PSI - Issue 68

Vitalii Antonchenko et al. / Procedia Structural Integrity 68 (2025) 1305–1311 Vitalii Antonchenko et al. / Structural Integrity Procedia 00 (2025) 000–000

1306

2

precisely on analytical or “quick” methods of evaluation. Nowadays FEA plays a crucial role in all aspects of mechanical analysis and fracture mechanics calculations as well. Still there is a room in application of analytical methods, especially if we are talking about probabilistic fracture mechanics, where a huge amount of computations are required. One of central problem for the real RPV analysis is a stress discontinuity between the ferritic part and the cladding. To overcome this issue stress decomposition is proposed. It assumes that a stress field can be represented as monotonic in cladding and ferritic plus additional stress in cladding. This obvious solution complicates the calculations since in general case we should provide a SIF solution from the loading through the whole thickness, and for the cladding only. Due to the fact that cladding (austenitic steel) and base metal (ferritic steel) have different physical properties, namely Young’s modulus which ratio is varied thought the PTS, the proposed solution should also consider this fact. As state-of-the-art in pressurized thermal shock analysis for cladded components polynomial solution from [1] is used, which is well-known and included in standards like JRC VERLIFE [2], code for WWER countries. This equations and tables developed for cladded plate are recommended for RPV forgings, so it also worth test their applicability for WWER cylindrical part. In Ukraine for fracture analysis a special document was developed [3], which also has an appendix dedicated to SIF evaluation in cladded cylindrical components. Nevertheless, the continuous improvements of the document [3] itself, through the several years, the same procedure is used base on WFM. It should be noted here that SOU [3] has a SIF solution for the constant and linear stress field only, thus its application to real PTS event is limited. The idea of current paper is to test the proposed methods of SIF evaluation for cladded components. More specifically, we focus on the RPV cylindrical part, since the SIF evaluation for it is crucial for LTO. Also, an attempt is made based on the proposed Chapuliot [1] methodology develop a simple-to-use table specific for WWER-1000, to be included in the national standard. Nomenclature ! inner radius of vessel cladding thickness, thickness of the ferritic vessel Young's modulus, Poisson ratio normal to the crack surface stress polynomial coefficients stress intensity factor crack length, crack depth LTO Long-Term operation SIF Stress Intensity Factor FEM Finite Element Method / Finite Element Model PTS Pressurized thermal shock WFM Weight function method 2. Methodology Our primary goal is to develop simple and fast tool for SIF evaluation for WWER-type reactors. Thus in this study we focus on the WWER-1000 cylindrical part, which exhibit neutron embrittlement, thus is critical for LTO. On the figure below some mesh examples are shown. In our work, we consider a cylindrical part of the RPV with the following parameters: an inner radius is R i = 2068 mm, a thickness of the ferrite part is h = 192.5 mm and cladding thickness is r = 7mm. To build the model, we used a three-dimensional solid-state element of the highest order with 20 nodes. The mesh size is: 34032 elements and 146126 nodes. The average orthogonal quality is 0.9270. There are 10 element contours around the crack tip. The crack tip is split into 54 segments. The radius of the 1st contour is 0.1 mm, and the last one is 1 mm. It should be mentioned that separate models were created for circumferential and axial cracks. The images of these models are presented in the Fig. 1 and Fig. 2. !"# ! ! µ ! ! " ! ! "