PSI - Issue 42

Tereza Juhászová et al. / Procedia Structural Integrity 42 (2022) 1090–1097 Juhaszova/ Structural Integrity Procedia 00 (2019) 000–000

1093

4

Seitl et al. (2017). Indexing I describes mode of the crack propagating, this paper is focused on mode I, opening mode. As it will be described furthermore, another approach could be used to calculate SIF in the crack tip, using relation of the stress value on the distance from the crack tip, that determines SIF as: � = �→� √2 , (2) where r is the coordinate in cylindrical coordinate system with beginning in the crack tip. The value of K I could be calculated using a linear approximation of relation between SIF calculated and r . Therefore, the value of a constant in the linear equation stands for the value of SIF in the crack tip, Westergaard (1939). To characterize material properties of the specimens, commonly known Paris et al. (1961) or Paris-Erdogan (1963) law was used: � � � � = � � , (3) where C and m are the material constants dependent on stress ratio R, specific loading parameters and geometrical properties of specimen and the ratio d a/ d N is the crack growth rate, which evaluates crack length increment in number of loading cycles processed. 4. Numerical modeling To evaluate experimental results and to obtain fatigue parameters, numerical modelling took place in Ansys Mechanical APDL (2022). To make the calculation faster and to save memory space as well, only quarter of specimen was modelled, as the geometry allows for symmetry by replacing the rest of the specimen with corresponding boundary conditions, which constrained displacement in the direction of the missing body, see Fig. 2(a). Geometry of the specimen represents real structural profile/components, with thickness B of 10 mm, width W of 50 mm and the ratio of span of the supports to width S/W of 3. The material model of the high-strength steel material was defined as isotropic linear elastic with parameters:  Young’s modulus: E = 190 GPa  Poisson’s ratio:  = 0.3. Loads of each numerical model corresponding to maximal value of P max =25 kN from experimental campaign, see chapter 5. Because of the non-standard geometry, in the beginning of evaluation the data obtained from modelling environment needed to be compared with sources from literature. Therefore, the results from parametrical model with value S/W of 4, using least square method (LSM), were compared to results numerically calculated using Tada’s (2000) shape function and with data from 2D modelling, using CINT command, see Fig. 2(b) To obtain the values of SIF from numerical modeling, opening stress was determined on the path with the length of 1 mm, placed in the center of specimen, beginning in the crack tip and continuing through the undamaged part of the body. These values were used to determine the SIF in the crack tip using formula (2). Plastic zone in the vicinity of the crack needed to be neglected to obtain precise values, using the principles of linear elastic fracture mechanics (LEFM). The results showed in Fig. 2(b), obtained with these methods, shown good similarity, therefore was the numerical model assessed as convenient to use for further processing. It is also visible, how values from vicinity of the crack influence the results and could cause deviations (PZ incl.).