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Optimum design of symmetric composite patch repair to centre cracked metallic sheet
Composite Structures 49 (2000) 285±292
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Optimum design of symmetric composite patch repair to centre cracked metallic sheet A. Mahadesh Kumar, S.A. Hakeem * Aircraft Research and Design Centre, Hindustan Aeronautics Limited, Design Complex, Bangalore 560037, India
Abstract Composite patch repair of cracked metallic aircraft structures has recently been accepted as one of the means of improving fatigue life and attaining better structural integrity. The eectiveness of such patches for cracked sheets can be measured as an achievable reduction in the crack tip stress intensity factor (SIF). In this paper, a study has been conducted to get an optimum design of symmetric (balanced) composite patch to a centre cracked metallic sheet. It has been achieved considering the SIF at the crack tip of the sheet as constraint and the plan-form shape of patch and the thickness of patch as design variables. The results of square, circular, elliptical and rectangular patches are presented. The eectiveness of smaller patch length perpendicular to the crack compared to the full-length patch in the same direction has been brought out. A new con®guration called skewed patch is studied. Reduction in weight of the patch due to skewed con®guration has been brought out. The eectiveness of patch thickness over the patch plan-form shape in reducing SIF has been brought out. Ó 2000 Elsevier Science Ltd. All rights reserved. Keywords: Composite patch repair; Stress intensity factor; Optimum patch design; Skewed patch
1. Introduction Damage during the service life is a natural characteristic of any airframe. Performing repairs to damaged airframe components is virtually inevitable, from primarily economic reasons. A badly implemented repair can be more dangerous than the unrepaired con®guration. Out of various types of damages, cracks can possibly be repaired by either mechanically fastened doublers or bonded patches. The bonded patch oers many advantages over a mechanically fastened doubler which include improved fatigue life, reduced corrosion, in situ applications and easy conformance to complex aerodynamic contours. Bonded composite repairs have been shown to provide high levels of bond durability under the operating conditions. Researchers in Australia have extensively employed Boron±Epoxy bonded patches to repair cracks and to reinforce weak spots in airframes. Researchers in UK have employed carbon composite repairs to helicopter metallic primary structures. Most of the work is based on simple analysis or test data. This paper presents a scienti®c approach to the optimum design of composite repair patches.
*
Corresponding author. Tel.: +91-80-5233035; fax: +91-80-5234320.
Scienti®c approach to designing and assessing repairs before implementing started in 1970s. The work was pioneered by Baker [1] at Australian Research Laboratories (ARL) for Royal Australian Airforce (RAAF). By now, there are over 10 000 ¯ying patches at various locations on aircraft with dierent ¯eet. 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 call for intervention of the manufacturer for functional restoration. Most of the reported work is on composite patching of metallic airframe components. A bonded overlay of high strength composite material oers an ecient method for enhancing the structural integrity. Baker [1] has very precisely summarised a range of bene®ts derivable by application of selective composite reinforcement to existing metallic components. They include stiening under-designed regions, increasing static strength, restoring strength or stiness, reducing stress intensity, and improving damage tolerance in safe-life components. The team in Australia has very successfully employed Boron±Epoxy patch repairs to Macchi, Hercules, Mirage, Orion, F-111, B-727, B-767, B-747, Bell helicopter, and MD-82 [2]. Jones et al. [3] have studied the multi-site-damage problem on a test specimen representative of a fuselage lap joint in a commercial wide
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A.M. Kumar, S.A. Hakeem / Composite Structures 49 (2000) 285±292
bodied aircraft. The key feature, in addition to functional success, is the in situ repair, which leads to substantial savings in down time for the aircraft, at times repair can be performed overnight. Molent et al. [4] have presented an exhaustive eort undertaken at ARL for the repair of the integral stiener of the wing pivot ®tting of F-111C aircraft. The repair consisted of unidirectional boron/epoxy doublers bonded to the stiener, and co-cured with an adhesive at elevated temperature. In order to alleviate the thermally induced residual strains due to the elevated temperatures, the wing was preloaded during the doubler application. Finite element analysis was performed and validated using strain data survey conducted on the aircraft. As a proof of concept, simple test articles (dog bone specimen) were fabricated and tested. Following this work, the wing was successfully loaded to 100% proof load with no visible signs of deterioration. Finite element analysis of composite reinforcement by Mitchell et al. [5], appears to be the ®rst thorough attempt towards analytical understanding of this class of problems. He models the patch in two-dimensional (2D) plan-form as well as 2D longitudinal cross-section. The predicted strains were reported to be in good agreement with the experimental observations. At ARL, fairly early in their venture into repairs, Jones and Callinan [6] analytically investigated, using ®nite element method (FEM), the behaviour of composite patches to metallic sheets, permitting separate response of the sheet, adhesive and the patch to emerge. They emphasise patch tapering as a solution to stress reduction in the adhesive. Such an analysis can help optimise the patch con®guration [7]. They appear to be the only group to have analytically investigated repairs to thick sections [8] and the eects of expansion coecient on residual thermal stresses [9]. Rose [20±22] has applied integral equation approach to understand 2D idealisation of three-dimensional (3D) reinforced crack problems. Double symmetry eliminates the bending eects of unbalanced patches. Young et al. [10,11] have investigated eects of rectangular and elliptical balanced patches on stress intensity factors at crack tips in an uniaxially loaded sheet. They present a closed form approximate solution for large elliptic patches. More recently, Rooke et al. [12] developed the boundary element method and investigated the eect of central as well as oset patches on stress intensity factor at crack tips in stiened and unstiened sheets. Fatigue life was calculated using Paris law, and was found to depend in a complex way on the crack length and patch and stiener con®gurations. Central patches are found to be more useful for small cracks while oset patches are better for longer cracks. Similar observations have earlier been made by Chandra et al. [13], who used boundary collocation to solve in-
tegral equations representing patch eect on crack tip stress intensity factors. Liu and Fan [14] employed GreenÕs function approach and developed singular integral equations to evaluate stress singularities at crack tips and strip ends for bonded strip patch to cracked sheet. Arendt et al. [15] have quanti®ed bending eects of unsymmetrically bonded composite repairs on cracked aluminium panels, using plate linear ®nite element model. Stress intensity factors and strain energy release rates were obtained from the model using modi®ed crack closure method. They report negligible variation of stress intensity factor over the thickness of the cracked plate. On contrary Mahadesh et al. [16] report substantial variation through the thickness of sheet. An extensive review of patch repairs is reported by Ripudaman [17].
2. Problem de®nition It is required to repair a ¯at aluminium alloy sheet that has a centre crack, as shown in Fig. 1. The sheet width is 240 mm, length is 240 mm and thickness is 3 mm. The sheet is subjected to an uniaxial stress (r) of 166.67 MPa. The material properties of the aluminium alloy are YoungÕs Modulus E 71709 MPa, PoissonÕs ratio m 0:33, pK IC p plane strain fracture toughness 32:4 MPa M , Threshold SIF Kth 4:4 MPa M . The sheet under the uniaxial stress of 166.67 MPa has a critical crack length (2a) of 24 mm. The sheet with the crack length of 24 mm, therefore, has zero fatigue life. The sheet is to be repaired such that the fatigue life of
Fig. 1. Geometry of the sheet with central crack.
A.M. Kumar, S.A. Hakeem / Composite Structures 49 (2000) 285±292
the repaired sheet is restored to the same level as the sheet without crack. This is possible to be achieved by means of a composite patch bonded to the sheet. The design of the patch must be such that the crack tip stress intensity factor (SIF) must be reduced to the threshold SIF of the sheet. p In the problem de®ned, the sheet SIF is 32.4 MPa M , corresponding to r 166:67 MPa and 2a 24 mm. The composite patch bonded p tothe sheet must reduce the SIF from 32.4 Mpa M to the p threshold value of 4.4 Mpa M . There are two types of composite patches that can be employed. One is the composite patch bonded on one side of the sheet which is called as unsymmetric or unbalanced patch and the other is the patch bonded on both sides of the sheet which is called as symmetric or balanced patch. The symmetric patch is found more eective than the unsymmetric patch [16,18]. Therefore, a symmetric patch is chosen in the present study. The unidirectional carbon ®bre reinforced plastic (CFRP) patch has the properties of E1 135, E2 E3 9 GPa, m12 m13 0:3; m23 0:02; G12 G13 5 and G23 8 GPa. The ®bres are oriented normal to the crack line. The patch is bonded to the sheet by means of epoxy ®lm adhesive of 0.15 mm thickness. The properties of the epoxy ®lm adhesive (FM-73) are E 2158 MPa; m 0:35. The sheet with the patch is shown in Fig. 2.
287
well known and is widely used [19]. The MCCI method is used in the studies presented in this paper. 3.1. MCCI method In the MCCI method, the mesh around the crack should be suciently ®ne. The re®nement of the mesh is decided by taking distance between crack tip node and neighbouring nodes approximately equal to one-twentieth times the half-crack length. 3.2. Validation of MCCI method The FEM code numerically integrated elements for system analysis (NISA) is used for calculating the SIF using the MCCI method. The method is validated by comparing the FEM results with the closed form solution for the 240 240 3 mm3 sheet with the centre crack. Both 2D and 3D analysis have been performed. For the 2D analysis, the four noded general shell element (NKTP-20) is used. For the 3D analysis, the eight noded brick element (NKTP-4) is used. The element size near the crack tip is 0.6 mm which is one twentieth times the half-crack length. The ®nite element mesh is shown in Fig. 3. The results of FEM analysis and the closed form solution are presented in Table 1. The results are in good agreement and therefore validate the use of the MCCI method. The same mesh re®nement is used for all the patch repair studies in this paper.
3. Calculation of stress intensity factor
3.3. Use of eight noded brick element
A closed form solution for calculation of crack tip SIF of patch repaired cracks does not exist and therefore recourse to numerical techniques is taken. FEM is a powerful numerical technique for calculating SIF. Amongst the dierent methods of extracting SIF from FEM, modi®ed crack closure integral (MCCI) method is
A comparative study between eight noded brick element and 20 noded brick element is carried out to establish the error bounds associated with the solution. The SIF obtained for a square patch of side lengthp of 96 mm using eight noded brick element is 4.94 MPa M p and for 20 noded brick element is 5.08 MPa M . The dierence in the SIF is approximately 2.8%. However, solution using 20 noded brick element uses approximately 600 MB disk space and a CPU time of approximately 5500 s, whereas eight noded brick element of the same number of elements uses approximately 150 MB disk space and 600 s of CPU time on 64 MB RAM Pentium II processor PC. Since the error associated with the eight noded brick element is only 2.8% and since the present study involved about hundred solutions for dierent patch repair con®gurations, it is decided to use eight noded brick elements. 4. Design of patch
Fig. 2. Geometric model of the sheet with patch.
The sheet with a centre crack shown in Fig. 1 is to be repaired by bonding a symmetric composite patch, such that the SIF reduces to its threshold value of 4.4
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assumed constant. The geometry and the boundary conditions are doubly symmetric, therefore only one quarter is analysed. The adhesive is treated as cracked along with the sheet. The crack is modelled as the face free of traction. 4.1. Square patch For a square patch, the results of SIF variation with variation in patch size and thickness are shown in Fig. 4. From Fig. 4, it is observed that 1. thickness of patch has predominant eect on SIF, 2. the patch side length has lesser eect on SIF. 4.2. Circular patch For a circular patch, the results of SIF variation with variation in patch radius and thickness are shown in Fig. 5. From Fig. 5, it is observed that 1. thickness of patch has predominant eect on SIF, 2. the patch radius has lesser eect on SIF, 3. for given thickness there exists an optimum radius, below which the SIF rises sharply and above which the eect of radius on SIF is less. 4.3. Elliptical patch For an elliptical patch the variation in the SIF with the variation in the size of the patch and the thickness of the patch are shown in Fig. 6. From Fig. 6, it is observed that 1. for the same thickness and the same minor axis length, SIF reduces as major axis length increases, 2. there exists an optimum minor axis length, 3. elliptical patch (b < a) is more eective as compared to circular patch (b a), 4. elliptical patch (b > a) is less eective as compared to elliptical patch (b < a), 5. it is noted that the optimum minor axis length is 24 mm which is the length of the crack.
Fig. 3. Finite element mesh.
p Mpa M . The design variables are the plan-form shape and the thickness of the patch. The material properties of the patch and adhesive, the thickness of adhesive are
4.4. Rectangular patch For a rectangular patch, the results of variation in SIF with the size of the patch and the thickness of the
Table 1 Analysis to validate MCCI method Size of sheet (mm)
Crack length (mm)
Stress applied (MPa)
Type of Analysis
Closed-form p (MPa M )
MCCIp (MPa M )
% Error
240 240 3 240 240 3 240 240 3
24.0 30.0 24.0
166.67 166.67 166.67
2D 2D 3D
32.630 36.653 32.630
32.858 36.468 32.330
0.6 0.5 0.9
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Fig. 4. Square patch ± eect of thickness and side length of patch on SIF.
Fig. 5. Circular patch ± eect of thickness and radius of patch on SIF.
Fig. 6. Elliptical patch ± eect of variation of minor axis, major axis and thickness of patch on SIF.
patch are shown in Figs. 7 and 8. From Fig. 7, it is observed that 1. there exists an optimum length of the patch perpendicular to the crack line, 2. a rectangular patch (y < x) is more eective as compared to a square patch (y x),
289
Fig. 7. Rectangular patch ± eect of patch length perpendicular to crack line on SIF.
Fig. 8. Rectangular patch ± eect of patch length parallel to crack line on SIF.
3. a full-length patch (y 120 mm) in the direction perpendicular to the crack line is less eective, 4. it is noted that, as in the case of elliptical patch the optimum length of the patch perpendicular to the crack line is 24 mm, which is the length of the crack. From Fig. 8, it is observed that 1. thickness of patch has predominant eect on SIF, 2. increasing patch length along the crack line reduces SIF, 3. a full-length patch (x 120 mm) along the crack line is the most eective, 4. the SIF rises sharply as the patch length along the crack line is below a certain value. 4.4.1. Comparison of rectangular patch with elliptical patch The rectangular and the elliptical patch con®gurations are compared by keeping the volume of the patch constant. The results are presented in Table 2. From Table 2, it is observed that the rectangular patch is more eective in reducing SIF as compared to the elliptical patch of same volume.
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A.M. Kumar, S.A. Hakeem / Composite Structures 49 (2000) 285±292
Table 2 Comparison between rectangular and elliptical patch of same volume Case
Patch type
Size (mm)
Thickness (mm)
Volume (mm3 )
SIF (MPa
1
Elliptical Rectangular
a 36; b 24 x 28:27; y 24
2.25 2.25
12214.5 12214.5
4.02 3.91
2
Elliptical Rectangular
a 60; b 24 x 47:12; y 24
2.25 2.25
20357.5 20357.5
3.56 3.39
4.5. Skewed patch It was found in the studies of comparison of rectangular patch with elliptical patch, that the rectangular patch covers more of high stressed area of unpatched sheet as compared to the elliptical patch. This led to the concept of skewed patch. The skewed patch shape is arrived at in such a way that it covers more of high stress area and less of low stress area. The skewed patch con®guration is shown in Fig. 9. The skewed patch shown in Fig. 9 was found to be more eective in reducing SIF, than the rectangular patch, but the disadvantage is that it develops a region of high stress in the sheet, at the corner `S' as shown in Fig. 9. To eliminate the region of high stress the skewed patch is modi®ed as
p M)
shown in Fig. 10. The modi®ed skewed patch is de®ned by three lengths `p', `q' and `r'. 4.5.1. Skewed patch length `p' The variation of SIF with the length `p' of the skewed patch is shown in Fig. 11. The length `r' is related to length `p' in such a way that the patch area remains constant. From Fig. 11, it is observed that 1. there exists an optimum value for the length `p', 2. increasing length `q' is eective in reducing SIF, 3. the variation in SIF with length `p' is not signi®cant. 4.5.2. Skewed patch length `r' From Section 4.5.1, the optimum value of length `p' of the skewed patch is found to be 15 mm. Keeping the
Fig. 9. Skewed patch.
Fig. 11. Skewed patch ± eect of length `p' and length `q' on SIF.
Fig. 10. Skewed patch (modi®ed).
Fig. 12. Skewed patch ± eect of length `r' and length `q' on SIF.
A.M. Kumar, S.A. Hakeem / Composite Structures 49 (2000) 285±292
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Table 3 Comparison between skewed patch and rectangular patch Case
Patch type
Size (mm)
Thickness (mm)
Volume (mm3 )
SIF p (MPa M )
% Dierence in Volume
1
Rectangular Skewed
x 120; y 24 p 15; q 60; r 54
2.25 2.25
51840 37260
2.64 2.63
28.1
2
Rectangular Skewed
x 120; y 24 p 15; q 72; r 65
2.25 2.25
51840 51840
2.64 2.36
0.0
% Dierence in SIF 0.37 10.6
Table 4 Comparison between patch thickness and plan-form shape Case
Patch type
Size (mm)
Thickness (mm)
Volume (mm3 )
SIF p (MPa M )
% Dierence in SIF
1
Skewed
p 15; q 36; r 33 p 15; q 54; r 33
2.25 1.50
15552.0 15552.0
3.43 4.32
20.6
2
Rectangular
x 36; y 24 x 54; y 24
2.25 1.50
15552.0 15552.0
3.61 4.60
21.5
3
Elliptical
a 36; b 24 a 54; b 24
2.25 1.50
12214.5 12214.5
4.02 4.94
18.6
4
Square
a 30 a 36
2.25 1.50
16200.0 15552.0
4.02 5.21
22.8
5
Circular
R 30 R 36
2.25 1.50
12723.5 12214.5
4.27 5.52
22.6
Table 5 Order of merit of dierent patches Patch type
Size (mm)
Thickness (mm)
SIF (MPa
Skewed Rectangular Elliptical Square Circular
p 15; q 36; r 33 x 42; y 24 a 60; b 24 a 48 R 72
2.25 2.25 2.25 2.25 2.25
3.43 3.50 3.56 3.63 3.78
length `p' constant at 15 mm, the variation of SIF with the length `r' is shown in Fig. 12. From Fig. 12, it is observed that 1. increasing length `r' is eective in reducing SIF, 2. increasing length `q' is eective in reducing SIF. It is observed that increasing length `r' is restricted by the sheet stress. Beyond a certain length `r', the sheet stress near the skew end, shown as critical region in Fig. 10, would rise sharply. Therefore it is recommended that the slope of the patch edge ` r ÿ p=q' should not exceed 0.6±0.7. 4.5.3. Comparison of skewed patch with rectangular patch A rectangular patch having full length along the crack line, which is the most eective con®guration, is compared with the skewed patch and the results are shown in Table 3. From Table 3, it is observed that
p M)
Volume (mm3 ) 15552.0 18144.0 20357.5 41472.0 73287.1
1. for approximately the same value of SIF, a skewed patch is approximately 28% lesser in weight than a rectangular patch (case1), 2. for the same volume, the SIF of a skewed patch is approximately 10% lesser than a rectangular patch (case 2).
5. Patch thickness From the studies carried out on the repair of cracked sheet with composite patches, it is concluded that the patch thickness is the predominant design variable that determines the eectiveness of the patch. Table 4, shows the eect of patch thickness on SIF for dierent patch plan-form shapes. From Table 4, it is observed that, approximately more than 18% reduction
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A.M. Kumar, S.A. Hakeem / Composite Structures 49 (2000) 285±292
in SIF can be achieved by increasing thickness of patch instead of increasing plan-form area for the same volume of patch.
6. Patch plan-form Studies have been carried out on the repair of cracked sheet with composite patches. The patch plan-form studied includes square, circular, elliptical, rectangular and skewed. From these studies, it is concluded that the skewed plan-form is the most optimum. Table 5 shows the eectiveness of plan-form on SIF. From Table 5, it is observed that 1. for approximately the same SIF, the skewed planform has the least volume, 2. the order of merit of plan-form is skewed, rectangular, elliptical, square and circular.
7. Conclusions The results of the present study will lead to the optimum design of a symmetric composite patch repair to a centre crack metallic sheet. From the results, the following conclusions are drawn: 1. A skewed patch is the most optimum patch design. 2. Care should be taken while designing skewed patches to ensure that the stresses in the sheet are within the design limits. 3. A rectangular patch is the second optimum patch design and is more eective than elliptical, circular and square patches. 4. In the case of a rectangular patch full-length patch perpendicular to the crack line is less eective compared to smaller patch lengths. The optimum patch length perpendicular to the crack line happens to be equal to the crack length. A full-length patch in the direction of the crack line is the most eective. 5. An elliptical patch is the third optimum patch design. An elliptical patch with major axis parallel to the crack line is more eective than the patch with major axis perpendicular to the crack line. In the case of an elliptical patch also, the optimum minor axis length perpendicular to the crack line happens to be equal to the crack length. An elliptical patch with major axis dimension equal to the width of the sheet, is the most eective. 6. If there is a choice between increasing thickness of the patch or increasing the area of the patch, it is better to increase the patch thickness.
References [1] Baker AA. Repair of cracked or defective metallic aircraft components with advanced ®bre composites ± an overview of Australian work. Comp Struct 1984;2:153±81. [2] Baker AA, Chester RJ. Recent advances in bonded composite repair technology for metallic aircraft components. In: Chandra T, Dhingra AK, editors. Advanced composites 93, Proceedings of the International Conference on Advanced Composite Materials 1993:45±9. [3] Jones R, Bridgford N, Wallace G, Molent L. Bonded repair of multi-site damage. In: Atluri SN, Sampath SG, Tong P, editors. Structural integrity of ageing airplanes. Berlin: Springer, 1991, pp. 199±212. [4] Molent L, Callinan RJ, Jones R. Design of an all boron/epoxy doubler reinforcement for F-111C wing pivot ®tting: structural aspects. Comp Struct 1989;11:57±83. [5] Mitchell RA, Woolley RM, Chwirut DJ. Analysis of composite reinforced cut-outs and cracks. AIAA J 1975;4:744±9. [6] Jones R, Callinan RJ. Finite element analysis of patched cracks. J Struct Mech 1979;7(2):107±30. [7] Jones R, Callinan RJ. A design study in crack patching. Fibre Sci Technol 1981;14:99±111. [8] Jones R, Davis M, Callinan RJ, Mallinson GD. Crack patching analysis and design. J Struct Mech 1982;10(2):177±90. [9] Jones R, Callinan RJ. Thermal considerations in the patching of metal sheets with composite overlays. J Struct Mech 1980;8(2):143±9. [10] Young A, Cartwright DJ, Rooke DP. Model studies of repair patches. In: Proceedings of the International Conference on Fatigue, Corrosion, Cracking, Fracture Mechanics and Failure Analysis, Salt Lake City, 1989:339±46. [11] Young A, Rooke, DP, Cartwright DJ. Numerical study of balanced patch repairs to cracked sheets. Aer J 1989:327±34. [12] Rooke DP, Young A, Courtney TJ. Eect of repair patches on fatigue lifetimes. In: Atluri SN, Harris CE, Hoggard A, Miller N, Sampath SG, editors. Durability of metal aircraft structures. Atlanta Technology Publications, 1992, pp. 132±45. [13] Ramesh C, Murthy MVV, Ramamurthy TS, Rao AK. Analaytical estimation of stress intensity factors in patched cracked plates. Eng Frac Mech 1985;21(3):479±94. [14] Liu T, Fan W. Analysis for an adhesively bonded ®nite strip repair to a cracked plate. Eng Frac Mech 1994;47(5):629±37. [15] Arendt C, Sun CT. Bending eects of unsymmetric adhesively bonded composite repairs on cracked aluminium panels. NASA CP 1994;3274:33±48. [16] MahadeshKumar A, Ripudaman S. Modelling composite patch repairs to cracked metallic sheet. In: NISA UsersÕ Conference 1995, Bangalore, India. [17] Ripudaman S. Repairs to damage tolerant structures: issues and a viewpoint. J Aero Soc India 1996:169±86. [18] MahadeshKumar A, Ripudaman S. 3D ®nite element modelling of a composite patch repair. In: ICF9, Sydney, Australia, 1997:2159±66. [19] Rybiki EF, Kanninen EF. A ®nite element calculation of stress intensity factor by modi®ed crack closure integral. Eng Frac Mech 1977;9:931±8. [20] Rose LRF. An Application of inclusion analogy for bonded reinforcements. Int J Solids Struct 1981;17:827±38. [21] Rose LRF. A cracked plate repaired by bonded reinforcements. Int J Frac 1982;18:135±44. [22] Rose LRF. Crack reinforcement by distributed springs. J Mech Phys Solids 1987;35:383±440.
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Optimum design of symmetric composite patch repair to centre cracked metallic sheet A. Mahadesh Kumar, S.A. Hakeem * Aircraft Research and Design Centre, Hindustan Aeronautics Limited, Design Complex, Bangalore 560037, India
Abstract Composite patch repair of cracked metallic aircraft structures has recently been accepted as one of the means of improving fatigue life and attaining better structural integrity. The eectiveness of such patches for cracked sheets can be measured as an achievable reduction in the crack tip stress intensity factor (SIF). In this paper, a study has been conducted to get an optimum design of symmetric (balanced) composite patch to a centre cracked metallic sheet. It has been achieved considering the SIF at the crack tip of the sheet as constraint and the plan-form shape of patch and the thickness of patch as design variables. The results of square, circular, elliptical and rectangular patches are presented. The eectiveness of smaller patch length perpendicular to the crack compared to the full-length patch in the same direction has been brought out. A new con®guration called skewed patch is studied. Reduction in weight of the patch due to skewed con®guration has been brought out. The eectiveness of patch thickness over the patch plan-form shape in reducing SIF has been brought out. Ó 2000 Elsevier Science Ltd. All rights reserved. Keywords: Composite patch repair; Stress intensity factor; Optimum patch design; Skewed patch
1. Introduction Damage during the service life is a natural characteristic of any airframe. Performing repairs to damaged airframe components is virtually inevitable, from primarily economic reasons. A badly implemented repair can be more dangerous than the unrepaired con®guration. Out of various types of damages, cracks can possibly be repaired by either mechanically fastened doublers or bonded patches. The bonded patch oers many advantages over a mechanically fastened doubler which include improved fatigue life, reduced corrosion, in situ applications and easy conformance to complex aerodynamic contours. Bonded composite repairs have been shown to provide high levels of bond durability under the operating conditions. Researchers in Australia have extensively employed Boron±Epoxy bonded patches to repair cracks and to reinforce weak spots in airframes. Researchers in UK have employed carbon composite repairs to helicopter metallic primary structures. Most of the work is based on simple analysis or test data. This paper presents a scienti®c approach to the optimum design of composite repair patches.
*
Corresponding author. Tel.: +91-80-5233035; fax: +91-80-5234320.
Scienti®c approach to designing and assessing repairs before implementing started in 1970s. The work was pioneered by Baker [1] at Australian Research Laboratories (ARL) for Royal Australian Airforce (RAAF). By now, there are over 10 000 ¯ying patches at various locations on aircraft with dierent ¯eet. 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 call for intervention of the manufacturer for functional restoration. Most of the reported work is on composite patching of metallic airframe components. A bonded overlay of high strength composite material oers an ecient method for enhancing the structural integrity. Baker [1] has very precisely summarised a range of bene®ts derivable by application of selective composite reinforcement to existing metallic components. They include stiening under-designed regions, increasing static strength, restoring strength or stiness, reducing stress intensity, and improving damage tolerance in safe-life components. The team in Australia has very successfully employed Boron±Epoxy patch repairs to Macchi, Hercules, Mirage, Orion, F-111, B-727, B-767, B-747, Bell helicopter, and MD-82 [2]. Jones et al. [3] have studied the multi-site-damage problem on a test specimen representative of a fuselage lap joint in a commercial wide
0263-8223/00/$ - see front matter Ó 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 3 - 8 2 2 3 ( 0 0 ) 0 0 0 0 5 - 2
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bodied aircraft. The key feature, in addition to functional success, is the in situ repair, which leads to substantial savings in down time for the aircraft, at times repair can be performed overnight. Molent et al. [4] have presented an exhaustive eort undertaken at ARL for the repair of the integral stiener of the wing pivot ®tting of F-111C aircraft. The repair consisted of unidirectional boron/epoxy doublers bonded to the stiener, and co-cured with an adhesive at elevated temperature. In order to alleviate the thermally induced residual strains due to the elevated temperatures, the wing was preloaded during the doubler application. Finite element analysis was performed and validated using strain data survey conducted on the aircraft. As a proof of concept, simple test articles (dog bone specimen) were fabricated and tested. Following this work, the wing was successfully loaded to 100% proof load with no visible signs of deterioration. Finite element analysis of composite reinforcement by Mitchell et al. [5], appears to be the ®rst thorough attempt towards analytical understanding of this class of problems. He models the patch in two-dimensional (2D) plan-form as well as 2D longitudinal cross-section. The predicted strains were reported to be in good agreement with the experimental observations. At ARL, fairly early in their venture into repairs, Jones and Callinan [6] analytically investigated, using ®nite element method (FEM), the behaviour of composite patches to metallic sheets, permitting separate response of the sheet, adhesive and the patch to emerge. They emphasise patch tapering as a solution to stress reduction in the adhesive. Such an analysis can help optimise the patch con®guration [7]. They appear to be the only group to have analytically investigated repairs to thick sections [8] and the eects of expansion coecient on residual thermal stresses [9]. Rose [20±22] has applied integral equation approach to understand 2D idealisation of three-dimensional (3D) reinforced crack problems. Double symmetry eliminates the bending eects of unbalanced patches. Young et al. [10,11] have investigated eects of rectangular and elliptical balanced patches on stress intensity factors at crack tips in an uniaxially loaded sheet. They present a closed form approximate solution for large elliptic patches. More recently, Rooke et al. [12] developed the boundary element method and investigated the eect of central as well as oset patches on stress intensity factor at crack tips in stiened and unstiened sheets. Fatigue life was calculated using Paris law, and was found to depend in a complex way on the crack length and patch and stiener con®gurations. Central patches are found to be more useful for small cracks while oset patches are better for longer cracks. Similar observations have earlier been made by Chandra et al. [13], who used boundary collocation to solve in-
tegral equations representing patch eect on crack tip stress intensity factors. Liu and Fan [14] employed GreenÕs function approach and developed singular integral equations to evaluate stress singularities at crack tips and strip ends for bonded strip patch to cracked sheet. Arendt et al. [15] have quanti®ed bending eects of unsymmetrically bonded composite repairs on cracked aluminium panels, using plate linear ®nite element model. Stress intensity factors and strain energy release rates were obtained from the model using modi®ed crack closure method. They report negligible variation of stress intensity factor over the thickness of the cracked plate. On contrary Mahadesh et al. [16] report substantial variation through the thickness of sheet. An extensive review of patch repairs is reported by Ripudaman [17].
2. Problem de®nition It is required to repair a ¯at aluminium alloy sheet that has a centre crack, as shown in Fig. 1. The sheet width is 240 mm, length is 240 mm and thickness is 3 mm. The sheet is subjected to an uniaxial stress (r) of 166.67 MPa. The material properties of the aluminium alloy are YoungÕs Modulus E 71709 MPa, PoissonÕs ratio m 0:33, pK IC p plane strain fracture toughness 32:4 MPa M , Threshold SIF Kth 4:4 MPa M . The sheet under the uniaxial stress of 166.67 MPa has a critical crack length (2a) of 24 mm. The sheet with the crack length of 24 mm, therefore, has zero fatigue life. The sheet is to be repaired such that the fatigue life of
Fig. 1. Geometry of the sheet with central crack.
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the repaired sheet is restored to the same level as the sheet without crack. This is possible to be achieved by means of a composite patch bonded to the sheet. The design of the patch must be such that the crack tip stress intensity factor (SIF) must be reduced to the threshold SIF of the sheet. p In the problem de®ned, the sheet SIF is 32.4 MPa M , corresponding to r 166:67 MPa and 2a 24 mm. The composite patch bonded p tothe sheet must reduce the SIF from 32.4 Mpa M to the p threshold value of 4.4 Mpa M . There are two types of composite patches that can be employed. One is the composite patch bonded on one side of the sheet which is called as unsymmetric or unbalanced patch and the other is the patch bonded on both sides of the sheet which is called as symmetric or balanced patch. The symmetric patch is found more eective than the unsymmetric patch [16,18]. Therefore, a symmetric patch is chosen in the present study. The unidirectional carbon ®bre reinforced plastic (CFRP) patch has the properties of E1 135, E2 E3 9 GPa, m12 m13 0:3; m23 0:02; G12 G13 5 and G23 8 GPa. The ®bres are oriented normal to the crack line. The patch is bonded to the sheet by means of epoxy ®lm adhesive of 0.15 mm thickness. The properties of the epoxy ®lm adhesive (FM-73) are E 2158 MPa; m 0:35. The sheet with the patch is shown in Fig. 2.
287
well known and is widely used [19]. The MCCI method is used in the studies presented in this paper. 3.1. MCCI method In the MCCI method, the mesh around the crack should be suciently ®ne. The re®nement of the mesh is decided by taking distance between crack tip node and neighbouring nodes approximately equal to one-twentieth times the half-crack length. 3.2. Validation of MCCI method The FEM code numerically integrated elements for system analysis (NISA) is used for calculating the SIF using the MCCI method. The method is validated by comparing the FEM results with the closed form solution for the 240 240 3 mm3 sheet with the centre crack. Both 2D and 3D analysis have been performed. For the 2D analysis, the four noded general shell element (NKTP-20) is used. For the 3D analysis, the eight noded brick element (NKTP-4) is used. The element size near the crack tip is 0.6 mm which is one twentieth times the half-crack length. The ®nite element mesh is shown in Fig. 3. The results of FEM analysis and the closed form solution are presented in Table 1. The results are in good agreement and therefore validate the use of the MCCI method. The same mesh re®nement is used for all the patch repair studies in this paper.
3. Calculation of stress intensity factor
3.3. Use of eight noded brick element
A closed form solution for calculation of crack tip SIF of patch repaired cracks does not exist and therefore recourse to numerical techniques is taken. FEM is a powerful numerical technique for calculating SIF. Amongst the dierent methods of extracting SIF from FEM, modi®ed crack closure integral (MCCI) method is
A comparative study between eight noded brick element and 20 noded brick element is carried out to establish the error bounds associated with the solution. The SIF obtained for a square patch of side lengthp of 96 mm using eight noded brick element is 4.94 MPa M p and for 20 noded brick element is 5.08 MPa M . The dierence in the SIF is approximately 2.8%. However, solution using 20 noded brick element uses approximately 600 MB disk space and a CPU time of approximately 5500 s, whereas eight noded brick element of the same number of elements uses approximately 150 MB disk space and 600 s of CPU time on 64 MB RAM Pentium II processor PC. Since the error associated with the eight noded brick element is only 2.8% and since the present study involved about hundred solutions for dierent patch repair con®gurations, it is decided to use eight noded brick elements. 4. Design of patch
Fig. 2. Geometric model of the sheet with patch.
The sheet with a centre crack shown in Fig. 1 is to be repaired by bonding a symmetric composite patch, such that the SIF reduces to its threshold value of 4.4
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assumed constant. The geometry and the boundary conditions are doubly symmetric, therefore only one quarter is analysed. The adhesive is treated as cracked along with the sheet. The crack is modelled as the face free of traction. 4.1. Square patch For a square patch, the results of SIF variation with variation in patch size and thickness are shown in Fig. 4. From Fig. 4, it is observed that 1. thickness of patch has predominant eect on SIF, 2. the patch side length has lesser eect on SIF. 4.2. Circular patch For a circular patch, the results of SIF variation with variation in patch radius and thickness are shown in Fig. 5. From Fig. 5, it is observed that 1. thickness of patch has predominant eect on SIF, 2. the patch radius has lesser eect on SIF, 3. for given thickness there exists an optimum radius, below which the SIF rises sharply and above which the eect of radius on SIF is less. 4.3. Elliptical patch For an elliptical patch the variation in the SIF with the variation in the size of the patch and the thickness of the patch are shown in Fig. 6. From Fig. 6, it is observed that 1. for the same thickness and the same minor axis length, SIF reduces as major axis length increases, 2. there exists an optimum minor axis length, 3. elliptical patch (b < a) is more eective as compared to circular patch (b a), 4. elliptical patch (b > a) is less eective as compared to elliptical patch (b < a), 5. it is noted that the optimum minor axis length is 24 mm which is the length of the crack.
Fig. 3. Finite element mesh.
p Mpa M . The design variables are the plan-form shape and the thickness of the patch. The material properties of the patch and adhesive, the thickness of adhesive are
4.4. Rectangular patch For a rectangular patch, the results of variation in SIF with the size of the patch and the thickness of the
Table 1 Analysis to validate MCCI method Size of sheet (mm)
Crack length (mm)
Stress applied (MPa)
Type of Analysis
Closed-form p (MPa M )
MCCIp (MPa M )
% Error
240 240 3 240 240 3 240 240 3
24.0 30.0 24.0
166.67 166.67 166.67
2D 2D 3D
32.630 36.653 32.630
32.858 36.468 32.330
0.6 0.5 0.9
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Fig. 4. Square patch ± eect of thickness and side length of patch on SIF.
Fig. 5. Circular patch ± eect of thickness and radius of patch on SIF.
Fig. 6. Elliptical patch ± eect of variation of minor axis, major axis and thickness of patch on SIF.
patch are shown in Figs. 7 and 8. From Fig. 7, it is observed that 1. there exists an optimum length of the patch perpendicular to the crack line, 2. a rectangular patch (y < x) is more eective as compared to a square patch (y x),
289
Fig. 7. Rectangular patch ± eect of patch length perpendicular to crack line on SIF.
Fig. 8. Rectangular patch ± eect of patch length parallel to crack line on SIF.
3. a full-length patch (y 120 mm) in the direction perpendicular to the crack line is less eective, 4. it is noted that, as in the case of elliptical patch the optimum length of the patch perpendicular to the crack line is 24 mm, which is the length of the crack. From Fig. 8, it is observed that 1. thickness of patch has predominant eect on SIF, 2. increasing patch length along the crack line reduces SIF, 3. a full-length patch (x 120 mm) along the crack line is the most eective, 4. the SIF rises sharply as the patch length along the crack line is below a certain value. 4.4.1. Comparison of rectangular patch with elliptical patch The rectangular and the elliptical patch con®gurations are compared by keeping the volume of the patch constant. The results are presented in Table 2. From Table 2, it is observed that the rectangular patch is more eective in reducing SIF as compared to the elliptical patch of same volume.
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Table 2 Comparison between rectangular and elliptical patch of same volume Case
Patch type
Size (mm)
Thickness (mm)
Volume (mm3 )
SIF (MPa
1
Elliptical Rectangular
a 36; b 24 x 28:27; y 24
2.25 2.25
12214.5 12214.5
4.02 3.91
2
Elliptical Rectangular
a 60; b 24 x 47:12; y 24
2.25 2.25
20357.5 20357.5
3.56 3.39
4.5. Skewed patch It was found in the studies of comparison of rectangular patch with elliptical patch, that the rectangular patch covers more of high stressed area of unpatched sheet as compared to the elliptical patch. This led to the concept of skewed patch. The skewed patch shape is arrived at in such a way that it covers more of high stress area and less of low stress area. The skewed patch con®guration is shown in Fig. 9. The skewed patch shown in Fig. 9 was found to be more eective in reducing SIF, than the rectangular patch, but the disadvantage is that it develops a region of high stress in the sheet, at the corner `S' as shown in Fig. 9. To eliminate the region of high stress the skewed patch is modi®ed as
p M)
shown in Fig. 10. The modi®ed skewed patch is de®ned by three lengths `p', `q' and `r'. 4.5.1. Skewed patch length `p' The variation of SIF with the length `p' of the skewed patch is shown in Fig. 11. The length `r' is related to length `p' in such a way that the patch area remains constant. From Fig. 11, it is observed that 1. there exists an optimum value for the length `p', 2. increasing length `q' is eective in reducing SIF, 3. the variation in SIF with length `p' is not signi®cant. 4.5.2. Skewed patch length `r' From Section 4.5.1, the optimum value of length `p' of the skewed patch is found to be 15 mm. Keeping the
Fig. 9. Skewed patch.
Fig. 11. Skewed patch ± eect of length `p' and length `q' on SIF.
Fig. 10. Skewed patch (modi®ed).
Fig. 12. Skewed patch ± eect of length `r' and length `q' on SIF.
A.M. Kumar, S.A. Hakeem / Composite Structures 49 (2000) 285±292
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Table 3 Comparison between skewed patch and rectangular patch Case
Patch type
Size (mm)
Thickness (mm)
Volume (mm3 )
SIF p (MPa M )
% Dierence in Volume
1
Rectangular Skewed
x 120; y 24 p 15; q 60; r 54
2.25 2.25
51840 37260
2.64 2.63
28.1
2
Rectangular Skewed
x 120; y 24 p 15; q 72; r 65
2.25 2.25
51840 51840
2.64 2.36
0.0
% Dierence in SIF 0.37 10.6
Table 4 Comparison between patch thickness and plan-form shape Case
Patch type
Size (mm)
Thickness (mm)
Volume (mm3 )
SIF p (MPa M )
% Dierence in SIF
1
Skewed
p 15; q 36; r 33 p 15; q 54; r 33
2.25 1.50
15552.0 15552.0
3.43 4.32
20.6
2
Rectangular
x 36; y 24 x 54; y 24
2.25 1.50
15552.0 15552.0
3.61 4.60
21.5
3
Elliptical
a 36; b 24 a 54; b 24
2.25 1.50
12214.5 12214.5
4.02 4.94
18.6
4
Square
a 30 a 36
2.25 1.50
16200.0 15552.0
4.02 5.21
22.8
5
Circular
R 30 R 36
2.25 1.50
12723.5 12214.5
4.27 5.52
22.6
Table 5 Order of merit of dierent patches Patch type
Size (mm)
Thickness (mm)
SIF (MPa
Skewed Rectangular Elliptical Square Circular
p 15; q 36; r 33 x 42; y 24 a 60; b 24 a 48 R 72
2.25 2.25 2.25 2.25 2.25
3.43 3.50 3.56 3.63 3.78
length `p' constant at 15 mm, the variation of SIF with the length `r' is shown in Fig. 12. From Fig. 12, it is observed that 1. increasing length `r' is eective in reducing SIF, 2. increasing length `q' is eective in reducing SIF. It is observed that increasing length `r' is restricted by the sheet stress. Beyond a certain length `r', the sheet stress near the skew end, shown as critical region in Fig. 10, would rise sharply. Therefore it is recommended that the slope of the patch edge ` r ÿ p=q' should not exceed 0.6±0.7. 4.5.3. Comparison of skewed patch with rectangular patch A rectangular patch having full length along the crack line, which is the most eective con®guration, is compared with the skewed patch and the results are shown in Table 3. From Table 3, it is observed that
p M)
Volume (mm3 ) 15552.0 18144.0 20357.5 41472.0 73287.1
1. for approximately the same value of SIF, a skewed patch is approximately 28% lesser in weight than a rectangular patch (case1), 2. for the same volume, the SIF of a skewed patch is approximately 10% lesser than a rectangular patch (case 2).
5. Patch thickness From the studies carried out on the repair of cracked sheet with composite patches, it is concluded that the patch thickness is the predominant design variable that determines the eectiveness of the patch. Table 4, shows the eect of patch thickness on SIF for dierent patch plan-form shapes. From Table 4, it is observed that, approximately more than 18% reduction
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in SIF can be achieved by increasing thickness of patch instead of increasing plan-form area for the same volume of patch.
6. Patch plan-form Studies have been carried out on the repair of cracked sheet with composite patches. The patch plan-form studied includes square, circular, elliptical, rectangular and skewed. From these studies, it is concluded that the skewed plan-form is the most optimum. Table 5 shows the eectiveness of plan-form on SIF. From Table 5, it is observed that 1. for approximately the same SIF, the skewed planform has the least volume, 2. the order of merit of plan-form is skewed, rectangular, elliptical, square and circular.
7. Conclusions The results of the present study will lead to the optimum design of a symmetric composite patch repair to a centre crack metallic sheet. From the results, the following conclusions are drawn: 1. A skewed patch is the most optimum patch design. 2. Care should be taken while designing skewed patches to ensure that the stresses in the sheet are within the design limits. 3. A rectangular patch is the second optimum patch design and is more eective than elliptical, circular and square patches. 4. In the case of a rectangular patch full-length patch perpendicular to the crack line is less eective compared to smaller patch lengths. The optimum patch length perpendicular to the crack line happens to be equal to the crack length. A full-length patch in the direction of the crack line is the most eective. 5. An elliptical patch is the third optimum patch design. An elliptical patch with major axis parallel to the crack line is more eective than the patch with major axis perpendicular to the crack line. In the case of an elliptical patch also, the optimum minor axis length perpendicular to the crack line happens to be equal to the crack length. An elliptical patch with major axis dimension equal to the width of the sheet, is the most eective. 6. If there is a choice between increasing thickness of the patch or increasing the area of the patch, it is better to increase the patch thickness.
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