VERIFICATION ANALYSES FOR NEWLY DEVELOPED AUTOMATIC 3D FINITE ELEMENT CRACK PROPAGATION SYSTEM

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1 Proceedings of the ASME 214 Pressure Vessels & Piping Conference PVP214 July 2-24, 214, Anaheim, California, USA PVP VERIFICATION ANALYSES FOR NEWLY DEVELOPED AUTOMATIC 3D FINITE ELEMENT CRACK PROPAGATION SYSTEM Hiroaki Doi Nuclear Regulation Authority (NRA, Japan) Roppongi, Miantoku, Tokyo , Japan Hitoshi Nakamura ITOCHU Techno-Solutions Corp.(CTC) Kasumigaseki Chiyodaku, Tokyo 1-68, Japan Wenwei Gu ITOCHU Techno-Solutions Corp.(CTC) Kasumigaseki Chiyodaku, Tokyo 1-68, Japan Do-Jun Shim Engineering Mechanics Corporation of Columbus 3518 Riverside Drive, Suite 22 Columbus, Ohio, USA Gery Wilkowski Engineering Mechanics Corporation of Columbus 3518 Riverside Drive, Suite 22 Columbus, Ohio, USA ABSTRACT In order to calculate the crack propagation in complicatedshaped locations in components such as weld in penetration structures of reactor pressure vessel of nuclear power plants, an automatic 3D finite element crack propagation system (CRACK-FEM) has been developed by the Nuclear Regulation Authority (NRA, Japan). To confirm the accuracy and effectiveness of this analysis system, a verification analysis was performed. The program used for comparison is PipeFracCAE developed by Engineering Mechanics Corporation of Columbus, which has been used for many crack propagation analyses in various applications. In this paper, the axial crack propagation analysis for primary water stress corrosion cracking (PWSCC) in a steam generator inlet nozzle of a pressurized water reactor (PWR) plant is presented. The results demonstrate that the two codes are in good agreement. The contents of this paper were conducted as a research project of the Japan Nuclear Energy Safety Organization (JNES) when one of the authors (Doi) belongs to JNES. After this project, JNES was abolished and its staff and task were absorbed into NRA on March 1, 214. INTRODUCTION About one third of the nuclear power plants in Japan have been operated for more than 3 years and cracks produced by stress corrosion cracking (SCC) have been detected in various components during in-service inspections in recent years. Therefore, it is becoming increasingly important to predict the lifetime of the components subjected to crack propagation initiated from detected cracks in order to decide the timing of repairing the components for maintaining the integrity of the plant. In order to calculate the crack propagation in complicatedshaped components such as weld in penetration structures of reactor pressure vessel, an automatic 3D finite element crack propagation system CRACK-FEM has been developed by the Nuclear Regulation Authority (NRA, Japan). We explained the structure and functions of the system. Also, we calculated stress intensity factors (SIF) for basic problems such as a tension of circular crack by the CRACK-FEM and compared them with analytical values to confirm the accuracy of the CRACK-FEM [1]. However, for crack propagation in complicated-shaped components, it is not easy to confirm the results of the CRACK-FEM, because cracks in such components tend to have random shapes, whereas only the SIF for cracks having an elliptical or semielliptical shape in a simple shaped component are available in the literature. Therefore, we decided to make a comparison analysis between the CRACK-FEM and other crack propagation program. However, crack propagation program practically used was much limited. NRA found a crack propagation program: the PipeFracCAE developed by Engineering Mechanics Corporation of Columbus, which has been used for many crack propagation analyses in various 1 Copyright 214 by ASME

2 applications [2]. NRA conducted a verification analysis and compared the result with that of the PipeFracCAE. The PipeFracCAE makes the crack propagation analyses for pipes. Therefore, we selected an axial crack propagation analysis for primary water stress corrosion cracking (PWSCC) in a steam generator inlet nozzle of a pressurized water reactor (PWR) plant as a verification problem. Since this problem deals with pipes. In this paper, we present this verification problem. Because a PWSCC crack propagates only in the weld, the shape of the propagated crack shape is affected by the weld boundary. FEA analysis is indispensable for analyzing this crack propagation, and so the problem is practically important for the CRACK- FEM. The contents of this paper were conducted as a research project of the Japan Nuclear Energy Safety Organization (JNES) when one of the authors (Doi) belongs to JNES. After this project, JNES was abolished and its staff and task were absorbed into NRA on March 1, 214. Data Input Analysis Step Mesh Generation Stress Analysis Stress Intensity Factor Calculation Crack Propagation Calculation Data Output Propagated Crack Shape OUTLINE OF CRACK-FEM Figure 1 shows the flow chart of the CRACK-FEM. First, data for the crack propagation analysis are inputted. The total time for the estimation is divided into multiple successive periods, which correspond to analysis steps in CRACK-FEM. In each analysis step, the increase in crack size produced in the period is calculated as follows. The CRACK-FEM automatically generates meshes of the analysis object with initial cracks or propagated cracks at the first step or each analysis step respectively. Stress analyses are then conducted for these meshes using a commercially-available finite element analysis (FEA) stress analysis code (ABAQUS and FINAS/STAR) for all the stresses (for SCC cracks) and stress ranges (for fatigue cracks) acting on the crack in the period. SIFs used to estimate the increase in crack size are calculated using these stress analysis results. The analysis steps are repeated for the analysis object with propagated cracks until the end of the period of estimation. FEA MESH AND METHOD OF SIF CALCULATION USED IN CRACK-FEM FEA meshes with hexahedron elements are usually necessary for three-dimensional crack propagation analyses to ensure the analysis accuracy of the SIF solution. The use of hexahedron meshes, however, restricts the scope of application of the system, because hexahedron (re)meshing is not always possible for complicated geometries. The CRACK-FEM can use three different methods of SIF calculation, thus avoiding the problem of hexahedron automeshing. Figure 1 Flow chart of CRACK-FEM Table 1 indicates these methods of SIF calculation and the FEA meshes used for each method. The methods are the Virtual Crack Extension Method (VCEM), the Virtual Crack Closure Integral Method (VCCM) [3] and the Domain Integral Method (DIM) [4]. VCEM uses tetrahedron elements and hexahedron elements, VCCM and DIM use only tetrahedron elements. Figure 2 shows an example of FEA meshes for each SIF calculation method in CRACK-FEM. The FEA mesh of VCEM and VCCM have a doughnut-like domain surrounding the crack front. In this domain, hexahedron elements and tetrahedron elements are used for VCEM and VCCM, respectively. CRACK PROPAGATION CALCULATION IN CRACK- FEM The crack advance at each node on the crack front line is calculated from the obtained stress intensity factor using the crack growth rate characteristics in the CRACK-FEM. The crack advance at each node is assumed to have the normal direction of the front line. The new crack front line is determined from the previous crack front line using the crack advance for all the nodes on the crack line. 2 Copyright 214 by ASME

3 No. A Table 1 Method of SIF calculation and FEA mesh Method of Calcurating Stress Intensity Factor Virtual Crack Extension Method (VCEM) Element Type 1 node Tetrahedron Element and 2 node Hexahedron Element Stress Analysis Code ABAQUS and FINAS/STAR AXIAL CRACK PROPAGATION ANALYSIS FOR A PWSCC IN A STEAM GENERATOR INLET NOZZLE OF A PWR PLANT Analysis Model B C Virtual Crack Closure-Integral Method (VCCM) 1 node Tetrahedron Element ABAQUS Domain Integral Method (DIM) 1 node Tetrahedron Element Crack front ABAQUS and FINAS/STAR Figure 3 shows a cross-sectional drawing of a steam generator inlet nozzle of a PWR plant used for the crack propagation verification analysis. The outer diameter D o is 94 mm and the thickness t is 81 mm for the weld part of the inlet nozzle. An initial crack with a depth of a = 1.5 mm and length of 2c = 9 mm is assumed on the inner surface of the welding and buttering area at the central position. The welding and buttering is made of Ni-based alloy. The safe end and cladding are made of stainless steel and the nozzle is made of low alloy steel. Since only Ni-based alloy has sensitivity to PWSCC crack propagation, the PWSCC crack propagates in the welding and the buttering of the Ni-based alloy but does not go through the boundaries formed between the Ni-based alloy and other materials. The rate of PWSCC crack growth used in the crack propagation analysis is given by [5]: da at = K 2.24 where, da/dt is crack growth rate (m/s) and K is SIF (MPa m). (a)vcem Do=94mm t=81mm Crack front 2Cladding 1Nozzle 4Welding(Ni-based Alloy) (b)vccm Initial crack 5Safe End Growing crack Crack front Figure 3 Cross-sectional drawing of steam generator inlet nozzle of PWR plant Applied Stress (c)dim Figure 2 Example of FEA mesh for three SIF calculation method in CRACK-FEM Internal pressure of 15.4 MPa and weld residual stress were considered for the PWSCC crack propagation. The internal pressure was applied on the inner surface of the inlet nozzle and on the crack surfaces. Also, the pressure was applied to the inlet nozzle as an axial stress. Figure 4 shows the distribution of the weld residual stress applied to the crack which was determined from measured data. 3 Copyright 214 by ASME

4 Weld Residual Stress (MPa) Normalized distance from the inner surface the crack propagation results, the three methods of SIF calculation of the CRACK-FEM and PipeFracCAE show fairy good agreement. Looking into the detail among these, the VCCM of CRACK-FEM shows the fastest crack propagation and the PipeFracCAE shows the slowest crack propagation. The example of difference in time to reach a crack length (4mm) and a depth (2mm) for the two results are approximately 5%. The difference is probably due to the difference in the element type and mesh between them. The verification analysis results suggest that the three methods of SIF calculation of the CRACK-FEM have sufficient accuracy and effectiveness for practical applications. Figure 4 Weld residual stress distribution applied to crack Analysis Results The crack propagation analysis was made by the three methods of SIF calculation of the CRACK-FEM mentioned in the previous section and by the PipeFracCAE. The CRACK- FEM used ABAQUS as the FEA code. Figure 5 shows one of the meshes of the analysis object with initial crack for the CRACK-FEM (SIF calculation of VCEM). Although the number of nodes used for the analysis object changes slightly with propagating crack, the number of nodes used for them with the initial crack are about 47. Figure 6 shows the SIF distribution along the crack front line obtained by the CRACK- FEM, when the crack is in the initial condition. Although the SIF of DIM has small fluctuations, the distribution of the three methods of SIF calculation of CRACK-FEM agree well with each other. Figure 7 shows example results of crack growth and their meshes (SIF calculation of VCEM). Meshes of a doughnut-like domain of concentrically arranged hexahedron elements surrounding the crack front and other area made of tetrahedron elements are automatically produced. Figure 8 shows the example results of crack propagation and their meshes of the steam generator inlet nozzle by the PipeFracCAE. The PipeFracCAE uses mapped meshes with hexahedron elements and updates them during the crack propagation analyses. The PipeFracCAE used ABAQUS as the FEA stress analysis code. The SIF calculation method is VCEM (the post-processor of ABAQUS), the used crack growth rate and the applied stress are the same as those of the CRACK-FEM. The elements used are 8 node hexahedron elements, which is different from those used for the CRACK- FEM. Figure 9 shows the changes in the crack front line shape with time obtained from the crack propagation result by the CRACK-FEM (SIF calculation method is VCEM). The time used for each analysis (model producing and analysis) by the CRACK-FEM was about 5 hours using 2CPUs of the Intel Xeon processor (6cores, 2.93 GHz). Figures 1 and 11 show the changes in crack length and depth with time obtained from the crack propagation result by the CRACK-FEM and PipeFracCAE, respectively. In both of Crack Figure 5 Mesh of steam generator inlet nozzle with initial crack by CRACK-FEM 4 Copyright 214 by ASME

5 Stress intensity factor (MPa mm) CRACK-FEM(VCEM) 4 CRACK-FEM(DIM) 3 CRACK-FEM(VCCM) Positions at crack front (degree) ②Cladding Figure 6 Distribution of SIF by three methods of SIF calculation of CRACK-FEM Figure 8 Example result of propagated crack shapes and their meshes by PipeFracCAE ①Nozzle Outer surface Groove Groove Initial Crack front line 449 Doughnut-like domain 439 ④Welding ⑤Safe end 49 ②Cladding (a)about 7-year later (Years) Inner surface ①Nozzle Figure 9 Changes in crack front line shape with time by CRACK-FEM Crack front line Doughnut-like domain ④Welding ⑤Safe end (b)about 1-year later Figure 7 Example result of propagated crack shapes and their meshes by CRACK-FEM 5 Copyright 214 by ASME

6 Crack length( mm) 8 7 PipeFracCAE 6 CRACK-FEM(VCEM) CRACK-FEM(DIM) 5 CRACK-FEM(VCCM) 4 Width of Weld Time (years) Figure 1 Changes in crack length with time by CRACK- FEM and PipeFracCAE Crack depth (mm) 9 8 PipeFracCAE 7 CRACK-FEM(VCEM) 6 CRACK-FEM(DIM) 5 CRACK-FEM(VCCM) Pipe Thickness Time (years) Figure 11 Changes in crack depth with time by CRACK- FEM and PipeFracCAE SUMMARY This paper presented a verification analysis of the newly developed CRACK-FEM, and compared the results with those of the PipeFracCAE program. For verification, an axial crack propagation analysis for primary water stress corrosion cracking (PWSCC) in a steam generator inlet nozzle of a pressurized water reactor (PWR) plant was conducted. Because a PWSCC crack propagates only in the weld, the shape of the propagated crack is affected by the weld boundary. The results of this study demonstrated that the two codes are in good agreement, thus confirming the accuracy and effectiveness of the CRACK-FEM for practical applications. REFERENCES 1. Doi, H., Nakamura, H., Gu, W. and Okada, H., Development of an Automatic 3D Finite Element Crack Propagation System, 214, PVP , Anaheim, California, USA. 2. Shim, D.-J., Kalyanam, S., Punch, E., Zhang, T., Brust, F., Wilkowski, G., Goodfellow, A. and Smith, M., 21 Advanced Finite Element Analysis (AFEA) Evaluation for Circumferential and Axial PWSCC Defects, PVP , Bellevue, Washington, USA. 3. Okada, H., Kawai, H. and Araki, K., 28, A Virtual Crack Closure-Integral Method (VCCM) to Compute the Energy Release Rate and Stress Intensity Factors Based on Quadratic Tetrahedral Finite Elements, Engineering Fracture Mechanics, 75, pp , Elsevier. 4. Nagai, M., Ikeda, T. and Miyazaki, N., 27, Stress Intensity Factors Analyses of Three-Dimensional Interfacial Cracks Using Tetrahedral Finite Elements, Proceedings of The Japan Society for Computational Engineering and Science (in Japanese), 12, pp Japan Nuclear Energy Safety Organization, 25, Fiscal 25 Report on Investigation of Evaluation Technique for Stress Corrosion Cracking in Ni-Based Alloy (Constant Load Test), (in Japanese). 6 Copyright 214 by ASME