PSI - Issue 68

Jan Klusák et al. / Procedia Structural Integrity 68 (2025) 660–665 Jan Klusák, Kamila Kozáková/ Structural Integrity Procedia 00 (2025) 000–000

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Taylor, 2006). TCD typically analyses the stress distribution in the vicinity of a stress concentrator. Neuber observed that the notched component is in its fatigue limit state when the average stress over a given distance is equal to the fatigue limit of a smooth specimen. The method is known as the Line Method (LM). Peterson simplified this approach by evaluating the stress at a single point from the notch tip. This is now known as the Point Method (PM). The distance for averaging the stress (in the case of LM) or for evaluation of the point stress (in case of PM) is called critical distance and it can be determined in several ways. The most commonly used method is a calculation from a formula using basic material properties. The critical distance L is considered as a material constant which can be found by using the equation (1), where 0 and K th represent the plain fatigue limit and the threshold value of the stress intensity factor range (Vargiu et al., 2017). = " ! % #$ !" #% # & & (1) Nomenclature D the narrowest diameter of the specimen G shear modulus K th threshold value of the stress intensity factor range K tm stress concentration factor of the model notch K tp stress concentration factor of the predicted notch L critical distance (from literature) l cr critical distance from fatigue data of the model notch l p critical distance of the predicted notch N f number of cycles to fracture SED strain energy density TCD theory of critical distances w strain energy density ( average strain energy density a n strain energy density amplitude of notched specimens a pn strain energy density amplitude of specimens with predicted notch a s strain energy density amplitude of smooth specimens +, component of strain tensor Poisson’s ratio 0 plain fatigue limit +, component of stress tensor Another method is to determine the critical distance based on experimental data and the stress distribution in front of a notch tip. The critical distance can be calculated from two fatigue S-N curves obtained from smooth and notched specimens (Susmel & Taylor, D., 2007). TCD finds a wide range of applications in fracture and fatigue assessment of different types of materials such as ceramics (Taylor, 2004), fibre composite materials (Morgan et al., 2022), metals (Borges et al., 2019), concrete (Radhika, and Chandra Kishen, 2023) and polymers (Cicero et al., 2012). The relationship between critical distance and microstructural parameters has also been investigated (Taylor, 2016). However, there are still influences that affect the critical length parameter. The critical distance depends on the material, number of cycles to failure, notch radius, stress ratio and surface quality. In this paper, the line method is used to determine the critical distance, but the quantity averaged in front of the notch is represented by the strain energy density (SED). The strain energy density w is defined as the total energy