Numerical analysis of the behavior of repaired
cracks with composite patch in thick metallic
structures
A. ACHOUR
a, B. BACHIR BOUIADJRA
b, L. AMINALLAH
c,
N.
Benseddiq
d, D. Ouinas
e, A. Albedah
f, B. Serier
g,
a. LMNEPM, Mechanical engineering department, University abdelhamid ibn badis,
Mostaganem, 27000, Algeria , E-mail address : [email protected]
b. LMPM, Department of Mechanical engineering, University of Sidi Bel Abbes, BP 89 Cité
Ben M'hidi, Sidi Bel Abbes, Algeria , E-mail address: [email protected]
Abstract :
In this study, the behavior of repaired cracks with bonded composite patch is analyzed numerically. The stress-intensity factor at the crack tip is chosen as fracture criterion in order to estimate the repair performances. This factor at the crack front is computed using three-dimensional finite element method. The obtained results show that the stress intensity factor at the crack front is highly reduced by the presence of the patch repair. The increase of the thickness of the repaired structure has a negative effect on the repair efficiency. The effects of the geometrical parameters on the stress intensity factors were analyzed. These parameters must be optimized in order to improve the repair performances.
Key words : Bonded composite repair; Aluminum alloy; Adhesive; Stress
intensity factor; Finite element method.
1
Introduction
Service life damage is a natural characteristic of any structure subjected to fatigue loading, compromising integrity and safety. Economic reasons make repairs to damaged structures components virtually inevitable. Design, analysis and technology for integrity enhancement of damaged or even under-designed structures continue to be an engineering challenge. A badly implemented repair can be more dangerous than the un-repaired configuration. Out of the various classes of damage, if we limit ourselves to cracks in sheets, then either a mechanically fastened doubler or a bonded patch can possibly repair these. The bonded patch offers many advantages over a mechanically fastened doubler, which include improved fatigue behavior, reduced corrosion and easy conformance to complex aerodynamic contours (Jones R et al.,1991; Molent L and Jones R.1993). The scientific approach to designing and assessing repairs before implementing probably started in the early 1970. Alan Baker at the Aeronautical and Maritime Research Laboratory (AMRL) pioneered the work for the Royal
Australian Airforce (RAAF) and later in USA in early 1980 s. (Baker AA.,1984; Baker AA.,1993). Adopting and following repair guidelines given by the manufacturer for typical minor damages is a routine activity with many airline operators. Damages not listed in such repair manuals, naturally call for intervention of the manufacturer for functional restoration. Extensive experimental studies have demonstrated the effectiveness of bonded repairs as a cost-effective means of repairing cracked structures, in terms of restoring the residual strength to the design level and significantly reducing fatigue crack growth rate (WOO and KWANG SUNG.,2008 ; C.N. Duong et al.,2006). For un-patched cracks, it is now possible to obtain satisfactory predictions of the effects of stress ratio and variable amplitude loading on the rate of fatigue crack growth using crack-closure models. A repaired crack can be viewed as being bridged by a series of distributed springs sprang between the crack faces. Under fatigue loading, these springs restrain the opening of the crack, and thus reducing the stress-intensity factor. To analyze the effect of this bridging mechanism on the residual plastic wake behind the crack tip, the crack bridging theory (Rose LRF.,1997) is employed together with a crack-closure model to analyse the steady-state closure of patched cracks subjected to constant amplitude loading. The analytical consideration proves that under small-scale yielding condition, (the applied stress is far smaller than the material’s yield stress), the steady-state crack closure level depends only on the applied stress ratio and is almost identical to that corresponding to un-repaired cracks subjected to the same applied stress ratio. This finding has been verified by a finite element analysis. Furthermore, the transient crack closure behaviour following an overload, which is the main mechanism responsible for crack growth retardation, has also been investigated by the finite element method. The results reveal that patched cracks exhibit the same transient decrease/increase in the crack-closure stress as un-patched cracks. Based on these findings, a correspondence principle relating the transient crack-closure behaviour of patched cracks to that of un-patched cracks is proposed. Several authors (H. Fekirini et al., 2008 ; B Bachir Bouiadjra et al., 2008) showed that the stress intensity factor for patched crack exhibits an asymptotic behaviour as the crack length increases. This is due to the stress transfer toward the composite patch throughout the adhesive layer. The analysis of the effects of the geometrical properties of the composite on the repair performance was retained great interest in the literature. Heller and Kaye (M. Heller and R. Kaye.,2002) used the genetic algorithm to optimise the patch shape. Kaddouri et al,.2008, Ouinas et al.,2009 , analysed numerically the performance of the octagonal, circular and elliptical shape of the patch. They showed that the patch shape has a significant effect on the value of the stress intensity factor at the crack tip. In addition, the use of appropriate patch shape can reduce the level of the thermal residual stresses due to the adhesive curing (B. Bachir Bouiadjra et al.,2002) ,analysed the effect of the patch thickness, they showed that the patch thickness must also be optimised. The comparison between the double symmetric patch and the single was analysed by several authors (M. Belhouari et al.,2004; B. Bachir Bouiadjra et al.,2010). All these authors showed that the use of double symmetric patch improves the fatigue life of the repaired structures. This improvement is due to the double stress transfer in the double patch configuration. In addition, the double symmetric patch annuls the bending effect due to the eccentricity of the composite patch in the case of single sided patch. The double symmetric patch has two main disadvantages: the first is the difficulty to follow the crack propagation and the second is the relatively higher levels of the thermal residual stresses because of the double adhesive curing. The objective of this study is to analyze the distribution of the stress intensity factor along the crack front for repaired crack with bonded composite patch. The effect of the thickness of the repaired plate is specially analyzed in order to show the difference of the repair performance for thick and thin plates.
The basic geometry of the cracked structure considered in this study is shown in Fig. 1. Consider a rectangular elastic aluminum plate with the following dimensions: length Lp= 200 mm, width Wp = 80
mm, thickness ep = 6 mm. The plate is subjected to uniaxial tensile load giving a remote stress state of
σr = 65 MPa. A lateral crack of length a perpendicular to the loading axis is supposed to exist in the
plate. This crack is repaired with two kinds composite patch carbon/epoxy and boron/epoxy of dimensions: length Lr = 50 mm, width Wr = 50 mm and thickness er = 2 mm. The ply orientation is
parallel to the loading axis. The adhesive used for bonding is the adekit A140 with thickness ea = 0.2
mm. The mechanical characteristics of analyzed materials are given in Table 1.
Lp Wr Wp Lr Plate Patch a Adhesive ep er ea Y X Y Z
Fig. 1. Geometrical model.
The mechanical characteristics of analyzed materials are given in Table 1.
Table 1 Mechanical properties of different materials. EL (GPa) Longitudinal Young Modulus ET (GPa) Transversal Young Modulus G (GPa) Shear Modulus L Longitudinal Poisson’s ratio T Transversal Poisson’s ratio Aluminium alloy 2024-T3 73 73 0.33 0.33 Carbon / Epoxy 74.80 37.60 16.95 0.37 0.02 Boron / Epoxy 210 19.6 5.46 0.3 0.028 Adekit A140 2.69 2.69 1 0.3 0.3
3 Finite element modeling
Stress analysis of the repair was performed using 3-D FE models developed with the commercial FE code ANSYS [31]. The metallic sheet, composite patch and epoxy adhesive were modelled as different bodies using the 8-noded 3-D ANSYS SOLID45 element. The patch lay-up is the unidirectional [0°]. Due to symmetry of geometry and loading only one half of the repair was modelled. Fig. 2 and 3 shows the FE meshes of the repair parts and complete repair.
Adhesive
Patch Plate
Crack
Fig. 2. Typical mesh model of the half of the structures.
Position 0 Position 1 Position 2 Position 3 Position 4 Position 5 Position 6 Plate Adhesive Patch Crack
Fig. 3. Sites of analysis of the stress intensity factor (SIF).
A fine mesh was adopted in the area around the crack tip to allow a satisfactory accuracy in SIF calculation. The number of elements used in this study is 17,028 elements: 12,216 elements in the aluminum plate, 3,208 elements in the composites patch and 1,604 elements in the adhesive layer. The Stress intensity factor (SIF) at the crack front was computed using the virtual crack closure technique (VCCT). This technique was originally proposed in 1977 by Rybicki and Kanninen [32], is a very attractive SIF extraction technique because of its good accuracy, and a relatively easy algorithm of application capability to calculate SIF for all three fracture modes. The proposed technique has been extended by other authors [33,34]. Currently, the three-dimensional virtual crack closure technique (3D VCCT) is often chosen as a tool for SIF calculations [33].
The VCCT is based on the energy balance proposed by Irwin. In this technique, SIF are obtained for three fracture modes from the equation:
where Gi is the energy release rate for mode i, Ki the stress-intensity factor for mode i, E the elastic modulus.
The idea presented by Rybicki and Kanninen [32] is based on the calculation of the energy release rate, using Irwin assumption that the energy released in the process of crack expansion is equal to work required to close the crack to its original state as the crack extends by a small amount Δa. Irwin computed this work as:
Where u is the relative displacement, σ the stress, r the distance from the crack tip, and Δa the change in virtual crack length.
Therefore, the energy release rate is:
The work W can be expressed by:
Where F is the force needed to close the crack virtually, u is the crack opening displacement. Equation 3 allows the calculation of the energy release rate for 2D FE models (mode I and II).
The application of the VCCT in 3D FE models is commonly called the 3D VCCT. The extension of the method from 2D to 3D requires replacing Eq. (3) with Eq. (5)
Where Δa the distance from the crack tip in the third direction and h is the element size in the third direction .
To apply Equation 5 to FE models comprising 8-node brick elements, the integrals in Eq. 5 are replaced with the sum:
Where index i controls direction and index k controls the node b number.
The stress intensity factor is analyzed along the thickness of the specimen characterized by positions as it is shown in Fig. 3.
4 Analysis and results
4.1 Effect of the plate thickness
Extending the fatigue of structures initially damaged by cracking is analyzed in terms of reducing the stress intensity factor along repaired crack front. A numerical study by the finite element method was conducted to analyze the SIF along the crack front for patched and unpatched plate (Fig. 4, 5, 6 and 7). The analysis of these figures shows that, whatever the plate thickness, this SIF resulting from unrepaired crack does not vary practically along this thickness. This means that the propagation of this crack is done uniformly in the volume of the plate. For repaired structures with high thicknesses (ep= 6 mm), the stress intensity factor increases linearly from the patched face towards the un-patched one, the values of the SIF at this last face approaches that of un-repaired structures (Figure 4 and 5). When the plate thickness decreases (Figure 5, 6 and 7) the Stress intensity factor decreases significantly at the un-repaired faces of the plate. The patching effect is thus more significant for thin plate. The fatigue life of repaired structures can be highly improved by the bonded composite patch for thin plate. These results are in concordance with those of the literature. Hosseini (H. Hosseini-Toudeshky.,2006) analyzed the effect of the ply number of the composite on the repair performance, he concluded that the crack growth life of the panel with the thickness of 2.29 mm, may increase about 65% and 236% by implementing a 4 or 16 layers patch respectively (H. Hosseini-Toudeshky.,2006). However, for 6.35 mm thickness, the life of repaired structures may be improved with 21–35% only according to Hosseini (J. Wang et al.,2009). We can conclude that it is more efficient to repair thick plates with double symmetric patch
0 1 2 3 4 5 6 4 6 8 10 12 14 16 18 20 22 ea = 0.2 mm er = 2 mm ep = 6 mm a / W = 0.2
: Plate without patch : Plate with patch
K ( M P a.m 0 ,5 ) Position
Fig. 4. Comparison of the SIF between patched and un-patched cracks (ep = 6 mm).
0 1 2 3 4 5 6 4 6 8 10 12 14 16 18 20 22 K ( M P a .m 0 ,5 ) Position ea = 0.2 mm e r = 2 mm ep = 4 mm a / W = 0.2
: Plate without patch : Plate with patch
Fig. 5. Comparison of the SIF between patched and un-patched cracks (ep = 4 mm).
0 1 2 3 4 5 6 4 6 8 10 12 14 16 18 20 22 K ( M P a .m 0,5 ) Position ea = 0.2 mm er = 2 mm ep = 2 mm a / W = 0.2
: Plate without patch : Plate with patch
0 1 2 3 4 5 6 4 6 8 10 12 14 16 18 20 22 K ( MPa. m 0,5 ) Position ea = 0.2 mm er = 2 mm ep = 1 mm a / W = 0.2
: Plate without patch : Plate with patch
Fig. 7. Comparison of the SIF between patched and un-patched cracks (ep = 1 mm).
4.2 Effect of the cracks length
In this paragraph The effect of the crack length on the SIF for repaired crack is analysed . Figure 8 presents the variation of the SIF along the crack front for different ratios a/W. It can be seen, that the increase of the size of repaired cracks involves an increase in the stress intensity factor at the crack fronts. This behavior is normal because the crack propagation leads to an increase of the stress around the crack front which is the cause of the higher values of the SIF. However, it can be noted, according to the results of figure 8, the effect of the crack length on the SIF variation is very weak at the unrepaired face but this effect is very significant at the un-repaired face of the plate. This is due to the presence of the composite patch on the repaired face of the plate. The stress transfer between the plate and the composite patch is important at the repaired faced and it is inexistent at the un-repaired face of the plate. This disequilibria may leads to an instability of the crack propagation. This problem can be solved by repairing thick plate with double sided symmetric patch.
0 1 2 3 4 5 6 3 6 9 12 15 18 21 24 27 30 33 36 K ( MP a.m 0,5 ) Position ea = 0.2 mm er = 2 mm ep = 6 mm : a/W = 0.2 : a/W = 0.3 : a/W = 0.4 : a/W = 0.5
4.3 Effect of the patch thickness
Figure 9 illustrates this effect by displaying the SIF variation along the crack front for various patch thicknesses. It can be seen that the increase of the patch thickness reduces significantly the stress intensity factor at the crack front. For example, the relative reduction of the SIF is about 30% when the wrap thickness varies between 1and 5 mm . These results allow us to confirm that the choice of thicker patches makes it possible to increase significantly their performances. For a better distribution of the stresses, it is preferable to use a multiple layers of bonded composite patch for repairing cracks. stresses, it is preferable to use a multiple layers of bonded composite patch for repairing cracks.
0 1 2 3 4 5 6 4 6 8 10 12 14 16 18 20 22 K ( MPa. m 0,5 ) Position ea = 0.2 mm ep = 6 mm a / W = 0.2 : er = 1 mm : er = 2 mm : er = 3 mm : er = 4 mm : er = 5 mm
Fig. 9. Effect of the patch thickness on the variation of the SIF.
4.4. Effect of the adhesive thickness
The adhesives used in bonded repairs are often required to carry a high level of stresses. The effect of the adhesive thickness on the distribution of the stress on the adhesive layer is very important. This effect will have a significant incidence on the repair performances. Figure 10 shows the variation of the stress intensity factors along the crack front for this adhesive thickness. It can be seen that a reduction in the adhesive thickness decreases the stress intensity factor, when the adhesive thickness varies between 0.1 and 0.3 mm. This means that lower adhesive thickness is desirable for repairing crack. When the adhesive thickness exceeds the value of 0.3 mm, its effect on the SIF variations becomes insignificant. In addition, it is recommended by the designers of the bonded composite repair that the adhesive thickness must be ranged between 0.1 and 0.3 mm in order to avoid the increase peel stresses.
0 1 2 3 4 5 6 4 6 8 10 12 14 16 18 20 22 K ( MP a .m 0,5 ) Position er = 2 mm ep = 6 mm a / W = 0.2 : e a = 0.1 mm : e a = 0.2 mm : ea = 0.3 mm : ea = 0.4 mm : e a = 0.5 mm
Fig. 10. Effect of the adhesive thickness on the variation of the SIF
5. Conclusions
The reduction of the stress intensity by the composition patch repair is very significant at the crack front, which improves the fatigue of repaired aircraft structures. The repair performances are highly reduced for thick plate. This is because there is a great difference in the SIF values between patched and un-patched faces. It is recommended to repair thick plates with double symmetric composite patch. The optimization of the geometrical properties of the adhesive and the patch can improve significantly the repair performances and durability. The use of multiple composite layers for repair can also improve the repair performances. In this case the ply orientations must be optimized. Acknowledgment
Authors Bel Abbes Bachir Bouiadjra and Abdulmohsen Alvedah extend their appreciation to the Deanship of Scientific Research at King Saud University for funding the work through the research group No. RGP-VPP-035
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