PSI - Issue 57

124 Mohammad F. Tamimi et al. / Procedia Structural Integrity 57 (2024) 121–132 Mohammad F. Tamimi & Mohamed Soliman/ Structural Integrity Procedia 00 (2023) 000 – 000 4 employed to calculate the work per unit fracture surface area and link it to the SIF. The relationship between the J integral and the SIF, specifically in the context of Mode I loading, which is of interest herein, is: = √ ′ (2) in which ′ is equal to the modulus of elasticity ( E ) for plane stress and [ /(1 − 2 )] for plane strain conditions and is Poisson’s ratio. In this paper, FE modeling is employed to calculate the J -integral given the crack size and applied stresses. Residual stresses that arise during fabrication and welding significantly impact crack propagation behaviour (Nussbaumer et al., 1999). Welding induces high residual tensile stresses near the stiffener and compressive stresses between stiffeners. This paper utilizes Faulkner's (1975) idealized welding-induced residual stress model to outline the distribution of the residual stresses across stiffened panels. The model suggests a triangular tensile stress distribution around the weld, and uniform compressive residual stresses in remaining areas. Residual stresses can also appear in the stiffeners due to welding. Gannon, (2011) defined a triangular tensile stress distribution in the stiffener web around the welds. The residual stress in the stiffener flanges was found to vary significantly but is generally small compared to the material yield strength (Gannon, 2011). Figure 1 shows the adopted residual stress distribution in the main panel and stiffeners. Faulkner’s model was chosen as it aligned closely with the actual residual stresses observed in the specimens investigated experimentally in Mahmoud and Dexter (2005).

Fig. 1 . Idealized residual stress distribution due to welding in the main panel and stiffeners. In this paper, a numerical finite element model is utilized to compute the crack driving parameter (i.e., J -integral) for the stiffened panels. The calculated crack driving parameter encompasses both externally imposed loads and residual stresses. Coupled with the analytical crack growth rule provided by Equations 1 and 2, the established computational model assists in computing the crack growth rate for each cycle under the applied cyclic load. However, given the large number of cycles considered in this simulation, machine learning is integrated to surrogate the numerical analysis and quantify the crack driving force for a specific set of input parameters. 4. ANN-Assisted Crack Growth Prediction Artificial Neural Networks (ANNs) can assist in modeling complex relationships or approximation of intricate, high order models (Avcar & Saplioglu, 2015). After training and validation, an ANN can accurately predict the output for a specific input within its training domain (Avcar and Saplioglu, 2015). There are various neural network types suitable for modeling complex computational problems, such as feedforward, radial basis function, convolutional, recurrent, and modular neural networks (Avcar and Saplioglu, 2015). Feedforward ANNs, adopted herein, exhibit notable computational efficiency, especially for highly nonlinear problems such as crack propagation in welded stiffened panels (Ma et al., 2021; Mortazavi & Ince, 2020). In this paper, a Feedforward ANN is adopted to assist in reducing the computational cost of the crack propagation FE simulations. Feedforward ANNs comprise input, hidden, and output layers. The input layer collects data from an external source for further processing in the hidden layers. In post-