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Procedía Engineering 10 (2011) 3)285-3290
Fatigur propagation of induerd eraeks by stiffrnrrs in repaired panrls with eompositr patehrs
H. Hossrini-Toudrshkya'* M.A. Ghaffaria and B. Mohammadib
aDepartment of Aerospace Engineering, Amirkabir University of Technology, Tehran, Iran bSchool of Mechanical Engineering, Iran University of science & Technology, Tehran, Iran
Abstract
In this study, finite element method is used to investigate crack propagation of stiffened aluminum panels repaired with composite patches. For this purpose, 3-D crack-front in general mixed-mode conditions is considered for the analyses. The cracks are considered to be near the stiffener around a rivet and are capable to propagate under a cyclic loading. Effects of rivets distances and their diameter on the crack growth life of repaired panels are investigated. Moreover, the obtained crack-front shapes at various crack growth steps, crack trajectories and life of the unrepaired and repaired panels with various glass/epoxy patch lay-ups are discussed.
© 2011 Published by Elsevier Ltd. Selection and peer-review under responsibility of ICM11
Keywords: Crack propagation; composite patch; repair; Stiffened cracked panel; rivet
1. Introduction
Most of the previously performed studies on bonded composite patch repair have involved plane aluminum panels without considering stiffeners. Fredell et al. [1] conducted fatigue experiments using bonded glare and boron/epoxy patches on the cracked panels. Naboulsi and Mall [2] performed several FE analyses to predict fatigue crack growth rate of cracked aluminum panels repaired with composite patch and compared the results with fatigue crack growth rate of cracked unrepaired panels. Chung and Young [3] presented fatigue crack growth tests for repaired thick plates with an inclined edge crack. Hosseini-Toudeshky et al. [4-6] conducted three-dimensional FEM analyses and experiments to obtain
* Corrrsponding author. Trl.: +98-21-64543224; fax: +98-21-66959020. E-mail address: hossrini@aut.ae.ir.
1877-7058 © 2011 Publi d by Elsevier Ltd. doi:10.1016/j.proeng.2011.04.542
fatigue crack growth life and crack trajectory of the repaired panels with a central inclined crack in general mixed-mode fracture conditions and real crack-front modeling.
Actual aircraft structures are not generally flat aluminum panels without any reinforcement; they are stiffened structures consist of skin, stiffener, webs, and spars. Stiffened panels are often subjected to fatigue loading. A considerable amount of research on crack tip stress intensity analysis, cracked panels with multiple intact stiffeners and broken stiffeners, bending flexibilities of panels and stiffeners, nonlinear shear deformation of fasteners, and cracked stiffeners have been already performed [7-13]. Poe [7] performed fatigue tests on stiffened panels constructed with bolted and integral stringers. It was experimentally observed that crack growth rate in stiffened panel is reduced by the bolted stringers. Vlieger [8] presented a method to predict the residual strength of a cracked sheet structure contains of stiffening elements that can act as crack stoppers. Chu et al. [9] conducted an experimental study to characterize the fatigue crack growth behavior of stiffened panels under uniform lateral pressure loading. Mellings et al. [10] presented a new method for automatically predicting the growth of cracks in stiffened panels and they realized that the rate of crack growth is reduced when stiffeners are used and that the life is increased correspondingly. Schubbe and Mall [11] studied the effects of patch geometry and stiffness ratios on single sided repairs of thick plates. Jones et al. [12] presented design formulae for composite repairs rib stiffened wing skins. They also examined the crack growth history of a range of specimens, and cracks repaired with a composite patch, and showed that in the low to mid-range AK region, there is a nearly linear relationship between the log of the crack length and the number of cycles. Sabelkin et al. [13] investigated fatigue crack growth in a stiffened thin panel repaired with single-side composite patch through experiments and analyses.
In this study, effects of various characteristics of both repair and stiffener's on fatigue crack growth of repaired panels containing stiffeners are studied. The major objective of this study is to deal with the used rivets to attach the stiffeners to the panel. Effects of Rivet's diameter and rivets spacing on crack growth rate and fatigue life of panels are discussed. Moreover, influences of composite patch lay-ups in fatigue crack growth of the stiffened panels are perused. For these purposes, three-dimensional finite element crack growth analyses are performed considering real crack-front modeling.
2. Computational fracture analysis
Fig. 1 shows a typical geometry and loading of the stiffened single-side repaired panels containing typical induced cracks by a rivet. Having the displacement and stress fields around the crack-tip, fracture parameters such as K, Kn and Km are calculated, and then they are used to predict the crack-front shape, crack propagation path and fatigue crack growth life of the repaired panels. These analyses are performed using linear elastic fracture mechanics (LEFM) assumptions. The computational fracture analyses are based on the calculation of separated energy release rates (SERRs) by the aid of the modified virtual crack closure technique (MVCCT) to obtain the local SERR along the crack front. Formulations, more details, and crack-front modeling are fully explained in [6]. For three-dimensional general mixed-mode problems the Richard criteria [14] have been used for crack growth analyses. Deflection angles of and can be calculated by the relationships in reference [6,14]. Another component to calculate the fatigue crack growth is definition of a law relating the crack length to the loading cycles. For this purpose the well known Paris Law is used.
3. Finite elements analysis
The cracked panels and stiffeners are made of 2024-T3 aluminum alloy, the patches material is glass/epoxy composite, and the adhesive material is FM-73. Material properties are given in Table 1. The material constants used in the Paris law were C = 2.29e-14 and d = 3.7927 [5].
L=120mm Lp =72mm
Ls =24mm W=80mm
Ws (Variable)=20,25,30mm
t=2.29mm
ta=0.1016mm
tp =0.7mm(4layer:4x0.175mm) Dr (Variable)=5,6,7,8mm a(initial-crack)=0.5mm
Fig. 1. Typical geometry and loading of a repaired stiffened panel
Table 1. Material properties of glass/epoxy patch, 2024-T3 aluminum alloy (panel and stiffener) and adhesive [5]
Elasticity Shear modulus
modulus (GPa) (GPa)
Poisson's ratio
Elasticity modulus (GPa)
Poisson's ratio
41 27.82 G12 2.56 U 12 0.31 2024-T3
'22 5.83 G13 2.56 U 13 0.31 Aluminum alloy E 71.02 u 0.3
'33 5.83 G23 2.24 u 23 0.41 Glue FM-73 E 1.83 u 0.33
G=110MPa
The right picture is presented to clearly show the crack trajectory and crack front shape when crack propagated from the middle rivet.
Fig. 2. (a) Typical mesh and elements of stiffener, panel, adhesive and patch; (b) Crack trajectory and crack front shape
In the three dimensional analysis, an isotropic 8-node-solid element with extra shape function was used to model the aluminum panel and adhesive layer. Furthermore, a layered 8-node-solid element was used to model the composite patch. Fig. 2(a) shows a typical mesh of the component. In these analyses a fine mesh was generated near the cracks, 8 elements along the panel thickness, 2 elements along the stiffener thickness, 2 elements along the adhesive thickness and 2 elements along the patch thickness were also used. The front view of the model and the elements along the thickness are shown in Fig. 2(a).
Crack trajectory that has begun from middle rivet and arrives near the other rivets in last steps of crack growth analyses is shown in Fig. 2(b).
4. Results and Discussions
To verify the developed FEM procedure, the predicted crack growth behavior of the un-repaired panel without stiffener and containing a 45o central inclined crack is compared with the available experimental results from [5] in Fig. 3(a). The predicted crack growth behavior is also obtained for the same panel with a single side composite repair of [105]4 glass/epoxy and compared with the experimental results in Fig. 3(b). It shows a well agreement between the experimental and FEM results indicating the verification of both the FEM analyses for crack propagation modeling and material data in Paris law.
10000 20000 30000 N (Cycle)
Fig. 3. Comparison between the predicted crack growth behaviors with experimental results [5]; (a) un-repaired panel, (b) repaired panel with patch lay-up of [105]4 at un-patched surface
4.1. Effect of patch lay-ups
To study the effects of various composite patch lay-ups on fatigue crack growth of repaired stiffened panels, they considered with 6mm diameter rivets, 20mm rivets spacing and 5 different patch lay-ups. Fig.4 shows the crack-front shape development of the repaired panels with the typical patch lay-ups of [90]4 and [-45]4 in X-Z plane. The cracks extended up to a certain crack growth with crack tip X coordinate of XCtip =10 mm at un-patched side (the side with stiffener) of the repaired panels. It is observed that the crack grows non-uniformly along the panel's thickness for all patch lay-ups. This behavior is due to the asymmetry conditions of the repaired panels which lead to the existence of out-of-plane bending. This figure show that the crack-front shape curvature of the repaired stiffened panels with the patch lay-up of [90]4, is more bended than that from [-45]4. For all patch lay-ups in Fig. 4, in the early stages of crack growth which the crack front is still under the stiffener, crack growth rates at the stiffened side is smaller than the patched side especially for the patch lay-up of [-45]4. This growth rate at stiffened side is progressively increased, thus the curvature of crack-front is changing during the next stages. The obtained crack growths versus X crack-tip position are depicted in Fig. 5(a). It shows that using the patch lay-ups of [90]4, [902/02] and [105]4 lead to significant crack growth life extension than the patch lay-ups of [-45]4 and [-45/45]2. It's due to the loading conditions and patch layers angles. The patch lay-ups with angles closer to 90o have a high strength leading to stronger bridges for load transfer.
Fig. 5(b) shows comparison of the obtained crack-front shapes at XCtip=16.5 mm (near the next rivet) for repaired stiffened panels with various patch lay-ups in X-Z plane. This figure shows that the obtained crack-front shapes for the panels with the patch lay-ups of [90]4, [105]4 and [902/02] have almost similar behavior in X-Z plane. The same conclusion maybe made for the panels with the patch lay-ups of [45/-45]2 and [-45]4. It is also noted that the curvature of the crack-front shapes of the panels with the patch lay-up of [90]4, [105]4 and [902/02] are larger than the panels with the other two patch lay-ups. The crack-
front shapes of the panel with the patch lay-up of [902/02] is slightly smoother than the panel with the patch lay-up of [105]4 and [90]4. This is also due to the existence of out-of-plane bending as a result of patch lay-up configuration which is against the primary out-of-plane bending due to the single-side repair. Fatigue crack growth lives of repaired panels with the patch lay-ups of [90]4, [105]4, [902/02], [45/-45]2 and [-45]4 are 124727, 116498, 110407, 94014 and 90894 cycles respectively when the crack tips meet the next rivets. It shows that the best patch lay-up for reducing the crack growth rate is [90]4.
i:[90/90/90/90]
Patched Surfac
Stiffened Surface
iy-up [-45/-45/-45/-4S]
Stiffened Surfac
Fig. 4. Crack-front development for repaired panels with various patch lay-ups in X-Z plane; (a) [90]4 ;(b) [-45]4
60000 80000 100000 120000 N (Cycle)
^. Patched Surface
—ti- [-45/-45/-45/-45]
-♦-[45/-45/45/-45]
^ Hie [90/90/0/0]
-»-[105/105/105/105]
D(rivet) : 6mm Ck-d- [90/90/90/90]
Rivet spacing 20mm
" Stiffened Surface
15.5 16 X (mm)
Fig. 5. (a) Predicted crack growth versus number of cycles for repaired stiffened panel with various patch lay-ups; (b) Comparison of the obtained crack-front shapes at Xctip=16.5mm for repaired stiffened panels with various patch lay-ups
x (mm)
4.2. Effect of rivets diameter
In this section effect of rivets diameters on fatigue crack growth behavior and life of the repaired stiffened panel are studied for typical patch lay-up of [-45/45]2. With considering of 80 mm panel width and rivets diameters of 5, 6, 7 and 8mm, the constant rivet spacing for all rivets, is calculated 25 mm that the rivet spacing and the edge distance for all presented rivets are compatible with standard recommendation in design. Fig. 6(a) shows that fatigue crack growth life is increased with decreasing the rivets diameter. When the diameter of rivets is decreased, the distance that cracks can propagate and the load transfer area becomes larger between the middle rivet and adjoining rivets. Various crack growth rates at the early to middle stages of crack growth indicating various load transfer area between the rivets, but when the cracks become closer to the next rivet the crack growth rates become almost similar.
4.3. Effect of rivet spacing
In this section, effect of rivets spacing on fatigue crack propagation and life of repaired panels are studied. In these analysis the rivet with 6mm diameter have used and the chosen patch lay-up is similar to the previous section, [-45/45]2. Fig. 6(b) shows that for a constant rivet diameter as the rivets spacing is
increased fatigue crack growth rates and crack growth lives are decreased. This result indicating that
Fig. 6. Predicted crack growth versus number of cycles for repaired stiffened panel; (a) with various rivets diameter; (b) with various rivets spacing
5. Conclusion
It was discussed that in the early stages of crack growth which the crack front is still under the stiffener, crack growth rate in the stiffened side is smaller than the patched side especially for the patch lay-ups of [-45]4 and [-45/45]2. It was shown that the patch lay-up has significant effect on the fatigue crack growth life extension of the repaired stiffened panels. Rivets diameters influence the fatigue crack growth behavior significantly and fatigue crack growth rate is decreased with increasing the rivet spacing.
References
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