Microsoft Word - numero_60_art_05_3361.docx M. A. Bouchelarm et alii, Frattura ed Integrità Strutturale, 60 (2022) 62-72; DOI: 10.3221/IGF-ESIS.60.05 62 Numerical analysis of bonded composite patch efficiency in the case of lateral U and V-notched aluminium panels Bouchelarm Mohammed A., Boulenouar Abdelkader, Chafi Meriem Laboratoire de Matériaux et Systèmes Réactifs- LMSR, Djillali Liabes University of Sidi Bel-Abbes- 22000, Algeria m.bouchelarm@yahoo.com, aek_boulenouar@yahoo.fr, chafi.meriem@yahoo.com ABSTRACT. In this study, the finite element method is applied to investigate the mechanical behavior of aluminium notched structures reinforced by composite patch. In order to evaluate the efficiency of patches in the case of lateral U and V-notches repaired with a semi-circular patch shape, it is very important to analyze the stress distribution at the notch tip and to take in consideration the influence of the geometrical and mechanical properties of the patch and the adhesive. The effect of the patch size, thickness and type was highlighted. Furthermore, the effect of the adhesive thickness on the normal stress distribution was investigated. Simple and double patch were used as reinforcement techniques. Results showed that the increase of the contact area between the plate and the patch contributes to the normal stress reduction in the ligament of the plate. The adhesive thickness must be chosen carefully to keep the positive effects of the patch. The normal stress as well as the stress concentration factor are reduced at the notch tip by using a double patch reinforcement. This reduction becomes more noticeable when the patch thickness increases. KEYWORDS. Bonded composite patch; Adhesive; Stress concentration factor; Finite element method; Notch. Citation: Bouchelarm, M. A., Boulenouar, A., Chafi, M., Numerical analysis of bonded composite patch efficiency in the case of lateral U and V-notched aluminium panels, Frattura ed Integrità Strutturale, 60 (2022) 62- 72. Received: 23.11.2021 Accepted: 28.12.2021 Online first: 27.01.2022 Published: 01.04.2022 Copyright: © 2022 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. INTRODUCTION onsiderable attention is given through composite repair and reinforcement to enhance the life cycle of damaged structures, which is a primary focus from an economic perspective. The high level of durability under operating conditions provided by adhesively bonded composite patches approves their use as a reinforcement of mechanical structures. Baker [1] pioneered repair of aircraft structures by bonded adhesives in the 1970s, since, considerable work has been achieved to develop the technique of using the composite patches on different structures [2-7]. To understand the mechanical behavior of defects reinforced by patches, several authors used finite element method [8-14] The focus of these studies was repairing cracks in thin plates. In the case of three-dimensional problems, Boulenouar et al. [15] used finite element method for the repair of semicircular cracks in a finite-thickness plate. Merzoug et al. [16] carried out simulations to analyze the behaviour of repaired surface cracks with a bonded composite patch. Meran and Samanci C https://youtu.be/PQ5ezmGkuuQ M. A. Bouchelarm et alii, Frattura ed Integrità Strutturale, 60 (2022) 62-72; DOI: 10.3221/IGF-ESIS.60.05 63 [17] studied a various composite patches effect on mechanical properties of notched Al-Mg plate. Cetisli and Kaman [18] investigated the stress intensity factors for an interfacial edge crack between two dissimilar composite plates jointed with a single side composite patch. A three-dimensional finite element approach was used by Maligno et al. [19] to investigate the behaviour of fatigue crack growth in a thick aluminium alloy plate repaired with a bonded composite patch. The ultimate failure pressure of corroded pipes reinforced with composite repair systems was investigated by Chen et al. [20], a numerical model of the ultimate failure in a repaired pipe was established. Saffar et al. [21] studied the prediction of failure pressure in pipelines with localized defects repaired by composite patches. El-Sagheer et al. [22] analyzed the multi-effects of the glass fiber reinforced polymer (GFRP) composite patch to repair the inclined cracked 2420-T3 aluminum plate. In this paper, a three-dimensional finite element modeling is carried out using Ansys APDL program; the aim of this study is to examine the efficiency of bonded composite patches in the case of lateral U and V-notched aluminium panels repaired with a semicircular patch shape. The effect of the patch size, thickness and type is investigated. In addition, the effect of the adhesive thickness on the normal stress distribution is investigated. Two types of repair are used as reinforcements, the simple and double patch. Their effect on the variation of normal stresses and on the stress concentration factor (Kt) at the front of U-notches and V-notches with different angles will be considered. NUMERICAL MODELING OF LATERAL U-NOTCHES onsider a thin plate made of a 2024-T3 aluminium alloy with a lateral U-notch having the following dimensions: height H = 203.2 mm, width 2W = 152.4 mm, thickness ep = 1 mm and notch radius ρ = 12.7 mm. The mechanical properties of the plate, the patch and the adhesive are given in table 1. The plate is subjected to uniaxial tensile load giving a remote stress state of σ = 100 MPa. Fig. 1 presents the geometrical model of a simple and double composite patch bonded to the plate. The plate was reinforced with semi-circular patches. The patch dimensions were chosen according to the notch: the radius ρp = 3.ρ et and the thickness er = 1 mm. Figure 1: Geometrical model of the plate with lateral U-notch. a) non-reinforced, b) reinforcement with semi-circular patch, c) reinforcement technique configurations. The notched plate is represented in fig. 2 by a 3D meshing. The finite element model consists of three subsections to model the notched plate, the adhesive, and the composite patch, the considered volumes are then combined and overlapped into one volume. For symmetrical considerations, only one half of the structure was modeled by three dimensional elements with an applied load σ in the y axis. A total number of 4440 elements was considered to model the structure. A solid186 element is considered for the simulation, it is defined by 20 nodes having three degrees of freedom per node: translations in the nodal x, y, and z directions. The mesh size close to the notch tip is considered small enough to accurately describe the deformation and stress gradients. However, for the remaining regions coarse mesh is used in order to reduce the computational costs. Note that the mesh size has the same dimensions in the common part of materials. C M. A. Bouchelarm et alii, Frattura ed Integrità Strutturale, 60 (2022) 62-72; DOI: 10.3221/IGF-ESIS.60.05 64 Properties Aluminium 2024-T3 Boron/Epoxy Graphite/Epoxy Glaxy/Epoxy Adhesive E1 (GPa) 72 200 134 50 2.21 E2 (GPa) 19.6 10.3 14.5 υ12 0.33 0.33 0.1677 0.33 0.43 G12 (GPa) 7.2 5.5 2.56 G13(GPa) 5.5 5.5 2.56 G23(GPa) 5.5 3.2 2.24 Table 1: Mechanical properties of the different materials. Figure 2: Typical 3D finite element mesh for simple and double patch reinforcement Normal stress reduction at the notch tip Fig. 3 illustrates the distribution of normal stresses along the ligament of the plate. The stress distribution taken from the middle point along the plate thickness is compared for an unpatched plate, a plate reinforced with simple patch and another plate reinforced with double patch. It can be seen that the presence of the patch contributes to the stress reduction at the notch tip especially in the case of a double patch reinforcement. This reduction is seen because of a transfer of stresses through the adhesive towards the Boron-Epoxy patch. M. A. Bouchelarm et alii, Frattura ed Integrità Strutturale, 60 (2022) 62-72; DOI: 10.3221/IGF-ESIS.60.05 65 Figure 3: Distribution of the normal stresses along the ligament of the plate. Effect of patch size Using the first technique of reinforcement (simple patch), the effect of different patch sizes on the normal stress distribution along the ligament of the plate, is presented in fig. 4. This effect is investigated for three different patch types: Boron/epoxy, Graphite/Epoxy and Glass/Epoxy. One can notice that whatever is the patch type, the contact area between the plate and the patch plays an important role in the normal stress distribution. In fact, the increase of this area contributes to the normal stress reduction in the ligament of the plate, which also reduces the stress concentration. Figure 4: Effect of the patch size on the distribution of normal stresses along the ligament of the plate: a) Graphite/Epoxy, b) Glass/Epoxy and c) Boron/Epoxy. M. A. Bouchelarm et alii, Frattura ed Integrità Strutturale, 60 (2022) 62-72; DOI: 10.3221/IGF-ESIS.60.05 66 Effect of the adhesive thickness In the notched plates, the adhesive thickness is a key parameter for the transfer of the loads towards the patch and to prevent the adhesive failure. In this section, we have analyzed the effect of the adhesive thickness on the normal stress distribution in plates reinforced by simple and double Boron/Epoxy patches. From fig. 5, one can observe that for an adhesive thickness from 0.10 mm to 0.30 mm, the influence on the stress distribution is almost the same. However, the thickness must be chosen carefully, because a thicker adhesive reinforces adhesion, but minimizes the transfer of the loads into the patch, which cancels all the positive effects of the patch. Figure 5: Effect of the adhesive thickness on the distribution of normal stresses along the ligament of the plate: a) simple patch, b) double patch Effect of the patch thickness In order to exhibit the effect of the patch thickness on the mechanical behavior of a notched structure, fig. 6 shows the evolution of the normal stress along the ligament of the plate. The results are plotted for the two reinforcement techniques (simple and double Boron/Epoxy patch). It can be observed that the increase in the patch thickness leads to a decrease of the maximum stresses at the notch tip. This behavior is noted whatever the reinforcement technique is. Figure 6: Effect of the patch thickness on the evolution of the normal stress along the ligament of the plate. a) Simple patch, b) Double patch. The patch thickness have an important role on the stress variation in the contact area between the patch and the plate. In fact, a higher patch thickness reduces the stresses in the contact area. This is illustrated in fig. 7 for 2 and 4 mm patch thicknesses respectively, where the reduction of the stresses is about 18 % for the 4 mm simple patch and about 30% for M. A. Bouchelarm et alii, Frattura ed Integrità Strutturale, 60 (2022) 62-72; DOI: 10.3221/IGF-ESIS.60.05 67 the 4 mm double patch. One can conclude that the choice of the patch thickness is one of the best ways for a better efficiency of the patch repair. Figure 7: Effect of the patch thickness on the evolution of the normal stress along the ligament of the plate. a) er = 2mm, b) er = 4mm In a notched plate, the stress field around the notch tip is dominated by the normal stress. Increasing the normal stress leads to a higher stress concentration, which can cause the adhesive failure. The variation of the stress concentration factor defined by ( Kt = σmax/ σ0) is plotted as a function of the patch thickness in fig. 8. As can be seen, the increase of the patch thickness decreases the stress concentration factor (SCF) at the notch tip. In addition, the double patch reinforcement technique presents more reduction of the stress concentration factor than the simple patch. This reduction is remarkably observed when the patch thickness becomes higher, with 27% reduction versus 15% reduction for the double and the simple patch, respectively. Note that the SCF reduction is calculated by the following relation:   1 /reduction repaired unrepairedK K K (1) Figure 8: Effect of the patch thickness on the stress concentration factor. Fig. 9 illustrates the evolution of stress concentration factor as a function of the patch thickness. The results are presented for different patch types: Boron/Epoxy, Graphite/Epoxy and Glass/epoxy. One can notice that the values of stress M. A. Bouchelarm et alii, Frattura ed Integrità Strutturale, 60 (2022) 62-72; DOI: 10.3221/IGF-ESIS.60.05 68 concentration factor are strongly affected by the patch type. Indeed, the maximum reduction is observed with the Boron/Epoxy patch when compared with Graphite/Epoxy and Glass/Epoxy patches. To reach a reduction of Kt similar of that obtained with Boron/Epoxy, the patch thickness must be more than 4 mm for the other types. So, it can be concluded that the Boron/Epoxy patch allows a better absorption of the stress transmitted by the notch than the other patch types. From a 0.5 to 4 mm patch thickness, the drop of the stress concentration factor is 16.7%, 21 % and 27% for Graphite/Epoxy, Glass/Epoxy and Boron/Epoxy double patch respectively. Figure 9: Effect of the patch thickness on the stress concentration factor for different patch types. a) Simple patch, b) Double patch. NUMERICAL MODELING OF LATERAL V-NOTCHES harp V-notches present a danger of crack initiation and propagation because of the high stress concentration at the notch tip. To evaluate the behavior of these notches, we consider a thin plate made of 2024-T3 aluminium alloy with a lateral V-notch having the following dimensions: height H = 203.2 mm, width 2W = 152.4 mm, thickness ep = 1 mm. The mechanical properties of the plate, the patch and the adhesive have already been given in table 1. It is noted that only the Boron/Epoxy patch will be used in this section. The geometrical model is shown in fig. 10, the notched plate is reinforced with simple and double bonded composite patch with a semicircular form. The plate is subjected to uniaxial tensile load giving a remote stress state of σ = 50 MPa. Figure 10: Geometrical model of the plate with lateral V-notch. a) non-reinforced, b) reinforcement with semi-circular patch, c) reinforcement technique configurations. S M. A. Bouchelarm et alii, Frattura ed Integrità Strutturale, 60 (2022) 62-72; DOI: 10.3221/IGF-ESIS.60.05 69 Effect of the V-notch angle Fig. 11 shows the distribution of the normal stress along the plate ligament. The results are presented for different V-notch angles α (30°, 75°et 120°). It can be observed that the maximum stresses in plates with V-notches plates are higher than those of the U-notches, which means that the values of the stress concentration factor for sharp V-notches are also higher than the U-notches. The stress levels for a low notch angle are bigger than those obtained for a high notch angle. These values are generally sufficient for the crack initiation and propagation. Figure 11: Distribution of the normal stress along the plate ligament for different V-notch angles. a) α = 30°, b) α = 75°, c) α = 120°. The stress concentration factor is affected by the notch geometry. In the fig. 12 the Kt variation as a function of the V-notch angle α is presented for reinforced and non-reinforced plate. In this figure, the stress concentration factor decreases by increasing the notch angle which leads to a stress reduction. One can say that for the small angles, the risk for the failure becomes higher. The plotted results show that the variation of Kt presents a linear evolution expressed by the relation:   .tK A B (2) where: A and B are constants to determine The coefficients A and B are parameters dependent to the applied load and the mechanical and geometrical properties of the reinforced plate, the patch and the adhesive. Table 2 presents the values of A and B identified from the curves. M. A. Bouchelarm et alii, Frattura ed Integrità Strutturale, 60 (2022) 62-72; DOI: 10.3221/IGF-ESIS.60.05 70 Figure 12: Variations of the stress concentration factor as a function of the V-notch angle. Coefficient Without patch Simple patch Double patch A 27.56367 23.83085 20.91013 B -0.15392 -0.13467 -0.11846 Table 2: Values of the coefficients A and B identified from the curves. Effect of the patch thickness We have analyzed in fig. 13 the effect of the patch thickness on the stress concentration factor for different notch angles α (30°, 75°et 120°). One can observe that the increase in the patch thickness leads to a decrease of the stress concentration factor at the notch tip. This behavior is noted whatever the reinforcement technique is. The reduction of Kt values is more noticeable for the double patch than the simple patch reinforcement technique. It can also be observed that the low notch angles presents a higher stress concentration at the notch tip. Figure 13: Effect of the patch thickness on the stress concentration factor for different notch angles α (30°, 75°et 120°). a) Simple patch, b) Double patch. M. A. Bouchelarm et alii, Frattura ed Integrità Strutturale, 60 (2022) 62-72; DOI: 10.3221/IGF-ESIS.60.05 71 All the variables considered in this study are summarized in Table 3. U-notch V-notch Patch size 3 x 12.7 mm 4 x 12.7 mm 5 x 12.7 mm - Adhesive thickness From 0.1 to 0.3 mm - Patch thickness From 0.5 to 4 mm From 1 to 3 mm Notch angle - 30° 75° 120° Table 3: Considered variables with the relevant values. It is noted that the drop of the stress concentration factor values in the reinforced U-notches is more important than that observed for the reinforced V-notches. This is due to the higher stress concentration at the V-notch tip. This problem can be attenuated by increasing further the patch thicknesses. CONCLUSION sing a three dimensional finite element analysis, we have investigated the performance of bonded composite patches used as reinforcements of aluminium panels in the case of U and V-notches. A semicircular patch shape was used in both cases. The stress distribution at the notch tip was investigated by taking in consideration the effect of various parameters. The effect of the patch size, type as well as the patch and the adhesive thickness was explored. The simple and the double patches were used to reinforce the aluminium panels. The important findings can be summarized as follows:  The presence of the patch contributes to the stress reduction at the notch tip because of a transfer of stresses through the adhesive towards the patch.  The increase of the contact area between the patch and the plate contributes to the normal stress reduction in the ligament of the plate.  The increase in the patch thickness leads to a decrease of the maximum stresses as well as the stress concentration factor at the notch tip.  The double patch reinforcement presents more reduction of the stress concentration factor (about 27%) compared to the simple patch reinforcement.  The use of Boron/Epoxy patch leads to an improved absorption of the stress transmitted by the notch than Graphite/Epoxy and Glass/Epoxy patches.  The drop of the stress concentration factor in the reinforced U-notches is more important than that observed for the reinforced V-notches.  As a conclusion, we can say that the use of a Boron/Epoxy double patch with an optimized patch thickness can be one of the most efficient ways to increase the performance of the patch reinforcement. 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