Parametric investigation of one-sided composite patch efficiency for repairing crack in mixed mode considering different thicknesses of the main plate

Abstract

In this paper, parameters affecting the performance and durability of a one-sided composite patch for mixed-mode crack repairing is investigated, considering different thicknesses of the main plate. In different references, there is no unity of opinion on the effect of various parameters on the performance and durability of one-sided patches. In the present study, to eliminate this disagreement, 3D finite element method is employed. It is clear that the effect of each parameter strongly depends on the thickness of the repaired plate. Among the investigated parameters, the patch material, length and width of the patch, and adhesive thickness are more important and studied in this paper. Results reveal that the effect of different parameters on the performance and durability of one-sided patches depends not only on the thickness of the main plate but also on the patch material.

Keywords

Finite element method fracture damage tolerance stress intensity factor bonded composite repair

Introduction

In many industries, the repair is performed when replacement is not possible or economical. There are various methods to repair plates, tanks, pipes, etc. such as welding the crack or defect site, the use of rivet-attached metal, the use of adhesive-bonded composite patches, etc. One of the best methods to repair metal and composite parts is to use adhesive-bonded composite patches. Composite patches have many advantages over other types of repair methods. Composites have a higher strength-to-weight ratio compared to metals and are more resistant to corrosion and damage.¹ The composite patch improves fatigue behavior, reduces corrosion, and is easily formed.² Ideally, the repair is expected to restore the structure to its original state. The most important advantage of a composite patch is that no new holes are created in the main structure during installation, and the structure does not get weaker. The required thickness for the composite patch is from 33% to 50% of the aluminum patch.³ The composite patch reduces the stress intensity factor (SIF), thereby slowing down and stopping the crack growth. The main advantage of the patch repair technology is that the weight of the structure is not greatly increased.⁴ The composite patch does not require high temperature, does not create stress concentration, and requires less skill than welding. For offshore oil and gas resources, because hot work cannot be done, patches are much more suitable for repair than welding.¹ Lightness, shape flexibility, variety of patches, etc. have made composite patches popular.⁵ In a multi-axial loading case, the adhesive-bonded metal patch performs better than the composite patch. In uniaxial loading, the composite patch is more appropriate. Anyway, the metal patch does not form in any shape as easy as a composite patch.⁶

Repair strength depends on the adhesive strength, patch strength, and strength of the repaired structure and all three should be examined. There is an asymptotic value for SIF in structures containing crack repaired with the composite patch, and as long as the SIF is below this value, the method is conservative.⁷ The repair material must have a minimum load-bearing capacity equal to the base material.⁸ Composite patches are used in many industries. The use of these patches is very common in aircraft maintenance and is limited to helicopters. Basically, in helicopters, any repairs to its dynamic components such as blades and shafts are not allowed, and, as explained by Shahani and Mohammadi,^9,10 these parts will be replaced after the service life is over. However, in emergency cases, such as when a helicopter shaft is damaged in the battlefield by bullet strikes, these patches can be temporarily used to repair helicopter components.^11–13 The success of the patch depends first on the adhesive and then on the patch material.⁷ Although the use of the composite patch dates back to 30 years ago, it has now been approved only for grade 2 important members.^14,15 Reasons for the patch failure include increasing the SIF on the main plate, increasing shear strain or peal stress on the adhesive, separation (poor surface preparation and poor adhesion selection), delamination, sudden failure (high stress), moisture absorption, residual thermal stresses, etc.^1,16 Thermal stress increases the SIF and decreases fatigue life.¹⁷

One of the results presented by Karr et al.¹⁸ shows that the effect of the number of the patch layers on the SIF reduction is much greater than its length and width and the thickness of the patch has a great effect on the static and fatigue strength of the plate. The material of the patch has little effect on the static strength and a great effect on the fatigue strength. Applying a one-sided patch on thin plates is more useful than thick plates. The performance of one and two-sided circular patch for surface crack repair was compared through the maximum SIF.¹⁹ The effect of different parameters was investigated and the results show that the choice of one or two-sided patch depends on both the crack depth and the patch thickness. Repaired samples with the hybrid method, composite patch, and bolt clamping exhibited up to 49%, 44%, and 24% increase in tensile strength under pure tensile stress, respectively.²⁰ Experimental and analytical studies were conducted to characterize the fatigue crack growth behavior of pre-cracked aluminum plates repaired with an asymmetric bonded composite patch.²¹ The analytical predictions of both the crack front shape evolution and the fatigue life were in good agreement with the experimental observations. Many research works, such as Bhise et al.²² and Braun et al.,²³ have investigated composite patch optimization. The effectiveness of the patch, as well as the influence of various parameters on the repair efficiency, has been analyzed by Shokrieh et al.²⁴ and Horn et al.²⁵

In this paper, parameters affecting the performance and durability of a one-sided composite patch for mixed-mode crack repairing is investigated, considering different thicknesses of the main plate. In different references, there is no unity of opinion on the effect of various parameters on the performance and durability of one-sided patches. In the present study, to eliminate this disagreement, 3D finite element method is employed. It is clear that the effect of each parameter strongly depends on the thickness of the repaired plate. Among the investigated parameters, the patch material, length and width of the patch, and adhesive thickness are more important and studied in this paper. To the best knowledge of the author, no research work has investigated the effect of different parameters on the performance and durability of the one-sided patch in the mixed-mode considering different thicknesses of the main plate.

Problem definition and validation analysis

An elastic aluminum plate with dimensions of 254 ×190 mm is considered and for different thicknesses of the main plate (2, 3.5, 5, 6.5, and 8 mm) effect of various parameters on the efficiency and durability of the patch is investigated using 3D finite element method. Most of the previous investigations have studied the crack repair in mode I, but, in the present study, to investigate the problem in a more general case, the crack is considered in the mixed-mode with a 45 ° angle relative to the load direction. Figure 1 shows a schematic of the problem under study and Figure 2 shows the model in abacus software with its meshed state. For meshing the model, C3D8R elements are used and contour integral method is considered for modeling the crack and the SIF calculation. The boundary conditions are considered such that the displacements at the two ends of the plate are restricted in perpendicular directions to the load and the plate can move freely along the load. The tensile stress of 100 MPa is applied at both ends of the plate in the y-direction. Very small size elements are used around the crack tip for obtaining better SIF results. The thickness of the adhesive is 0.1 mm, the crack length is 12.7 mm, and the thickness of the patch and the main plate is 2 mm. The main plate is made of aluminum 2024-T3, which is widely used in aerospace industries and the adhesive is considered to be FM-73. In addition, the fiber orientation is considered in line with the applied load. Four composite materials (boron-epoxy, graphite-epoxy, carbon-epoxy, and glass-epoxy) are considered for the patch. Table 1 presents the mechanical properties of the components used in the finite element analysis.

Table 1.

Mechanical properties of the components used in the FE analysis (G and E in GPa).⁶

Material	$E_{1}$	$E_{2}$	$E_{3}$	$G_{12}$	$G_{13}$	$G_{23}$	$ν_{12}$	$ν_{13}$	$ν_{23}$
Al2024-T3	72	–	–	–	–	–	0.33	–	–
Boron-epoxy	208.1	25.44	25.44	7.24	7.24	4.94	0.1677	0.1677	0.035
Graphite-epoxy	172.4	10.34	10.34	4.82	4.82	3.10	0.3	0.3	0.18
Carbon-epoxy	134	10.3	10.3	5.5	5.5	2.3	0.33	0.33	0.53
Glass-epoxy	27.82	5.83	5.83	2.56	2.56	2.24	0.31	0.31	0.41
Adhesive FM-73	–	–	–	0.42	–	–	0.3	–	–

In order to validate the model, the results of the finite element analysis are compared with the analytical equations. For the infinite plate under uniaxial tension, the SIF in modes I and II are obtained from equations (1) and (2), respectively. Because the dimensions of the plate considered in the present analysis are much larger than that of the crack, infinite plate relations are used to calculate the SIF.

K_{I} = σ \sqrt{π a} cos 2 β

(1)

K_{II} = σ \sqrt{π a} sin β cos β

(2)

In equations (1) and (2), σ is the applied stress, a is half the crack length, and β is the crack angle with the direction perpendicular to the load. Considering the applied stress of 100 MPa, $2 a = 12.7 mm$ and $β = 45^{\circ}$ , using equations (1) and (2), the SIF of modes I and II are obtained to be $K_{I} = K_{II} = 223.3 MPa \sqrt{mm}$ . The average values of K_I and K_II obtained by the finite element analysis are $232.35 MPa \sqrt{mm}$ and $232.8 MPa \sqrt{mm}$ , respectively. The difference between the numerical and analytical solutions is less than 5%. Figure 3 shows the effect of the crack angle on the SIF. As can be seen, by increasing the crack angle (β), the SIF decreases in mode I and increases in mode II. For all the crack angles studied, the SIF in mode I is slightly higher than the unrepaired state on the unrepaired side, but in mode II the SIF of the repaired plate is always lower than the unrepaired plate.

Effect of the patch material on the SIF reduction

Figure 4 illustrates the variation of K_I and K_II in terms of the dimensionless parameter percentage reduction in the SIF (RF_i) along the thickness of the main plate, considering different patch materials (left side of the graph shows the patched side of the plate). RF_i is defined as follows

R F_{i} = (1 - \frac{K_{ip}}{K_{iu}}) \times 100

(3)

In relation (3), indexes p and u represent the repaired and unrepaired state, respectively, and i can have the values I and II as modes I and II. In mode I, on the patched side RF_I has reached nearly 70%, but on the unpatched side of the plate, for all the patch materials, the value of this parameter is negative (Figure 4). Negative RF_I means that the SIF is higher than the unrepaired state. The higher SIF on the unpaired side compared to the unrepaired state is also reported in the previous references.⁶ However, in most portion of the main plate thickness, the RF_I value is positive, and the results presented in various references, show that the use of the one-sided patches is useful in extending the fatigue life of the structure.²⁶ For the boron-epoxy patch, the RF_I values on the patched and unpatched sides is 61.4% and −33.5%, respectively, and the average SIF in mode I is $198.7 MPa \sqrt{mm}$ , which is 14% less than the unrepaired value. Although, the difference in K_I for different patch materials is not so significant, as the patch stiffness increases, the repair efficiency increases too. In mode II, the RF_II value along the plate thickness is positive, and the boron-epoxy and the glass-epoxy patches have the highest (over 27%) and the lowest decrease in the SIF relative to the unrepaired state, respectively. Graphite-epoxy and carbon-epoxy patches have almost the same performance. For the boron-epoxy patch, the RF_II value on the patched and unpatched side is 41% and 24.4%, respectively.

Effect of the main plate thickness on the SIF

In this section, the effect of the main plate thickness (t_p) on the SIF in modes I and II is investigated, considering the carbon-epoxy patch and constant thickness of the patch t_r = 2 mm (Figure 5). Obviously, the K_I results, along the plate thickness, are not very different for different thicknesses of the main plate. In a one-sided patch, two factors opposed each other. By increasing the main plate thickness, the longer the patch distance from the unpatched side can lead to an increase in the SIF and another factor (decrease in asymmetry intensity) leads to a decrease in the SIF. In mode II, as the thickness of the main plate increases, the maximum SIF along the thickness of the main plate increases, too. For low thicknesses of the main plate (2, 3.5, and 5 mm), increasing the thickness of the plate has a large effect on K_II, but at higher thicknesses (6.5 and 8 mm), increasing the thickness of the plate does not cause much variation in K_II.

In the following, the K_I and K_II changes along the thickness of the main plate are investigated, considering different thicknesses of the plate and various patch materials (Figure 6). It is clear from Figure 6 that in mode I, for almost all the patches used (except for the glass-epoxy patch), the variation of the SIF along the plate thickness is not significantly different. For the glass-epoxy patch, the SIF on the patched side is higher than the other materials and the maximum SIF on the unpatched side is lower. For K_II, it is obvious that by increasing the main plate thickness, the positive effect of the patch is lessened, and in case of using the glass-epoxy patch, for a plate thickness of 5 mm or more, the SIF is very close to that of the unrepaired state. Meanwhile, boron-epoxy and glass-epoxy patches have the highest and lowest efficiency, respectively, and the performance of graphite-epoxy and carbon-epoxy patches is almost the same.

In Figure 7, the variation of the maximum (unrepaired side), minimum (repaired side) and midpoint SIF is plotted in terms of the thickness of the plate in modes I and II. In mode I, as mentioned before, except for glass-epoxy, the performance of patches with various materials is not much different. However, these slight differences can be very effective in fatigue life. In addition, the average SIF obtained by using the glass-epoxy patch in both modes I and II is much higher than the other three patch materials, and as a result, glass-epoxy patch is not recommended for repair. In the use of the glass-epoxy patch, the average SIF increases with increasing the thickness of the main plate for the constant thickness of the patch, whereas for the other three patch materials the average SIF is not significantly affected by the thickness of the main plate. In mode II, it is obvious that, due to the lack of bending moment effect on this mode, the efficiency of the patch decreases significantly with increasing the plate thickness, and the midpoint SIF increases for all the patch materials. The best performance is for the boron-epoxy patch in the case of t_p = 2 mm.

Effect of the patch width on the SIF

In this section, the effect of the patch width on the SIF is investigated considering several patch materials and different patch thicknesses (1, 2, 3, and 4 mm). At first, the thickness of the main plate is assumed to be 2 mm and the patch width is changed from the initial value of 60–190 mm (equal to the width of the main plate) (Figure 8). The crack is in the mixed-mode and its angle with the loading direction is 45 degrees.

In Figure 9, the midpoint SIF of modes I and II and the maximum SIF (unpatched side) are plotted in terms of the patch width considering different patch thicknesses (tr). In mode I, for the 1 and 2 mm patch thicknesses, the maximum SIF exceeds the unrepaired state, and neither the maximum nor the midpoint SIF changes with increasing the patch width. For 3 and 4 mm patch thicknesses, both the maximum and the midpoint SIF are below the unrepaired state and as the patch width increases, the SIF decreases markedly.

In mode II, for all the patch thicknesses, the SIF is below the unrepaired state and, besides, the SIF does not change much with changing the patch width. Clearly, the use of a patch with a higher thickness leads to a further decrease in the SIF. In most previous studies, because the analysis has been performed for a specific thickness, the results show that the patch width has little or no effect on the repair efficiency.² But as shown in Figure 9, for certain thicknesses of the patch, its width has a great effect on the repair efficiency, and for other thicknesses, it may have no effect. This should be borne in mind during designing the patch. However, using a thicker patch may not be very welcomed aerodynamically and from this point of view, there is a need for further investigation.

From Figure 9, it is clear that changing the width of the patch affects the efficiency of the repair when using boron-epoxy and carbon-epoxy patches for 3 and 4 mm patch thicknesses. However, in the case of using the glass-epoxy patch, for all the patch thicknesses, the effect of changing the patch width on the SIF is low and negligible. Therefore, one important conclusion to be drawn from this analysis is that the effect of the patch width on the repair efficiency depends not only on the thickness of the patch but also on the patch material.

In Figure 10(a), the midpoint K_I is shown in terms of the patch width. For boron-epoxy and carbon-epoxy patches (3 and 4 mm thick patches) that are stiffer than the glass-epoxy patch, the SIF decreases with increasing the patch width. Therefore, in such cases, it is useful to increase the patch width. In Figure 10(b), midpoint and unpatched surface SIF are shown in terms of the patch thickness for a fixed width of 60 and 190 mm (t_p = 8 mm). It is evident that in all the studied cases, the average and maximum SIF in modes I and II decreased with increasing the patch thickness. In mode I, by increasing the patch thickness, the positive effect of the larger patch width is more evident and for the patch width of 190 mm, a greater decrease in the SIF occurs. In mode II, the opposite occurs, and as the patch thickness increases, the effect of the patch width becomes less important and the graphs get closer.

Effect of the patch length on its efficiency

In this section, the effect of the patch length on the repair efficiency is investigated. Initially, the thickness of the main plate is assumed to be 2 mm and the effect of the patch length is investigated for three lengths of 60, 90, and 120 mm, considering different materials and thicknesses of the patch. For the three patch lengths investigated, in the case of using the boron-epoxy patch, the total displacement results are shown in Figure 11. Due to the increasing asymmetry intensity, by using a longer length patch, the total displacement of all points on the plate increases too. For the patch lengths of 60 and 120 mm, the maximum displacement obtained is 1.43 and 3.19 mm, respectively. Figure 12 shows the variations of the midpoint SIF for different composite patch lengths, considering different patch materials and thicknesses. For the glass-epoxy patch, the variation of the patch length has no significant effect on the midpoint SIF in mode I. As the patch stiffness increases, the SIF variations in terms of the patch length are more important. However, as the patch length increases, the SIF also increases slightly in both modes I and II. Therefore, for all materials and thicknesses examined, the use of a longer length patch reduces the repair efficiency (Figures 12 and 13). Therefore, a long-length patch is not recommended for repair. Both the test results and numerical analysis show that with increasing the patch length, fatigue life decreases, and the SIF increases.²⁷

The variations of the midpoint K_I in terms of the patch thickness is shown in Figure 13 considering different thicknesses of the main plate. As can be seen, for smaller values of the main plate thickness and all the patch lengths, increasing the patch thickness initially results in an increase in K_I, and subsequently, a further increase in the patch thickness will result in a decrease in K_I. For example, for a 2 mm plate thickness, the average K_I increases as the patch thickness increases from 1 to 2 mm, and then it decreases with a further increase in the patch thickness. This is also the case for plates with thicknesses of 3 and 4 mm. But, for a 5 mm thick plate, increasing the patch thickness always results in a decrease in K_I. Therefore, a very important point to note is that at lower thicknesses of the plate, increasing the patch thickness does not always lead to a decrease in K_I and it should be examined on a case-by-case basis.

Effect of the adhesive thickness on the patch efficiency

In this section, the effect of the adhesive thickness (in the range of 0.1–0.3 mm) on the patch efficiency is investigated for different plate thicknesses (2, 5, and 8 mm). The carbon-epoxy is considered for the patch material. For different thicknesses of the patch, Figure 14 shows the average SIF (corresponding to the midpoint along the thickness of the main plate) in terms of the adhesive thickness (t_a). As can be seen, as the adhesive thickness increases, K_I and K_II increase too, resulting in a decrease in the patch efficiency (Figures 14 and 15). However, as can be seen in Figure 16, and is referred to in various references, as the thickness of the adhesive increases, the stress on the adhesive itself decreases.^2,28 By changing the thickness of the adhesive from 0.1 to 0.3 mm, the maximum Von Mises stress in the adhesive decreased from 18.5 to 11.7 MPa. Therefore, it can be said that increasing the adhesive thickness is detrimental to the patch performance but is useful for the durability of the patch. In addition, in both modes I and II, as the patch thickness increases, the effect of changing the adhesive thickness on the SIF increases, too (Figure 14). For example, by varying the thickness of the adhesive from 0.1 mm to 0.3 mm, for the 2 mm thick plate, the K_I variations for t_r = 1 mm is 4.6% and for t_r = 4 mm is 7.9%. In mode II, the corresponding values are 5.7% and 8.1%, respectively.

For three different adhesive thicknesses, the variation of the average SIF in terms of the patch thickness is shown in Figure 15. For the 2 mm thick plate, with increasing the patch thickness, unlike the 5 and 8 mm thick plates, the SIF initially increases and then decreases. As the patch thickness increases, two factors conflict. On the one hand, increasing the thickness of the patch gives more rigidity to the whole structure and on the other hand, by increasing the patch thickness, the intensity of asymmetry increases, too. At the beginning of the work, for a 2 mm thick plate, increasing the patch thickness has a large effect on increasing the asymmetry and, as a result, the SIF increases. In main plates with thicknesses of 5 and 8 mm, because the thickness of these plates is high, increasing the patch thickness results in increasing the whole structure rigidity and asymmetry has no predominant effect.

Summary and conclusion

Based on the finite element study, the following conclusions can be drawn from the present work:

In mode I, by changing the main plate thickness, except for the glass-epoxy patch, for almost all the patches used, the variation of the SIF along the plate thickness is not significantly different. For K_II, as the thickness of the main plate increases, the positive effect of the patch decreases.

Boron-epoxy and glass-epoxy patches have the highest and lowest efficiency, respectively, and the performance of graphite-epoxy and carbon-epoxy patches is almost the same.

The average SIF obtained by using the glass-epoxy patch in both modes I and II is much higher than the other three materials used, and as a result, the glass-epoxy patch is not recommended for repair.

The effect of the patch width on the repair efficiency depends not only on the thickness of the patch but also on the patch material. For some thicknesses and materials, changing the patch width may not affect its efficiency, and for others, changing the patch width can significantly reduce the SIF.

For all the materials and thicknesses examined, as the length of the composite patch increases, the SIF increases slightly. Therefore, the use of the longer length patches is not recommended for repair.

In general, increasing the patch thickness leads to a decrease in the SIF. However, for low-thickness plates, this should be checked as this may not always be the case when using one-sided patches, and in some cases, increasing the patch thickness may increase the SIF.

Increasing the thickness of the adhesive decreases the repair efficiency and increases its durability. In other words, as the adhesive thickness increases, the SIF increases, and the stress on the adhesive itself decreases. For thicker patches, changing the thickness of the adhesive has more effect on the SIF.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Sirvan Mohammadi

Appendix

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