284.65 (242)
T0 T0 T0 T0 T0 T0
¼ ¼ ¼ ¼ ¼ ¼
620⬚C 320⬚C 20⬚C and CRS 620⬚C 320⬚C 20⬚C and CRS
10 10 10 50 50 50
20.765 14.304 26.616 8.775 6.797 10.488
31.01 28.53 41.85 55.14 54.70 59.07
124.98 (136) 124.10 (130) 132.42 (136) 222.58 (276) 222.24 (276) 224.41 (276)
T0 T0 T0 T0 T0 T0
¼ ¼ ¼ ¼ ¼ ¼
620⬚C 320⬚C 20⬚C and CRS 620⬚C 320⬚C 20⬚C and CRS
CRS stands for cladding residual stresses and P 0 for the internal pressure MPa.
heat transfer coefficient is assumed to be 10 kW/m 2⬚C during the transient. The cladding residual stresses are introduced to the FE model in three different ways. First, it is assumed that the vessel is stress free at 620⬚C (the PWHT temperature), following a cooling to the ambient temperature. Second, it is assumed that the vessel is stress free at its operation temperature (320⬚C). Finally, it is assumed that the vessel is stress free at the ambient temperature, and a cladding residual stress profile similar to TG4 results are introduced to the model as initial prescribed stresses. Fig. 8 shows the cladding residual stresses at the ambient temperature obtained through these three ways compared with two reported measured data, TG4 and Rybicki [26]. The crack driving force K J, at the deepest point of the crack obtained from the analysis of the different cases are presented in Table 2. For each combination of crack geometry and cladding residual stresses, three different load cases are analyzed. In the third column of Table 2, only contribution of the cladding residual stresses (CRS) at the ambient temperature is given. The contribution of the cladding residual stresses and the internal pressure at 50⬚C (for instance during a cold pressurizing scenario) is presented in column four. The maximum crack driving force and its time of occurrence during the studied LOCA transient are given in column five for different cases.
7. Discussions The evaluated results presented in the previous sections indicate that, for the studied crack geometry, local cleavage fracture events can be expected in the cladding HAZ. The crack driving force K J compared with the material fracture toughness in the middle of the cladding HAZ during the transient are presented in Fig. 5. Providing that crack-tip constraint effects are small, a cleavage event can be
expected for the studied case at a time around 200 s into the transient. However, the results of the evaluation of the crack-tip constraint presented in Fig. 6 indicate substantial loss of constraint in the cladding HAZ compared with the SSY solutions. To make a more exact evaluation on the possibility and the occurrence time of a cleavage fracture event one needs to have access to cleavage fracture toughness data of the cladding HAZ material corresponding to the actual constraint conditions. One can expect that the loss of crack-tip constraint in the cladding HAZ may decrease the probability of any cleavage event or delay its occurrence time for the studied crack geometry. There are some sources of uncertainty which potentially can influence eventual cleavage fracture events in the studied case. These sources are the following. 1. Presented material data of the cladding HAZ show large scatter. The cladding HAZ is actually an inhomogeneous zone with varying material properties. This affects the crack driving forces and toughness properties estimated for the cladding HAZ. 2. The FE results indicate substantial loss of crack-tip constraint in the cladding HAZ compared with the SSY solutions. The constraint variations are very large in the cladding HAZ. This together with (1) cause practical difficulties to provide relevant fracture material data for the cladding HAZ. 3. The eventual intervention of warm prestressing may also make a cleavage fracture initiation difficult to achieve in the experiment. While the consideration of crack-tip constraint conditions and warm prestressing phenomena indicate difficulties in occurrence of a cleavage fracture event, there is a potential to promote the initiation of a cleavage fracture event. Investigation by Sattari-Far [19] shows that a thin hard layer (of about 100 mm) is formed at the cladding/base interface due
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to cladding. This relatively small hard zone has very low toughness properties and, therefore, can be a potential site for initiation of a brittle fracture event. Considering the effects of the cladding residual stresses presented in Table 2 and Fig. 7, it is observed that the cladding residual stresses have negligible contributions to critical situations of the studied crack geometries under a LOCA type transient. The critical crack driving forces are practically insensitive to the way the cladding residual stresses are introduced in the model, especially for deep cracks. However, the contribution of the cladding residual stresses can be considerable under other conditions, like hydro testing and cold pressurizing. For shallow cracks, the results are dependent on the way the cladding residual stresses are modeled. This is of importance when acceptance assessments are performed. For such cases, it is reasonable to assume that tensile residual stresses of the magnitude of the yield strength of the cladding material prevail in the cladding at ambient temperature. It is observed that, for the studied crack geometry, the critical situation occurs in a location (the cladding HAZ) where interactions of the material properties and the constraint effects are very complex. The performed sensitivity studies of influencing parameters indicate that the fracture toughness properties of the cladding HAZ are the strongest sources of uncertainty. Therefore, to perform a more accurate evaluation, relevant cleavage fracture toughness data of the cladding HAZ material are needed. These data should to some extent cover the constraint conditions prevailing in the cladding HAZ of the actual crack cases. It is worthy to note that the different constraint parameters used in this study give different degrees of loss of constraint in the studied cases. More studies are, therefore, needed to find the best measure to quantify the constraint effects. A post-test analysis on the spinning cylinder experiment will hopefully give more information to verify the utility of the J-integral concept for crack cases of this kind.
8. Conclusions Based on pretest fracture assessments of a surface breaking crack in the NESC-1 spinning cylinder, the following conclusions can be made. 1. For deep cracks under thermal transient of this kind, the critical situation does not occur at the deepest point of the crack front, but in or near the cladding HAZ, where the crack driving force can exceed the actual fracture toughness properties of the material. 2. Some limited ductile crack growth is expected to occur along the crack front in the cladding HAZ and adjacent base material in the studied crack geometry. 3. Consideration of the crack tip triaxiality indicates substantial loss of the crack-tip constraint in the cladding HAZ compared with the SSY solutions. In addition, the
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constraint variations in this zone are very large in the studied cases. 4. Providing that the constraint and warm prestressing effects do not substantially affect the situations in the studied cases, one can expect cleavage fracture to occur in the cladding HAZ at time around 200 s into the transient, using cleavage fracture data with 50% fracture probability. 5. Specific modelling of the cladding HAZ can significantly influence the calculated crack driving force in the cladding HAZ, but not at the deepest point of the crack. 6. The cladding residual stresses give negligible contribution in critical situations of the studied crack geometries under a LOCA type transient, but their contributions can be considerable under other conditions such as; fatigue, IGSCC and cold pressurizing. It is reasonable to assume that tensile residual stresses of the magnitude of the yield strength of the cladding material prevail in the cladding at the ambient temperature.
Acknowledgements Funding of this study was provided by the Swedish Nuclear Power Inspection (SKI). This support is greatly appreciated. The authors are also grateful to valuable discussions with Dr. Bjo¨rn Brickstad (SAQ).
References [1] Sattari-Far I. Pretest analysis of the NESC-1 spinning cylinder experiment. SAQ/FoU-Report 97/03, Stockholm: SAQ Kontroll AB, 1997. [2] Rice JR A path independent integral and the approximate analysis of strain concentration by notches and cracks. J. App. Mech., 1968;35:379–386. [3] Sharma SM, Aravas N Determination of higher-order terms in asymptotic elastoplastic crack tip solutions. J. Mech. Phys. Solids, 1991;39:1043–1072. [4] Hutchinson JW Singular behavior at the end of a tensile crack in a hardening material. J. Mech. Phys. Solids, 1968;16:13–31. [5] Rice JR, Rosengren GF Plane strain deformation near a crack tip in a power law hardening material. J. Mech. Phys. Solids, 1968;16:1–12. [6] O’Dowd NP, Shih CF Family of crack-tip fields characterized by a triaxiality parameter-I. Structure of fields. J. Mech. Phys. Solids, 1991;39:989–1015. [7] O’Dowd NP, Shih CF Family of crack-tip fields characterized by a triaxiality parameter-II. Fracture applications. J. Mech. Phys. Solids, 1992;40:939–963. [8] Sumpter JDG, Forbes AT. Constraint based analysis of shallow cracks in mild steels. In Proc. Int. Con. Shallow Crack Fracture Mechanics Tests and Applications. Cambridge, UK: TWI, 1992. [9] Dodds RH, Shih CF, Anderson TL Continuum and micromechanics treatment of constraint in fracture. Int. J. Fract., 1993;64:101–133. [10] Dodds RH, Tang M, Anderson TL. Effects of prior ductile tearing on cleavage fracture toughness in the transition region. Structural Research, Series No. 583, University of Illinois at Urbana-Champaign, IL, 1993. [11] Shih CF, O’Dowd NP, Kirk MT. A framework for quantifying crack tip constraint. In Constraint effects in fracture, ASTM STP 1171.
212
[12]
[13]
[14] [15]
[16] [17]
[18]
I. Sattari-Far, L. Dahlberg/International Journal of Pressure Vessels and Piping 75 (1998) 203–212 Philadelphia, PA: American Society for Testing and Materials, 1993:2–20. Kirk MT, Koppenhoefer KC, Shih CF. Effect of Constraint on specimen dimensions needed to obtain structurally relevant toughness measures. In Constraint effects in fracture, ASTM STP 1171. Philadelphia,PA: American Society for Testing and Materials, 1993:79–103. Faleskog J. Effects of local constraints along three dimensional crack fronts-A numerical and experimental investigation. J. Mech. Phys. Solids, 1996. Aurich D, Sommer E The effect of constraint on elastic-plastic fracture. Steel Research, 1988;59:358–367. Brocks W, Knecke G, Noak HD, Veith H On the transferability of fracture mechanics parameters to structures using FEM. Nucl. Eng. Design., 1989;112:1–14. Kordisch H, Sommer E, Schmitt W The influence of triaxiality on stable crack growth. Nucl. Eng. Des., 1989;112:27–35. Brocks W, Knecke G. On the influence of triaxiality of the stress state on ductile tearing resistance. In Elements of defect assessment. ESIS/ EGF Publication 9. London: Mechanical Engineering Publishers, 1991:189–201. Brocks W, Schmitt W. Quantitative assessment of the role of crack tip constraint on ductile tearing. In Constraint effects in fracture, ASTM
[19]
[20] [21] [22] [23]
[24]
[25]
[26]
STP 1171. Philadelphia, PA: American Society for Testing and Materials, 1993:64–78. Sattari-Far I Constraint effects on ductile crack growth in cladded components subjected to unaxial loading. Int. J. Fatigue Fract., 1995;18:1051–1069. Rintamaa R. NESC1 Spinning Cylinder Project: summary of material property data. Material Task Group, 1996. ABAQUS, User’s manual. Version 5.3. Hibbit, Karlsson and Sorenson, 1995. ANSYS, Users manual. Version 5.0. Swanson Analysis System, 1993. Sattari-Far I Constraint effects on behavior of surface cracks in cladded reactor pressure vessels subjected to PTS transients. Int. J. Pres. Ves. and Piping, 1996;67:185–197. Sattari-Far I, The significant of cladding material on the integrity of nuclear pressure vessels with cracks. SA/FoU-Report 89/03. Stockholm: SAQ Kontroll AB, 1989. Kockelman H. Residual stress measurement on cladding and adjacent base metal on NESC-1 spinning cylinder. Report No. NESCDOCTG3(97)03 TG4 Residual Stress Report, NESC TG4. Rybicki EF, Shadley JR, Sandhu AS. Experimental evaluation residual stresses in a weld clad plate and clad test specimens. US Nuclear Regulatory Commission Report NUREG/CR-4646, 1986.