PSI - Issue 66

Akash Shit et al. / Procedia Structural Integrity 66 (2024) 247–255

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Shit and Prakash/ Structural Integrity Procedia 00 (2025) 000–000

2.3. Calculation of Effective Stress Intensity Factor In Abaqus®, the stress intensity factors, � , �� and  ��� , can be obtained directly under the contour integral evaluation module; alternatively, these factors can be derived through the  -integral. For materials exhibiting linear elastic behavior, the energy release rate (G) is equivalent to the -integral. Subsequently, the stress intensity factors can be computed from G using the equation (1), �� �  � � � � � � (1) Where, is the Young’s Modules, is the Poisson’s ratio, is the stress intensity factor and �  for plane strain condition and �  for plane stress condition. To incorporate both � and �� under biaxial loading, the effective stress intensity factor for plane stress condition is calculated by the below equation used by Pirondi, (2003) and Shi et al., (2006). ��� �  � � � � �� � (2) To address the square root singularity for linear elastic material behavior at the crack tip, the mid-side nodes of the 8-noded quadrilateral elements adjacent to the crack tip are moved by a quarter-point distance. 2.4. FE Model Validation and Boundary Conditions In-plane biaxial loading was applied in the X and Y directions at the pins. The displacement along the Y-axis was fixed for the left and right side pins, allowing them to move freely along the X-axis. For the joint aligned in the Y direction, the displacement along the X-axis was fixed for the top and bottom side pins, allowing them to move freely along the Y-axis. The contact properties between the pin and holes were established through surface-to surface contact behaviour. A friction coefficient of 0.2 was applied to define the tangential behaviour of the contacts, and the Augmented Lagrange (Standard) constraint enforcement method was employed to model the normal behaviour. A maximum force of 240 kN was applied to generate a remote stress of 60 MPa in both the X and Y directions for equi-biaxial loading. In this study, it was assumed that the load is equally shared by the rivets. Subsequently, three different tension-tension load ratios were considered, 0.75, 0.5, and 0.25, by varying the load in the X-direction while keeping the load in the Y-direction constant. The FE model is validated with the results by Morishita et al., (2021). The quarter model of the specimen is considered under the uniaxial loading condition, Fig. 2(a). A unit stress is applied perpendicular to the crack surface according to the literature. The mesh size of 0.02 mm was applied near the crack and then gradually increased. CPS8, an 8-node biquadratic plane stress quadrilateral element, is used for the entire analysis. This current model is validated with less than a 2% difference with the literature shown in Fig. 2(b). (a) (b)

Literature

This study Model

10

8

Stress Intensity Factor K:

6

4

2

[Mpa.mm^0.5]

0

0

5

10

15

20

Half crack length: b [mm]

Fig. 2. (a) Meshed quarter model of the specimen [Morishita et al., (2021)] (b) Model validation with the literature [Morishita et al., (2021)]