PSI - Issue 46

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

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Saurabh Gairola et al. / Structural Integrity Procedia 00 (2021) 000–000

demanded in aerospace and automotive industries. Especially, the extended finite element method (XFEM) introduced by Belytschko, (Qian & Zhao, 2019) which is used extensively to predict the fatigue life of materials and structures with the mechanical characterization data generated using experimental techniques. The conventional finite element method requires the mesh to be conformed along the crack geometry, and hence as the crack propagates, the crack tip needs constant remeshing. On the other hand, the extended finite element method allows the crack to be independent of the mesh and therefore eliminates the need for remeshing. This reduces the computational efforts required for the simulation, which makes XFEM unique and highly suitable for simulating the complex static and dynamic behaviour of materials relevant to industrial applications. Mazlan et al. (Mazlan et al., 2020) predicted fatigue life of the Al 2024 T3 using the stress life equation and observed good agreement between simulated and experimental data. Mohanty e al, (Mohanty et al., 2015) investigated fatigue crack growth rate (FCGR) via genetic algorithm and reported good correspondence between simulated and experimental data. The literature on fatigue behaviour of Al 2024 alloy simulated using XFEM is scarce. Therefore, the present work is focused on predicting the fatigue life of Al 2024 using the combined FEM and stress life approach. The fatigue crack growth of Al 2024 alloy was simulated using AFGROW software (Developed by the US Air force research laboratory). It has a damage tolerance analysis framework that can be readily used to predict fatigue crack propagation (Zou et al., 2011). The prediction of fatigue life can be made by using damage accumulation models, namely, stress life and strain life methods. These approaches are used to predict the crack initiation period (Chang, 2015). Stress based approach operates under the assumption that the stress involved is within the elastic range, and these approaches work well for high cycle fatigue behavior but have inferior accuracy for the low cycle fatigue. These equations are developed for completely reversed loading or loading with zero mean stress. For other stress, i.e., loading with mean stress, various mean stress correction methods such as Goodman, Gerber, Marrow mean stress correction were developed. In the current study, the prediction of fracture and fatigue behavior of Al 2024 alloy is made using the stress life approach and XFEM method, respectively. 2. Simulation Procedure 2.1. XFEM XFEM uses the partition of unity method (PUM) to integrate the discontinuities into the conventional finite element mesh. PUM method introduces additional enrichment functions in the vicinity of discontinuities, as depicted in the equation below (Qian & Zhao, 2019). � � ���� � � �. � � � �� �. � � � � � �. � � � ��� � ��� ��� The elements along the crack path are modified using the Heaviside enrichment function H(x), and the elements on the crack tip are enriched using crack tip enrichment function F a (x), as shown by blue and red color, respectively in fig. 1. Heaviside function represents the jump in the displacement across the crack, whereas the crack tip enrichment function deals with the singularities at the crack tip. Crack tip enrichment function is given by � � � � ��� . ��s � 2� � � ��� . sin � 2� � � ��� . sin� � sin � 2� � � ��� . sin� � . ��s � 2� �2� Here r and θ are the local polar coordinates of the crack tip. The movement of discontinuities in the mesh is handled by level set functions. Two distance functions, φ, and ψ, are used to define the crack geometry. The function φ defines the crack surface, and the ψ defines the orthogonal surface at the crack tip. Function φ takes a positive value above the crack surface and becomes negative below crack surface. The function ψ is positive on the right side of the normal at the crack tip.