Improvement of the return mapping algorithm based on the implicit function theorem with application to ductile fracture analysis using the GTN model

Mano, Akihiro; Imai, Ryuta*; Miyamoto, Yuhei*; Lu, K.; Katsuyama, Jinya; Li, Y.

International Journal of Pressure Vessels and Piping, 199, p.104700_1 - 104700_13, 2022/10

https://doi.org/10.1016/j.ijpvp.2022.104700

Elastic-plastic analyses based on finite element methods are widely applied to simulate the nonlinear behaviors of materials. When the analysis is conducted by an implicit method, the stress values are generally updated with a time increment by using the so-called return mapping algorithm. This algorithm requires solving simultaneous nonlinear equations related to a constitutive model. In the present paper, we proposed a general method to reduce the number of equations in the return mapping algorithm based on the implicit function theorem. In addition, the proposed method was applied to the Gurson-Tvergaard-Needleman (GTN) model that considers the influence of damage due to nucleation and growth of microscopic void in materials in the simulation of the nonlinear behaviors. By using the GTN model with the proposed method, an elastic-plastic analysis was performed by the implicit method for a 4-point bending test of pipe with a through-wall crack. The numerical solution of the variation of the load-load line displacement from the analysis agreed with experimental result. Thus, we concluded that the proposed method is useful for simulating nonlinear behaviors, including void nucleation and growth in materials.

Event tree analysis for material relocation on core catcher in a sodium-cooled fast reactor

Yamano, Hidemasa; Kubo, Shigenobu; Kan, Taro*; Shibata, Akihiro*; Hourcade, E.*; Dirat, J. F.*

Proceedings of 29th International Conference on Nuclear Engineering (ICONE 29) (Internet), 10 Pages, 2022/08

In this paper, the approach to event tree development and the scope of the event tree analysis were described with key points on core catcher loading. For the analytical conditions, two core catcher loading conditions were given as bounding and conservative cases. For important heading of the event tree, key important phenomena were included: strong back design, fuel-coolant interaction and quench in the sodium plenum design, jet attack, criticality and coolability on the core catcher. In this paper, preliminary trial quantification was attempted using a probability ranking table which is based on engineering judgement. This event tree analysis has identified the dominant sequence, and clarified the effect of the core catcher loading and effectiveness of design measures. This study suggests that the criticality measure is very important for the core catcher study.

Failure estimation methods for steam generator tubes with wall-thinning or crack

Yamaguchi, Yoshihito; Mano, Akihiro; Li, Y.

Proceedings of ASME 2022 Pressure Vessels and Piping Conference (PVP 2022) (Internet), 10 Pages, 2022/07

The steam generator (SG) tube is one of the important components in pressurized water reactors. Flaws such as wall-thinning or stress corrosion cracking have been reported in SG tubes. The burst pressure where both the internal and external pressures from the primary and secondary coolant systems are considered must be predicted to assess the structural integrity of SG tubes. Burst tests were performed by various organizations. On the basis of the test results, failure estimation methods were proposed. In this study, previous burst test data and existing failure estimation methods for SG tubes with wall-thinning or crack were investigated. As a result, the coefficient of the existing estimation method for SG tube with uniform wall-thinning was updated. In addition, failure estimation methods that are suitable for SG tubes with crack or local wall-thinning were proposed by considering the effects of the flaw shape and size on the burst pressure. The applicability of the failure estimation methods was confirmed by comparing the predicted results with the burst test data in actual SG tubes.

CSNI leak-before-break benchmark; Summary of phase 1

Tregoning, R.*; Wallace, J.*; Bouydo, A.*; Costa-Garrido, O.*; Dillstrm, P.*; Duan, X.*; Heckmann, K.*; Kim, Y.-B.*; Kim, Y.*; Kurth-Twombly, E.*; et al.

Transactions of 26th International Conference on Structural Mechanics in Reactor Technology (SMiRT-26) (Internet), 11 Pages, 2022/07

Fourteen organizations, representing eleven countries, participated in a leak-before-break (LBB) benchmark exercise that compared results from analyses among participating countries and identified the effects of weld residual stress (WRS) and crack morphology on crack opening displacement (COD), critical bending moment (CBM), and leak rate (LR) results. The participants determined whether the initial problem would meet their country's LBB acceptance criteria and then evaluated the effects of crack morphology and WRS for a prescribed crack size, geometry and loading. Six out of fourteen participants indicated that the initial problem met their LBB requirements. In the follow-on tasks, differences among the participant's CBM predictions were principally due to the material properties used in the analysis while the type of failure model chosen contributed much less. Most of the differences in the LR predictions were directly attributable to differences among the COD models, but a portion was attributable to the treatment of crack face pressure (CFP). The benchmark identified several aspects of an LBB analysis that could support a more realistic evaluation.

Improvement of probabilistic fracture mechanics analysis code PASCAL-SP regarding stress corrosion cracking in nickel based alloy weld joint of piping system in boiling water reactor

Mano, Akihiro; Yamaguchi, Yoshihito; Katsuyama, Jinya; Li, Y.

Journal of Pressure Vessel Technology, 144(1), p.011506_1 - 011506_9, 2022/02

https://doi.org/10.1115/1.4052449

In the past few decades, the cracks because of stress corrosion cracking (SCC) have been detected in the dissimilar weld joints welded using nickel based alloy in piping system of boiling water reactors. Thus, the structural integrity assessment for such weld joints has become important. Nowadays, probabilistic fracture mechanics (PFM) analysis is recognized as a rational method for structural integrity assessment because it can consider inherent uncertainties of various influencing factors as probability distributions and quantitatively evaluate the failure probability of a cracked component. The Japan Atomic Energy Agency has developed a PFM analysis code PASCAL-SP for a probabilistic structural integrity assessment of weld joint in pipe in nuclear power plant. This study improves the analysis functions of PASCAL-SP for weld joint welded using nickel based alloy in boiling water reactor susceptible to SCC. As an analysis example of the improved version of PASCAL-SP, the failure probability of a weld joint is quantitatively evaluated. Furthermore, sensitivity analyses are conducted concerning the effect of leak detection and in-service inspection. From the analysis results, it is concluded that the improved version of PASCAL-SP is useful for structural integrity assessment.

A Novel method to uniquely determine the parameters in Gurson-Tvergaard-Needleman model

Zhang, T.; Lu, K.; Mano, Akihiro; Yamaguchi, Yoshihito; Katsuyama, Jinya; Li, Y.

Fatigue & Fracture of Engineering Materials & Structures, 44(12), p.3399 - 3415, 2021/12

https://doi.org/10.1111/ffe.13568

The Gurson-Tvergaard-Needleman (GTN) model is considered a promising approach in failure prediction as it takes the micromechanical behavior of ductile metals into consideration and its function exhibits a relatively clear physical meaning. Although the GTN model has been widely investigated in the past decades, its engineering applications have scarcely progressed due to the difficulty in determining the eight strongly coupled parameters. Based on the physical background of GTN model, a set of methods was established to determine the parameters in the GTN model. The knowledge of continuum damage mechanics was used to experimentally determine the development of void volume fraction through the variation of effective Young's modulus in a uniaxial tensile test, and three parameters regarding void nucleation were analytically derived using a newly established method. Other parameters in the GTN model were also uniquely determined through a joint use of the chemical composition analysis (for the initial void volume fraction), the cell model analyses (for the two constitutive parameters), and the inverse finite element method (for the two failure parameters). The reliability of this novel parameter determination method was verified through the failure prediction of both cracked and uncracked specimens of carbon steel STPT410.

User's manual and analysis methodology of probabilistic fracture mechanics analysis code PASCAL-SP Ver. 2 for piping (Contract research)

Yamaguchi, Yoshihito; Mano, Akihiro; Katsuyama, Jinya; Masaki, Koichi*; Miyamoto, Yuhei*; Li, Y.

JAEA-Data/Code 2020-021, 176 Pages, 2021/02

JAEA-Data-Code-2020-021.pdf:5.26MB

In Japan Atomic Energy Agency, as a part of researches on the structural integrity assessment and seismic safety assessment of aged components in nuclear power plants, a probabilistic fracture mechanics (PFM) analysis code PASCAL-SP (PFM Analysis of Structural Components in Aging LWR - Stress Corrosion Cracking at Welded Joints of Piping) has been developed to evaluate failure probability of piping. The initial version was released in 2010, and after that, the evaluation targets have been expanded and analysis functions have been improved based on the state-of-the art technology. Now, it is released as Ver. 2.0. In the latest version, primary water stress corrosion cracking in the environment of Pressurized Water Reactor, nickel based alloy stress corrosion cracking in the environment of Boiling Water Reactor, and thermal embrittlement can be taken into account as target age-related degradation. Also, many analysis functions have been improved such as incorporations of the latest stress intensity factor solutions and uncertainty evaluation model of weld residual stress. Moreover, seismic fragility evaluation function has been developed by introducing evaluation methods including crack growth analysis model considering excessive cyclic loading due to large earthquake. Furthermore, confidence level evaluation function has been incorporated by considering the epistemic and aleatory uncertainties related to influence parameters in the probabilistic evaluation. This report provides the user's manual and analysis methodology of PASCAL-SP Ver. 2.0.

Improved Bayesian update method on flaw distributions reflecting non-destructive inspection result

Katsuyama, Jinya; Miyamoto, Yuhei*; Lu, K.; Mano, Akihiro; Li, Y.

Proceedings of ASME 2020 Pressure Vessels and Piping Conference (PVP 2020) (Internet), 8 Pages, 2020/08

https://doi.org/10.1115/PVP2020-21430

We have developed a probabilistic fracture mechanics (PFM) analysis code PASCAL4 for evaluating failure frequency of reactor pressure vessels (RPVs). It is known that flaw distributions have an important role in failure frequency calculation in PFM analysis. Previously, we proposed likelihood function to obtain more realistic flaw distributions applicable for both case when flaws are detected and when there is no flaw indication as the inspection results based on Bayesian update methodology. Here, it can be applied to independently obtain posterior distributions of flaw depth and density. In this study, we improve the likelihood function to enable them to update flaw depth and density simultaneously. Based on the improved likelihood function, an example is presented in which flaw distributions are estimated by reflecting NDI results through Bayesian update and PFM analysis. The results indicate that the improved likelihood functions are useful for estimating flaw distributions.

A New probabilistic evaluation model for weld residual stress

Mano, Akihiro; Katsuyama, Jinya; Miyamoto, Yuhei*; Yamaguchi, Yoshihito; Li, Y.

International Journal of Pressure Vessels and Piping, 179, p.103945_1 - 103945_6, 2020/01

https://doi.org/10.1016/j.ijpvp.2019.103945

Weld residual stress (WRS) is one of the most important factors in the structural integrity assessment of piping welds, and it is considered a driving force for crack growth. It is characterized by large uncertainty. For more rational assessment, it is important to consider the uncertainty of WRS for evaluating crack growth behavior in probabilistic fracture mechanics (PFM) analysis. In existing PFM analysis codes, WRS uncertainty is set by statistically processing the results of multiple finite element analyses. This process depends on the individual performing PFM analysis, which may lead to uncertainties whose sources would be different from the original WRS. In this study, we developed a new WRS evaluation model based on Fourier transformation, and the model was incorporated into PASCAL-SP, which has been developed by Japan Atomic Energy Agency. Through improvements to the code, WRS uncertainty can be considered automatically and appropriately by inputting multiple WRS analysis results directly as input data for PFM analysis.

Improvement of probabilistic fracture mechanics analysis code PASCAL-SP with regard to PWSCC

Mano, Akihiro; Yamaguchi, Yoshihito; Katsuyama, Jinya; Li, Y.

Journal of Nuclear Engineering and Radiation Science, 5(3), p.031505_1 - 031505_8, 2019/07

https://doi.org/10.1115/1.4042115

Probabilistic fracture mechanics (PFM) analysis is expected as a rational method for the structural integrity assessment because it can consider the uncertainties of various influence factors and can evaluate the quantitative value such as failure probability of a cracked component as the solution. In the Japan Atomic Energy Agency, a PFM analysis code PASCAL-SP has been developed for the structural integrity assessment of piping welds in nuclear power plants. In the latest few decades, a number of cracks due to primary water stress corrosion cracking (PWSCC) have been detected in the nickel-based alloy welds in the primary piping of pressurized water reactors (PWRs). Thus the structural integrity assessment taking account of PWSCC has become important. In this paper, we improved PASCAL-SP for the assessment considering PWSCC by introducing the several analytical functions such as the evaluation models of crack initiation time, crack growth rate and probability of crack detection. By using improved PASCAL-SP, the failure probabilities of pipes with a circumferential crack or an axial crack due to PWSCC were evaluated as numerical examples. We also evaluated the influence of a leak detection and a non-destructive examination on the failure probabilities. On the basis of the numerical results, we concluded that the improved PASCAL-SP is useful for evaluating the failure probability of pipe taking PWSCC into account.