Progressive failure analysis of bonded composite repairs

Composite Structures 81 (2007) 331–340 www.elsevier.com/locate/compstruct

Progressive failure analysis of bonded composite repairs Xi Liu a

a,*

, Guoping Wang

b

Department of Aircraft Design, Beijing University of Aeronautics and Astronautics (BUAA), Beijing 100083, China b Hafei Aviation Industry Co. Ltd., Harbin 150066, China Available online 5 October 2006

Abstract To study the tensile behavior of open-hole composite plates bonded with external composite patches, experimental tests were conducted and a 3-D progressive damage model is developed. Good agreement of the experimental results with the numerical predictions is obtained. Using this analysis model, the effects of several repair parameters on the failure initiation strength, ultimate strength and failure mechanism of these repaired structures are investigated. Four high stress concentration locations, where damages mostly initiate, are detected. Three types of final failure modes of these repaired structures subjected to tensile loads are concluded, with each corresponding to a different damage progression process.  2006 Elsevier Ltd. All rights reserved. Keywords: Progressive damage; Failure mode; Bonded repair; Finite element; Composites

1. Introduction Owing to the increasing applications of composite materials to both commercial and military aircraft structures, especially to the primary load-bearing structures [1,2], coupled with budget limitation and ever increasing requirements for maximum return on money invested, considerable attention has been drawn to the maintenance of those composite structures. The conventional ‘‘replace rather than repair’’ policy for metallic structures proves costly and sometimes unnecessary. More and more structures with defects or local damages will be repaired. After many years of study, various repair techniques have been successfully applied. Among them, adhesively bonded structural repair has gained more favor than mechanically fastened structural repair for the reason that fiber reinforced composites are essentially bonded in nature. Therefore, in recent years, considerable experimental [3–6] and numerical studies [7–12] have been conducted to investigate the influence of different repair parameters on the stress distribution, ultimate strength, and stress intensity factor of the bonded repaired structures. How*

Corresponding author. E-mail address: [email protected] (X. Liu).

0263-8223/$ - see front matter  2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2006.08.024

ever, relatively little research work has been carried out to analyze the failure mechanism of these repaired structures, a good knowledge of which is essential for the repair design and certification [13]. In this paper, a 3-D progressive damage model is built and verified by experimental study. Using this model, various repair parameters are studied and the failure initiation strength and ultimate strength of these bonded repaired structures are predicted. Moreover, extensive studies are carried out to provide an insight into the influence of different repair parameters on the failure mechanism of these structures. 2. Experimental study The parent plates ([(0/90/±45/90/0)2]s) and patches used in the experiments were fabricated with T300/QY8911 prepreg, the mechanical properties of which are listed in Table 1. To simulate the damages in the structures, B30 mm holes were drilled in the center of the parent plates, and rounded composite patches were bonded on both sides by using epoxy film adhesive (J159) of 0.12 mm thickness, as shown in Fig. 1. During the tests, specimens were subjected to longitudinal tensile loads on MTS8101-13 as shown in Fig. 2. In

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Table 1 Mechanical properties of materials Materials

T300/QY8911

E1 (GPa) E2, E3 (GPa) m12, m13 m23 G12, G13 (GPa) G23 (GPa) Xt (MPa) Xc (MPa) Yt (MPa) Yc (MPa) S (MPa)

135.00 8.80 0.33 0.48 4.47 3.20 1548 1226 55 218 89

J159 1.00 0.30

45

100mm

Patch

Parent plate

Adhesive

Φ30mm

2.88mm

Fig. 2. Specimen on MTS8101-13.

260mm

Fig. 1. Geometry of the repaired structure.

order to obtain valid results, three identical specimens were tested per group (as listed in Table 2). In the experiment, the experimental phenomenon and ultimate strength of these specimens were recorded. Photographs were also taken for studying their failure mechanisms, as shown in Fig. 3. From the comparative study of these test specimens (see Fig. 3a), two types of final failure modes can be concluded: Mode A: Due to the high shear and peel stresses in the adhesive near the patch edges, damages initiated and propagated swiftly in the adhesive, and then the patches and parent plates were partly or completely detached. Finally,

the plates were broken apart along the transverse direction through the holes, leaving the patches undamaged, as shown in Fig. 3b. Mode B: The patches failed to sustain the load transferred from the plates and broke along the edges of the holes. Almost simultaneously, the parent plates were also drawn apart along the transverse direction (Fig. 3c). 3. Progressive damage modeling 3.1. Finite element model Consider a plate with a B30 mm central hole, which is bonded with round composite patches on both sides, the configuration of which is the same as that shown in Fig. 1. To avoid the limitation of the 2-D models [14], and to investigate the failure mechanism at layer level, a three dimensional finite element analysis model is adopted. However, due to the dimension of the lamina in the thick-

Table 2 Configurations selected for failure study Group label

Parent plate

Adhesive thickness (mm)

Patch size (mm)

Patch stacking sequence

1 2 3 4 5 6

[(0/90/±45/90/0)2]s [(0/90/±45/90/0)2]s [(0/90/±45/90/0)2]s [(0/90/±45/90/0)2]s [(0/90/±45/90/0)2]s [(0/90/±45/90/0)2]s

0.12 0.12 0.12 0.12 0.12 0.12

B40 · 0.35 B40 · 0.7 B50 · 0.875 B60 · 1.4 B70 · 0.7 B80 · 0.875

[±45] [0/±45/90] [02/±45/90] [02/±452/902] [0/±45/90] [02/±45/90]

X. Liu, G. Wang / Composite Structures 81 (2007) 331–340

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bottom corner of the mid-plane. In the virtual tests, the following boundary and load conditions are applied: x ¼ 0 mm; u ¼ v ¼ w ¼ 0; 1 x ¼ 260 mm; F Applied ¼ F Actual ; 2 z ¼ 0 mm; w ¼ 0;

ð1Þ

where u, v, w are the displacements along the x, y, z directions. FApplied, FActual are the applied load in the model and the actual load, respectively. 3.2. Failure criterion and property degradation 3.2.1. Plate and patch For the parent plates and patches, stiffness reduction is carried out at layer level in each element considering three types of damages: fiber breakage, matrix cracking and delamination. To detect them, a set of 3-D stress based failure criteria are selected. Specifically, the following Tsai– Wu criterion [15] is used to detect fiber breakage and matrix cracking in the laminated structures. 3.2.1.1. Failure criterion. f ðrk ÞF i ri þ F ij ri rj ¼ 1;

ð2Þ

where: F 1 ¼ 1=X t  1=X c ;

F 2 ¼ 1=Y t  1=Y c ;

F 3 ¼ 1=Z t  1=Z c ; F 11 ¼ 1=X t X c ; F 22 ¼ 1=Y t Y c ;

F 33 ¼ 1=Z t Z c ; ð3Þ

2

F 44 ¼ F 55 ¼ F 66 ¼ 1=S ; 1

F 12 ¼ 0:5ðX t X c Y t Y c Þ 2 ;

1

F 13 ¼ 0:5ðX t X c Z t Z c Þ 2 ;

1

F 23 ¼ 0:5ðY t Y c Z t Z c Þ2 :

Fig. 3. Failure modes of the tested specimens.

ness direction and considering the effect of aspect ratio, an extremely fine mesh will have to be used to achieve reliable outcomes in the traditional laminates modeling method. The time to run such a model will be intolerable. Therefore, in this paper, the 20-node layered element SOLID191 in ANSYS is adopted to model the laminates, which allows up to 100 different material layers in the thickness direction in each element without much increase of counting time. In the analysis model, the adhesive is assumed to be isotropic and a normal 20-node brick element (SOLID186) is used. Due to the symmetry of the two-sided repaired structure with respect to the mid-plane of the parent plate, only the upper half of the repaired structure is modeled. And the x–y plane of the Cartesian coordinate system is located at the mid-plane of the plate with x-axis along the longitudinal direction of the parent plate and its origin is at the left

The Ye [16] delamination is used to detect the delamination onset, which takes the form: r 2 r 2  r 2 3 5 4 þ þ ¼ 1; r3 > 0; Y S ST ð4Þ r 2  r 2 5 4 þ ¼ 1; r3 6 0; S ST where Y and S are the transverse tensile and shear strength, respectively. ST is the shear strength in the plane perpendicular to the fibers. 3.2.1.2. Stiffness degradation method. When the Tsai–Wu criterion mentioned above finds that a layer in an element has damaged, then the next step is to compute the contribution of each stress component towards the failure index to identify which one contributes the maximum. 3.2.1.3. Fiber breakage. If r1 contributes the maximum, then the damage of the layer within a certain element is fiber breakage. The following stiffness degradation method is adopted:

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E01 ¼ ksrc E1 ; G013 ¼ ksrc G13 ; m013 ¼ ksrc m0xz ;

G012

¼ ksrc G12 ;

ð5Þ

m012 ¼ ksrc m12 :

is used for the second time. If more times of shear failure occur in the same element, a very small value 0.00001 is assigned to kAdhesive. 3.3. Progressive damage analysis

3.2.1.4. Matrix cracking. If the failure is due to r2 or r6, then the damage mode is matrix cracking. The following material properties are degraded: E02 ¼ ksrc E2 ; G023 ¼ ksrc G23 ; G012 ¼ ksrc G12 ; m023 ¼ ksrc m023 ; m012 ¼ ksrc m12 :

ð6Þ

3.2.1.5. Delamination. If the Ye delamination criterion detects any delamination, then: E03 ¼ ksrc E3 ; G023 ¼ ksrc G23 ; m023

¼

ksrc m023 ;

G012 ¼ ksrc G13 ; m012

ð7Þ

¼ ksrc m13 ;

where E01 , E02 , E03 , G012 , G023 , G013 , m012 , m023 , m013 are the degraded material properties, and ksrc is stiffness reduction coefficient. Extensive comparative studies are carried out to study the effect of ksrc, which indicates that ksrc would greatly influence the strength prediction and failure mechanism in the progressive damage model. After a careful comparative study, ksrc = 0.001 is applied in the current model. In case of mixed damage modes, for example, if fiber breakage and delamination both occur in the same layer of an element, then the corresponding material properties of this layer are reduced to nearly 0. However, to avoid numerical problems, ksrc = 106 is applied. 3.2.2. Adhesive 3.2.2.1. Failure criterion. To simplify the analysis and to still capture the essential feature, the major damage mode considered in the adhesive is adhesive shear failure, and the maximum shear stress criterion is used to judge it in the adhesive at element level: r1  r3 P S: ð8Þ 2 Here r1 and r3 are the maximum and minimum principal stresses in the adhesive; sys is the shear strength of the adhesive.

A program, the algorithm of which is shown in Fig. 4, is created to analyze the failure mechanism of bonded repaired structures. Before the analysis begins, a finite element model is set up in the program by using the APDL language of ANSYS. All the material properties are set to their initial values. Within each load step, damage analysis is carried out by applying these failure criteria mentioned above. If any damage occurs, the material properties in the damaged region will be degraded according to the corresponding degradation rules, and then the analysis will be restarted without load increment until no damage is found in this load step or final failure of the repaired structure is determined. Theoretically, the smaller the load increment between successive steps, the more accurate analysis result can be achieved. However, a reasonable load increment should be prescribed to avoid too much analysis time and also to ensure accuracy. After a careful convergence study, DF = 2 kN is proved to be a good compromise between accuracy and time consumption. 3.4. Model verification To verify the progressive damage analysis model, three repair cases are analyzed, the configurations of which are the same as those listed in Table 2 (Groups 1–3). As shown in Fig. 5, the predicted ultimate strength corresponds well with the experimental results. Furthermore, the failure mechanism predicted by the model is also compared with the records of the experimental phenomenon as discussed in the following parts. Group 1: The experimental record shows that the patches were driven apart along the hole edges nearly simultaneously

Start

FE model setup Stress analysis

3.2.2.2. Stiffness degradation method. In case of any shear failure being detected, the following stiffness degradation method is applied: E0Adhesive ¼ kAdhesive EAdhesive ;

ð9Þ

where E0Adhesive is Young’s modulus after degradation; kAdhesive is the stiffness reduction coefficient. Considering the plastic nature of the adhesive, a gradual degradation method is adopted. When shear failure is found in an element for the first time, kAdhesive = 0.1 is applied, and 0.01

Material property degradation Failure analysis

NO

Load increment

YES Check for final failure

NO

Check for failure

YES

Fig. 4. Progressive damage algorithm.

Stop

X. Liu, G. Wang / Composite Structures 81 (2007) 331–340

Ultimate strength (MPa)

300

Analysis Experiment

250 200 150 100 50 0 1

2

3

Group label

Fig. 5. Predicted ultimate strength vs. experiment data.

with the parent plates, which is the failure ‘‘Mode B’’ as defined in Section 2 of this paper. The failure process predicted by the model analysis, as shown in Fig. 6, also presents the same failure process: before the final failure, the

335

damages of the parent plate are mainly near the hole edge. Simultaneously, obvious damages along the hole edge in the patch occur, mainly matrix cracking (see Fig. 6a). The final failure is sudden: as shown in Fig. 6b, the parent plate breaks along the transverse direction, and the patch is taken apart along the hole edge, the same as noticed in the experimental tests. It is hard to tell which component breaks apart first. Groups 2 and 3: The experimental record indicates that Groups 2 and 3 presented nearly the same failure mechanism: the parent plates were taken apart, leaving the patches unbroken or even intact (‘‘Mode A’’), and so do the numerical analysis results. Therefore, take Group 2 as an example, the analysis results are shown in Fig. 7. When the load increases to the failure load, no damage occurs in the patch, however, as shown in Fig. 7a, a large area of shear failure has already appeared in the adhesive. So the patches are peeled away from the parent plate, with just some matrix cracking in the 90 layers. Having lost the support from the patches, the plate snaps along the transverse direction as shown in Fig. 7b.

Fig. 6. Failure process of Group 1: (a) F = 55 kN, (b) F = 61 kN (final failure).

Fig. 7. Failure process of Group 2: (a) F = 65 kN (earlier stage), (b) F = 65 kN (final failure).

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The comparison above shows that the progressive damage analysis model not only predicts the ultimate strength very well, but also provides a reasonable failure mechanism for the two-sided bonded repair. 4. Results and discussion 4.1. High stress zone and main final failure modes Using this progressive damage analysis model, about 40 repaired structures with different repair parameters are analyzed. The results of these virtual tests reveal that when these ‘‘specimens’’ are subjected to tensile loads, there are mainly four groups of locations, as shown in Fig. 8, where high stress concentration always occurs and damages mostly initiate. Failure analysis of these virtual test results reveals that there are mainly three types of final failure modes of these repaired structures, named ‘‘Mode A’’, ‘‘Mode B’’ and ‘‘Mode C’’ respectively in this paper, as shown in Fig. 9. After a comparison between Figs. 9 and 3, it is interesting to notice that ‘‘Mode A’’ and ‘‘Mode B’’ also occur in the experiments. But the ‘‘Mode C’’ has not happened in the limited experimental tests. Further investigation of the failure process of these repaired structures indicates that different final failure modes of these repaired structures correspond to different failure modes of the parent plates

and patches, details of which are listed in Table 3. And the corresponding failure configurations of plates and patches are shown in Figs. 10 and 11. Taking the repair parameters into consideration, analysis of the ‘‘specimens’’ with different final failure modes reveals the following results. ‘‘Mode A’’ always occurs when the parent plates are bonded with relatively strong patches, and high stresses are induced in the covered region, which incurs high shear stress in the adhesives. So the adhesives invariably fail first and the patches are detached from the parent plates. Once without the support from the patches, the parent plates soon break along the transverse direction under remote tensile loads. ‘‘Mode B’’ is more likely to occur when the patches are not strong enough. Less stresses are induced in the adhesives, so the patches can be bonded to the parent plates in the whole process. Moreover, a comparative study shows that patches in failure ‘‘Mode Pa-A’’ enjoy higher stiffness than those in ‘‘Mode Pa-B’’. Table 3 Final failure modes of the components Final failure mode of the structures

Plate

Patch

Mode A Mode B Mode C

Mode Pl-A Mode Pl-A Mode Pl-B

Not damaged Mode Pa-A or Mode Pa-B Not damaged

Note: For the definition of these failure modes please refer to Figs. 9–11. Overlap region

Overlap region

Overlap region

Overlap region

Failure path

A

B

C

Overlap region

Failure path

Overlap region

D

Fig. 8. High stress concentration locations. Mode Pl-A

Failure path

Overlap region

Failure path

Overlap region

Failure path

Overlap region

Fig. 10. Main final failure modes of the parent plates.

Failure path

Final failure Mode A

Final failure Mode B

Mode Pl-B

Overlap region

Failure path

Overlap region

Final failure Mode C Mode Pa-A

Fig. 9. Three main final failure modes of the repaired structures.

Mode Pa-B

Fig. 11. Main final failure modes of the patches.

X. Liu, G. Wang / Composite Structures 81 (2007) 331–340

4.2. Effect of patch size To study the effect of patch size on the ultimate strength and failure mechanism of the repaired structures, as given in Table 4, only the patch size, represented in terms of the patch diameter in the current model, is changed in the model. As shown in Fig. 12, both the failure initiation strength and the ultimate strength start from a low value and generally increase with larger patches. Especially when the patch diameter is less than 60 mm, the curves are relatively steep. However, when the patch diameter exceeds 60 mm, the slope of both curves decreases obviously and enters a stable stage. It is not clear why this should be the case without further investigation on the failure mechanisms of these repaired structures. For structures repaired with small patches, take the structure bonded with B40 mm patches as an example, due to its narrow overlap length, when the adhesive transfers load between the parent plate and patches, high stress concentration zone will be formed more easily in the narrow overlap region, especially near the patch edges, where shear failure occurs first in the adhesive (see Fig. 13a) and propagates quickly to most of the overlap region under the same outer load, as shown in Fig. 13b. Then the plate and patches are partly or wholly detached. Without the support from the patches, it is natural that the parent plate will soon break apart, resulting in low ultimate strength, and exhibiting ‘‘Mode A’’ failure as listed in Table 5. Structures with larger patches have wider overlap lengths, where the stresses transferred from parent plates and patches are more evenly distributed over the adhesives. The analysis of the failure process of a structure with B50 mm or larger patches reveals that no shear failure occurs in the adhesives until ultimate failure loads are applied. The final failure pictures of the adhesives, as shown in Fig. 14, indicate smaller shear failure areas for larger patches. Because of the linkage of adhesives during the whole process, the patches successfully protect the plates all through. So it is natural that these repaired structures enjoy higher ultimate strength. Furthermore, from Fig. 12, it is interesting to notice that the difference between failure initiation strength and ultimate strength becomes

400

Failure initiation Ultimate failure

380 360 340

Applied stress (MPa)

‘‘Mode C’’ happens when the regions covered by the patches have higher strength than the original plates and the adhesives do not fail first, so the failure paths have to make their way around the edges of these patches, where high stress concentration occurs.

337

320 300 280 260 240 220 200 40

45

50

55

60

65

70

Patch diameter (mm)

Fig. 12. Effect of patch size.

Fig. 13. Failure initiation and propagation in the adhesive of the plate with B40 mm patches.

Table 5 Effect of patch diameter on failure mode Patch diameter (mm)

Plate

40 50 60 70

Mode Mode Mode Mode

Pl-A Pl-A Pl-A Pl-B

Patch

Repaired structure

Not damaged Mode Pa-A Mode Pa-B Not damaged

Mode Mode Mode Mode

A B B C

Note: For the definition of these failure modes please refer to Figs. 9–11.

larger with bigger patches, which indicates that the failure progress of structures with larger patches is more stable and slow. The reason why when the patch diameter exceeds a certain extent, B60 mm in this paper, its influence is weakened can be found by the comparative study of the final failure pictures of adhesive with different overlap lengths in Fig. 14. Although the discussion above mentioned that wider overlap length would make the stress within the adhesive more evenly distributed, the stresses are mostly carried in the narrow regions near the patch and hole

Table 4 Model parameters for studying the effect of patch size

Size (L · W · T) Materials Stacking sequence

Plate

Patch

Adhesive

260 · 100 · 2.88 mm T300/QY8911 [(0/90/±45/90/0)2]s

Change in diameter, T = 0.875 mm T300/QY8911 [02/±45/90]

T = 0.20 mm J159 –

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X. Liu, G. Wang / Composite Structures 81 (2007) 331–340

Fig. 14. Final failure pictures of adhesive.

edges. The stress level of other locations in the adhesive will keep low no matter how wide the overlap length is. So for B70 patch, the adhesive only has shear failure near the patch edge, which explains why too large patches fail to enhance the ultimate strength as expected. Furthermore, in practical situations, large patches are hard to be bonded without any local deficiencies such as air trapment and uneven distribution of the adhesive, not to mention the weight penalty associated with large patches. 4.3. Effect of patch thickness The same parent plate, as listed in Table 4, bonded with B50 patches is used to assess the effect of patch thickness. In order to avoid the influence of other factors, the patches are laid up with only ±45 plies. In Fig. 15, n is the ratio of patch thickness TPatch to the parent plate thickness TPlate, n¼

T Patch : T Plate

ð10Þ

As shown in Fig. 15, there is an optimum patch thickness, which is about 60% of the parent plate thickness for current repair configuration. When n < 0.6, the strength of the repaired structures increases with thicker patches; however, when n > 0.6, the slope of the curves becomes negative, indicating that too thick patches will deteriorate the strength of the repaired structures. The reason for the above phenomenon can be found in the following failure analysis. 300

Failure initiation Ultimate failure

280 260

Applied stress (MPa)

240 220 200 180

As Fig. 16a shows, since the thin patches are relatively weak, they cannot effectively suppress the crack propagation near the hole edge. So, before the final failure of the structures, large areas of local damages in the patches have occurred along the hole edge. When thicker patches are applied, as shown in Fig. 16b, damages of the plate switch to the regions around the patch edge, and the expanding of the crack along the hole edge is obviously slowed down, which accounts for the rising of the strength of the repaired structures. However, thicker patches also bring problems. A comparison of the failure pictures of the adhesives in Figs. 16a–c indicates that thick patches increase shear stress in the adhesives. Therefore, before the final failure, the adhesive of the structure repaired with [±45]8 patches has already had a large area of shear failure, and the plate and patches are almost detached, with large areas of delamination occurring near the hole edge during the peeling process, as shown in Fig. 16c. The early detachment of the patches from the plate results in its low ultimate strength, which explains the heading down of the curves in Fig. 15. 4.4. Effect of patch stacking sequence For the laminates, careful design of their stacking sequence can also contribute to its strength under different circumstances. To study its role in the repair, the same plate as in Table 4 bonded with different patches, as listed in Table 6 is analyzed. The comparison of the strength shown in Fig. 17 indicates that the stacking sequence of the patches has little influence on the failure initiation strength and ultimate strength. So does its effect on these repaired structures’ failure mechanism. Only in Groups 4, 5 and 6, the matrix cracking is more likely to initiate and expand in the 90 layers near the hole edges at an early stage, for its closeness to the adhesive and weakness in the longitudinal direction. However, matrix cracking in 90 layers has little influence on the ultimate strength of the whole structure. 4.5. Effect of adhesive thickness

160 140 120 0.0

0.2

0.4

ξ

0.6

0.8

Fig. 15. Influence of patch thickness.

1.0

The adhesives, which bond the patches and parent plates together, are always regarded as the weakest chain in the bonded repair, and play an essential role. Therefore, careful selection of its parameters is very important. In this paper, its thickness effects are studied with a model that has

X. Liu, G. Wang / Composite Structures 81 (2007) 331–340

339

Fig. 16. Repaired structures before final failure: (a) [±45], (b) [±45]4, (c) [±45]8.

Table 6 Parameters of patches Case number

Patch material

Size (mm)

Stacking sequence

1 2 3 4 5 6

T300/QY8911 T300/QY8911 T300/QY8911 T300/QY8911 T300/QY8911 T300/QY8911

B50 · 0.875 B50 · 0.875 B50 · 0.875 B50 · 0.875 B50 · 0.875 B50 · 0.875

[0/45/45/45/90] [45/0/±45/90] [±45/0/45/90] [90/45/45/45/0] [45/90/±45/0] [±45/90/45/0]

Failure initiation Ultimate failure 300

Fig. 18 shows the strength of the repaired structure with respect to adhesive thickness, which suggests that there is an optimum choice of adhesive thickness in the repair design. If the adhesive is too thin, it will be stiff and brittle. Shear failure is more likely to initiate from these high stress regions near the patch and hole edges as shown in Fig. 19. And the damages will soon expand to the whole overlap region, causing the early detachment of patches, resulting in low ultimate strength and ‘‘Mode A’’ failure of the repaired structures, as listed in Table 7. On the other hand, too thick adhesive goes to the opposite. The adhesive will be too plastic. Under outer load, large deformation of the adhesive weakens the effectiveness of load transfer between the parent plates and patches.

200

150

100

50

0 1

2

3

4

5

6

Case number

Fig. 17. Strength of structures repaired with patches of different stacking sequences.

the same parent plate as listed in Table 4, which is bonded with patches ([02/±45/90]), but with different adhesive thickness.

Applied stress (MPa)

Applied stress (MPa)

250

370 360 350 340 330 320 310 300 290 280 270 260 250 240 230 220 210 200 190 180

Failure initiation Ultimate failure

0.0

0.2

0.4

0.6

0.8

Adhesive thickness (mm)

Fig. 18. Influence of adhesive thickness.

1.0

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Fig. 19. Shear failure initiation and propagation in the 0.12 mm thick adhesive.

Table 7 Final failure modes of repaired structures with different adhesive thickness Adhesive thickness (mm)

Plate

0.12 0.16 0.20 0.30 0.50 1.00

Mode Mode Mode Mode Mode Mode

Pl-A Pl-A Pl-B Pl-B Pl-A Pl-A

Patch

Repaired structure

Not damaged Not damaged Not damaged Not damaged Mode Pa-B Mode Pa-B

Mode Mode Mode Mode Mode Mode

A A C C B B

Note: For the definition of these failure modes please refer to Figs. 9–11.

Because of the low load transferring capability of the adhesive, although the patches are still bonded on the parent plates, the plates have to bear most of the outer loads themselves, which causes the decrease of the ultimate strength. When the adhesive thickness is about 0.2–0.3 mm, the ultimate strength of the structures reaches the highest point, and the failure mechanisms of the structures are also changed. As listed in Table 7, because of the reasonable choice of adhesive thickness, the adhesives successfully bond the components together all through, so the strength of the patched region will exceed that of the original parent plates, and the failure paths have to make their way around the patch edges, where high stress concentration occurs. 5. Conclusions In the present study, both experimental tests and numerical study are carried out to investigate different repair parameters’ effects on the ultimate strength and failure mechanism of adhesively bonded repaired structures, and the following conclusions can be drawn from the above study. 1. Under tensile loads, there are mainly three types of final failure modes for the repaired structures, each occurring under different circumstances. 2. Four sets of high stress concentration zones are found, where damages mostly initiate and propagate. 3. Delamination scarcely occurs in two-sided bonded repair under tensile loads, but most likely in the layers close to the adhesive or near the hole edges, when the patches are peeled away from the parent plates. 4. Structures bonded with different patches may have the same strength, but their failure process and final failure modes can be totally different.

5. The parameters of patches will not only influence the patches performance, but also more importantly, it will change the failure process of the adhesives, and finally the failure mechanism of the repaired structures. 6. Optimum repair designs can be achieved with careful choice of repair parameters and by taking into consideration other factors, such as structure configuration limit, structure accessibility, etc.

Acknowledgments The authors thank Prof. Ying Yan, Prof. Chuanxian Cheng, Dr Bingshan Liu, and Lulu Wang in Beijing University of Aeronautics and Astronautics (BUAA) for their help and valuable advices on the finite element analysis model. References [1] Baker AA, Rose LRF, Jones R. Advances in bonded composite repair of metallic aircraft structure. 2V. Amsterdam: Elsevier; 2003, ISBN 0-08-042699-9. [2] Baker Alana. Bonded composite repair of fatigue-cracked primary aircraft structure. Compos Struct 1999;47(1–4):431–43. [3] Charalambides MN, Hardouin R, Kinloch AJ, Matthews FL. Adhesively-bonded repairs to fibre-composite materials I. Experimental. Composites A 1998;29(11):1371–81. [4] Schubbe JJ, Shankar Mall, Fatigue behavior in thick aluminum panels with a composite repair, AIAA-98-1997. p. 2434–43. [5] Baker AA, Chester RJ, Hugo GR, Radtke TC. Scarf repairs to highly strained graphite/epoxy structure. Int J Adhes Adhes 1999;19(2–3): 161–71. [6] Bartholomeusz RA, Baker AA, Chester RJ, Searl A. Bonded joints with through-thickness adhesive stresses – reinforcing the F/A-18 Y470.5 bulkhead. Int J Adhes Adhes 1999;19(2–3):173–80. [7] Naveen Rastogi, Soni SR, Denney JJ, Analysis of bonded composite patch repaired metallic structures – an overview of aging aircraft, AIAA98-1883. p. 1578–88. [8] Soutis C, Duan D-M, Goutas P. Compressive behaviour of CFRP laminates repaired with adhesively bonded external patches. Compos Struct 1999;45(4):289–301. [9] Hu FZ, Soutis C. Strength prediction of patch-repaired CFRP laminates loaded in compression. Compos Sci Technol 2000;60(7):1103–14. [10] Achour T, Bouiadjra B Bachir, Serier B. Numerical analysis of the performances of the bonded composite patch for reducing stress concentration and repairing cracks at notch. Comput Mater Sci 2003;28(1):41–8. [11] Seo Dae-Cheol, Lee Jung-Ju. Fatigue crack growth behavior of cracked aluminum plate repaired with composite patch. Compos Struct 2002;57(1–4):323–30. [12] Charalambides MN, Kinloch AJ, Matthews FL. Adhesively-bonded repairs to fibre-composite materials II. Finite element modelling. Composites A 1998;29(11):1383–96. [13] Jones R, Chiu WK, Smith R. Airworthiness of composite repairs: failure mechanisms. Eng Failure Anal 1995;2(2):117–28. [14] Randolph A Odi. A comparative study of finite element models for the bonded repair of composite structures. J Reinforced Plastics Composites 2002;21(4):311–32. [15] Stephen W Tsai, Edward M Wu. A general theory of strength for anisotropic materials. J Compos Mater 1971;5:58–81. [16] Ye L. Role of matrix resin in delamination onset and growth in composite laminates. Compos Sci Technol 1988;33:257–77.