Jai Hak Park

Simulation of stress corrosion crack growth in steam generator tubes

Abstract Assuming a small axial surface crack inside a steam generate (S/G) tube, stress corrosion crack growth is simulated by using finite element method. Pressure difference and residual stresses induced from the roll expansion are considered as applied forces and Scotts crack growth equation based on the stress intensity factor is used. Stress intensity factor distribution along crack front, variation of crack shape and crack growth rate are obtained during the crack growth. From the results, it is noted that for the given residual stress distribution, variation curve of the crack aspect ratio during the crack growth is uniquely determined. In addition, the curve shows nearly constant crack aspect ratio during the initial crack growth stage. When adjacently growing two small cracks are coalesced to form a longer crack, the growth rate of crack depth is increasing but that of crack length is decreasing, and the crack aspect ratio is converging to the original variation curve during the subsequent crack growth.

Reconsideration of the Allowable Local Thickness of Straight Pipes in ASME CC N-597

It becomes a hot issue to assess the structural integrity of thin-walled pipes and pipe items. ASME Section XI Code Case N597-2 [1] provides a criterion for acceptance of the pipes. But the code has several limitations for application and sometimes gives too conservative or non-conservative results. So works are in progress to modify and extend the code. For that purpose it is necessary to understand fully the technical bases of the code. In this paper technical bases were explained and the equations in the code were derived for the allowable local thickness of straight pipes. In N-597 code, the allowable local thickness of a thinned straight pipe is given for three different methods. Because of the different technical base, each method gives different thickness values and sometimes gives contradictory values. So in this paper attempts were made in order to propose a unified rule for the allowable local thickness and in order to remove or relax the restrictions on the application of the code. For this purpose elastic stress analyses were made using the finite element method and the stress results were examined. Based on the obtained bending stress results, a very simple procedure was proposed to obtain the consistent allowable local thickness for the thinned straight pipes.Copyright

Probability of Burst in Steam Generator Tubes Using Monte Carlo Method

A statistical assessment model for structural integrity of steam generator tubes was proposed using Monte Carlo method. The growth of flaws in steam generator tubes was predicted using statistical approaches. The statistical parameters that represent the characteristics of flaw growth and initiation were derived from in-service inspection (ISI) non-destructive evaluation (NDE) data. Based on the statistical approaches, flaw growth models were proposed and applied to predict distribution of flaw size at the end of cycle (EOC). Because NDE measurement results differ from that of real ones in steam generator tubes, a simple method for predicting the physical number of flaws from periodic in-service inspection data was proposed. The probabilistic flaw growth rate was calculated from the in-service non-destructive inspection data. And the statistical growth of flaw was simulated using the Monte Carlo method. Probabilistic distributions of the flaw size and the probability of burst were obtained from numerously repeated simulations using the proposed assessment model.Copyright

Development of a Code for 2D Elasto-Plastic Fracture Mechanics Analyses Using the Finite Element Alternating Method

The development of an efficient and accurate crack analysis method remains an important task to ensure safe operation and economical efficiency of structures. A robust code is developed, based on the finite element alternating method (FEAM), to obtain fracture mechanics parameters such as stress intensity factors and J-integrals in two dimensional stress fields. Necessary analytical elastic solutions are obtained by solving the integral equations formulated by Cheung and Chen. For elasto-plastic analysis of curved cracks the initial stress method proposed by Zienkiewicz and co-workers and the iteration procedure proposed by Nikishkov and Atluri are used after modification. In the finite element method for cracked structures, Modeling of crack mesh demands great time and effort but is inevitably required for appropriate solution. But the solution of the developed code is obtained in an iteration procedure, which alternates independently between finite element method (FEM) solution for the uncracked body, and the analytical solution for the crack in an infinite body. In order to check the accuracy and efficiency of the proposed method, several example problems are solved and compared with published solutions and finite element analysis solutions. Introduction Many crack analysis methods have been suggested for the structural integrity assessment. But an efficient and accurate method is demanded until now because of drawbacks and limitations of each method. The analytical method gives accurate crack tip stress fields and stress intensity factors, but the method can be applied only for a body with simple geometry and loading conditions. On the other hand, the numerical method can consider complex geometries easily but it takes much time to include cracks in the model. The finite element alternating method intends to use the benefits of the two methods. The finite element alternating method (FEAM) has been known to be an effective method for obtaining accurate fracture mechanics parameters such as stress intensity factors (SIF) [1,2]. And the method is extended further in order to solve general problems with arbitrarily shaped cracks. The required analytical solution for an arbitrarily curved crack in an infinite isotropic plate is obtained by solving the integral equations formulated by Cheung and Chen [3,4]. Park, Atluri and Nikishkov [5,6,13] solved three-dimensional cracks and multiple curved cracks. Kim and Park [7] further extended the method for multiple curvilinear cracks in an orthotropic plate. The FEAM code developed in this paper can be applied to obtain the SIF values for general multiple collinear or curvilinear cracks in an isotropic or orthotropic plate. Elasto-plastic alternating algorithm proposed by Nikishkov and Atluri [8] is modified for elasto-plastic analysis of multiple cracks. Also this code is very effective for fatigue crack growth simulation of multiple curved cracks. In order to verify the usefulness of the developed code, several example problems are solved. The obtained stress intensity factors and stress fields are compared with other results obtained from published references and commercial FEM programs. Key Engineering Materials Online: 2004-08-15 ISSN: 1662-9795, Vols. 270-273, pp 1159-1164 doi:10.4028/www.scientific.net/KEM.270-273.1159

Analysis of Burst Pressure of Damaged Tubes Using Plastic Instability Analysis

Generally rupture of steam generator tubes occurs accompanying significant plastic deformation. In this study, the burst pressure of a damaged steam generator tube is calculated from the plastic instability analysis using the finite element method. Two wear types, flat and circumferential types are considered. An equation for the burst pressure is proposed by using the concept of strength reduction factor and the Svensson equation. The analysis results are also compared with the experiment data from published references and they show a good agreement with the experiment data.

Elasto-Plastic Analysis of 3-D Inner Cracks Using the Finite Element Alternating Method

The finite element alternating method (FEAM) was extended to obtain fracture mechanics parameters and elasto-plastic stress fields for 3-D inner cracks. For solving a problem of a 3-D finite body with cracks, the FEAM alternates independently the finite element method (FEM) solution for the uncracked body and the solution for the crack in an infinite body. As the required solution for a crack in an infinite body, the symmetric Galerkin boundary element method formulated by Li and Mear was used. For elasto-plastic numerical analysis, the initial stress method proposed by Zienkiewicz and co-workers and the iteration procedure proposed by Nikishkov and Atluri were used after modification. The extended FEAM was examined through comparing with the results of commercial FEM program for several example 3-D crack problems.

Estimation of the Number of Physical Flaws from Periodic ISI Data of SG Tubes Using Effective POD

It is necessary to know the number of flaws and their size distribution in order to calculate the probability of failure or to estimate the amount of leakage through the tube wall of steam generators. But in-service inspection (ISI) flaw data is different from the physical flaw data. In case of a single inspection, it is easy to estimate the number of physical flaws using the POD curve. However, we may be faced with some difficulties in obtaining the number of physical flaws from the periodic in-service inspection data. In this study a simple method for estimating the number of physical flaws from periodic in-service inspection data is proposed. In order to obtain the flaw growth history, the flaw growth is simulated using the Monte Carlo method and the flaw size and the corresponding POD value are obtained for each flaw at each periodic inspection time. The flaw growth rate used in the simulation is statistically calculated from the in-service inspection data. By repeating the simulation numerous flaw growth data can be generated and the effective POD curve can be obtained as a function of flaw size. From the effective POD curve the number of physical flaws and their size distributions are obtained. The effective POD value is affected by flaw growth rate and POD of the used inspection method. The usefulness and convenience of the proposed method is evaluated from several applications and satisfactory results are obtained.

Analysis of Three-Dimensional Cracks with Independent Crack Mesh

In order to simulate the growth of arbitrarily shaped three-dimensional cracks, the finite element alternating method is extended. As the required solution for a crack in an infinite body, the symmetric Galerkin boundary element method formulated by Li and Mear is used. In the study, a crack is modeled as distribution of displacement discontinuities, and the governing equation is formulated as singularity-reduced integral equations. With the proposed method several example problems, such as a penny-shaped crack, an elliptical crack in an infinite solid and a semi-elliptical surface crack in an elbow are solved. And their growth under fatigue loading is also considered and the accuracy and efficiency of the method are demonstrated.

Finite Element Alternating Method for Solving Two-Dimensional Cracks Embedded in a Bimaterial Body

The finite element alternating method based on the superposition principle has been known as an effective method to obtain the stress intensity factors for general multiple collinear or curvilinear cracks in an isotropic plate. In this paper the method is extended further to solve two-dimensional cracks embedded in a bimaterial plate. The main advantage of this method is that it is not necessary to make crack meshes considering the stress singularity at the crack tip. The solution of the developed code is obtained from an iteration procedure, which alternates independently between the finite element method solution for an uncracked body and the analytical solution for cracks in an infinite body. In order to check the validity of the method, several crack problems of a bimaterial body are solved and compared with the results obtained from the finite element analysis.

Crack Growth Simulation of Arbitrarily Shaped 3D Cracks Using Finite Element Alternating Method

In order to simulate the growth of arbitrarily shaped three dimensional cracks, the finite element alternating method is extended. As the required analytical solution for a crack in an infinite body, the symmetric Galerkin boundary element method formulated by Li and Mear is used. In the study, a crack is modeled as distribution of displacement discontinuities, and the governing equation is formulated as singularity-reduced integral equations. With the proposed method several example problems for three dimensional cracks in an infinite solid, as well as their growth under fatigue, are solved and the accuracy and efficiency of the method are demonstrated.