Leon Cizelj

Automatic finite element meshing of planar Voronoi tessellations

Abstract The concept of Voronoi tessellation has recently been extensively used in materials science, especially to model the geometrical features of random microstructures like aggregates of grains in polycrystals, patterns of intergranular cracks and composites. Solution of the underlying field equations usually requires use of numerical methods such as finite elements. The framework for automatic generation of quadrilateral finite element meshing of planar Voronoi tessellation is proposed in the paper, resulting in a powerful set of tools to be used in the rather wide field of micromechanics. As far as feasible, the implementation of features built in commercially available mesh generators was pursued. Additionally, the minimum geometric requirements for a “meshable” tessellation are outlined. Special attention is given to the meshes, which enable explicit modelling of grain boundary processes, such as for example contact (closure of cracks) or friction between grains. This is inline with numerical examples, which are oriented towards the fracture mechanics, in particular to the development of intergranular microcracks and/or their impact on the effective behaviour of the polycrystal. The examples were evaluated using the commercially available general-purpose finite element code abaqus . The usual continuum mechanics based numerical methods and boundary conditions were safely applied to aggregates of randomly oriented polycrystals with anisotropic elastic material behaviour as computational domains.

Application of first and second order reliability methods in the safety assessment of cracked steam generator tubing

Abstract The First- and Second Order Reliability Methods (FORM and SORM) have been applied in the safety assessment of steam generator tubes with through-wall axial stress corrosion cracks. The underlying probabilistic fracture mechanics model takes into account the scatter in tube geometry, material properties and stable crack propagation. Also, the effect of the maintenance strategy has been considered. A realistic numerical example has been given to compare the failure probabilities calculated by FORM and SORM to those obtained by different versions of Monte Carlo simulations. The relative errors of the numerical methods employed have been analysed, which has shown that FORM performs in an acceptable and SORM in an excellent manner. Some changes in failure surface properties, caused by different maintenance strategies, are indicated and a sensitivity analysis of influencing parameters is made. The results obtained demonstrate the applicability of FORM and SORM in the safety assessment of stress corrosion cracked steam generator tubing.

Propagation of stress corrosion cracks in steam generator tubes

Abstract A model suitable to describe the propagation of stress corrosion cracks in steam generator tubes made of Inconel-600 is proposed in this paper. It concentrates on axial cracks located in the tube expansion transition zones which are assumed to be through-wall. The residual stress field is therefore considered as the major contributing factor driving short cracks while operational stresses dominate the growth of longer cracks. An estimate of residual hoop stresses is obtained using a non-linear finite element simulation of the tube to tube-sheet rolling process. Scatter of the residual stresses due to the stochastic variations of the dominant influencing parameters was studied. The crack propagation model utilizes linear-elastic fracture mechanics theory. In particular, both crack tips are modelled to propagate with different velocities due to the highly asymmetric stress field. Provisions are also made to account for the reactor coolant temperature and chemical composition effects. The model performance is demonstrated by a numerical example considering the crack propagation data from D4 steam generators during a 15 month operational cycle as recorded by subsequent non-destructive tube examinations.

Reliability of steam generator tubes with axial cracks

An approach for estimating the failure probability of tubes containing through-wall axial cracks has already been proposed by the authors. It is based on probabilistic fracture mechanics and accounts for scatter in tube geometry and material properties, scatter in residual and operational stresses responsible for crack propagation, and characteristics of nondestructive examination and plugging procedures (e.g., detection probability, sizing accuracy, human errors). Results of preliminary tests demonstrated wide applicability of this approach and triggered some improvements. The additions to the model are extensively discussed in this paper. Capabilities are demonstrated by results of analysis of steam generator no. 1 in Slovenian nuclear power plant located in Krsko after the 1992 inspection and plugging campaign. First, the number of cracked tubes and the crack length distribution were estimated using data obtained by the 100-percent motorized pancake coil inspection. The inspection and plugging activities were simulated in the second step to estimate the efficiency of maintenance in terms of single and multiple-tube rupture probabilities. They were calculated as a function of maximum allowable crack length. The importance of human errors and some limitations of present nondestructive examination techniques were identified. The traditional wall thickness and crack-length-based plugging criteria are compared. The crack-length-based criterion is shown to be more efficient and more safe, especially because of strong suppression effect on probability of multiple-tube rupture. The results are considered to be important for safety and maintenance of existing plants and for further research.

Intergranular stress distributions in polycrystalline aggregates of irradiated stainless steel

Abstract In order to predict InterGranular Stress Corrosion Cracking (IGSCC) of post-irradiated austenitic stainless steel in Light Water Reactor (LWR) environment, reliable predictions of intergranular stresses are required. Finite elements simulations have been performed on realistic polycrystalline aggregate with recently proposed physically-based crystal plasticity constitutive equations validated for neutron-irradiated austenitic stainless steel. Intergranular normal stress probability density functions are found with respect to plastic strain and irradiation level, for uniaxial loading conditions. In addition, plastic slip activity jumps at grain boundaries are also presented. Intergranular normal stress distributions describe, from a statistical point of view, the potential increase of intergranular stress with respect to the macroscopic stress due to grain-grain interactions. The distributions are shown to be well described by a master curve once rescaled by the macroscopic stress, in the range of irradiation level and strain considered in this study. The upper tail of this master curve is shown to be insensitive to free surface effect, which is relevant for IGSCC predictions, and also relatively insensitive to small perturbations in crystallographic texture, but sensitive to grain shapes.

Safety and availability of steam generator tubes affected by secondary side corrosion

The outside diameter stress corrosion cracking at tube support plates became the dominating ageing mechanism in steam generator tubes made of Inconel 600. A variety of maintenance approaches were developed and implemented world-wide to enable safe and reliable plant operation with affected tubes. Despite different philosophical and physical backgrounds involved, all applied approaches satisfy relevant regulatory requirements. The main goal followed in this paper is to quantify the degree of safety which is achieved through the implementation of selected maintenance approaches. A method is proposed which measures the operational safety and availability through three efficiency parameters: probability of steam generator tube rupture; predicted accidental leak rates through the defects in the tube bundle; and number of plugged tubes. An original probabilistic model quantifies the probability of tube rupture, while procedures available in literature were used to evaluate the accidental leak rates. A numerical example is based on data from the Krsko NPP (PWR 623 MWe). The maintenance strategies analyzed are: (a) traditional defect depth (40%) plugging criterion; (b) alternate plugging criterion (bobbin coil voltage as defined by EPRI and US NRC); (c) combination of traditional and alternate plugging criteria; and (d) no plugging at all. Advantages of the defect specific approaches (b) and (c) over the traditional one (a) are clearly shown. The efficiency of the traditional approach (a) is shown to be comparable to the no plugging at all approach (d). Finally, a sensitivity analysis aimed at ranking of the input parameters is presented. Uncertain failure models are shown to be the major contributor to the scatter of obtained results.

Vulnerability Analysis of a Nuclear Power Plant Considering Detonations of Explosive Devices

The needs for vulnerability analyses picked up the pace after the military threats to a nuclear power plant in the year 1991 and after the 9/11 events in 2001. The methodology which was proposed for complex assessment of possible consequences following a deliberate damage, shortly after the year 1991 is here further developed to correspond to requests for further studies identified after the events 9/11. The new methodology integrates phenomenological models of the cause of damage, material strength and injuries of human beings with nuclear power plant models used in probabilistic safety assessment. The damage source studied is an explosion of a device brought to the location by land transport. The description of the method and its results are only illustrative and not very detailed in order that the results cannot be used for malicious purposes. A straightforward example analyzing the response of a simplified process facility to a ground explosion outside the building is shown, although the methodology was tested also on a power plant. The results indicate that sizable explosions are required to inflict any damage to the reinforced concrete walls. Much larger explosions are needed to break the equipment behind such walls. The performed analysis shows that the facility can be even better secured at relatively low costs.

Modelling the early development of secondary side stress corrosion cracks in steam generator tubes using incomplete random tessellation

Abstract A thorough understanding of the secondary side stress corrosion cracking of Inconel 600 in steam generator (SG) tubes seems to be still somewhat in the future. Especially the early phase of the development of cracks, also called the initiation phase, is beyond the present state-of-the-art explanations. An effort was, therefore, made to propose modelling and visualisation of the kinetics of secondary side stress corrosion crack initiation and growth on the grain-size scale: • An incomplete random tessellation is used to approximate the random planar grain structure. • The crack initiation is modelled by random processes, taking into account the most important factors such as proximity of the aggressive medium and the orientation of the grain boundaries relative to the stress field. • The stochastic process describing crack growth accounts for crack branching, coalescence and interference between neighbouring cracks. Several numerical examples are provided to demonstrate the versatility of the proposed method. Reasonable qualitative agreement with metallographic results is shown.

Probabilistic assessment of excessive leakage through steam generator tubes degraded by secondary side corrosion

Abstract A probabilistic approach aimed at predicting the probability of excessive leakage through degraded steam generator (SG) tubes is proposed in the paper. The excessive leakage is assumed to occur during postulated hypothetical accidental conditions when the sum of all individual leak rates through degraded tubes exceeds the predefined acceptable value. The leak rates through the individual defects were evaluated using models developed by EPRI for assessment of outside diameter stress corrosion cracking (ODSCC) at the tube support plate intersections. Additionally, a brief description of the procedures which are used in the field to obtain conservative estimates of the total leak rate under accident conditions is given. The conservativeness of those methods is quantified through failure probability in the numerical examples. Two numerical examples are provided. They are based on inspection data obtained from Slovene and Belgian plants with 3/4 in. tubes made of Inconel 600 MA. The numerical examples analyze the behavior of the model for both small ( 10 V). The discussion of the results includes: (i) prediction and discussion of the probability of excessive leakage; (ii) the conservativeness of the approximate summation procedures used in the field to obtain conservative estimates of the total leak rate under accident conditions; (iii) some comments on the sensitivity of the probability of excessive leakage to the major uncertainties inherent in the data and models used. As a conclusion, some suggestions to improve both the efficiency of the numerical procedures and models used to estimate the leak rates through individual defects are given.

Failure probability of axially cracked steam generator tubes; A probabilistic fracture mechanics model

In this paper a model for estimating the failure probability of axially cracked steam generator tubes is proposed. The model compares observed crack length distribution with critical crack length distribution by means of probabilistic fracture mechanics. The observed crack length is influenced by measured data, measurement reliability, sizing accuracy, and predicted crack growth rate. The critical crack length is defined by a deterministic mechanical model. All cracks are conservatively assumed to extend through the tube wall. The effect of the plugging limit is studied along with the number of cracked tubes to perform risk-based lifetime optimization of steam generators. A numerical example presented considers hypothetical accidental operating conditions during a feedwater line break.