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.

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.

An Estimation method of flaw distributions reflecting inspection results through Bayesian update

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

Proceedings of Asian Symposium on Risk Assessment and Management 2017 (ASRAM 2017) (USB Flash Drive), 9 Pages, 2017/11

Nowadays, probabilistic fracture mechanics (PFM) has been utilized in several countries as a rational method for structural integrity assessment of important structural components such as reactor pressure vessels (RPVs). In PFM analyses, potential flaws in target components are used to evaluate the failure probability or frequency. Therefore, flaw distributions (i.e., flaw depth and density distributions) in an RPV shall be rationally set as one of the most important influential factors, which are developed during the manufacturing process such as welding. Recently, a Bayesian updating methodology was applied to reflect the inspection results into flaw distributions, and the likelihood functions applicable to the case when flaws are detected in inspections were proposed. However, there may be no flaw indication as the inspection results of some RPVs. The flaw distributions in this situation are important while the corresponding likelihood functions have not been proposed. Therefore, this study proposed likelihood functions to be applicable for both case when flaws are detected and when there is no flaw indication as the inspection results. Based on the proposed likelihood functions, several application examples were given in which flaw distributions were estimated by reflecting the inspection results through Bayesian update. The results indicate that the proposed likelihood functions are useful for estimating the flaw distribution for the case when there is no flaw indication as the inspection results.

Chemistry in mega-gravity; Preparation of molecular-scaled graded materials from radical copolymerization

Ihara, Hirotaka; Abe, Yasuyuki*; Miyamoto, Akihiro*; Nishihara, Masamichi*; Takafuji, Makoto*; Ono, Masao; Okayasu, Satoru; Mashimo, Tsutomu

Chemistry Letters, 37(2), p.200 - 201, 2008/02

https://doi.org/10.1246/cl.2008.200

The molecular-graded structures have been realized through direct copolymerization of halogenated styrene and 2-ethylhexyl methacrylate under ultra-strong gravitational field. The graded structures were clearly confirmed by EPMA and NMR spectroscopy.

Preparation of poly(N-isopropylacrylamide)/liquid-crystalline clay composite gels by -ray irradiation

Shimasaki, Kotaro*; Yamaki, Tetsuya; Sawada, Shinichi; Hiroki, Akihiro; Maekawa, Yasunari; Miyamoto, Nobuyoshi*

no journal, , 

Anisotropic hydrogels of poly(N-isopropylacrylamide) hybridized with liquid-crystalline clay mineral (fluorohectorite or montmorillonite) nanosheets were synthesized by a -ray-induced polymerization and crosslinking techniques. The obtained gels exhibited better mechanical properties; their modulus of compressive elasticity was 17 times higher than that of the conventional crosslinker-based gels.

Multiple-wavelength superfluorescence in helium following FEL excitation; Ultrafast experiments and simulations

Harries, J.; Ohae, Chiaki*; Iwayama, Hiroshi*; Kawaguchi, Kentaro*; Kuma, Susumu*; Miyamoto, Yuki*; Nagasono, Mitsuru*; Nakajima, Kyo*; Yabashi, Itsuo*; Shigemasa, Eiji*; et al.

no journal, , 

A New probabilistic evaluation model on weld residual stress

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

no journal, , 

Weld residual stress (WRS) is one of the most important factors with a great deal of uncertainty, which is considered as a driving force for crack growth in the structural integrity assessment of piping welds. For more rational assessments, it is important to consider the uncertainty of WRS in probabilistic fracture mechanics (PFM) analysis. In the existing PFM analysis codes, the uncertainty of WRS is set through statistical process of multiple finite element analysis (FEA) results. This process depends on persons who perform PFM analysis, and it may give different uncertainties. In this study, we developed a new WRS evaluation model based on the Fourier transformation, and the model was introduced into PASCAL-SP which has been developed by Japan Atomic Energy Agency. Through these improvements of the code, the uncertainty of WRS can be taken into account automatically and appropriately by inputting multiple WRS analysis results directly as input data of PFM analysis.