PSI - Issue 42

M. Yakovlev et al. / Procedia Structural Integrity 42 (2022) 1619–1625 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction When there is a crack in the body, in order to assess crack propagation and, consequently, to assess the strength, it is necessary to know the pattern and intensity of the stress state in the region surrounding the crack tip. The stress field in the vicinity of a crack tip is determined by the stress intensity factor K (SIF). SIF calculation is an important issue in fracture mechanics. SIF is a value that depends on the level of stresses in the structure, the geometry of the crack and the geometry of the structure itself. For a correct description of the crack growth process, it is necessary to know SIF distributions for a large number of different typical cracks. Such data can be obtained from the analysis of tests on a large number of specimens or from finite element (FE) analysis. The authors (2022) proposed the specimen geometry for the surface crack growth rate test interpretation at elevated temperature. The crack growth data are usually presented in terms of the crack growth rate as a function of the range of SIF. This dependence is described by the Paris ’ law (1961, 1963):

/ ( ) m da dN С K =  ,

(1)

where da is the с rack length increment for a load cycle dN . The material coefficients C and m are obtained experimentally. The range of SIF is defined as the difference between the maximum and minimum SIF in load cycle:

max min K K K  = − .

(2)

The application of the crack growth rate test results to the assessment of the residual life of structural elements containing surface cracks is presented in the articles (2016, 2021). When determining the values of SIF, the equations of fracture mechanics are used. The SIF for an arbitrary crack is often represented as:

i nom i K K Y = ,

(3)

where SIF for a crack in an infinite plate is often taken as the base value in calculations, which is determined by the formula: nom nom K a   = , (4) where σ is the nominal stress in the plate at some distance from the crack tip, a is the half-length of the crack. Y is a specimen geometry-dependent SIF function. Consequently, the problem is reduced to determining this function. There are no equations describing the SIF distributions in the specimen geometry proposed by authors (2022). Thus, the aim of this paper is to numerically determine the specimen geometry-dependent SIF functions based on FE analysis for the geometry of a specimen with a surface semi-elliptical crack that allow to interpret the experimental data of the surface crack growth rate tests of the specimen at elevated temperatures. 2. Stress intensity factor calculation As mentioned above, the determination of the specimen geometry-dependent SIF functions was carried out by conducting a numerical calculations. The finite element method (FEM) is widely used to determine the stress fields at the crack tip. When using the FEM to obtain SIF two methods is often applied. One of them is a direct method, according to which the SIF value is determined from the stress or displacement field. In the second method, the SIF value is determined indirectly - through relationships with other quantities, such as compliance, elastic energy or J integral. In the present study we applied direct method to SIF calculations. The SIFs were calculated based on principles for building the topology of FE meshes, the sizes of the elements, and their distribution densities in the radial and