PSI - Issue 36

Halyna Krechkovska et al. / Procedia Structural Integrity 36 (2022) 43–50 Halyna Krechkovska, Viktor Sylovanyuk, Oleksandra Student et al./ Structural Integrity Procedia 00 (2021) 000 – 000 5 47

formation of defects of corresponding sizes along their interfaces (Fig. 3 a ). Indeed, as a result of the action of pulsating cyclic loads with high loading ratio (which is typical for steam pipelines of TPPs), defects will inevitably form around such large inclusions and their merging will result in the formation of intergranular cracks (Nykyforchyn et al. (2010)).

a

b

c

d

Carbides

Fig. 3. Schematic representation of the arrangement of carbides along grain boundaries, favourably oriented with respect to tensile stresses, in the operated steel ( a ) and corresponding models to illustrate the choice of favourably oriented micro cracks ( b ) and designation of characteristic dimensional parameters important for the destruction of ligaments between defects (along boundaries between carbides and matrix) under the action of tensile stresses ( c , d ). Under uniaxial tension, among the microcracks randomly located in the working section of the element, the most dangerous of them are oriented perpendicular to the direction of tensile stresses and are located as close as possible to each other (Fig. 3 b ). These cracks will determine the tensile strength of the steel σ UTS under bulk damages. From the standpoint of the metal’s strength theory, any other variants of orientation of cracks relative to the applied stresses are considered less dangerous. Thus, to analyse the loss of strength of steel damaged in operation (due to the precipitation of carbides along the grain boundaries, the formation of defects in the form of pores along their interfaces with the matrix, the formation of a collinear system of cracks due to the destruction of bridges between the nearest pores located along the grain boundaries, oriented almost perpendicular to the applied stresses), an idealized model of an elastic isotropic medium was chosen. This approach makes it possible to predict the lower threshold of the strength of steel damaged during operation. There was used the well-known solution of the problem of body tension with a periodic system of collinear cracks (Nazarov (1997)) obtained earlier in the framework of the mathematical theory of cracks (Vytvytskiy (1970)). This made it possible to record the relationship between the intensity of tensile forces σ, the distance between the crack tips, their length, and the size of the pre-fracture zones in the vicinity of these defects as follows: (1) where 0 is the ultimate strength of steel in the initial state; 2 l corresponds to total length of the crack with pre fracture zones in its tips; 2 а characterises the distance between the centres of the nearest cracks; 2 d denotes to the crack length (it was considered that 2 d value corresponds to the carbide diameter). The parameters a , b , l are variables in the chosen mathematical model. Their change depends on the operation life term and the number of cycles of additional loading of the structural elements by thermal stresses caused by block shutdowns. After all, as shown by the calculations of circular thermal stresses at all stages of operation (stationary mode for steam pipelines or with planned or abnormal block shutdowns), significant thermal stresses additionally arise in the vicinity of the outer surface of pipes ( Krechkovs’ka 3 et al. (2019)). These additional stresses promote the intensification of both structural transformations in steel and the deterioration of its characteristics. And the hydrogenation of the metal during high-temperature operation only stimulates these harmful effects (Student 4 (1998), Smiyan et al. (2021)). Taking into account the fact that both the high- temperature operation term of steel τ op and the number of block shutdowns N op affect its structural and mechanical state, the (τ op ٠ N op ) / (τ N ٠ N N ) indicator was introduced. It characterizes the fraction of the exhaustion of the regulated values of the operational indicators τ N and N N during steel operation. For steel in the initial state, this indicator tends to zero. However, for critically degraded steel with an actual service life τ op and the corresponding number of shutdowns of blocks N op reaching the normalized levels of        = − a l a d UTS    2 sin 2 sin arccos 2 1 0  