PSI - Issue 46

Saurabh Gairola et al. / Procedia Structural Integrity 46 (2023) 182–188 Saurabh Gairola et al./ Structural Integrity Procedia 00 (2021) 000–000

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Fig. 1. Node enrichment in XFEM

2.2. XFEM Paris law is the most commonly used fatigue crack growth equation. It is used to predict the crack growth rate during the progression of a fatigue crack. It provides the linear fit in da/dN-∆K relationship and is applicable in region II only. Furthermore, the effect of stress ratio is not considered in Paris law (Eq.3). � �∆ � � ��� Forman modified the Paris law to include the effect of stress ratio and to extend its applicability to region III. Contrary to the Paris law, which requires different sets of parameters for different stress ratios, the Forman law (Eq.4) can use a single set of parameters for a wide range of stress ratios (Akramin et al., 2020). � �∆ � � ����� � �∆ �4� In the current study, the Forman constants were calculated for different conditions, as shown in fig. 2. The average value of different conditions is taken as the final input value for simulation.

Fig. 2. Curve fitting of Forman constants (a) center cracked specimen (Saeed, 2015) (b) Single edge notch tension (Hudson, 1969)

2.3. Computational Model Compact Tensile (CT) specimen was used for numerical analysis of fracture toughness. Fig. 3(a) illustrates the geometry and boundary condition of the CT specimen as per ASTM E399 (Alexopoulos & Papanikos, 2008). Reference point A and B were kinematically coupled with the corresponding holes, and displacement type loading was applied on both ends. Pre-crack of crack length 5 mm was introduced in the CT specimen, as shown in fig. 3(a).