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

1308

4

the ferritic part, represented by the nodes 4, 5 and 6 (Fig. 4). But for this point, as the node directly at the interface is affected by the cladding, the shape factor for point C is only calculated using points 4 and 5.

Fig. 3 Parameters of the considered defect, with point representation

The average shape functions are obtained from the following relations: & 2 = / 3 ' 45!67 / + 4 ∙ 45!67 9 + 45!67 : , ; = / < ' 45!67 < + 4 ∙ 45!67 = , ,

(3)

When decomposing the stress field into polynomials, the main difficulty is to represent the stress discontinuity at the interface between the cladding and base metal. This is because, during thermal shock, the continuity of deformations at the interface between the cladding and the base metal lead to an unstable stress distribution at the interface. Therefore, the stress field is divided along the thickness into two: the field in the base metal and the field in the cladding. Using the extrapolation and polynomial expansion functions, we obtain a smooth curve over the full wall thickness. And subtracting the resulting smooth function from the original stress function, we get the stress jump that occurs in the cladding due to the difference in physical and mechanical properties. Then SIF can be found using equation: / = .∑ " " 0 * > + + , , 1 " < "?@ + ∑ ", ", 0 * > + + , , 1 " / "?@ 2 3 ( + ) , (4) To obtain different polynomial coefficients, various types of loadings should be applied. The most convenient way is to use a crack loading approach, in this case the crack is loaded using different polynomial loading fields. 3. Results Table 1 and Table 2 show the shape coefficients for the axial and circumferential orientation of the crack. We considered the most relevant defect with a depth of 10% of the total wall thickness of the WWER-1000 RPV and an ellipse axis ratio of 0.3