Effect of the Fibers Orientation of the Different Types of Composite Plates Notched of U-Shape Repaired by Composite Patch

Abstract The main objective of this work is to repair a structure of composite materials by gluing composite patches with different fiber directions. The effects of stress distribution, damaged area ratio, stress intensity factor KIC and imposed stacking sequence were highlighted by a comprehensive study that contained two sides, an applied experimental side and a numerical model side. The composite materials plates studied in this work are 8-layer of graphite/epoxy, glass/epoxy and boron/epoxy, with different angles. The results obtained clearly show with respect to the experimental side that the orientation of the fibers affects the ultimate strength of failure and that the fibers oriented longitudinally in the direction of the tensile strength give us an ideal performance of the composite material. As for the model aspect of this study, the effects of stress intensity factor and the relationship between the damaged area and the fiber orientation on the performance of these patches were studied. We can conclude from this study that the orientation of the fibers has an important role in the performance of the composite material and its efficiency in repair.


Introduction
In recent times the use of composite materials has become increasingly important in modern advanced industries.Due to its remarkable advantages in terms of lightness, hardness, corrosion resistance, and dealing with moisture and various weathers efficiently, as well as the price and durability and in terms of being easily formed but also in terms of dynamic, electrical or thermal.This type is currently replacing metallic materials in many industries (aviation, marine, civil engineering, sports and health uses, etc.) [1][2][3] .In order to develop and improve parts for various uses, it is necessary to understand and analyze the long-term properties of composite materials (durability).Another advantage of these materials is their ability to dissipate energy, which makes them less brittle than their conventional counterparts [4][5][6] .
One of the most important factors affecting the performance of composite materials for their duty is Humidity, an experimental study of water effect was conducted on the mechanical and dynamic properties of composite materials to analyze the effect of water absorption and fiber direction by Khouloud et al. 7 .Mokhtari et al. 8 identified all the stresses present in the adhesive joint in order to improve the nature of the material, as well as the nature and orientation of the fibers 8 .Among the factors affecting the behavior and performance of the composite material is the heat factor.Mechab et al. examined the deterioration of composite panels under convection in order to evaluate the effects of the mechanical properties of the composite on the orientation angle of the panel fibers and to prove the effect on the values of j integral 9 .The researcher Berrahou Mohamed has done several works regarding the study of the behavior of corroded aluminum plates under thermal stresses 10 , these Studies show that the higher the temperature, the more the composite material is affected negatively which in some cases may lead to significant damage.
The main objective of this study was to analyze the effect of fiber orientation on the performance of the composite material.We conducted a Library search on the most important studies that dealt with this phenomenon in particular, and among these studies.An experimental study by Ngoc -Hung Vu et al. on the mechanical behavior of a fiber-reinforced multilayer composite plate in order to study the assembly of a composite plate 11 .In addition, Long Pham et al. 12 examined the effect of steel fiber length and fragmentation size on the mechanical properties of plates 12 .
The analytical results of a study by Doo-YeolYoo and NemkumarBanthia showed that the assumption of 2-D fiber random orientation is suitable for unreinforced UHPFRC beam, while 3-D random fiber orientation assumption is suitable to reinforce with steel, UHPFRC beams and GFRP rebar due to fiber alignment disturbance from internal reinforcements 13 .Materials Research Achache et al. 14 also made a study aimed at the numerical analysis of the energy release rate factor G of a composite laminated board (glass or boron/epoxy) cross layer [+a, −a] in the presence of a crack between two circular slits under the influence of several parameters such as fiber orientation a and orientation crack 14 .Some studies have shown that the difference in fiber orientation and stacking sequence affects the performance and selection of the composite material and that by adding additional layers, it can strengthen the patch until its performance is optimal 15,16 .
In addition to all these studies, there is a large body of research in this field to study fiber orientation on the performance and efficiency of composite materials used in repair [17][18][19][20][21] .
This article also included an analysis of the effect of fiber orientation and layer stacking on the damaged area of the adhesive.It also studies the behavior of composite materials under mechanical influence.The study of the theory of the damaged area of the adhesive in recent years has received great attention from the researcher Berrahou Mohamed [22][23][24][25] .
Sabarinathan et al. 26 evaluated of thermal stability and damping behavior of electrical insulator waste reinforced thermoset polymer composite, addressing the effect of inorganic electrical insulator waste filler on the properties of glass fiber reinforced epoxy composite.They highlight the possibility for reprocessing electrical insulator waste as low-cost reinforcement in polymer composites, by uniformly mixing waste dielectric fillers into the resin through ultrasonic technology.Experimental results showed an increase in water absorption and density of the composites with the increase in electrical insulator waste filler in the polymer matrix.Moreover, the filler addition reduces the tensile strength and increases the flexural strength.Ramraji et al. 27 investigated the effect of cross-linked, alternate, neutral and flax basalt/ flax texture and leather on the mechanical and vibrational properties of newly designed polymeric laminate, followed by two layers of interwoven leather basalt layered linen (B4F5).The addition of the flax layer increased the natural frequency to the highest value.It was found that the skin basalt layer with intertwined flax layered B2F7 design structure exhibits maximum damping value with acceptable mechanical properties.
The composite patch and the adhesive layer have many effective mechanical and geometric parameters which are taken into account in the quality of the repair.As well, the shapes of the composite patches are a determinant of the effectiveness of the repair.This became the goal of many researchers among them: Bouchiba and Serier 28 , Salemet al. 25 have developed a static approach to optimize the shape of the composite patch.They concluded that the shape reduces the fracture energy at the crack front and minimizes shear stresses in the adhesive layer.Rachid et al. 29 , by designing a new shape of patch, called double arrow patch, show that compared to the conventional rectangular shape, this shape gives rise to a more efficient and effective repair in terms of reduction of the normal tensile stresses very concentrated at the crack tip.
In this work, we investigate the relationship between the numerical and experimental results of different cracked plates repaired with composite materials.The results focus on the specific stress concentrations in the composite as well as the effect of the composite properties mechanicals.In this article we have conducted a study from two aspects, the applied Experimental side and the Numerical modeling side.We focused on analyzing and studying several influences, such as fiber type and its orientation, on stress distribution.Next, we determined the effect of fibers orientation on the damaged area ratio and the change in stress intensity factor according of the crack length, and then examined the effect of the stacking sequence on the stress distribution.We investigate the relationship between the numerical and experimental results of cracked plate repaired with different types of composites.

Geometric Model
The structural model is a rectangular shaped geometric plate, The normalized dimensional data is (Hpl = 204mm, Wpl = 152mm, epl = 3mm) with a U-shaped notch of radius of r=15.2 see Figure 1.The plate was repaired with a U-shaped patch with a thickness epat = 1.6mm; three patch fibers orientation was used in this study (longitudinal, transverse and inclined) to investigate the influence of patch materials (boron / epoxy, glass / epoxy, graphite / epoxy).as shown in Figure 1.
The properties of the composite plates are: We repaired these cracks using a composite material, which is epoxy boron, to focus on the performance of the plates and to study the tensile factor and stress at the crack tip.
The patch dimensions are in Figure 1.Being glued to the plate by an FM73 adhesive (high performance structural epoxy adhesive) of thickness ea = 0.127 mm, Young's modulus Ea = 2.55 GPa and Poisson's ratio γ = 0.32.The 120 MPa load is applied to the end of the plate to be repaired length direction (x direction).
The finite element analysis of the configuration described in Figure 2 was performed using the ABAQUS program 30 .In this illustration we see the shape of the broken composite plate with a U-shaped notch (Semi circle), the construction consists of three subsections.The glue as well as the composite component (patch).As the break in the center of the plate causes stress concentration, a refined mesh is created around it.The total number of elements of the structure is 12148 quadratic hexahedral elements of type c3d20r, with 68829 nodes.The geometric shape of the crack is 3d.The plate has eight layers of elements in the thickness direction, the  adhesive has only one layer of elements through thickness and the patch has four layers of elements through thickness.To generate crack front some brick elements are replaced by "crack block".These crack-blocks are meshes of brick elements which are mapped into the original element space and merged with surrounding mesh.

Results and Discussion
This research was conducted in two parts.The first part consisted in carrying out an experimental research on the behavior of composite plates made of the following composite materials: boron / epoxy, graphite / epoxy and glass / epoxy with various fiber orientation angles (θ = 0 °, θ = 45 ° etθ = 90 °).In the second part we used the type of glass/ epoxy composite for crack reinforcement because it gives good resistance in the repair.In this part, we studied the effect of the fibers orientaion of plate on the variation of stress intensity factor for U-shaped notched plates according of crack length, on stress distribution σxx and σyyas , on the damaged area ratio and the effect of the stacking sequence of the patch versus the stress concentration factor, von mises stress and stresses of shear.

Ultimate strength depending on the fibers orientation
In this part, we will present a experimental study aiming at the analysis of the ultimate strength as a function of the fibers orientations of a composite material plate of three types of composites (graphite / epoxy, glass / epoxy and boron / epoxy).
This study shows that for all types of composites, the longitudinal orientation of the used patch fibers is preferable because the ultimate strength value is very high compared to the other orientations, by up to 20% compared to the inclined fibers and by an estimated 35% compared to the composites with the transverse orientation of the fibers at angle 90 degree, which proves the importance of fiber orientation in composite material stiffness and structure resistance.
After studying the data of Figures 4-6, it is clear that the graphite / epoxy composite material gives the largest value for the ultimate strength of failure compared to the other composites, as it reaches 1100 MPa at an angle of 0 degrees (longitudinal direction), while the other composites record values of 504 MPa for boron / epoxy and 410MPa for glass / epoxy for the same angle.Which allows us to say that the graphite / epoxy composite is the best type in this work in resisting mechanical stress.

Single and double glass / epoxy patch repair
Figure 7 presents the variation of the force according to the displacement, for a notch repaired by simple patch and double symmetrical patch.The beneficial effect of the patch is clearly visible.Indeed, the rigidities and the stress at failure of the repaired specimens are improved; it is because the patch absorbs the forces transferred by the plate through the adhesive as and when mechanical loading increases.The results of this figure clearly show that the double patch exhibits a considerable beneficial effect compared to the single patch.For the double patch, the stresses at the bottom of the notch are doubly absorbed by the patch; in this case the service life of the structure can be improved.
Table 1 groups together the stiffnesses and stresses at failure of laminates repaired by a simple and double patch.The presence of a notch weakens the structures by local stress concentration in the vicinity of the notch.This geocentric singularity reduces the rigidity and the stress at failure of the test specimen.Indeed, the highest values of stiffness and ultimate strength are obtained in the smooth structure without notch.These two parameters decrease respectively by 40% and 60% in a notched specimen.
The presence of the single or double patch in a damaged composite increases its rigidity and resistance to failure.sequence ply [45 / -45 / 90/0] S results in a weak improvement in rigidity, ie an increase of 6%.The double patch of this sequence results in slightly small increases as the 8-ply laminate [0/45 / -45 / 90] S.
Several studies have shown that the use of the double patch increases the fatigue life of two times compared to the single patch.The beneficial effect of the double patch can be enhanced if one takes into account the flexing effect that occurs with the use of the single patch.This bending is due to the displacement of the neutral axis of the structure when the composite patch is glued.The symmetrical double patch completely eliminates this effect.
We can therefore confirm that the advantages acquired by the use of the symmetrical double patch are quite significant.However, this double patch technique has certain drawbacks.In fact, in the case of the double patch, the visual detection of the crack initiated at the edge of the notch is impossible, which makes inspections quite difficult.

Simulation part
This part of the work is related to the modeling study of a cracked composite structure that we repaired using another composite material where the composite patch technique plays an important role in repairing failed structures [23, In this research, we examine the quality and reliability of patches constructed from carbon / epoxy, graphite / epoxy and boron / epoxy with different fibers orientation.In this numerical study was to highlight the evolution of the distribution of the stresses according to the crack length, and the variation of the damaged area ratio (D R ) and stress intensity factor (FIC) according of fibers orientation for the type of glass / epoxy composites and also the influence of the stacking sequence of the patch on the stresses.

Constrained distribution according to fibers orientation of patch
The Figures 8-9 illustrate the distribution of the von Mises stresses σ xx and σ yy according to path1 and of path 2 for different fibers directions (θ = 0 °, θ = 90 °, θ = 45 °) of a notched and cracked plate by a length crack of a = 15mm.A glass / epoxy patch was used to repair this plate.In the two graphs of Figures 8-9, we can see that the higher σ xx and σ yy focus is around the crack.also show that the interval of the stress concentration is maximum between 5 <x <15mm according to xx (path 1) and between 5 <x <40mm according to yy (path 2) and that the stresses values According to the plane xx are greater than those of plane yy.We notice that the orientation of the fibers in the longitudinal direction θ = 0° gives better behavior compared to the other orientations.We noted that the stresses of Von mises to be stable with  the increase of the length of path1 according to the interval 0 <x <5 and 15 <x <45.On the other hand, the length of path2 must be stable at the interval e 0 <y <5 and 40<y<75.
In conclusion, we can say that the fibers orientation has an important role in the performance of patches and the efficiency of their repair.The more the angles of fibers directing are close to the direction of the tensile stress, the better their performance compared to other angles.

Variation of the adhesive damaged area for different fibers orientation of patch
The development of the damaged U-shaped adhesive area is shown in the figure below.In the case of a = 5mm, the damaged area appears in small areas at the edges of the adhesive and around the crack, in the three types of fiber directions.Then in the case of a = 15mm it is noticed that the damaged area is relatively larger than the previous case at the level of the patch dimensions and appears at the level of the crack.Whereas at the crack length a = 40, this region evolved to take on a massive appearance at the margins of the central fissure.The increase in the value of the damaged area is due to the length of the incision.We find that the damaged area is in the middle of the board and larger at a = 40.
The theory's Main assumption of is that the adhesive and crack initiation in the bonded patch occurs after a damaged area develops.Under low amplitude of load, the localized damages arrive at the edges of patch.This damage occurs because the material is locally subjected to strains higher than the ultimate material strain.Under medium load amplitude, the damaged zones grow in size and the concentration of points of the damaged areas increases.As the failure load is reached the damaged area in the adhesive grows to a critical size and the individual components of the damage coalesce and form a crack.Numerically, the damaged area is identified by marking items for which a failure criterion is exceeded.The adhesive tested is a toughened ductile adhesive which is expected to fail in performance.Consequently, the failure criterion used for the cohesive damage of the adhesive layer is the equivalent Von Mises strain criterion: Where equiv ε is the equivalent stain, pi ε are the plastic strains in the different directions and ϑ the Poisson ratio.
This criterion is satisfied when the maximum principal strain in the material reaches the ultimate principal strain.For each failure criterion an ultimate strain will be defined and the corresponding damage zone size at failure is determined.The damaged area theory is based on the principle that the adhesive joint is assumed to fails when the damaged area reaches a certain critical value.The damaged zone can be determined by either a stress or a strain criterion.Therefore, the adhesive fails to perform its functions when the cohesive failure criterion is satisfied the adhesive joint.Since adhesive failure occurs at the adhesive joint, the adhesive failure criterion for the damaged area should be used.For isotropic materials, failure criteria such as the Von-Mises and Tresca criteria can be used to better understand the adhesive failure.Where Chang-Su Ban proved that the area where the equivalent strain of the adhesive exceeds the ultimate strain of 7.87%.After conducting studies on the FM-73 adhesive they concluded that this adhesive fails when the DR (Damaged area ratio) reaches a percentage exceeding 0.24 which is considered critical 31

Effect of fiber direction on damaged area ratio
Figure 11 clearly shows that for all fiber directions used (θ = 0°, θ = 90°, θ = 45°), the damaged area ratio values increase with crack length.The minimum value of DR is in the longitudinal orientation patch, compared to the transverse and inclined orientation patches, and this allows us to conclude that the crack repair efficiency is better in this orientation (longitudinal direction).Unlike the other two angles.We also note that the values of DR are less than DRc in the case of the longitudinal direction of the fibers, as for the other two directions, we reach the critical value DRc for a crack length equal to a27 mm for transversely oriented fibers and a length equal to 37 mm for a structure with inclined fibers.
We can conclude that longitudinally oriented fiber composites are better and more efficient compared to the other directions because they give the lowest value of DR.

Effect of patch fibers orientation on KIC reduction
To demonstrate the effect of the fibers direction of the composite material on the repair of a central circular notch, we consider different cases of orientation of the patch fibers.Figure 12 shows the effect of the patch fibers orientation on the variations of the stress intensity factor.The beneficial effect of the patch is clearly visible.Indeed, the stress concentrations of the repaired specimen are improved compared to those not repaired, it is because the patch absorbs the forces transferred by the plate through the adhesive.The results in this figure clearly show that repair performance is best when the patch orientation fibers is parallel to the direction of loading.This efficiency decreases when the orientation of the fibers increases.
Longitudinal orientation of the patch and the plate leads to a reduction in KIC of 70%.This reduction goes to 40% for a transverse orientation of the patch fibers.The other orientations of the fibers of the patch generate almost similar values of the variation of the KIC.From these results it is clearly seen that the patch fiber orientation directly affects the stress intensity at the notch edge.This effect increases with the increase in the rigidity of the patch.These results are justified by the values of the transverse and longitudinal Young's modulus and the direction of the stresses of the notched plates.We also can see that increasing the length of the crack produces an increase in the stress intensity factor.

Effect of patch lamination
In order to study the influence of the ply orientation of the composite patch on the level of normalized stresses and shear, we must fix the plate stacking sequence and vary that of the patch.Then we choose the optimal patch stacking sequence that minimizes these constraints.
The effect of the patch stacking sequence to the damaged laminate composite, these present the variation of the normalized stresses σ * and τ * for different sequence of stacking of the patch and shown in Figures 13-16.
The plate plies orientation has a significant influence on repair performance.Indeed; the lowest level of maximum normalized stresses is obtained when the adjacent plies of the plate (first ply) and of the patch (last ply) are oriented at 0 °.This stress is minimized when the overall rigidity of the patch increases [0] 4.An orientation of 90 °, 45 or -45 of the patch last ply leads to significant variations in the maximum stresses, the level of which also depends on the plate stacking sequence.As for the shear stresses τ * we observe that these stresses are minimal in the plate when the rigidity of the patch decreases or when all the plies are oriented in a 90 ° transverse direction, This non-optimal stacking sequence.
The effect of the ply fiber orientation adjacent to the bonded joint is not negligible; it has a significant influence on repair performance.This setting can change the damage scenario and therefore it should be optimized.The structure performance repaired by gluing is improved when the patch has a significant longitudinal Young's modulus.The use of one-way patch is optimal since this provides the highest reinforcement efficiency in the load direction.The difference between the Young's modulus of the different plies generates a variation in rigidity.In fact, a patch with a high longitudinal Young's modulus absorbs the majority of the stresses at the bottom of the notch through the adhesive.On the other hand, a composite patch of low longitudinal Young's modulus does not absorb all the stresses, this leads to an increase in stresses in the plate.

Conclusion
In this paper, we studied the mechanical behavior of the repaired cracked and notched plates using of composite patch.This study consists of an experimental test and numerical analysis using the ABAQUS program.We can deduce the following conclusions based on the results: *Experimental study: Composite plates oriented longitudinally in the direction of tensile strength gave the best results in terms of improving the ultimate strength of the composite , while the double repair technique showed efficiency compared to the simple repair.
*Modeling study: -The higher concentration of σxx and σyy is particularly around the crack region.
-The greater the crack length, the greater the stress intensity factor of plate and the proportion of the adhesive damaged area.
-The sequence has a significant effect on the stress level.The lowest maximum normal stresses are obtained when the adjacent layers of the plate (first layer) and the patch (last layer) are oriented in the direction of the tensile strength at degree 0.
-The use of unidirectional patching is optimal because it provides the highest reinforcement efficiency in the load direction.

Figure 3 .
Figure 3. Plies orientation in the patch and plate.

Figure 4 .
Figure 4. Ultimate strength depending on the fibers orientation of graphite/epoxy.

Figure 5 .
Figure 5. Ultimate strength depending on the fibers orientation of boron/epoxy.

Figure 6 .
Figure 6.Ultimate strength depending on the fibers orientation of glass/epoxy.

Figure 8 .
Figure 8. Distribution of σxx stresses for a cracked plate.

Figure 9 .
Figure 9. Distribution of σyy stresses for a cracked plate.

see Figure 4 .
Figure10presents the graphs simulated by the FEM using the ABAQUS code, these graphs clearly show the size of the damaged zone in the adhesive (in gray) following the fibers orientation from θ =0° up to θ =90°.The percentage of the damaged zone is evaluated by calculating the damaged zone in gray in relation to the adhesive total area.

Figure 10 .
Figure 10.The damaged area of FM73 adhesive for a Glass / epoxy patch of V-shaped.

Figure 11 .
Figure 11.Variation of the damaged area ratio DR as a function of the fibers orientation (°) for a glass / epoxy patch.

Figure 12 .
Figure 12.Stress intensity factor variation KIC (MPa.m 1⁄2 ) as a function of the fibers orientation according to crack length a (mm).

Figure 13 .
Figure 13.Influence of the patch stacking sequence on the shear stress σ * for a plate [0/45] 2s.

Figure 14 .
Figure 14.Influence of the patch stacking sequence on the shear stress τ * for a plate [0/45] 2s.

Figure 16 .
Figure 16.Influence of the patch stacking sequence on the shear stress τ * for a plate [45/90] 2s.

Figure 15 .
Figure 15.Influence of the patch stacking sequence on the stress σ * for a plate [45/90] 2s.

Table 1 .
Comparison of stiffness and ultimate strength at failure of repaired specimens.