PSI - Issue 66

Akash Shit et al. / Procedia Structural Integrity 66 (2024) 247–255 Shit and Prakash/ Structural Integrity Procedia 00 (2025) 000–000

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1. Introduction Rivets play a pivotal role of joining in engineering for centuries, providing reliable solutions across a wide range of applications and under complex loading conditions. The rivet holes act as the stress riser; so, in most of the engineering components the failure initiates from the rivet holes due to stress concentration; in some cases by fretting or fretting corrosion. The crack propagation many a times is not plane perpendicular to the direction of loading which is the ideal case of opening mode of cracking (Mode-I). Thus, it is essential to calculate the mixed mode Stress Intensity Factor (SIF) or even better, the effective SIF to accurately predict the severity of cracks at a riveted joint, as the initiated crack experiences a combination of opening mode (Mode-1) and sliding mode (Mode-2) loading. Vlieger examined the fatigue behavior of riveted joints subjected to bi-axial loading through experimental and numerical techniques [H. Vlieger, (1994)]. Studies on riveted lap joints under mixed-mode loading have found that under biaxial loading, SIF values are higher at lower crack depths compared to uniaxial loading, with a gradual increase in SIF from the crack middle region towards the bottom of the plate [Suresh Kumar et al., (2017)]. Investigation on the aircraft fuselage riveted lap joints have also shown that crack growth is significantly accelerated under biaxial loading conditions as a result of out-of-plane deformations [Müller, (1995)]. The Lozenge or diamond pattern riveted joint, characterized by its economical use and unique rivet arrangement, offers enhanced load distribution, strength, and stability. Its widespread application in structures such as bridges, trusses, and cranes requires a study based on fracture mechanics to ensure structural integrity. However, there are fewer studies on this pattern compared to chain or zig-zag patterns. Hithendra and Prakash, (2021) investigated the stress intensity factor (SIF) for cracks at various rivet hole locations in Lozenge patterns, identifying critical points and exploring residual stress fields to reduce SIF. They also determined the optimal crack length and interference levels for minimizing SIF, assuming initial crack propagation perpendicular to the loading direction considering uniaxial loading [Karakampalle and Prakash, (2021)]. This study investigates the effective Stress Intensity Factor (SIF) in 3-2-1 Lozenge pattern riveted joints under biaxial loading conditions. The analysis incorporates the maximum principal stress direction to locate the initial crack and estimates the crack propagation angle using the maximum energy release rate (MERR) criterion. A standard cruciform specimen and four different in-plane tension-tension biaxial load ratios (0.25, 0.5, 0.75 and 1) is considered to assess the effect on the SIF. Additionally, the study explores the presence of a shadow crack at row 2 on the effective SIF of the primary crack at row 1 by considering two different configurations of the location of the

shadow crack. Nomenclature 2a

Crack length (mm) E Elastic Modulus (GPa) Poisson's Ratio Applied Stress (MPa) σ y

Tensile Yield stress (MPa) Ultimate Tensile Strength (MPa) Energy Release Rate � �  � Mode I Stress Intensity Factor ����  √ � Mode II Stress Intensity Factor ����  √ � Effective stress intensity factor ����  √ �

σ ut

G

KI

KII K eff

2. Methodology The Stress Intensity Factor (SIF) for the fatigue cracks emanating from one or more holes of a typical 3-2-1 Lozenge pattern riveted joints under biaxial loading is studied using numerical technique by considering a standard cruciform specimen shown in Fig. 1(a). The determination of the initial crack location and orientation is based on the maximum principal stress direction, while the direction of crack propagation is determined in accordance with the maximum energy release rate criterion. To investigate the influence of load ratio on the stress intensity factor, four distinct biaxial load ratios (ratio of load along x- and y- direction) of 0.25, 0.5, 0.75, and 1 are considered. Plane