Determination of SIF for patched crack in aluminum plates by the combined finite element and genetic algorithm approach

Abstract

A B S T R A C T In this paper, the finite element method is used to analyze the behaviour of repaired cracks in 2024-T3 aluminum with bonded patches made of unidirectional composite plates. The problem is considered in Mode I condition. First the K I stress intensity factor (SIF) is calculated by the finite element method using displacement correlation technique. Different plate and patch thicknesses and crack lengths are considered in the analyses.Then an equation is determined by using genetic algorithms for the calculation of stress intensity factor without any further finite element analysis. The equation gives reasonably accurate results.Keywords finite element analysis; genetic algorithm approach; patched crack; stress intensity factors. N O M E N C L A T U R Ea = crack length E = modulus of elasticity GAPD = genetic algorithm patch design K I = stress intensity factor for mode I condition K IP = SIF for patched condition K IC = fracture toughness p = patch thickness R 2 = coefficient of determination SIF = stress intensity factor t = aluminum thickness t a = adhesive thickness w = aluminum plate width v = poisson ratio σ = applied stress I N T R O D U C T I O NIn aircraft structures, traditional repair methods such as bolt and rivets cause stress concentration due to drilling of additional fastener holes. Therefore, the development of bonding technology has been accelerated. Adhesively bonded repairs cause minimum stress concentration and alter the load path that induces efficient load transfer from cracked structure to reinforcement. Thus, the reduction of the stress intensity factor caused by bonded patch repair prevents or retards crack re-initiation or further growth.The bonded patch offers many advantages over mechanically fastened doublers, which include improved fatigue behaviour, reduced corrosion and easy conformance to complex aerodynamic contours. 2,3 Baker pioneered studies about bonded composite repairs in aircraft and marine structures, most of which have been focused on Mode I opening of crack. Megueni et al. 4 used the finite element method to compute the stress intensity factor for repairing cracks with bonded composite patches taking account of the disbond. In the case of disbond, the increase of patch thickness reduces the negative effects of disbond. Tsai and Shen 5 performed stress analyses for four different aluminum plates, including no crack, with crack, with

Finite element analysis of cracks in aging aircraft structures with bonded composite-patch repairs

“…It has been one of the most prevalent numerical tools in the field of fracture mechanics since the early 1960s. Researchers have been developing new techniques to improve the accuracy of FEM in application to fracture mechanics [3][4][5][6][7][8][9][10][11]. The use of quarter point elements in improving the accuracy of the solution around the crack tip was suggested by Henshel and Shaw [12] and Barsoum [13].…”

“…Most of computational models of the composite-patch-repaired plates utilized a simplified two-dimensional model [3,4,8,14]. However a plate under in-plane loading would develop highly complicated three-dimensional stresses if patches are bonded to its surfaces regardless of single or double sided patch.…”

Determination of SIFs, crack‐tip coordinates and crack angle of anisotropic materials

“…However, this method requires both displacement and stress fields that often cause experimental difficulties. The least‐squares or correlation methods 16,17 do not have this problem, so this method was used in this study. The sum of the squares of the normalized residue for m points with u and v displacements is where u i and v i are the u and v displacements of point i obtained from experiments.…”

Fracture analysis of Kevlar-49/epoxy and e-glass/epoxy doublers for reinforcement of cracked aluminum plates

“…A two dimensional finite element code, utilizing plane stress elements to mimic the repaired plate, referred to as FRacture ANalysis Code for 2D Layered structure (FRANC2DL), is being used by many researchers [11][12][13]. However, 2D models cannot capture the out-of-plane deformation along the crack front which has considerable impact on the stress intensity factor across the plate thickness [14].…”