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                                                                           T. Fekete, Frattura ed Integrità Strutturale, 36 (2016) 99-111; DOI: 10.3221/IGF-ESIS.36.10 
 

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Focused on Fracture Mechanics in Central and East Europe 

 
 
 
 
Review of pressurized thermal shock studies of  
large scale reactor pressure vessels in Hungary 
 
 
Tamás Fekete 
HAS Centre for Energy Research, Department of Fuel and Reactor Materials, Structural Integrity Group 
tamas.fekete@energia.mta.hu 
 

 
ABSTRACT. In Hungary, four nuclear power units were constructed more than 30 years ago; they are operating 
to this day. In every unit, VVER-440 V213-type light-water cooled, light-water moderated, pressurized water 
reactors are in operation. Since the mid-1980s, numerous researches in the field of Pressurized Thermal Shock 
(PTS) analyses of Reactor Pressure Vessels (RPVs) have been conducted in Hungary; in all of them, the concept 
of structural integrity was the basis of research and development. During this time, four large PTS studies with 
industrial relevance have been completed in Hungary. Each used different objectives and guides, and the 
analysis methodology was also changing. This paper gives a comparative review of the methodologies used in 
these large PTS Structural Integrity Analysis projects, presenting the latest results as well. 
  
KEYWORDS. Structural Integrity Analyses; Reactor Pressure Vessels; Pressurized Thermal Shock. 
 
 
 
INTRODUCTION 
 

n a preceding paper [2], the concept and the general methodology of Pressurized Thermal Shock (PTS) Structural 
Integrity analyses of large scale Reactor Pressure Vessels (RPV) were presented. The PTS phenomenon was known 
to specialists earlier, but became widely known and consequently, subject to intensive research when in the late 

1970’s, two accidents occurred in the US. Those accidents showed that transients can occur in pressurized water reactors, 
resulting in a severe overcooling that causes thermal shock in the vessel, concurrent with or followed by re-pressurization. 
These are the transients generally known under the name of PTS. The very high tensile stress caused by thermal shock at 
the inner surface of the vessel wall can cause the cleavage initiation of a pre-existing flaw of a certain dimension to occur 
(i. e. crack-like defect). Concern about brittle crack initiation during PTS can arise because during operation the neutron 
irradiation exposure around the energy-generating core makes the material of the Reactor Pressure Vessel (RPV) 
increasingly susceptible to cleavage fracture initiation. 
Although PTS calculations have been part of RPV safety evaluations since the first half of the 1980’s, there are various 
approaches that are analogous in general, but have many differences in details. There exists no internationally recognized 
standard; there are guidelines in Europe that are recommended to use (e. g. specifically for VVER units [4] and [16]); 
various approaches are used at a national level in different countries. In Hungary, the HAEA Guide 3.18v3 [3] is currently 
in effect. 
During the last three decades, four large PTS studies have been conducted in Hungary. Each used different objectives and 
guides, and the Analysis methodology has also been changing. In the preceding paper [2], the conceptual model of PTS 
Structural Integrity calculations was presented. It was shown that using the conceptual model –that is based on the notion 
of typed graph-transformation systems– the calculations and their evolution can be described on a theoretical level. Using 

I 



 

T. Fekete, Frattura ed Integrità Strutturale, 36 (2016) 99-111; DOI: 10.3221/IGF-ESIS.36.10                                                                                
 

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the model, the structure and the key aspects of a more proper description of the PTS Calculation methodology were 
presented, as follows: 
 Objective of the study; 
 Codes and guides used during the project definition; 
 Geometry definition: 

o Parts of the RPV modeled during the study and the geometric model,  
• locations selected for Fracture mechanics analyses; 

o Flaw-size and geometrical distribution at selected locations;  
• relation of postulated flaws vs. detected flaws; 

 Description of neutron-transport calculations; 
 Materials: 

o Description of materials; 
o Description of constitutive models:  

•  thermo-mechanics model and its parameters  
   description of ageing;  
•  fracture model and its parameters;  
   description of ageing; 

o Qualification of material test methods; 
 Thermal-hydraulics:  

o Selection of overcooling sequences; 
o Thermal-hydraulic assessments; 

 Modeling of physical fields: 
o Kinematical model; 
o Physical fields; 
o Fracture mechanics model; 

 Integrity criteria. 
Applying the results mentioned above, these points will be discussed in the course of this review concerning the evolution 
of PTS Calculation Methodologies in Hungary. Considering the changing context, the objectives of the study, as well as 
the codes and guides used during the problem definition and solution will also be presented. 
 
 
PHASE 0.: DESIGNER’S AND MANUFACTURERS PTS STRUCTURAL INTEGRITY CALCULATIONS 
 
Designer’s and Manufacturers PTS Structural Integrity Calculations  

he VVER-440 V213-type RPV design was developed by OKB Gidropress without PTS assessments in the first 
half of the 1970s; as at that time the PTS safety evaluations of the RPVs were not part of the design requirement. 
Normal operating events and anticipated emergency events were addressed in the loading specifications. 

Calculations of protection against brittle fracture were part of the original strength calculations, and followed the rules set 
by the Russian standard valid at the time. According to the rule, brittle fracture resistance was analyzed on the basis of the 
material’s static strength properties, but did not use fracture mechanics criterion. 
The Integrity of the RPV met the brittle fracture requirements if:  
 Twall ≥Tk, where Twall is the component’s wall temperature, Tk is the critical temperature of brittleness of the 

component’s material, or 
 when Twall <Tk and σred<Rp0,2T/n, where σred denotes Mohr’s reduced stress, Rp0,2T is yield stress of the material at the 

component’s wall temperature, n is the safety factor; n=2 if the component is regularly examined by non-destructive 
tests (NDT), otherwise n=4 [14]. 

 
Later, starting in the mid-80s, several PTS calculations were performed by OKB Gidropress and by other institutes, but in 
most cases, these studies assumed a generic RPV; so plant-specific conditions were neglected. 
 
The Manufacturer’s PTS Structural Integrity Calculations  
As part of the manufacturer’s strength-calculation documentations, Škoda provided a PTS analysis for a few accidental 
situations chosen based on engineering judgments, using linear elastic fracture mechanics. 

T 



 

                                                                           T. Fekete, Frattura ed Integrità Strutturale, 36 (2016) 99-111; DOI: 10.3221/IGF-ESIS.36.10 
 

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Concerning geometry definition, Weld No5/6, and an ECCS nozzle were selected, taking the geometrical dimensions of 
the components into account, as it was given in the documentation. At both locations, embedded elliptical cracks were 
selected with 2a0= 5 mm, with fatigue crack growth of 1 mm, postulated up to End Of Life (EOL) conditions. 
The thermo-mechanical material parameters of the base material type 15Ch2MFA were selected from the strength 
calculations documentation. For fracture mechanics calculation, the equation 

 

   86400, ( )
86 ( )

IR k
k

K T T kg m
T T


 

        (1) 

 
described material fracture toughness. 
Results of ageing evaluation gave Tk=136 °C for Weld No5/6, and Tk=32 °C for the ECCS Nozzle. 
Selection of overcooling sequences was based on empirical, engineering experience: the loss of coolant accident cases 
(LOCA) rupture of pipelines Ø135, Ø250 and Ø492 were analyzed. 
The PTS calculations were performed by a code developed at Skoda. 
The Integrity of the RPV was accepted for brittle fracture, if:  
 Twall ≥Tk, where Twall is the component’s wall temperature, Tk is the critical temperature of brittleness of the 

component’s material, or 
 when Twall <Tk, then 

o ac/a0 ≥ 2, where ac is the critical crack size (where KI=KIR) and 
o KI(x=2c)/KIR(x=2c) = nk ≥√; 

 
Summary  
The above-reviewed analyses –performed by the manufacturer in the early 1980s– were based on engineering models. 
They analyzed only a very limited set of thermal-hydraulic transients, and used linear-elastic material models (that is, a 
Linear Elastic Fracture Mechanics (LEFM) methodology); the results of the fracture mechanics evaluation were adequate. 
 
 
PHASE 1: PTS STRUCTURAL INTEGRITY CALCULATIONS IN THE 1980S 
 
Objective of the study: 

he objective of the study was to provide results for the safety report that was necessary for the renewal of the 
operating license after each, 4-year inspection cycle. 
 

 
Codes and guides used during problem definition: 
The Interatomenergo rule 38.434.55-84 was used during the calculations. 
 
Geometry definition: 
 The RPV Beltline Region was selected for the study, with geometrical dimensions selected from the manufacturer’s 

documentation, 
o in the beltline region, an axial, semielliptical shaped, through clad crack with depth a=35 mm and c=52,5 

mm, and 
o in weld No 5/6 a circumferential, semielliptical shaped, through clad crack with depth a=35 mm and c=52,5 

mm was defined, 
 
Description of neutron-transport calculations: 
The fluence calculations were based on a semi-empirical approach. During generic studies, the lead factors for the critical 
beltline region and for the weld No 5/6 were determined, and data from fluence-measurement results were used to assess 
factual neutron fluencies for EOL conditions at the selected locations. 
 
Materials, constitutive models: 
 Both the cladding and the ferritic materials (15Ch2MFA forging and the welding metal) were modeled during 

calculations. For thermal and strength calculations, the data were derived from the manufacturer’s documentation. 

T 



 

T. Fekete, Frattura ed Integrità Strutturale, 36 (2016) 99-111; DOI: 10.3221/IGF-ESIS.36.10                                                                                
 

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 In thermal calculations, the thermo-physical parameters were independent from temperature; during calculations, 
averaged values of the manufacturer’s documentation were used. 

 In strength calculations, the Neumann-Duhamel constitutive model was used with temperature-independent, averaged 
values of the manufacturer’s documentation. 

 For the description of fracture toughness of the structural materials, the equation: 
 

    0.02, 26 36 kT TIc kK T T e
            (2) 

 
was used; the ageing was modeled by using the temperature-shift (∆Tk) of the critical temperature of brittleness in the 
following form: 

 
3

0k k k kT T T T A               (3) 
 

where Φ is neutron fluence. ∆Tk values were evaluated from plant surveillance data. 
 The above material parameters were based on experimental results, performed in a qualified laboratory. 
 
Thermal-hydraulic assessments: 
 The selection of overcooling sequences was based on engineering judgments.  

Loss of coolant accident cases (LOCA) rupture of pipelines Ø135, Ø250 and Ø492 were selected for calculations. 
 The thermal-hydraulic assessments were performed by Relap 4 – Mode 6 version. During thermal-hydraulic 

assessments, a simplified model of the primary system was used; the model assumed that all primary loops are 
identical, the model was called ‘One Loop model’ of the primary system. For mixing calculations, a home-developed 
code was used. 

 
Main features of the model used for PTS Structural Mechanics calculations: 
 For Structural Mechanics calculations, an analytical code was used [10], which had been validated with a Finite 

Element Code [13] earlier. The model and the solution of the problems had the following features: 
o In the thermal problem solution, the code used a thick-plane model of the beltline area that touches the 

liquid-wall interface. The solution of the thermal problem was determined in terms of Fourier series. The 
boundary conditions of the problem were received from results of thermal-hydraulic assessments at selected 
points in the downcomer. 

o In the solution of the strength problem, the software used analytical stress-formulae to generate the solution. 
o In fracture mechanical calculations, the crack tip driving force was calculated using the method published by 

Westergaard [17]. 
o The cladding residual stresses were taken into account, applying stress-free temperatures (Tsf), which were 

chosen equal to the operating temperature of the component. 
o The weld residual stresses were neglected. 

 
Integrity Criterion: 
The crack initiation condition in the form: 
 

I IcK K            (4) 
 
was used during calculations. 
 
Summary  
The analyses shown above were based on an analytical approach of the underlying thermo-elastic problem. The 
overcooling sequences were selected based on engineering judgments; this resulted in a limited set of transients. The 
Structural Mechanics calculations were based on the ‘force method’ that had been widely used in mechanical engineering 
since the early days of the field of Strength of Materials. The fracture mechanics module worked with an LEFM 
methodology. The ageing characteristics of structural materials were derived from the experimental results of the 
surveillance program. 



 

                                                                           T. Fekete, Frattura ed Integrità Strutturale, 36 (2016) 99-111; DOI: 10.3221/IGF-ESIS.36.10 
 

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PHASE 2: PTS STRUCTURAL INTEGRITY CALCULATIONS IN THE 1990S 
 
Objective of the study: 

he main objective of the study was to reassess the safety of Paks NPP using internationally accepted design- and 
safety -codes and guidelines. Experiences from various international PTS-related projects were used in the 
elaboration of the methodology [1, 5, 9, 15]. 

 
Codes and guides used during problem definition: 
The PNAE G-7-002–86 [8], the ASME BPVC XI, and the 10 CFR 50.61 were used during the project. 
 
Geometry definition: 
 The RPV Beltline Region was selected for the study, with geometrical dimensions selected from the manufacturer’s 

documentation, 
o in the beltline region, axial, semielliptical shaped through clad cracks with depths a=13, 23 and 35 mm and 

shape factor a/c=2/3; and 
o in weld No 5/6 a circumferential, semielliptical shaped through clad crack with depths a=13, 23 and 35 mm 

and shape factor a/c=2/3, were defined. 
 
Description of neutron-transport calculations; 
The fluence calculations were based on a semi-empirical approach. During generic studies, the lead factors for the critical 
beltline region and for the weld No 5/6 were determined, and data from fluence-measurement results were used to assess 
factual neutron fluencies for EOL conditions at the selected locations. 
 
Materials, constitutive models: 
 Both the cladding and the ferritic materials (15Ch2MFA forging and the weld metal) were modeled during 

calculations. For thermal and strength calculations, the data were derived from the manufacturer’s documentation. 
 In thermal calculations, the thermo-physical parameters were independent from temperature; during calculations, 

averaged values of the manufacturer’s documentation were used. 
 In strength calculations, the Neumann-Duhamel constitutive model was used with temperature-independent, averaged 

values of the manufacturer’s documentation. 
 For describing the fracture toughness of the structural materials, the equation: 

 

   0.0217, 35 53 kT TIc kK T T e
            (5) 

 
was used; the ageing was modeled by using the temperature-shift (∆Tk) of the critical temperature of brittleness in the 
following form: 

 
3

0k k k kT T T T A               (6) 
 

where Φ is neutron fluence. 
 The above material parameters were based on experimental results, performed in a qualified laboratory. 
 
Thermal-hydraulics: 
 The selection of the overcooling sequences was based on engineering judgments integrated with conclusions of 

international experiences [15] as well.  
A broad spectrum of various overcooling sequences, various loss of coolant accident (LOCA) scenarios, e.g. rupture 
of various pipelines (e.g. Ø90, Ø135, Ø233 and Ø492) were selected for calculations. 

 The thermal-hydraulic assessments were performed by the system thermal-hydraulic codes Relap 5 – Mode 2 and 
Athlet – mod 1.4.. During thermal-hydraulic assessments, a simplified ‘One Loop model’ of the primary system was 
used. For mixing calculations, the Remix code was used. 

T 



 

T. Fekete, Frattura ed Integrità Strutturale, 36 (2016) 99-111; DOI: 10.3221/IGF-ESIS.36.10                                                                                
 

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Main features of the models used for PTS Structural Mechanics calculations: 
 For Structural Mechanics calculations, a Hungarian code (called ACIB-RPV) was used [11], which was validated to 

Finite Element Codes [12]. The model and the solution of the problems has the following features: 
o In the thermal problem solution, the code used a thick-plane model of the beltline area that touches the liquid 

wall interface. The solution of the thermal problem was determined in terms of Fourier series. The boundary 
conditions of the problem were received from results of thermal-hydraulic assessments at selected points in 
the downcomer. 

o In the solution of the strength problem, the software used analytical stress-formulae to generate the solution. 
o In fracture mechanical calculations, the crack tip driving force was calculated using the method published by 

Westergaard [17]. 
o The cladding residual stresses were taken into account, applying stress free temperatures (Tsf), which were 

chosen equal to the operating temperature of the component. 
o The weld residual stresses were neglected. 

 
Integrity Criterion: 
The crack initiation condition in the form: 
 

 
1.1 I IcK K             (7) 

 
was used during calculations. 
 
Summary  
The PTS project assessed above made a larger effort in selecting the overcooling sequences and their assessments. This 
led to a larger set of transients, so the reliability of results increased. The analysis methodology was based on an analytical 
approach of the underlying problem. The fracture mechanics module worked with LEFM methodology. The ageing 
characteristics of structural materials were derived from the experimental results of the surveillance program. 
 
 
PHASE 3: PTS STRUCTURAL INTEGRITY CALCULATIONS IN THE NEW MILLENNIUM 
 
Objective of the study: 

he objective of the study was to reassess the safety of RPVs providing Time Limited Ageing Analysis (TLAA) 
results for Paks NPP for license-application beyond the designed service lifetime. Although the designed service 
lifetime of the RPVs was set to 40 years of operation, the analyses were conducted for the 30+ years of operation. 

 
Codes and guides used during problem definition: 
The HAEA Guide 3.18 [3], the IAEA PTS Guide for VVER units [4] and an earlier version of VERLIFE [16] were used 
during the project. 
 
Research and developmental works before the study: 
Beginning around the new Millennium, intensive research was initiated at KFKI AEKI in order to clarify the ageing 
properties of cladding materials, as well as to clarify the damage-mechanisms of various impurities in structural materials, 
with special emphasis on phosphorous segregation. AEKI joined a number of international projects. A full review of the 
activities would exceed the extent of the present paper. Many of the research results have been incorporated into the 
updated analysis methodology. 
 
Geometry definition: 
 The full RPV body was selected for the study, with geometrical dimensions derived from the manufacturer’s 

documentation. Two main sub-models of the model were constructed, in order to reduce the costs of the project in 
terms of IT and human resources. The aim of the development was to make parametric studies on simpler models 
using conservative assumptions; and after the selection of the worst transient loading cases, perform a calculation on 
the more detailed model, if necessary. Two types of models have been worked out: 

T 



 

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o a model designed for elastic calculations; the geometrical model is composed from two sub-models:  
1. a 3D Finite Element (FE) model of a lower-cylindrical part of the vessel with the bottom; the purpose of 
the model was the calculation of through wall temperature, stress and strain distributions occurring during 
PTS transients, and provide inputs to subsequent fracture mechanics calculations. The FE mesh models the 
welds, and includes quadratic, iso-parametric brick-type elements with 20 nodal points, but does not model 
the crack in the mesh. The developed model contains 58240 elements and 247405 nodal points. The 
geometrical model is presented on Fig. 1. 

 

 
 

Figure 1: 3D Finite Element model of a lower cylindrical part, bottom and welds of a VVER-440 RPV. 
 

2.  3D models of the main coolant pipeline nozzles 492; the purpose of the models was to calculate 
through wall temperature, stress and strain distributions occurring during PTS transients, and provide inputs 
to subsequent fracture mechanics calculations. The FE mesh includes quadratic, iso-parametric brick-type 
elements with 20 nodal points. The developed model contains 7320 elements and 34144 nodal points. The 
geometrical model is presented on Fig. 2. 
 
 

 

 
Figure 2: 3D Finite Element model of a main coolant pipeline nozzle 492. 

 



 

T. Fekete, Frattura ed Integrità Strutturale, 36 (2016) 99-111; DOI: 10.3221/IGF-ESIS.36.10                                                                                
 

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3  For elastic calculations, a series of crack locations were selected for fracture mechanics calculations, as it 
is presented on Fig. 3. The aim of this development was to make the calculations suitable for an algorithmic 
evaluation of the crack locations in any transient case. 
 

45° 90° 135° 225° 270° 315°180°
167° 193°

0° 360°

1
4
0
0

1
7
3
5

2
7
0
0

1
8
2
5

1
9
0
0

2
0
0
0

1
1
0
0

11128
 

 

Figure 3: Locations selected for fracture mechanics calculations on a VVER-440 RPV. 
 

At each location, two types of cracks have been defined, as follows: one type was a semi-elliptic, underclad 
crack; the other type was a through clad crack, both shown on Fig. 4. The a/c ratio was set to 1/3 [3]. The 
depth of the cracks varied between 2 and 14 mm from the cladding-base metal interface; the maximal crack-
depth was 0,1s. The use of this maximal postulated crack-depth parameter was allowed to calculate with 
because NDE tests were qualified according to international standards. NDE results also proved that the 
cladding could be seen free from critical defects, so the use of underclad cracks was also allowed. The 
through-clad cracks served for parametric studies. 
 

2c 2c 

A 

C 

A 

C a 
tpl 

ta 

 
 

Figure 4: The two crack types defined for Fracture Mechanics analyses [6, 7]. 
 



 

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o The other type of the model was designed for elastic or elastic-plastic calculations with a crack embedded into 
the mesh; it is the 3D FE model of the lower cylindrical part of the vessel with the bottom, including a crack 
embedded into the mesh. The model was developed with the purpose of simulating through wall 
temperature, stress and strain distributions occurring during PTS transients, and also performing subsequent 
fracture mechanics calculations on the embedded crack. The FE mesh models the welds, and includes 
quadratic, iso-parametric brick-type elements with 20 nodal points. The model was designed to study 
plasticity effects too. The developed model contains 160 540 elements and 709 826 nodal points. The 
geometrical model is presented on Fig. 5. The crack location was selected after long series of calculations 
performed on the simpler model, in order to reduce the time-consuming work of developing a mesh around 
the crack front. The crack model is an underclad, semi-elliptical crack with a=14 mm, a/c=1/3; the crack 
model is shown on Fig. 5 below. 

 

 
 

Figure 5: 3D Finite element model of a lower cylindrical part with embedded crack of a VVER-440 RPV. 
 
Description of neutron-transport calculations: 
The fluence data were provided by full 3D neutron-transport calculations that took the full loading-history of the 
energetic core into account. This fact made a complete re-evaluation of material ageing possible. 
 
Materials, constitutive models: 
 Both the cladding and the ferritic materials (15Ch2MFA forging and the weld metal) were modeled during 

calculations. For thermal and strength calculations, the data were derived from the manufacturer’s documentation. 
 In thermal calculations, the thermo-physical parameters were temperature-dependent. 
 In thermo-mechanical strength calculations, the Neumann-Duhamel constitutive model was used with temperature-

dependent parameters of the manufacturer’s documentation. In the case of elastic-plastic calculations, plastic material 
properties were derived from the re-evaluation of the material tests performed in the frame of the manufacturer’s 
surveillance program. 

 For describing the fracture toughness of the structural materials, the equation: 



 

T. Fekete, Frattura ed Integrità Strutturale, 36 (2016) 99-111; DOI: 10.3221/IGF-ESIS.36.10                                                                                
 

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   0.02, 26 36 kT TIc kK T T e
            (8) 

 
was used; the ageing was modeled by using the temperature-shift (∆Tk) of the critical temperature of brittleness in the 
following form: 
 

  0 ,age temp fat irr n fat operk k k k k kT T T T T A T F T                (9) 
 

where Φ is neutron fluence, a is fatigue damage, Toper is the operational temperature, ∆Tkirr is the temperature shift 
caused by neutron irradiation, ∆Tktemp is the temperature shift caused by thermal activation and ∆Tkfat is the 
temperature shift caused by fatigue. 

 The above-described material parameters were evaluated on the basis of experimental results, performed in qualified 
laboratories. 

 
Thermal-hydraulics: 
 The deterministic selection of the PTS transients was based on engineering judgment using the design basis accident 

analysis approach combined with the operational experience accumulated at the plant. In this deterministic selection, 
only the individual initiating events were taken into account. A broad spectrum of various overcooling sequences was 
selected for calculations. Complementary to the deterministic analysis of the limiting scenarios, a selection of 
additional transients with the help of probabilistic event-tree methodology was also performed. 

 The thermal-hydraulic assessments were performed by Relap 5 – Mode 3 and Athlet Ver 2.3. system codes. For 
mixing calculations, the Remix code was used. In the system’s thermo hydraulic calculations, the six-loop model of 
VVER 440 systems were used. so inhomogenities of the temperature and the velocity fields occurring in the 
downcomer were taken into account in some approximation as well. The FE model has more refined structure at the 
coolant-solid interface than the TH system model, a sophisticated interface was developed for the generation of 
thermal boundary conditions from thermal-hydraulic calculation results. The relation of the points used in thermal-
hydraulic analyses and the FE model solid interface is presented on Fig. 6. 

 

1

1

11

21

31

41

12 13 14 15 16

22 23 24 25 26

32

42 43 44 45 46

33 34 35 36

50

90

92

 
 

Figure 6: Locations of thermal-hydraulic data supplying points at the inner surface of the RPV. 
 



 

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Main features of the models used for PTS Structural Mechanics calculations: 
 For Structural Mechanics Calculations, the MSC.Marc code was used which is a validated, general-purpose Finite 

Element Code, developed specifically for non-linear calculations. The model and the solution of the problems 
featured the followings: 

o In the case of thermal-elastic or thermal-elastic-plastic problems supplemented by fracture mechanics 
calculations, the problem-solving strategy was to solve the coupled physical problem in its coupled form. The 
coupling was manageable using a staggered scheme, but for future applications, the couplings could be made 
stronger. 

o While solving the strength problem, the software used the classical deformation-based FE approach. 
o In fracture mechanical calculations, in case of the simpler model (described above), the crack tip driving force 

was calculated using the method published by S. Marie and S. Chapuliot [6, 7], which was implemented into a 
home-developed software package. 

o In calculations integrating the crack into the FE model, the crack tip driving force was calculated along the 
crack-front using the J-integral. 

o The cladding residual stresses have been taken into account, applying stress-free temperatures (Tsf), which had 
been chosen equal to the operating temperature of the component. 

o The weld residual stresses were integrated into the model. 
 
Integrity Criterion: 
The crack initiation condition in the form: 
 
 I IcK K            (10) 

 
was used during calculations. 
 
Summary  
Within the frame of the PTS project presented above, a more detailed FE model has been developed and tested. Two 
models were developed: a simpler linear model of the RPV and a more detailed model for studying the plastic effects 
occurring during PTS transients. The number of overcooling sequences has increased significantly. The neutron-transport 
calculations provided more precise results concerning neutron-physics data. That made it possible for the ageing 
assessments to lower the uncertainty of results. The thermal-hydraulic system model was also considerably improved. The 
increasing number of selected transients and the more complex models together led to more resource-demanding 
calculations; however, they also made the deeper understanding of the problem domain possible. 
 
 
CONCLUSIONS 
 

uildings, structures and systems of large scale and high value are designed for a certain, limited service lifetime, 
taking the standards and guidelines of the time into account. The standards applied during the design process of a 
large-scale structure reflect the scientific and technological level of the previous years or decades. However, the 

standards and guidelines are evolving over time, and the goals and requirements may also change during the service time 
of the equipment. That means that the context of safe operation is part of an advancing world, where the meaning of 
safety must remain unchanged. 
During the last three decades, four large PTS studies have been conducted in Hungary. Each used different objectives and 
guides, and the Analysis methodology has also been changing. In the preceding paper, the conceptual model of PTS 
Structural Integrity calculations was presented. It was shown that using the conceptual model –that is based on the notion 
of typed graph-transformation systems– the calculations and their evolution can be described on a theoretical level. Using 
the model, the structure and the key aspects of a more proper description of the PTS Calculation methodology were 
presented, as follows: The main stages of this evolutionary process were: 
 The analyses performed by the manufacturer in the early 1980s; these calculations were based on engineering models, 

analyzed only a very limited set of thermal-hydraulic transients, used linear-elastic material models a Linear Elastic 
Fracture Mechanics (LEFM) methodology; the results of fracture mechanics evaluation were adequate. 

B 



 

T. Fekete, Frattura ed Integrità Strutturale, 36 (2016) 99-111; DOI: 10.3221/IGF-ESIS.36.10                                                                                
 

110 
 

 The analyses performed in Hungary during the second half of the 1980s were based on an analytical solution of the 
underlying thermo-elastic problem. The overcooling sequences were selected based on engineering judgments, and 
this resulted in a limited set of transients. The Structural Mechanics calculations were based on the ‘force method’ that 
has been widely used in mechanical engineering since the early days of the field of strength of materials. The fracture 
mechanics module worked with LEFM methodology. The ageing characteristics of structural materials were derived 
from the experimental results of the surveillance program. 

 The PTS project conducted in the first half of the 1990s made a larger effort in selecting the overcooling sequences 
and their assessments. This lead to a larger set of transients and results, so the reliability of results increased. The 
analysis methodology was based on analytical solutions of the underlying problem. The fracture mechanics module 
worked with LEFM methodology. The ageing characteristics of structural materials were derived from the 
experimental results of the surveillance program. 

 After the Millennium, the numerical problem-solving methodology has been changed fundamentally, as higher-
capacity IT infrastructure and large-scale FE software tools became available. A more detailed FE model has been 
developed and tested. The team developed a simpler linear model of the RPV and a more detailed model for studying 
the plastic effects occurring during PTS transients. The number of overcooling sequences has increased significantly. 
The neutron-transport calculations provided more precise results concerning neutron-physics data. That made it 
possible for the ageing assessments to lower the uncertainty of results. The increasing number of selected transients 
and the more complex models led to more resource-demanding calculations; however, they also made the deeper 
understanding of the problem domain possible. For lack of space, a more detailed presentation of results is left for 
future publications. 

The main conclusion of the review of the various PTS projects carried out in Hungary during the last three decades is that 
in projects with industrial relevance, both the simplified engineering models and the highly sophisticated simulation tools 
have their own application domain; in each project it is the responsibility of the analysts to find a balance between the 
goals of the study; the complexity of the approach chosen for problem-solving; the available resources; and the time 
limits. The purpose of the research is to achieve a deeper understanding of the problem and develop robust engineering 
tools that can be used in later projects. 
 
 
ACKNOWLEDGMENT 
 

he kind help of Dr. J. Gadó and Dr. F. Gillemot for many years is gratefully acknowledged. The support of Dr. Á. 
Horváth, Prof. P. Trampus and Prof. L. Tóth is thankfully acknowledged. The work of L. Tatár, D. Antók and J. 
Pirkó is kindly acknowledged. 

 
 
REFERENCES 
 
[1] Blauel, J.G. et. al., An Updated and extended Safety Analysis for the Reactor Pressure Vessel of the Nuclear Power 

Plant Stade (KKS). in: F. Gillemot (Editor) IAEA Specialist's Meeting on Integrity of Pressure Components of 
Reactor Systems. Paks 1992 May. IAEA, Vienna, (1993) 15–26. 

[2] Fekete, T., Methodological Developments in the Field of Structural Integrity Analyses of Large Scale Reactor 
Pressure Vessels in Hungary, Frattura ed Integrità Strutturale, 36 (2016) 79-99; DOI: 10.3221/IGF-ESIS.36.09. 

[3] HAEA, Evaluation of brittle-fracture resistance of VVER-440/213 reactor pressure vessel for normal operation, 
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[4] IAEA, Guidelines on Pressurized Thermal Shock Analysis for WWER Nuclear Power Plants Revision 1, IAEA-EBP-
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[5] Iskander, K., et al.; Reactor Pressure Vessel Structural Implications of Embrittlement to the Pressurized-Thermal 
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[6] Marie, S., Menager, Y., Chapuliot, S., Stress intensity factors for underclad and through clad defects in a reactor 
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[7] Marie, S., Chapuliot, S., Improvement of the calculation of the stress intensity factors for underclad and through-clad 
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                                                                           T. Fekete, Frattura ed Integrità Strutturale, 36 (2016) 99-111; DOI: 10.3221/IGF-ESIS.36.10 
 

111 
 

[8] PNAE G-7-002-86: Equipment and pipelines strength analysis norms for nuclear power plants, (in Russian), 
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    /NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken die zijn geoptimaliseerd voor prepress-afdrukken van hoge kwaliteit. De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 5.0 en hoger.)
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    /ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing.  Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.)
  >>
  /Namespace [
    (Adobe)
    (Common)
    (1.0)
  ]
  /OtherNamespaces [
    <<
      /AsReaderSpreads false
      /CropImagesToFrames true
      /ErrorControl /WarnAndContinue
      /FlattenerIgnoreSpreadOverrides false
      /IncludeGuidesGrids false
      /IncludeNonPrinting false
      /IncludeSlug false
      /Namespace [
        (Adobe)
        (InDesign)
        (4.0)
      ]
      /OmitPlacedBitmaps false
      /OmitPlacedEPS false
      /OmitPlacedPDF false
      /SimulateOverprint /Legacy
    >>
    <<
      /AddBleedMarks false
      /AddColorBars false
      /AddCropMarks false
      /AddPageInfo false
      /AddRegMarks false
      /ConvertColors /ConvertToCMYK
      /DestinationProfileName ()
      /DestinationProfileSelector /DocumentCMYK
      /Downsample16BitImages true
      /FlattenerPreset <<
        /PresetSelector /MediumResolution
      >>
      /FormElements false
      /GenerateStructure false
      /IncludeBookmarks false
      /IncludeHyperlinks false
      /IncludeInteractive false
      /IncludeLayers false
      /IncludeProfiles false
      /MultimediaHandling /UseObjectSettings
      /Namespace [
        (Adobe)
        (CreativeSuite)
        (2.0)
      ]
      /PDFXOutputIntentProfileSelector /DocumentCMYK
      /PreserveEditing true
      /UntaggedCMYKHandling /LeaveUntagged
      /UntaggedRGBHandling /UseDocumentProfile
      /UseDocumentBleed false
    >>
  ]
>> setdistillerparams
<<
  /HWResolution [2400 2400]
  /PageSize [612.000 792.000]
>> setpagedevice