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Towards optimization of patch shape on the performance of bonded composite repair using FEM
Composites: Part B 45 (2013) 710–720
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Composites: Part B journal homepage: www.elsevier.com/locate/compositesb
Towards optimization of patch shape on the performance of bonded composite repair using FEM M. Ramji ⇑, R. Srilakshmi, M. Bhanu Prakash Department of Mechanical Engineering, Engineering Optics Lab, Indian Institute of Technology Hyderabad, Hyderabad 502 205, India
a r t i c l e
i n f o
Article history: Received 8 March 2012 Received in revised form 18 May 2012 Accepted 17 July 2012 Available online 23 August 2012 Keywords: Bonded composite repair A. Carbon fiber B. Fracture C. Finite element analysis (FEA)
a b s t r a c t Composite repair is gaining importance for extending the service life of aging aircrafts. There are many parameters like patch thickness, patch layup configuration and patch shape influencing the performance of composite repair. Therefore a need exists to prioritize them. In this work a 3-D finite element analysis has been conducted to get an optimum composite patch shape applied on an inclined center cracked panel, repaired by symmetrical patch. The patch shapes considered are circle, rectangle, square, ellipse and octagon. Also SIF reduction is compared for the same volume of patch. It is observed that extended octagonal patch shape performs better in case of SIF reduction. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Integrity enhancement of damaged structures through composite repair is attracting considerable engineering attention in recent years. In particular lot of application is in aerospace sector where extension of service life is of primary interest from an economic perspective. Repair involving composite patch applied to cracked metallic sheets is done using either mechanical fastening or adhesive bonding. Mechanical fasteners introduce stress concentration there by reducing the residual strength of the repaired plate. Adhesively bonded composite patch have been shown to provide high levels of bond durability under the operating conditions. It also offers an efficient method for enhancing the structural integrity which includes stiffening of under-designed regions, increasing static strength, restoring strength or stiffness and reducing stress intensity factor (SIF) [1]. Further, composite laminates have high directional stiffness, high failure strain, durability under cyclic loading, low density and excellent formability. Therefore, it is preferred over isotropic patches which are predominantly made of metal [1]. Adhesively bonded repair of aircraft structures has been initiated by Baker in the early 1970s [1]. Two kinds of patch work are generally employed in composite repair: single sided (un-symmetrical) and double sided (symmetrical). Mostly double sided patch work is preferred as more reduction in SIF is seen [2]. There ⇑ Corresponding author. Address: Department of Mechanical Engineering, Indian Institute of Technology Hyderabad, ODF Campus, Yeddumailaram, Medak Dist., Hyderabad 502 205, India. Tel.: +91 040 23 01 6078; fax: +91 040 23 01 6032. E-mail address: [email protected] (M. Ramji). 1359-8368/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compositesb.2012.07.049
are many parameters like patch thickness, patch layup and patch shape which influences the performance of the repair. From the literature, it is identified that patch shape plays a major role in repair performance. Over the last two decade, a paradigm shift has happened in computational mechanics especially in the area of finite element method (FEM) and its application has penetrated into every engineering discipline. A detailed review of application of FEM to composite repair is available in the literature [3–12]. Umamaheswar and Singh [3] performed finite element based study of single sided patch repairs applied to thin aluminum sheets. They showed the SIF variation through the thickness of the panel assuming a straight crack front. Mahadesh Kumar and Hakeem [4] conducted the numerical analysis for optimum patch shape in case of symmetric repair of center cracked panel. They have used different patch shapes such as circular, elliptical and rectangular and have estimated SIF reduction. But their work dealt with only mode I crack problem. Brighenti [5] has developed the optimum design procedure for repair using genetic algorithm. He showed that patch shapes significantly affects the fracture and fatigue life of double sided repaired components. Chukwujekwu Okafor et al. [6] developed a finite element model for analyzing the stress distribution of cracked plates repaired with a single sided octagonal patch. They have studied in detail the stress distribution in the skin, patch and adhesive layer. Albedah et al. [7] have conducted finite element analysis to estimate SIF for single and double sided repairs having a circular patch shape. They have compared the mass gain for both the cases. Recently, Rachid et al. [8] have found that the H shape patch performs better than the rectangular patch. They also concluded that the H
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M. Ramji et al. / Composites: Part B 45 (2013) 710–720 Table 1 Material properties.
a b c
Material
Exa (GPa)
Ey, Ez (GPa)
txyb, txz
tyz
Gxyc, Gxz (GPa)
Gyz (GPa)
Aluminum Adhesive Carbon/epoxy
73.1 4.59 135
– – 9
0.3 0.47 0.3
– – 0.02
– – 5
– – 8
E – Young’s modulus. t – Poisson’s ratio. G – Shear modulus.
Fig. 1. Geometry of the repair model having square patch symmetrical patch (a) front view, and (b) side view (all dimensions are in mm).
shape patch with arrow head improves the performance of the bonded repair. But they considered only mode I crack for their analysis. Bachir Bouiadjra et al. [9] have carried out the finite element analysis to compare the repair performance of patches with rectangular and trapezoidal shapes applied to mode I problem. They concluded that the trapezoidal patch shape works far better than the rectangular patches up to certain crack length. All these above works have been exclusively carried out for mode I problem and none addresses the repair of mixed mode cracked panel. Hosseini-Toudeshky et al. [10] have carried out experimental investigation for single sided repaired panels containing inclined center crack. Also they did FEM simulation of fatigue crack growth for a single sided repaired panel. But they have not studied impact of patch shape on the repair performance. Recently, Ramji et al. [11,12] have investigated that in the case of an unsymmetrical patch, there is no significant impact of patch shape on SIF reduction for mixed-mode problem.
In this work FEM based study of optimum patch shape applied to mixed mode cracked panel is carried out under linear elastic fracture mechanics (LEFM) frame work. Only static analysis has been performed. Different patch shapes like circle, rectangle, square, ellipse, and octagon are considered. Comparison of the performance of bonded repair is done by analyzing SIF reduction at the crack tip. Only double sided patch model is considered in this work. It is found that extended octagonal and rectangular patch shape perform better for mixed mode problem.
2. Technological and mechanical challenges in patch repair The adhesively bonded repair to the metallic structure allows the restoration of strength and stiffness of the structure, as well as slowing crack growth by reducing SIF. Application of bonded composite repair technology is challenging from both the scientific
Fig. 2. Estimation of KI/KII ratio (a) two coincident nodes near the crack tip before loading, and (b) two nearest nodes near the crack tip after loading.
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Fig. 3. Finite element model of cracked panel (a) entire panel, and (b) zoomed portion around the crack tip.
and engineering point of view, in particular repair of primary and secondary load bearing aircraft structures. This is because composite repair technology involves interdisciplinary inputs from several fields such as aerodynamic loading, stress analysis, fiber composite manufacturing, structural adhesive bonding, fracture mechanics
and fatigue. In general composite repair can be broadly classified into passive and active repair. Over last two decades only passive patch repair work has been studied and currently researchers are working on the active patch repair study involving smart materials [13]. The role of active smart patches made of piezoelectric actuators has been explored for active restoration of the repaired structures by introducing a local moment/force in opposite sense thereby reducing the SIF [14]. These piezoelectric patches are transversely isotropic by nature and it can be adhesively bonded. Still, this technology is explored at the lab scale and more work needs to be done for making it to certification stage. Till date, composite repair is mainly carried out on defective secondary load bearing structures and not on primary one. The technological challenge for the next decade will be on application of composite repair to defective primary load bearing structures. Because the application of bonded composite repairs to cracked primary structures is generally acceptable only on the basis of continuous monitoring of patch performance to ensure that the load transfer is maintained and also able to monitor damage growth in the parent/patch material. In case of composite patch damages like delamination, matrix cracking, and fiber pull out. should be detected and prevent further catastrophic failures. Therefore, a suitable non-destructive testing system should be devised for continuous online monitoring. The active patch material can also be used as sensors for predicting failures in the repaired system with slight adjustment utilizing their sensitivity to electro-mechanical coupling [13]. From the mechanical standpoint, two major challenges exist; firstly, proper adhesion/bonding of the patch on the defective panel
Fig. 4. Finite element model of composite repair model having patches of different shapes (a) circular, (b) rectangular, (c) square, (d) elliptical, (e) regular octagon, and (f) extended octagon.
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Fig. 5. Comparison of analytical SIF variation through the thickness with the numerical values from FEM for the center cracked panel having an inclined crack at b = 45°.
surface and secondly selection of appropriate adhesive. For better adhesion a good surface preparation is required and various techniques such as etching, shot peening or sand blasting are cited in the literature [1]. Depending upon nature of adhesive and panel surface, appropriate surface preparation techniques should be employed. A lot of research is currently going on in this direction for better surface preparation. Secondly, the choice of adhesive and its thickness plays a major role on the integrity aspect and supposedly it is the weakest link. Adhesives are generally classified as brittle,
intermediate and ductile [15]. Depending upon the combination of parent and patch material one can choose the kind of adhesive. In this work the patch is bonded symmetrically to the panel using AV138/HV998 adhesive material. This adhesive is highly stiff and brittle in nature having a very high elastic modulus [15] (see Table 1). The maximum shear strength of the brittle adhesive AV138 is 30 MPa and yield strength is 25 MPa [16]. Normally the upper limit of the interface strength can be taken as 30 MPa for the modeling behavior for doing damage propagation studies.
Fig. 6. Variation of SIF and factor R with the diameter D of circular patch (a) KI, (b) KII, and (c) R.
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Fig. 7. Variation of SIF and factor R against rectangular patch size B or H (a) KI, (b) KII, and (c) R.
Lastly, the adhesive thickness influences the strength of the joint as the load is transferred from the base metal to the patch via the adhesive. Thin adhesive layers are better than the thick layers because it gets the patch to be softer. But thickness provides good durability to the entire patch as thick adhesive layer attracts lesser strains. Good adhesive bonds are produced only in the range of thickness 0.125–0.25 mm [6] and in the present modeling the adhesive thickness (ta) is taken as 0.1 mm which is just sufficient to transfer the load. 3. Geometry and material properties The typical model for the cracked specimen is shown in Fig. 1. The panel is made of aluminum alloy 2014 T6 having the dimension of 160 39 3.175 mm3. It contains an inclined center crack ‘2a’ of length 10 mm. The panel thickness (ts) is taken as 3.175 mm. The crack is inclined at an angle of b = 45° with the horizontal as shown in Fig. 1. The plate is subjected to an uni-axial load of 15 kN (r = 121.11 MPa). The patch material is made of unidirectional carbon/epoxy composite laminate better known as carbon fiber reinforced plastic (CFRP). Later, isotropic patch having the same property as parent metal is also employed for overall comparison. The layer thickness of the laminate is taken as 0.375 mm and being four layered the patch thickness is (tp). The patch is bonded symmetrically to the panel using AV138/HV998 adhesive material. The general material properties of aluminum panel, composite patch and adhesive are given in Table 1. The composite
patch properties are taken from the Ref. [4]. The specimen dimensions follow the ASTM E-647 standard and it is taken from Ref. [10]. The effectiveness of patch depends on the stiffness ratio which is nothing but the ratio of patch stiffness to the panel stiffness (Eptp/Ests). Normally the recommended stiffness ratio ranges from 1 to 1.6 as mentioned in Ref. [6]. In this study the stiffness ratio is around 1 and it would definitely reinforce the panel at the defect area helping in more load transfer happening across the defect thereby reducing SIF at the crack tip. Being a symmetric patch repair maximum strengthening would happen surrounding the defect area.
4. Fracture analysis In this analysis, it is assumed that the crack-front remains perpendicular to the panel’s surface lying on a plane and therefore mode-III SIF is neglected. The SIF are deduced from J-integral using equation as given below:
J ¼ K 2I =E0 þ K 2II =E0
ð1Þ
where E0 is modulus of elasticity, E0 = E for plane stress conditions and E0 = E/(1 m2) for plane strain condition. In case of three dimensional analysis, plane strain condition is considered for estimating SIF [10]. The J-integral value is evaluated using domain integral method [17] as shown in the following equation:
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Fig. 8. Variation of SIF and factor R with the size b of square patch (a) KI, (b) KII, and (c) R.
J¼
Z
Wn1 rij nj
@ui ds @xi
ð2Þ
The ratio of KI over KII is evaluated as mentioned in Ref. [10] and is shown below:
K I Duy ¼ K II Dux
ð3Þ
where Dux is the horizontal displacement and Duy is the normal displacement between two closest nodes (see Fig. 2). The relative displacements are evaluated between loading and unloaded state. 5. Finite element modeling 5.1. Modeling of the cracked panel FEM is the most effective tool for computing SIF in 3D fracture models. In this work modeling and analysis is done using ANSYS 12.1 software which is a commercially available finite element package. To capture the high stress gradient existing at crack tip, a very fine meshing has been done around the tip as mentioned in Ref. [12]. In the present analysis the radial extent of the outer most nodes is 0.8766t and the crack tip element size is 0.0005t. The crack tip mesh has a total of 7128 elements (36 circumferential, 33 radial; six elements through the thickness) around the
crack tip region. Outside the disk, structured area mesh is created and later all the areas are extruded in thickness direction to generate volume. Finally, all the generated volumes are meshed with 20noded solid-186 element through sweep mode as shown in Fig. 3a and the zoomed portion of the crack tip is shown in Fig. 3b. The panel, patch and adhesive are modeled with 20-noded solid elements as per the dimensions shown in Fig. 1. In the thickness direction, the panel is meshed with six elements, adhesive with two elements and patch with four elements. Mesh surrounding the crack tip alters with respect to the patch shape considered. A tensile load of 15 kN is being applied as a pressure load of 121.11 MPa on the top surface of the panel. The bottom face is arrested in x and ydirection and the mid plane nodes of the panel are constrained in z-direction. Then J-integral values for the unrepaired panel is directly obtained from the ANSYS software using domain integral approach [17]. From the J-integral values KI and KII are estimated as explained in previous section. 5.2. Modeling of the repaired panel As patch is made of composite laminate having different layup orientation, the layer angles are defined by assigning element coordinate system to each layer of the patch [18]. Every layer is assigned one element in thickness direction. In this work circular, rectangular, square, elliptical, and octagonal patches having
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Fig. 9. Variation of SIF and factor R with major axis 2a for elliptical patch (a) KI, (b) KII, and (c) R.
different areas are modeled and analyzed upfront. All the patches are centered with respect to the panel and bonded above the crack. In this analysis the composite patch with fibers oriented parallel to the loading direction is considered. It is observed from our earlier study that the unidirectional laminate with 90° layup angle (oriented parallel to loading direction) gives highest reduction of SIF at the crack tip as compared to the other layup angle for a double sided repair of inclined crack panel [12]. As the repair panel is subjected to in-plane tensile load, the maximum principal stresses field is along the loading direction and therefore the axes of the CFRP patch is kept along the maximum principal stress field as it provides more stiffness in the loading direction. Fig. 4 shows the finite element model of the symmetrically repaired panel having different patch shapes.
is also studied by maintaining constant patch height (H) as 25 mm and varying its width (B) as 26, 28, 30 and 32 (all are in mm). The corresponding areas are 650, 700, 750 and 800 (in mm2). Similar to circular patch model around the crack tip a circular mesh pattern is created and then encompassed with in another circular area. Finally, a rectangular area is built around it as shown in Fig. 4b. Finally, each area is meshed individually.
5.2.1. Circular patch In this study circle of four different radii is considered and they are 12.5, 14, 15 and 16 (in mm) corresponding to an area of 490, 616, 706 and 804 (in mm2) respectively. Firstly, around the crack tip a circular mesh pattern is created. Encompassing the circular pattern another circular area is created, so that it encloses the circular patch area sufficiently. Finally, each area is meshed individually as shown in Fig. 4a.
5.2.4. Elliptical patch Elliptical patch area is generated by appropriately scaling the circular area. In this work two cases are considered: firstly horizontal ellipse, having the major axis along x-axis and secondly rotated ellipse where major axis is along y-axis. In this work the minor axis of the ellipse is taken as 25 mm and four different major axis lengths of 26, 28, 30 and 32 (all are in mm) are considered. The corresponding areas are 510, 550, 589 and 629 (in mm2). The meshing is done similar to that of circular patch model (see Fig. 4d).
5.2.2. Rectangular patch Two possible models are studied in case of rectangular patch. Firstly maintaining a constant width (B) of 25 mm and varying patch height (H). They are varied as 26, 28, 30 and 32 (all are in mm) leading to four different cases. Similarly an opposite scenario
5.2.3. Square patch Square patch is also modeled same as rectangular patch with side length varying as 22, 24, 26, 28 (all are in mm) having areas rounded to 490, 616, 706 and 804 (in mm2) respectively. The meshing is also done similar to that of rectangular patch model (see Fig. 4c).
5.2.5. Octagonal patch The octagon is created by circumscribing circle with radius ‘R’ which is shown in Fig. 4e. For the first case a regular octagon is considered having sides of length 10.3, 11.5, 12.4, 13.25 (all are
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Fig. 10. Variation of SIF and factor R with the distance d for regular and extended octagonal patches (a) KI, (b) KII, and (c) R.
in mm) circumscribed within the circle radii of 12.5, 14, 15 and 16 mm respectively. The corresponding areas are 517, 648, 744 and 848 (in mm2). For the second case, extended octagon is created by increasing two parallel sides length in such a way that the area of extended and regular octagon is kept same. But the corners are chamfered at 45°. For this model meshing is done similar to the rectangular patch model (see Fig. 4f). It is assumed that patch is perfectly bonded to the panel by adhesive. Appropriately the nodes are coupled at the respective interfaces to reflect the perfectly bonded behavior. During coupling, all the three degrees of freedom are coupled at each node. Similar boundary condition as mentioned in the previous sub-section is applied on the repaired panel too. Later, SIF’s are estimated using the same approach as discussed previously. 6. Results and discussions 6.1. Comparison of analytical and numerical SIF of the cracked panel Fig. 5 shows the SIF distribution through the thickness of the panel having inclined center crack at 45°. In this work, both analytical SIF [19] and numerical values (from FEM) is being compared. In case of numerical SIF distribution, one can see that there is a reduction of KI at edge and it peaks at the center of the panel while KII is higher at the edges and it reduces at the center of the panel. This variation at the free edge is because of the corner singularity effect [20]. The order of corner singularity is different from the crack tip
singularity. It is also shown that the SIF obtained is very close to analytical SIF, confirming the adequacy of the mesh considered. Thus similar kind of mesh is considered for further analysis. 6.2. SIF reduction parameter For quantitative estimation of effective patch shape for the mixed mode cracked panel a parameter R is introduced which is defined in the following equation:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u2 !2 !2 3 u U R K UII K RII 5 u4 K I K I R¼t K UI K UII
ð4Þ
where K UI and K UII represents unrepaired mode I and mode II SIF value, K RI and K RII represents mode I and mode II SIF value for the repaired model. This parameter combines both mode I and mode II SIF reduction into one value so that comparison becomes easier and straight forward. Higher the R value, better the patch performance with respect to SIF reduction. For comparison purpose SIF and R value at the mid-plane location is considered. 6.2.1. Circular patch Fig. 6 shows the variation of KI, KII and R with respect to the diameter D of circular patch. From Fig. 6a and b it can be observed that as the diameter of patch increases, overlapping area increases hence SIF decreases. Same trend is also seen in Fig. 6c, where R
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Fig. 11. Comparison of SIF variation for different patch shapes with respect to the crack inclination angle b (a) KI, (b) KII, and (c) R.
value increases with patch diameter as more load transfer by patch happens with increased area. Hence, patch having maximum permissible area is preferred in the case of circular shape. 6.2.2. Rectangular patch Fig. 7 shows the variation of KI, KII and R with respect to size of the rectangular patch. From Fig. 7a it can be observed that for fixed height and increasing width of rectangle KI gets lowered and KII becomes greater. For the other case, fixed width and increasing height of rectangle KII gets lowered and KI becomes greater (see Fig. 7b). Looking at Fig. 7c it can be found that R is higher for the rectangular patch with fixed width and increasing height. Hence it can be concluded that rectangular patch with larger height performs better as compared to the one with larger width. Because stiffness offered by a lengthier patch along loading direction is greater compared to the one in the width direction. 6.2.3. Square patch Fig. 8 shows the variation of KI, KII and R with the size of square patch. From Fig. 8a and b it is evident that as the size of patch increases, overlapping area increases hence SIF decreases similar to that of circular patch. Also the R value increases with increasing patch area as shown in Fig. 8c similar to that of circular patch model behavior. 6.2.4. Elliptical patch Two forms of elliptical patch shape are considered. One with the major axis along x-axis (horizontal ellipse) and other with the major axis along y-axis (rotated ellipse). Fig. 9 shows the variation
of KI, KII and R with respect to increasing major axis length while maintaining a fixed minor axis length. Looking at Fig. 9a and b, it can be found that for rotated ellipse KI is higher and KII gets reduced with increasing major axis length. The behavior of elliptical patch is similar to that of rectangular patch. From Fig. 9c it can be observed that R is higher for the rotated elliptical patch. The stiffness offered by rotated elliptical patch along loading direction is more as compared to the horizontal one. 6.2.5. Octagonal patch Fig. 10 shows the variation of KI, KII and R values with respect to distance between two parallel sides (d). Looking at Fig. 10a and b it can be seen that KI is higher whereas KII is lower in case of extended octagon as the distance d of octagon increases and vice versa in case of regular octagon. From Fig. 10c it can be observed that R is higher for the extended octagonal patch shape compared to regular octagonal patch shape. Hence extended octagonal shape is preferred. 6.3. Performance of different patch shapes on panel having different crack inclination angles In this section the influence of patch shape on SIF reduction for different inclined cracks are analyzed for a fixed patch area of 804 mm2, corresponding to the circle of radius 16 mm. Fig. 11 shows the variation of SIF (KI and KII) and R at the mid plane location for different crack inclination angles. By closely observing Fig. 11a one can see that KI is maximum at b = 0° and is minimum at b = 90°. The reason for this is that at b = 0° there is a maximum
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Fig. 12. Variation of SIF and factor R with the patch area for different patch shapes (a) KI, (b) KII, and (c) R.
crack opening displacement whereas at b = 90° it is nil. It is also observed that for a double sided patch there is a significant reduction of KI for the square, rectangular and octagonal patch shapes. From Fig. 11b it can be seen that KII is maximum at 45° and zero at crack angles b = 0° and 90°. On overall observation there is bigger reduction in SIF with the rectangular and extended octagonal patches. Fig. 11c shows the variation of R with different crack inclination angles. At b = 90° the SIF is nil hence R is not considered for this case. It is found that R is maximum at all the inclination angles in case of extended octagon and rectangular patch shape. On careful observation of Fig. 11, one can surely state that patch shape influences SIF and its impact is different for different crack inclinations. Therefore one needs to do a trade off for arriving at an optimum patch shape. The subsequent sub-section of manuscript deals with the patch performance against fixed patch volume. 6.4. Comparative study of different patch shapes on SIF reduction In the previous Section 6.2, we have studied the effect of SIF reduction for various possibilities within a given patch shape.
Based on that study certain patch shapes are chosen. In this section a comparative study is done among those chosen patch shape to identify the best performing shape for the mixed mode cracked panel with crack inclination angle of 45°. In this section authors have carried out a detailed study on the influence of patch shape on SIF reduction maintaining same volume. Three different patch areas are considered: 804, 706 and 616 (in mm2) and they correspond to the circle of radius 16, 15 and 14 (in mm) respectively. The patch thickness is kept same and all the patch shapes are arrived at by fixing only one dimension such as height/major axis length same as that of circle diameter. From the previous section it is shown that rectangular patch with greater height performs better than the one with greater width. Hence the rectangular patch with greater height than width is considered here. Square patch is also considered having similar areas with an exception that length is not same as that of circle diameter. Similarly rotated ellipse and extended octagon are chosen as they perform better compared to their counter parts. Fig. 12 shows the variation of SIF at mid plane location with respect to area for all the patch shape considered. Looking at Fig. 12a and b it can be observed that the SIF is
Table 2 Comparison of R value with different patch shapes for different patch areas. Patch area in mm2
Circular
Rectangular
Square
Rotated elliptical
Extended octagon
616 706 804
0.9940 1.0085 1.0202
1.0084 1.0217 1.0337
1.0063 1.0205 1.0310
0.9964 1.0111 1.0205
1.0077 1.0229 1.0388
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Table 3 Comparison of R value with different patch material for octagonal and rectangular patches. Patch shape in mm2
Patch is same as parent panel material
CFRP patch
Extended octagon Rectangle
0.94 0.93
1.04 1.03
decreasing with increasing patch area because load transfer by patch increases with increasing patch area. In Fig. 12c, R value is compared against the patch area for different patch shapes. It is found that extended octagonal patch is more efficient in terms of SIF reduction followed closely by rectangular patch. Compared to rectangular patch extended octagonal patch performs better because its width is more for a given area compared to the rectangular patch and load transfer is kept away from the crack tip. Also in most of the repair work researchers [1,2,6] have preferred extended octagonal patch shape in their study which further strengthens our prediction. Also the sharp corners are avoided in the extended octagonal patch making it more resistant against debonding as compared to the rectangular patch. Table 2 gives the comparison of R value obtained for different patch shapes. From Table 2 it is clearly evident that on overall comparison extended octagonal patch has the highest R value and therefore it is preferred for mixed-mode cracked panel. The performance of rectangular patch (having greater height) is also comparable to extended octagonal patch but from debonding perspective octagon is preferred. First limitation of this approach is that one cannot arrive at an optimum patch dimension and secondly it is applicable only to fixed panel size and one cannot generalize it for other panel dimensions. The optimization of patch dimension such as width, length and thickness for an extended octagon or rectangular patch shape needs to be deduced and it is part of future study. In the next subsection we have considered the overall comparison of SIF reduction parameter R for extended octagonal and rectangular patch shapes obtained with isotropic and CFRP composite patch. 6.5. Comparative study of different patch materials for extended octagonal and rectangular patch shape In this section the authors have studied the repair involving an isotropic patch identical to panel material. It is kept as same as that of parent material to account for better thermal expansion. Also the dimensions are kept similar to rectangular and octagonal patches. Table 3 gives the comparison of R value obtained with different patch materials for octagonal and rectangular patches. From Table 3 it is observed that the SIF reduction parameter R obtained for the isotropic patches are lower compared to CFRP patches of same dimension thereby confirming low reinforcement around the fault. Therefore, it is of no improvement in using isotropic patch of same stiffness and also in CFRP patches, fibers oriented parallel to the loading direction leads to high directional stiffness compared to the isotropic patch. Hence CFRP patch is best when compared to the isotropic patch. 6.6. Conclusion A finite element analysis based study has been carried out to understand the influence of patch shape on inclined center crack
panel having a crack inclination angle of 45°. Five different patch shapes such as circular, rectangle, square, elliptical and octagonal are considered. Irrespective of the patch shape in case of double sided repair there is a drastic reduction in mode I and mode II SIF value as compared to the unrepaired one. Rectangular patch shape having greater height has performed better compared to the one with greater width. On the other hand rotated elliptical patch has performed better than the horizontal one. Finally in case of octagonal patch, one with the extended side length has performed well. Also greater the patch area, higher the SIF reduction because of increased load transfer by the patch. Including the circular and square patch on overall comparison, extended octagon has performed better showing highest R value. It is closely followed by the rectangular patch shape. Further on overall comparison R is higher for CFRP patch as compared to isotropic extended octagonal patch having same dimensions. Therefore, extended octagonal patch shape made of CFRP with maximum permissible area is recommended in case of repair of inclined cracked panel.
References [1] Baker AA, Rose LRF, Jones R. Advances in the bonded composite repair of metallic aircraft structure. Killington: Elsevier Publications; 2002. [2] Duong CN, Wang CH. Composite repair – theory and design. Amsterdam: Elsevier Publications; 2007. [3] Umamaheswar Turaga VRS, Singh Ripudaman. Modelling of a patch repair to a thin cracked sheet. Eng Fract Mech 1999;62:267–89. [4] Mahadesh Kumar A, Hakeem SA. Optimum design of symmetric composite patch repair to center cracked metallic sheet. Comp Struct 2000;49:285–92. [5] Brighenti Roberto. Patch repair design optimization for fracture and fatigue improvements of cracked plates. Int J Solids Struct 2007;44:1115–31. [6] Chukwujekwu Okafor A, Singh Navdeep, Enemouh UE, Rao SV. Design, analysis and performance of adhesively bonded composite patch repair of cracked aluminium aircraft panels. Comp Struct 2005;71:258–70. [7] Albedah, Bachir Bouiadjra B, Mhamdia R, Benyahia F, Es-Saheb M. Comparison between double and single sided bonded composite repair with circular shape. Mater Des 2010;32:996–1000. [8] Rachid Mhamdia, Serier B, Bachir Bouiadjra B, Belhouari M. Numerical analysis of the patch shape effects on the performances of bonded composite repair in aircraft structures. Composites Part B – Engineering 2011;71:1–7. [9] Bachir Bouiadjra B, Fari Bouanani M, Albedah A, Benyahia F, Es-Saheb M. Comparison between rectangular and trapezoidal bonded composite repairs in aircraft structures: a numerical analysis. Mater Des 2011;32:3161–6. [10] Hosseini-Toudeshky Hossein, Bijan Mohammadi, Hamid Reza Daghyani. Mixed mode fracture analysis of aluminium repaired panels using composite patches. Comp Sci Technol 2006;66:188–98. [11] Ramji M, Srilakshmi R, Bhanu Prakash M. Towards an optimum patch design in composite repair. In: Proceedings of fifth ICTACEM conference. Kharagpur, India; December 2010. [12] Ramji M, Srilakshmi R. Design of composite patch reinforcement applied to mixed mode cracked panel using FEA. J Reinf Plast Comp 2012;39(9):585–95. [13] Quan Wang, Nan Wu. A review on structural enhancement and repair using piezoelectric materials and shape memory alloys. Smart Mater Struct 2012:21. http://dx.doi.org/10.1088/0964-1726/21/1/01300. [14] Wang Q, Quek ST, Liew KM. On the repair of a cracked beam with a piezoelectric patch. Smart Mater Struct 2002;11:404–10. [15] Da Silva Lucas FM, Ramos JE, Figueiredo MV, Strohaecker TR. Influence of the adhesive, the adherend and the overlap on the single lap shear strength. J Adhes Interface 2006;7(4):1–9. [16] Lucas FM, Da Silva RAM, Chousal JAG, Pinto AM. Alternative methods to measure the adhesive shear displacement in the thick Adherend Shear Test. J Adhes Sci Technol 2008;22:15–9. [17] Ansys version 12.1, User’s Documentation, Pennsylvania, US; 2009. [18] Ever J. Barbero. Finite Element Analysis of Composite Materials. Boca Raton: CRC Press, Taylor and Francis group; 2008. [19] Murakami Y. Hand book of stress intensity factors. Tokyo: Pergamon Press; 1987. [20] Anderson KL. Fracture mechanics fundamentals and applications. Boca Raton: CRC Press, Taylor and Francis group; 2005.
Contents lists available at SciVerse ScienceDirect
Composites: Part B journal homepage: www.elsevier.com/locate/compositesb
Towards optimization of patch shape on the performance of bonded composite repair using FEM M. Ramji ⇑, R. Srilakshmi, M. Bhanu Prakash Department of Mechanical Engineering, Engineering Optics Lab, Indian Institute of Technology Hyderabad, Hyderabad 502 205, India
a r t i c l e
i n f o
Article history: Received 8 March 2012 Received in revised form 18 May 2012 Accepted 17 July 2012 Available online 23 August 2012 Keywords: Bonded composite repair A. Carbon fiber B. Fracture C. Finite element analysis (FEA)
a b s t r a c t Composite repair is gaining importance for extending the service life of aging aircrafts. There are many parameters like patch thickness, patch layup configuration and patch shape influencing the performance of composite repair. Therefore a need exists to prioritize them. In this work a 3-D finite element analysis has been conducted to get an optimum composite patch shape applied on an inclined center cracked panel, repaired by symmetrical patch. The patch shapes considered are circle, rectangle, square, ellipse and octagon. Also SIF reduction is compared for the same volume of patch. It is observed that extended octagonal patch shape performs better in case of SIF reduction. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Integrity enhancement of damaged structures through composite repair is attracting considerable engineering attention in recent years. In particular lot of application is in aerospace sector where extension of service life is of primary interest from an economic perspective. Repair involving composite patch applied to cracked metallic sheets is done using either mechanical fastening or adhesive bonding. Mechanical fasteners introduce stress concentration there by reducing the residual strength of the repaired plate. Adhesively bonded composite patch have been shown to provide high levels of bond durability under the operating conditions. It also offers an efficient method for enhancing the structural integrity which includes stiffening of under-designed regions, increasing static strength, restoring strength or stiffness and reducing stress intensity factor (SIF) [1]. Further, composite laminates have high directional stiffness, high failure strain, durability under cyclic loading, low density and excellent formability. Therefore, it is preferred over isotropic patches which are predominantly made of metal [1]. Adhesively bonded repair of aircraft structures has been initiated by Baker in the early 1970s [1]. Two kinds of patch work are generally employed in composite repair: single sided (un-symmetrical) and double sided (symmetrical). Mostly double sided patch work is preferred as more reduction in SIF is seen [2]. There ⇑ Corresponding author. Address: Department of Mechanical Engineering, Indian Institute of Technology Hyderabad, ODF Campus, Yeddumailaram, Medak Dist., Hyderabad 502 205, India. Tel.: +91 040 23 01 6078; fax: +91 040 23 01 6032. E-mail address: [email protected] (M. Ramji). 1359-8368/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compositesb.2012.07.049
are many parameters like patch thickness, patch layup and patch shape which influences the performance of the repair. From the literature, it is identified that patch shape plays a major role in repair performance. Over the last two decade, a paradigm shift has happened in computational mechanics especially in the area of finite element method (FEM) and its application has penetrated into every engineering discipline. A detailed review of application of FEM to composite repair is available in the literature [3–12]. Umamaheswar and Singh [3] performed finite element based study of single sided patch repairs applied to thin aluminum sheets. They showed the SIF variation through the thickness of the panel assuming a straight crack front. Mahadesh Kumar and Hakeem [4] conducted the numerical analysis for optimum patch shape in case of symmetric repair of center cracked panel. They have used different patch shapes such as circular, elliptical and rectangular and have estimated SIF reduction. But their work dealt with only mode I crack problem. Brighenti [5] has developed the optimum design procedure for repair using genetic algorithm. He showed that patch shapes significantly affects the fracture and fatigue life of double sided repaired components. Chukwujekwu Okafor et al. [6] developed a finite element model for analyzing the stress distribution of cracked plates repaired with a single sided octagonal patch. They have studied in detail the stress distribution in the skin, patch and adhesive layer. Albedah et al. [7] have conducted finite element analysis to estimate SIF for single and double sided repairs having a circular patch shape. They have compared the mass gain for both the cases. Recently, Rachid et al. [8] have found that the H shape patch performs better than the rectangular patch. They also concluded that the H
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M. Ramji et al. / Composites: Part B 45 (2013) 710–720 Table 1 Material properties.
a b c
Material
Exa (GPa)
Ey, Ez (GPa)
txyb, txz
tyz
Gxyc, Gxz (GPa)
Gyz (GPa)
Aluminum Adhesive Carbon/epoxy
73.1 4.59 135
– – 9
0.3 0.47 0.3
– – 0.02
– – 5
– – 8
E – Young’s modulus. t – Poisson’s ratio. G – Shear modulus.
Fig. 1. Geometry of the repair model having square patch symmetrical patch (a) front view, and (b) side view (all dimensions are in mm).
shape patch with arrow head improves the performance of the bonded repair. But they considered only mode I crack for their analysis. Bachir Bouiadjra et al. [9] have carried out the finite element analysis to compare the repair performance of patches with rectangular and trapezoidal shapes applied to mode I problem. They concluded that the trapezoidal patch shape works far better than the rectangular patches up to certain crack length. All these above works have been exclusively carried out for mode I problem and none addresses the repair of mixed mode cracked panel. Hosseini-Toudeshky et al. [10] have carried out experimental investigation for single sided repaired panels containing inclined center crack. Also they did FEM simulation of fatigue crack growth for a single sided repaired panel. But they have not studied impact of patch shape on the repair performance. Recently, Ramji et al. [11,12] have investigated that in the case of an unsymmetrical patch, there is no significant impact of patch shape on SIF reduction for mixed-mode problem.
In this work FEM based study of optimum patch shape applied to mixed mode cracked panel is carried out under linear elastic fracture mechanics (LEFM) frame work. Only static analysis has been performed. Different patch shapes like circle, rectangle, square, ellipse, and octagon are considered. Comparison of the performance of bonded repair is done by analyzing SIF reduction at the crack tip. Only double sided patch model is considered in this work. It is found that extended octagonal and rectangular patch shape perform better for mixed mode problem.
2. Technological and mechanical challenges in patch repair The adhesively bonded repair to the metallic structure allows the restoration of strength and stiffness of the structure, as well as slowing crack growth by reducing SIF. Application of bonded composite repair technology is challenging from both the scientific
Fig. 2. Estimation of KI/KII ratio (a) two coincident nodes near the crack tip before loading, and (b) two nearest nodes near the crack tip after loading.
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Fig. 3. Finite element model of cracked panel (a) entire panel, and (b) zoomed portion around the crack tip.
and engineering point of view, in particular repair of primary and secondary load bearing aircraft structures. This is because composite repair technology involves interdisciplinary inputs from several fields such as aerodynamic loading, stress analysis, fiber composite manufacturing, structural adhesive bonding, fracture mechanics
and fatigue. In general composite repair can be broadly classified into passive and active repair. Over last two decades only passive patch repair work has been studied and currently researchers are working on the active patch repair study involving smart materials [13]. The role of active smart patches made of piezoelectric actuators has been explored for active restoration of the repaired structures by introducing a local moment/force in opposite sense thereby reducing the SIF [14]. These piezoelectric patches are transversely isotropic by nature and it can be adhesively bonded. Still, this technology is explored at the lab scale and more work needs to be done for making it to certification stage. Till date, composite repair is mainly carried out on defective secondary load bearing structures and not on primary one. The technological challenge for the next decade will be on application of composite repair to defective primary load bearing structures. Because the application of bonded composite repairs to cracked primary structures is generally acceptable only on the basis of continuous monitoring of patch performance to ensure that the load transfer is maintained and also able to monitor damage growth in the parent/patch material. In case of composite patch damages like delamination, matrix cracking, and fiber pull out. should be detected and prevent further catastrophic failures. Therefore, a suitable non-destructive testing system should be devised for continuous online monitoring. The active patch material can also be used as sensors for predicting failures in the repaired system with slight adjustment utilizing their sensitivity to electro-mechanical coupling [13]. From the mechanical standpoint, two major challenges exist; firstly, proper adhesion/bonding of the patch on the defective panel
Fig. 4. Finite element model of composite repair model having patches of different shapes (a) circular, (b) rectangular, (c) square, (d) elliptical, (e) regular octagon, and (f) extended octagon.
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Fig. 5. Comparison of analytical SIF variation through the thickness with the numerical values from FEM for the center cracked panel having an inclined crack at b = 45°.
surface and secondly selection of appropriate adhesive. For better adhesion a good surface preparation is required and various techniques such as etching, shot peening or sand blasting are cited in the literature [1]. Depending upon nature of adhesive and panel surface, appropriate surface preparation techniques should be employed. A lot of research is currently going on in this direction for better surface preparation. Secondly, the choice of adhesive and its thickness plays a major role on the integrity aspect and supposedly it is the weakest link. Adhesives are generally classified as brittle,
intermediate and ductile [15]. Depending upon the combination of parent and patch material one can choose the kind of adhesive. In this work the patch is bonded symmetrically to the panel using AV138/HV998 adhesive material. This adhesive is highly stiff and brittle in nature having a very high elastic modulus [15] (see Table 1). The maximum shear strength of the brittle adhesive AV138 is 30 MPa and yield strength is 25 MPa [16]. Normally the upper limit of the interface strength can be taken as 30 MPa for the modeling behavior for doing damage propagation studies.
Fig. 6. Variation of SIF and factor R with the diameter D of circular patch (a) KI, (b) KII, and (c) R.
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Fig. 7. Variation of SIF and factor R against rectangular patch size B or H (a) KI, (b) KII, and (c) R.
Lastly, the adhesive thickness influences the strength of the joint as the load is transferred from the base metal to the patch via the adhesive. Thin adhesive layers are better than the thick layers because it gets the patch to be softer. But thickness provides good durability to the entire patch as thick adhesive layer attracts lesser strains. Good adhesive bonds are produced only in the range of thickness 0.125–0.25 mm [6] and in the present modeling the adhesive thickness (ta) is taken as 0.1 mm which is just sufficient to transfer the load. 3. Geometry and material properties The typical model for the cracked specimen is shown in Fig. 1. The panel is made of aluminum alloy 2014 T6 having the dimension of 160 39 3.175 mm3. It contains an inclined center crack ‘2a’ of length 10 mm. The panel thickness (ts) is taken as 3.175 mm. The crack is inclined at an angle of b = 45° with the horizontal as shown in Fig. 1. The plate is subjected to an uni-axial load of 15 kN (r = 121.11 MPa). The patch material is made of unidirectional carbon/epoxy composite laminate better known as carbon fiber reinforced plastic (CFRP). Later, isotropic patch having the same property as parent metal is also employed for overall comparison. The layer thickness of the laminate is taken as 0.375 mm and being four layered the patch thickness is (tp). The patch is bonded symmetrically to the panel using AV138/HV998 adhesive material. The general material properties of aluminum panel, composite patch and adhesive are given in Table 1. The composite
patch properties are taken from the Ref. [4]. The specimen dimensions follow the ASTM E-647 standard and it is taken from Ref. [10]. The effectiveness of patch depends on the stiffness ratio which is nothing but the ratio of patch stiffness to the panel stiffness (Eptp/Ests). Normally the recommended stiffness ratio ranges from 1 to 1.6 as mentioned in Ref. [6]. In this study the stiffness ratio is around 1 and it would definitely reinforce the panel at the defect area helping in more load transfer happening across the defect thereby reducing SIF at the crack tip. Being a symmetric patch repair maximum strengthening would happen surrounding the defect area.
4. Fracture analysis In this analysis, it is assumed that the crack-front remains perpendicular to the panel’s surface lying on a plane and therefore mode-III SIF is neglected. The SIF are deduced from J-integral using equation as given below:
J ¼ K 2I =E0 þ K 2II =E0
ð1Þ
where E0 is modulus of elasticity, E0 = E for plane stress conditions and E0 = E/(1 m2) for plane strain condition. In case of three dimensional analysis, plane strain condition is considered for estimating SIF [10]. The J-integral value is evaluated using domain integral method [17] as shown in the following equation:
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Fig. 8. Variation of SIF and factor R with the size b of square patch (a) KI, (b) KII, and (c) R.
J¼
Z
Wn1 rij nj
@ui ds @xi
ð2Þ
The ratio of KI over KII is evaluated as mentioned in Ref. [10] and is shown below:
K I Duy ¼ K II Dux
ð3Þ
where Dux is the horizontal displacement and Duy is the normal displacement between two closest nodes (see Fig. 2). The relative displacements are evaluated between loading and unloaded state. 5. Finite element modeling 5.1. Modeling of the cracked panel FEM is the most effective tool for computing SIF in 3D fracture models. In this work modeling and analysis is done using ANSYS 12.1 software which is a commercially available finite element package. To capture the high stress gradient existing at crack tip, a very fine meshing has been done around the tip as mentioned in Ref. [12]. In the present analysis the radial extent of the outer most nodes is 0.8766t and the crack tip element size is 0.0005t. The crack tip mesh has a total of 7128 elements (36 circumferential, 33 radial; six elements through the thickness) around the
crack tip region. Outside the disk, structured area mesh is created and later all the areas are extruded in thickness direction to generate volume. Finally, all the generated volumes are meshed with 20noded solid-186 element through sweep mode as shown in Fig. 3a and the zoomed portion of the crack tip is shown in Fig. 3b. The panel, patch and adhesive are modeled with 20-noded solid elements as per the dimensions shown in Fig. 1. In the thickness direction, the panel is meshed with six elements, adhesive with two elements and patch with four elements. Mesh surrounding the crack tip alters with respect to the patch shape considered. A tensile load of 15 kN is being applied as a pressure load of 121.11 MPa on the top surface of the panel. The bottom face is arrested in x and ydirection and the mid plane nodes of the panel are constrained in z-direction. Then J-integral values for the unrepaired panel is directly obtained from the ANSYS software using domain integral approach [17]. From the J-integral values KI and KII are estimated as explained in previous section. 5.2. Modeling of the repaired panel As patch is made of composite laminate having different layup orientation, the layer angles are defined by assigning element coordinate system to each layer of the patch [18]. Every layer is assigned one element in thickness direction. In this work circular, rectangular, square, elliptical, and octagonal patches having
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Fig. 9. Variation of SIF and factor R with major axis 2a for elliptical patch (a) KI, (b) KII, and (c) R.
different areas are modeled and analyzed upfront. All the patches are centered with respect to the panel and bonded above the crack. In this analysis the composite patch with fibers oriented parallel to the loading direction is considered. It is observed from our earlier study that the unidirectional laminate with 90° layup angle (oriented parallel to loading direction) gives highest reduction of SIF at the crack tip as compared to the other layup angle for a double sided repair of inclined crack panel [12]. As the repair panel is subjected to in-plane tensile load, the maximum principal stresses field is along the loading direction and therefore the axes of the CFRP patch is kept along the maximum principal stress field as it provides more stiffness in the loading direction. Fig. 4 shows the finite element model of the symmetrically repaired panel having different patch shapes.
is also studied by maintaining constant patch height (H) as 25 mm and varying its width (B) as 26, 28, 30 and 32 (all are in mm). The corresponding areas are 650, 700, 750 and 800 (in mm2). Similar to circular patch model around the crack tip a circular mesh pattern is created and then encompassed with in another circular area. Finally, a rectangular area is built around it as shown in Fig. 4b. Finally, each area is meshed individually.
5.2.1. Circular patch In this study circle of four different radii is considered and they are 12.5, 14, 15 and 16 (in mm) corresponding to an area of 490, 616, 706 and 804 (in mm2) respectively. Firstly, around the crack tip a circular mesh pattern is created. Encompassing the circular pattern another circular area is created, so that it encloses the circular patch area sufficiently. Finally, each area is meshed individually as shown in Fig. 4a.
5.2.4. Elliptical patch Elliptical patch area is generated by appropriately scaling the circular area. In this work two cases are considered: firstly horizontal ellipse, having the major axis along x-axis and secondly rotated ellipse where major axis is along y-axis. In this work the minor axis of the ellipse is taken as 25 mm and four different major axis lengths of 26, 28, 30 and 32 (all are in mm) are considered. The corresponding areas are 510, 550, 589 and 629 (in mm2). The meshing is done similar to that of circular patch model (see Fig. 4d).
5.2.2. Rectangular patch Two possible models are studied in case of rectangular patch. Firstly maintaining a constant width (B) of 25 mm and varying patch height (H). They are varied as 26, 28, 30 and 32 (all are in mm) leading to four different cases. Similarly an opposite scenario
5.2.3. Square patch Square patch is also modeled same as rectangular patch with side length varying as 22, 24, 26, 28 (all are in mm) having areas rounded to 490, 616, 706 and 804 (in mm2) respectively. The meshing is also done similar to that of rectangular patch model (see Fig. 4c).
5.2.5. Octagonal patch The octagon is created by circumscribing circle with radius ‘R’ which is shown in Fig. 4e. For the first case a regular octagon is considered having sides of length 10.3, 11.5, 12.4, 13.25 (all are
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Fig. 10. Variation of SIF and factor R with the distance d for regular and extended octagonal patches (a) KI, (b) KII, and (c) R.
in mm) circumscribed within the circle radii of 12.5, 14, 15 and 16 mm respectively. The corresponding areas are 517, 648, 744 and 848 (in mm2). For the second case, extended octagon is created by increasing two parallel sides length in such a way that the area of extended and regular octagon is kept same. But the corners are chamfered at 45°. For this model meshing is done similar to the rectangular patch model (see Fig. 4f). It is assumed that patch is perfectly bonded to the panel by adhesive. Appropriately the nodes are coupled at the respective interfaces to reflect the perfectly bonded behavior. During coupling, all the three degrees of freedom are coupled at each node. Similar boundary condition as mentioned in the previous sub-section is applied on the repaired panel too. Later, SIF’s are estimated using the same approach as discussed previously. 6. Results and discussions 6.1. Comparison of analytical and numerical SIF of the cracked panel Fig. 5 shows the SIF distribution through the thickness of the panel having inclined center crack at 45°. In this work, both analytical SIF [19] and numerical values (from FEM) is being compared. In case of numerical SIF distribution, one can see that there is a reduction of KI at edge and it peaks at the center of the panel while KII is higher at the edges and it reduces at the center of the panel. This variation at the free edge is because of the corner singularity effect [20]. The order of corner singularity is different from the crack tip
singularity. It is also shown that the SIF obtained is very close to analytical SIF, confirming the adequacy of the mesh considered. Thus similar kind of mesh is considered for further analysis. 6.2. SIF reduction parameter For quantitative estimation of effective patch shape for the mixed mode cracked panel a parameter R is introduced which is defined in the following equation:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u2 !2 !2 3 u U R K UII K RII 5 u4 K I K I R¼t K UI K UII
ð4Þ
where K UI and K UII represents unrepaired mode I and mode II SIF value, K RI and K RII represents mode I and mode II SIF value for the repaired model. This parameter combines both mode I and mode II SIF reduction into one value so that comparison becomes easier and straight forward. Higher the R value, better the patch performance with respect to SIF reduction. For comparison purpose SIF and R value at the mid-plane location is considered. 6.2.1. Circular patch Fig. 6 shows the variation of KI, KII and R with respect to the diameter D of circular patch. From Fig. 6a and b it can be observed that as the diameter of patch increases, overlapping area increases hence SIF decreases. Same trend is also seen in Fig. 6c, where R
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Fig. 11. Comparison of SIF variation for different patch shapes with respect to the crack inclination angle b (a) KI, (b) KII, and (c) R.
value increases with patch diameter as more load transfer by patch happens with increased area. Hence, patch having maximum permissible area is preferred in the case of circular shape. 6.2.2. Rectangular patch Fig. 7 shows the variation of KI, KII and R with respect to size of the rectangular patch. From Fig. 7a it can be observed that for fixed height and increasing width of rectangle KI gets lowered and KII becomes greater. For the other case, fixed width and increasing height of rectangle KII gets lowered and KI becomes greater (see Fig. 7b). Looking at Fig. 7c it can be found that R is higher for the rectangular patch with fixed width and increasing height. Hence it can be concluded that rectangular patch with larger height performs better as compared to the one with larger width. Because stiffness offered by a lengthier patch along loading direction is greater compared to the one in the width direction. 6.2.3. Square patch Fig. 8 shows the variation of KI, KII and R with the size of square patch. From Fig. 8a and b it is evident that as the size of patch increases, overlapping area increases hence SIF decreases similar to that of circular patch. Also the R value increases with increasing patch area as shown in Fig. 8c similar to that of circular patch model behavior. 6.2.4. Elliptical patch Two forms of elliptical patch shape are considered. One with the major axis along x-axis (horizontal ellipse) and other with the major axis along y-axis (rotated ellipse). Fig. 9 shows the variation
of KI, KII and R with respect to increasing major axis length while maintaining a fixed minor axis length. Looking at Fig. 9a and b, it can be found that for rotated ellipse KI is higher and KII gets reduced with increasing major axis length. The behavior of elliptical patch is similar to that of rectangular patch. From Fig. 9c it can be observed that R is higher for the rotated elliptical patch. The stiffness offered by rotated elliptical patch along loading direction is more as compared to the horizontal one. 6.2.5. Octagonal patch Fig. 10 shows the variation of KI, KII and R values with respect to distance between two parallel sides (d). Looking at Fig. 10a and b it can be seen that KI is higher whereas KII is lower in case of extended octagon as the distance d of octagon increases and vice versa in case of regular octagon. From Fig. 10c it can be observed that R is higher for the extended octagonal patch shape compared to regular octagonal patch shape. Hence extended octagonal shape is preferred. 6.3. Performance of different patch shapes on panel having different crack inclination angles In this section the influence of patch shape on SIF reduction for different inclined cracks are analyzed for a fixed patch area of 804 mm2, corresponding to the circle of radius 16 mm. Fig. 11 shows the variation of SIF (KI and KII) and R at the mid plane location for different crack inclination angles. By closely observing Fig. 11a one can see that KI is maximum at b = 0° and is minimum at b = 90°. The reason for this is that at b = 0° there is a maximum
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Fig. 12. Variation of SIF and factor R with the patch area for different patch shapes (a) KI, (b) KII, and (c) R.
crack opening displacement whereas at b = 90° it is nil. It is also observed that for a double sided patch there is a significant reduction of KI for the square, rectangular and octagonal patch shapes. From Fig. 11b it can be seen that KII is maximum at 45° and zero at crack angles b = 0° and 90°. On overall observation there is bigger reduction in SIF with the rectangular and extended octagonal patches. Fig. 11c shows the variation of R with different crack inclination angles. At b = 90° the SIF is nil hence R is not considered for this case. It is found that R is maximum at all the inclination angles in case of extended octagon and rectangular patch shape. On careful observation of Fig. 11, one can surely state that patch shape influences SIF and its impact is different for different crack inclinations. Therefore one needs to do a trade off for arriving at an optimum patch shape. The subsequent sub-section of manuscript deals with the patch performance against fixed patch volume. 6.4. Comparative study of different patch shapes on SIF reduction In the previous Section 6.2, we have studied the effect of SIF reduction for various possibilities within a given patch shape.
Based on that study certain patch shapes are chosen. In this section a comparative study is done among those chosen patch shape to identify the best performing shape for the mixed mode cracked panel with crack inclination angle of 45°. In this section authors have carried out a detailed study on the influence of patch shape on SIF reduction maintaining same volume. Three different patch areas are considered: 804, 706 and 616 (in mm2) and they correspond to the circle of radius 16, 15 and 14 (in mm) respectively. The patch thickness is kept same and all the patch shapes are arrived at by fixing only one dimension such as height/major axis length same as that of circle diameter. From the previous section it is shown that rectangular patch with greater height performs better than the one with greater width. Hence the rectangular patch with greater height than width is considered here. Square patch is also considered having similar areas with an exception that length is not same as that of circle diameter. Similarly rotated ellipse and extended octagon are chosen as they perform better compared to their counter parts. Fig. 12 shows the variation of SIF at mid plane location with respect to area for all the patch shape considered. Looking at Fig. 12a and b it can be observed that the SIF is
Table 2 Comparison of R value with different patch shapes for different patch areas. Patch area in mm2
Circular
Rectangular
Square
Rotated elliptical
Extended octagon
616 706 804
0.9940 1.0085 1.0202
1.0084 1.0217 1.0337
1.0063 1.0205 1.0310
0.9964 1.0111 1.0205
1.0077 1.0229 1.0388
720
M. Ramji et al. / Composites: Part B 45 (2013) 710–720
Table 3 Comparison of R value with different patch material for octagonal and rectangular patches. Patch shape in mm2
Patch is same as parent panel material
CFRP patch
Extended octagon Rectangle
0.94 0.93
1.04 1.03
decreasing with increasing patch area because load transfer by patch increases with increasing patch area. In Fig. 12c, R value is compared against the patch area for different patch shapes. It is found that extended octagonal patch is more efficient in terms of SIF reduction followed closely by rectangular patch. Compared to rectangular patch extended octagonal patch performs better because its width is more for a given area compared to the rectangular patch and load transfer is kept away from the crack tip. Also in most of the repair work researchers [1,2,6] have preferred extended octagonal patch shape in their study which further strengthens our prediction. Also the sharp corners are avoided in the extended octagonal patch making it more resistant against debonding as compared to the rectangular patch. Table 2 gives the comparison of R value obtained for different patch shapes. From Table 2 it is clearly evident that on overall comparison extended octagonal patch has the highest R value and therefore it is preferred for mixed-mode cracked panel. The performance of rectangular patch (having greater height) is also comparable to extended octagonal patch but from debonding perspective octagon is preferred. First limitation of this approach is that one cannot arrive at an optimum patch dimension and secondly it is applicable only to fixed panel size and one cannot generalize it for other panel dimensions. The optimization of patch dimension such as width, length and thickness for an extended octagon or rectangular patch shape needs to be deduced and it is part of future study. In the next subsection we have considered the overall comparison of SIF reduction parameter R for extended octagonal and rectangular patch shapes obtained with isotropic and CFRP composite patch. 6.5. Comparative study of different patch materials for extended octagonal and rectangular patch shape In this section the authors have studied the repair involving an isotropic patch identical to panel material. It is kept as same as that of parent material to account for better thermal expansion. Also the dimensions are kept similar to rectangular and octagonal patches. Table 3 gives the comparison of R value obtained with different patch materials for octagonal and rectangular patches. From Table 3 it is observed that the SIF reduction parameter R obtained for the isotropic patches are lower compared to CFRP patches of same dimension thereby confirming low reinforcement around the fault. Therefore, it is of no improvement in using isotropic patch of same stiffness and also in CFRP patches, fibers oriented parallel to the loading direction leads to high directional stiffness compared to the isotropic patch. Hence CFRP patch is best when compared to the isotropic patch. 6.6. Conclusion A finite element analysis based study has been carried out to understand the influence of patch shape on inclined center crack
panel having a crack inclination angle of 45°. Five different patch shapes such as circular, rectangle, square, elliptical and octagonal are considered. Irrespective of the patch shape in case of double sided repair there is a drastic reduction in mode I and mode II SIF value as compared to the unrepaired one. Rectangular patch shape having greater height has performed better compared to the one with greater width. On the other hand rotated elliptical patch has performed better than the horizontal one. Finally in case of octagonal patch, one with the extended side length has performed well. Also greater the patch area, higher the SIF reduction because of increased load transfer by the patch. Including the circular and square patch on overall comparison, extended octagon has performed better showing highest R value. It is closely followed by the rectangular patch shape. Further on overall comparison R is higher for CFRP patch as compared to isotropic extended octagonal patch having same dimensions. Therefore, extended octagonal patch shape made of CFRP with maximum permissible area is recommended in case of repair of inclined cracked panel.
References [1] Baker AA, Rose LRF, Jones R. Advances in the bonded composite repair of metallic aircraft structure. Killington: Elsevier Publications; 2002. [2] Duong CN, Wang CH. Composite repair – theory and design. Amsterdam: Elsevier Publications; 2007. [3] Umamaheswar Turaga VRS, Singh Ripudaman. Modelling of a patch repair to a thin cracked sheet. Eng Fract Mech 1999;62:267–89. [4] Mahadesh Kumar A, Hakeem SA. Optimum design of symmetric composite patch repair to center cracked metallic sheet. Comp Struct 2000;49:285–92. [5] Brighenti Roberto. Patch repair design optimization for fracture and fatigue improvements of cracked plates. Int J Solids Struct 2007;44:1115–31. [6] Chukwujekwu Okafor A, Singh Navdeep, Enemouh UE, Rao SV. Design, analysis and performance of adhesively bonded composite patch repair of cracked aluminium aircraft panels. Comp Struct 2005;71:258–70. [7] Albedah, Bachir Bouiadjra B, Mhamdia R, Benyahia F, Es-Saheb M. Comparison between double and single sided bonded composite repair with circular shape. Mater Des 2010;32:996–1000. [8] Rachid Mhamdia, Serier B, Bachir Bouiadjra B, Belhouari M. Numerical analysis of the patch shape effects on the performances of bonded composite repair in aircraft structures. Composites Part B – Engineering 2011;71:1–7. [9] Bachir Bouiadjra B, Fari Bouanani M, Albedah A, Benyahia F, Es-Saheb M. Comparison between rectangular and trapezoidal bonded composite repairs in aircraft structures: a numerical analysis. Mater Des 2011;32:3161–6. [10] Hosseini-Toudeshky Hossein, Bijan Mohammadi, Hamid Reza Daghyani. Mixed mode fracture analysis of aluminium repaired panels using composite patches. Comp Sci Technol 2006;66:188–98. [11] Ramji M, Srilakshmi R, Bhanu Prakash M. Towards an optimum patch design in composite repair. In: Proceedings of fifth ICTACEM conference. Kharagpur, India; December 2010. [12] Ramji M, Srilakshmi R. Design of composite patch reinforcement applied to mixed mode cracked panel using FEA. J Reinf Plast Comp 2012;39(9):585–95. [13] Quan Wang, Nan Wu. A review on structural enhancement and repair using piezoelectric materials and shape memory alloys. Smart Mater Struct 2012:21. http://dx.doi.org/10.1088/0964-1726/21/1/01300. [14] Wang Q, Quek ST, Liew KM. On the repair of a cracked beam with a piezoelectric patch. Smart Mater Struct 2002;11:404–10. [15] Da Silva Lucas FM, Ramos JE, Figueiredo MV, Strohaecker TR. Influence of the adhesive, the adherend and the overlap on the single lap shear strength. J Adhes Interface 2006;7(4):1–9. [16] Lucas FM, Da Silva RAM, Chousal JAG, Pinto AM. Alternative methods to measure the adhesive shear displacement in the thick Adherend Shear Test. J Adhes Sci Technol 2008;22:15–9. [17] Ansys version 12.1, User’s Documentation, Pennsylvania, US; 2009. [18] Ever J. Barbero. Finite Element Analysis of Composite Materials. Boca Raton: CRC Press, Taylor and Francis group; 2008. [19] Murakami Y. Hand book of stress intensity factors. Tokyo: Pergamon Press; 1987. [20] Anderson KL. Fracture mechanics fundamentals and applications. Boca Raton: CRC Press, Taylor and Francis group; 2005.