PSI - Issue 70

Varsha S et al. / Procedia Structural Integrity 70 (2025) 51–58

52

computation of SIF for semi-elliptical cracks in structural elements has been achieved through different reported methods. Weight functions provide an efficient strategy because SIF reacts to the loading condition and crack shape variables. The weight functions create geometrical relationships to determine SIFs for single cracked bodies subjected to general loading types. During the last decade scientists have established single-dimensional weight functions to calculate SIF for deep and surface cracks by Ghajar, R., & Saeidi Googarchin, H. (2013) . They also noted that variations in k significantly affect the location of critical damage pointse. The research focuses on two-dimensional weight functions which scientists call point load weight functions. The researchers Ghajar et al. developed point load weight functions suitable for analyzing thick-walled cylinders, finite plates as well as semi-infinite domains. Zhao et al. established both a test specimen and its associated weight function to achieve SIF determination by Jin, M. et al (2012). The benefits of these 2D functions exist but they work with specific problems. The weight function by Saeidi Googarchin and Ghajar is limited to cylindrical structures with specific thickness-to-radius ratios. The requirement exists for adaptable SIF computation methods which use broadened weight functions. Most known classical solutions such as Sneddon's closed-form SIF for circular cracks in infinite bodies by Zhao, X. C., Levan, A., (2016), (1993) and Yong's 2D singular integral approach by Dhondt, G. (1997) require domains to be either infinite or semi-infinite. Liao and Atluri together with Vainshtok, Kuo et al. and Yu, H., & Kuna, M. (2021) analyzed circular cracks using different numerical and analytical approaches. Kitamura and Kamaya (2003) along with Souiyah, M. (2008) conducted studies on material irregularities and boundary influences. The correct analysis of fractures subjected to mixed-mode loading remains essential for understanding fundamental applications involving pressure vessels and pipelines. The combination of these situations produces challenging pathways for cracks to develop along with intricate material responses. Detailed studies about fracture types lead to better assessments of system damage tolerance and enhances reliability of operation. The current research determines exact SIF values for half-circular cracks that exist under any combination of two-dimensional stress field conditions in finite and infinite structures. The study utilizes point load weight function analysis to generate outcomes compatible with analytical and existing FEM data. The paper developed a general equation through this method that analyzes practical semi-circular cracks in structural systems. The weighted function method is a widely employed approach to calculate SIF. It characterizes the cracked geometry and remains unaffected by the specific loading condition. Once the reference load case and the corresponding crack face displacement, ur(x,a)u_r(x, a) ur (x,a), are known, the SIF for any other loading scenario can be derived. This is done by applying the known weighted function and using the SIF, Kr , from the reference case in a linear elastic cracked body. by Sham, T.-L. (1987). = ∫ ( ). ( , ) 0 (1) where the one-dimensional weight function is denoted by ( , ) and the distribution of stress on the virtual fracture face in the undamaged body is represented by σ(x). ( , ) = ( , ) (2) The crack length is denoted by a, the axis along the crack length by x, and a material constant by H in equation (2). Finding the corresponding SIFs in the literature was simple in contrast to the paucity of research on crack surface opening displacements. As a result, various generic forms of the estimated crack surface were presented on the basis of corresponding SIFs by Wang, X., & Glinka, G. (2009). Therefore, it is necessary to obtain the general form of the reference SIFs and load in order to determine the weight function. On the crack surface, at point P(x,y) two-unit forces, F = 1, are applied using the 2D point load weight function, m(x,y;P′), which helps in computing the SIFs on the fractured front at any random point P′. Integrating a 2D 2. Mathematical Modelling 2.1. Weight Function Concept