PSI - Issue 43

Lucie Malíková et al. / Procedia Structural Integrity 43 (2023) 264–269

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Lucie Malíková et al. / Structural Integrity Procedia 00 ( 2022) 000 – 000

Williams (1953), respectively. Generally, steels can fracture rapidly and/or can crack during welding, in fatigue or as a result of stress corrosion. It is essential to understand potential cracking mechanisms and risk factors to reduce the probability of failure. Cracks can be described as surface or subsurface fissures, that develop in a material, whose initiation and propagation are influenced for instance by mechanical, thermal, chemical, and/or metallurgical impacts. In metals, very often a combination of fatigue and corrosion damage occurs. Some overview works focused on metal fatigue were published by Cui (2002), Klesnil & Lukáš (1992 ) , Schütz (1996) or Zerbst et al. (2002) and instructions for assessment of lifetime of cracked structures can be found in papers by Geissler (2022), Hirt and Kunz (1996) or Seitl & Knésl (2008). Corrosion of various metals have been studied recently for instance in works by Chen et al. (2021), Kunz et al. (2012), Seitl et al. (2019), Kubzov á et al. (2020) or Xue et al. (2020). In this work, an influence of an elliptical corrosion pit on the basic fracture parameters of a close crack is analyzed. Linear elastic fracture mechanics concept is considered and besides the well-known stress intensity factors, also the higher-order terms of the Williams expansion are investigated for various selected configurations. A cracked bar with a perpendicular crack (in interaction with a corrosion pit) subjected to pure tensile loading was modelled by means of finite elements. The dimensions of the corrosion pit (length and depth) as well as the mutual distance between the pit and crack were selected based on the previous studies (Mal í kov á et al. (2022)) in order to analyze the effect of the corrosion on the initial crack propagation direction. 2. Description of the problem As mentioned above, a cracked bar with a perpendicular crack and a nearby corrosion pit subjected to pure remote tensile loading was modelled numerically in order to estimate the basic fracture parameters and describe the influence of selected variables on the fatigue crack propagation. Multi-parameter linear elastic fracture mechanics concept was considered, i.e. the stress intensity factors and also the higher-order terms of the Williams expansion were calculated. Williams expansion was originally derived for approximation of the stress and displacement crack-tip field in a specimen subjected to remote loading, see more details in Williams (1957). In this work, the numerical solution of the problem (displacement field in a set of nodes around the crack tip) and analytical description of the displacement field (Williams expansion) are combined for determination of the higher-order terms. This regression technique is referred to as the over-deterministic method (ODM), see for example Ayatollahi and Nejati (2011) for more details. Coefficients of the higher-order terms were rather ignored in the past and are generally not connected to any conventional fracture parameters. However, it has been shown that other higher-order terms can also possess an essential importance. One of the possibilities, how the higher-order terms can be utilized, is its integration into the fracture criterion for estimation of the initial crack propagation angle. This idea is applied within this paper. In Fig. 1, a scheme of the bar with a corrosion pit near the perpendicular edge crack can be seen (Fig. 1a) and an example of prism and round samples prepared under corrosion conditions (Fig. 1b). The values of the individual parameters were chosen based on the previous studies in order to analyze the configurations with the highest mutual interaction of the crack and the corrosion pit. This is the case, when the pit is very close to the crack and the pit is of larger size. Thus, the following dimensions and other parameters were considered: The distance between the crack and the edge of the corrosion pit was kept 0.1 mm. Simultaneously, the corrosion pit length, 2 P , was considered to be 4 mm, with the four times smaller depth of the pit, i.e. D = 1 mm. The total specimen length L = 100 mm, specimen width W = 10 mm, crack length varied between 0.05 and 4 mm ( a = 0.05, 0.25, 0.5, 1, 1.5, 2, 3 and 4 mm) and the applied tensile stress range was 300 MPa. A two-dimensional numerical model was created in accordance with the dimensions introduced in the commercial code ANSYS, see Ansys (2022). The plane strain conditions were defined, the crack was modelled as ideally sharp and the rectangular specimen was loaded via tensile stress on its upper and bottom side (see Fig. 1). Because the fracture parameters (stress intensity factors) at the crack tip were investigated, the finite element mesh needed to be fine enough at this location. Therefore, the 8-nodes quadrilateral PLANE183 elements were chosen for the numerical model. These elements enable (via the pre-defined command KSCON) shifting of the mid-side nodes towards to the crack tip, which ensures better approximation of the typical singular stress field. The material model was considered to be isotropic linear elastic. The elastic constants were set to be 210 GPa for the Young’s modulus and 0.3 for the Poisson’s ratio (in accordance with the real mechanical properties of high -strength steels that are extremely versatile materials for various engineering structures). These material properties are typical for high-strength steels, see Miki