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Fatigue behavior of thick center cracked aluminum plates repaired by two-sided composite patching
Materials and Design 88 (2015) 331–335
Contents lists available at ScienceDirect
Materials and Design journal homepage: www.elsevier.com/locate/jmad
Fatigue behavior of thick center cracked aluminum plates repaired by two-sided composite patching Hao Jian-Bin ⁎, Li Xu-Dong, Mu Zhi-Tao Naval Aeronautical Engineering Academy Qingdao Branch, Qingdao, 266000, Peoples Republic of China
a r t i c l e
i n f o
Article history: Received 21 January 2015 Received in revised form 1 September 2015 Accepted 2 September 2015 Available online 6 September 2015 Keywords: Fatigue behavior Thick center cracked plate Two-sided composite patches
a b s t r a c t Experimental investigations on the fatigue behavior of thick center cracked aluminum plates (10 mm) bonded with two-sided composite patches were conducted. Fatigue tests indicated that fatigue life of two-sided repaired specimens is 31 times greater than that of unrepaired specimens. The stress intensity factors (SIF) were calculated by using three-dimensional finite element method (FEM), which provide foundations to the prediction of fatigue life of two-sided repaired specimens based on Paris' law. Predictions are in good agreement with the experimental results. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction According to the standard of GB/T3880-1997, plates with the thickness of greater than 5 mm can be regarded as thick plates, which are often used as the bearing structures in the aircraft. Unavoidably, the bearing structures will also experience various forms of damages in the service life, and there are many defected plates had to be repaired and replaced every year. Adhesively-bonded composite patch repair over cracked or corrosion-damaged metallic aircraft structures has shown great promise for extending life of aging structures [1–6]. Due to the existence of the bonded patches, the stress concentration of the damaged areas is greatly improved [7–9]. Compared with the traditional mechanical repair methods, adhesively-bonded composite patch repair does not only minimize the weight increase but also improves the reliability of the structure since it can prevent introducing the new drilling hole in the damaged areas [10–12]. Fatigue characteristic of structures is one of the most important mechanical properties. To investigate the fatigue behavior of the repaired structures, many researchers have performed experimental tests and numerical analysis. D.C. Hart et al. [13] conducted fatigue tests of the patched plates at different applied stress levels, and they found that the benefit of the composite patch repair system increased with the levels of applied stress. F. Benyahia et al. [14] investigated the fatigue life of 7075 T6 aluminum alloy repaired with composite patch, and in their study, they found that the stress intensity factors (SIF) at the crack tip had a significantly decrease because of the presence of the patch. Ki-Hyun Chung and Won-Ho Yang [15] investigated the effect ⁎ Corresponding author. E-mail address: [email protected] (H. Jian-Bin).
http://dx.doi.org/10.1016/j.matdes.2015.09.011 0264-1275/© 2015 Elsevier Ltd. All rights reserved.
of composite patch lengths on the fatigue crack growth behavior in Al 6061-T6 panels with one-sided fiber reinforced composite patches. The results had shown that the sizes of composite patch could affect the fatigue life. Q.Y. Wang and R.M. Pidaparti [16] investigated the effect of different patch-ply on the fatigue life and SIF of one-sided patched plates. An experimental investigation was also conducted by S. Mall and D.S. Conley [17] to characterize the fatigue crack growth behavior in pre-cracked aluminum specimens of two thicknesses (1 and 6.35 mm) with asymmetrically bonded patches. Repairs were found to provide four and ten times improvement in the fatigue life of thick and thin panels over the unrepaired cases, respectively. Schubbe and Mall [18] measured the fatigue crack growth rates of the unpatched and patched faces in the pre-cracked 6.35 mm thick specimens, which were repaired asymmetrically with composite patches. Two-sided repair patching is usually used to increase the durability of damaged structures, especially when the thickness of the damaged plate is very large. In the present study, fatigue life and fatigue crack growth rates of 10 mm thick aluminum panels repaired with twosided bonded patches were evaluated. The SIF values of the patched plates were obtained by using 3-D finite element method (FEM) and the fatigue life prediction of two-sided repaired plates was investigated.
2. Experiments 2.1. Materials and specimens Aluminum plates ware made of LY12CZ. The composite patch was T300/E51 carbon-epoxy prepreg tape. The J150 Nitrile Modified Epoxy Resin adhesive (cured at 80 °C–120 °C, peel strength is 4.2 kN/m at room temperature) was used to bond the patches to the aluminum
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Table 1 Material properties. Young's modulus (GPa)
Al-plate Adhesive Patch
Shear modulus (GPa)
Poisson's ratio
E1
E2
E3
G12
G13
G23
γ12
γ13
γ23
73.8 2.9 134
– – 10.3
– – 10.3
– – 5.5
– – 5.5
– – 3.2
0.33 0.33 0.33
– – 0.33
– – 0.33
Fig. 3. The stress intensity factor (SIF) against different crack lengths in thickness direction.
Fig. 1. The geometry of two-sided repaired specimen.
plates. Material properties of aluminum plate, composite patch and adhesive are shown in Table 1. The plates were machined with the dimensions of 350 mm in length and 100 mm in width from the 10 mm thick LY12CZ aluminum sheets. A crack with the length of 20 mm was manually fabricated at the center of the plate by wire cutting as shown in Fig. 1. The surface of the aluminum plate was treated by phosphoric acid anodizing method to increase the adhesion force of the bonded surface [19]. The rectangular composite patches laminated of [0/45/− 45/90]4 with fibers oriented along the loading direction were bonded on two sides of the aluminum plate. The thickness of each ply for the carbon/epoxy patch was 0.1 mm. The average thickness of adhesive was 0.15 mm. The patches and adhesive were co-cured. The prepreg of composites was bonded to the aluminum plates layer by layer with hand-lay-up
Fig. 4. The average SIF values against different crack lengths.
process. The repaired areas of specimens were vacuum bagged and cured at 80 °C for 4 h and 120 °C for 2 h, and the pressure was kept at 0.1 MPa. The cure cycle involved a single ramp of heating at a rate of 3 °C/min and cooling down at a rate of 4 °C/min.
2.2. Experimental setup Fatigue tests of two-sided repaired and unrepaired specimens were carried out according to GB/T 6398-2000 and GB/T 3075-
Fig. 2. Finite element mesh of the repaired plate and near crack mesh refinement.
H. Jian-Bin et al. / Materials and Design 88 (2015) 331–335
333
Fig. 5. Distribution of the Von-Mises stresses (MPa) in cracked aluminum plate of unrepaired structures.
2008, respectively. Each group had five specimens, and a total number of ten specimens were tested. The fatigue tester used is MTS-810 tester with 50 ton capacity. All fatigue tests were operated at 10 Hz with sinusoidal wave form, the stress load ratio of 0.1 and the maximum stress of 150 MPa. The crack lengths of unrepaired specimens were measured by digital camera while the crack lengths of twosided repaired specimens were measured periodically during the fatigue test through nondestructive inspection technique (NDT) by stopping test and removing the specimen from the fatigue test machine. 3. Finite element analyses In the view point of Linear Elastic Fracture Mechanics (LEFM), fatigue crack is driven by SIF. To investigate the fatigue behavior, 3-D finite element analysis was performed to calculate the SIF of the patched plates. Emin Ergun et al. [20] calculated SIF using 3-D finite element
displacement correlation technique. In the present paper, SIF was obtained by using the fracture mechanics module post-processing program of the ABAQUS ver.6.10. Typical geometries and dimensions used in this study were shown as Fig. 1. The uniaxial load of 150 MPa was applied. In order to simplify the calculation, only one quarter of the patched plate was established due to symmetry. In the finite element analysis, twenty-node brick elements were employed to model the aluminum plate, eight-node 3-D cohesive elements were used to model the adhesive, and layered eight-node shell elements were employed to model the laminate composite patch. The plate had two elements in the thickness direction, the adhesive and the patch had one element through the thickness. The tie constraints were used in the contact surfaces. The global seed size was 2 mm. The mesh was refined for the regions close to the crack tip with an element dimension of 0.1 mm. Fig. 2 presents the overall mesh of the repaired plate and the mesh refinement in crack tip areas.
Fig. 6. Distribution of the Von-Mises stresses (MPa) in cracked aluminum plate of two-sided repaired structures.
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Fig. 7. Fatigue behavior of unrepaired plate and two-sided repaired plate.
Fig. 9. The SIF range ΔK against the crack length a.
4. Results and discussions 4.1. Numerical results Fig. 3 shows SIF variation in thickness direction against different crack lengths for two-sided repaired plates, where a is half of the crack length, W is half of the test section width, tplate is half of the thickness of the aluminum plate, K is SIF, tplate = 0, and tplate = 5 represents the location near the repaired surface and the center of the plate respectively. From the FEM model, it is found that in thickness direction of two-sided repaired plates, SIF reaches the maximum value at the center and the minimum value at the bonded surface, which is similar to SIF distribution of the unrepaired plates but totally different from that of the single-sided repaired plates. Sun CT et al. [4] showed that if the SIF value at the thickness did not vary much, the average SIF could be used to characterize the crack growth behavior. As can be seen in Fig. 3, the difference between SIF at the middle point of thickness and that at the surface is well within 10%. So the average SIF Kaver was used to characterize the crack growth behavior for the present twosided repaired plates. Fig. 4 shows the plot of the average SIF of two-sided repaired and unrepaired plates against different crack lengths. It can be noted that the crack tip SIF of two-sided repaired plates decreases significantly. And this decrease trend increases as the crack length grows, which agrees with the numerical results of Ki-Hyun Chung and Won-Ho Yang [15]. (When a/W = 0.25, SIF for unrepaired plate is 789 MPa·mm0.5 while the value for two-sided repaired plate is 559 MPa·mm0.5, and a 1.41 times decrease is achieved. When a/W = 0.875, SIF for unrepaired plate is 2739 MPa·mm0.5 while the value for two-sided plate is 786 MPa·mm0.5, and a 3.55 times decrease is achieved.)
Fig. 8. The failure figures of two-sided repaired specimens.
Figs. 5 and 6 present the distribution of Von-Mises stresses in cracked aluminum plate of unrepaired structure and two-sided repaired structure respectively. The crack length is taken to be 20 mm. From Fig. 6, it can be found that because of the stress transfer between the repaired plate and the patches mainly occurs in the patched side of the plate, the stress at the crack tip in the patched side of the plate is much smaller than that in the center of the plate, which accounts for SIF variation in thickness direction of the aluminum plate. Comparing the crack tip stresses distribution between Figs. 5 and 6, it can be also observed that with the help of the patches, the stress at the crack tip in two-sided repaired cracked aluminum plate is much smaller than that in the unrepaired structure, which accounts for the significant SIF difference between the repaired structures and unrepaired structures. 4.2. Fatigue tests results As shown in Fig. 7, the unrepaired plates and the two-sided repaired plates failed at an average of 4961 and 112,000 cycles, respectively. Fatigue life of the pre-cracked specimens with two-sided bonded composite patches is thirty-one times larger than that of unrepaired cracked specimen. Benyahia F et al. [14] showed that the fatigue life of cracked plates was increased fifteen times by one-sided composite patching. Sun CT et al. [4] claimed that the fatigue life of asymmetry patched plate increased about six times longer than un-patched plate. Q.Y. Wang and R.M. Pidaparti [16] showed that a life extension factor between five and fourteen could be obtained for the cracked specimens with different bonded patch plies by one-sided composite repair. From the above literatures, it is known that the increase ratio in the
Fig. 10. Comparisons of finite element results with experimental data for the fatigue life of unrepaired and two-sided repaired plates.
H. Jian-Bin et al. / Materials and Design 88 (2015) 331–335
fatigue life number of cycles brought by two-sided composite repair is about two to three times as the value obtained by one-sided composite repair, which indicates two-sided composite repair is more efficiency in improving the lifespan of aged aircraft structure. Fig. 8 presents the fractured figures of repaired specimens. It can be seen that the fatigue crack propagated along the direction perpendicular to the remote loading direction. The total crack extension length is equal to the full specimen width. In the tests process, it is also found that there was no obvious debond between the plates and the composite patches until the crack extend to the edge of the specimen width. As the plates failed, the patches failed simultaneously because of the delamination and debond. 4.3. Fatigue life prediction
References
ð2Þ
Based on the finite element analysis results of the SIF range ΔK and experimental constants C and m, the predictions of the fatigue life of two-sided repaired plates were calculated by the following integration equation: Z N¼
afinal
a0
da C ðΔK Þm
The authors would like to thank the projects (Grant No: 11272173) supported by NSFC.
ð1Þ
where N is the number of cycles, ΔK is the SIF range, C and m are material constants. By conducting fatigue tests on pre-cracked aluminum plates, the material constants of the present specimen were obtained as C = 6.3496 × 10−12, m = 3.72972. In the study, the Paris law's material constants of the two-sided repaired plate were assumed to be the same as the unrepaired plate. The SIF range Δ K of the two-sided repaired plate was calculated by the finite element analysis, and the results are shown in Fig. 9. The relationship between the SIF range ΔK and the crack length a can be presented by the following equation using quadratic polynomial fitting method: ΔK ¼ −6:67042 104 a2 þ 7:5189a þ 438:773:
(1)Numerical results showed that similar to unrepaired cracked plate, the crack tip SIF for two-sided repaired plate is the maximum at the center and minimum at the bonded surface in thickness direction, with a difference of less than 10%. Compared with unrepaired plates, the SIF in two-sided repaired plates is significantly reduced by the patches. And this decrease trend increases as the crack length grows. (2)The experimental results showed that the fatigue life of aluminum plates was increased by thirty-one times with two-sided bonded patches compared to unrepaired plates. (3)Based on Paris' law and the SIF, the fatigue life prediction of twosided repaired plates are in good agreement with the experimental observations.
Acknowledgments
Due to simplicity, Paris law is usually used to predict the fatigue life, which can be expressed as Eq. (1) da ¼ C ðΔKÞm dN
335
ð3Þ
where a0, afinal are the initial and final crack lengths, respectively (which is 10 mm and 40 mm in the paper). Fig. 10 is the plot of the comparisons of the fatigue life between experimental results and finite element results for all the patched configurations. As can be seen from the figure, the difference between the prediction and the experimental results of fatigue life for two-sided repaired plates is 6.66%, which shows the present method is valuable to give precise prediction of two-sided repaired structures. 5. Conclusions In this study, the performances of non-patched and two-sided bonded composite repair of cracked aluminum plates had been observed by conducting experimental and numerical investigations.
[1] A.A. Baker, Repair of cracked or defective metallic aircraft components with advanced fiber composites, Compos. Struct. 2 (1984) 153–234. [2] A.A. Baker, L.R.F. Rose, R. Jones, Advances in the Bonded Composite Repair of Metallic Aircraft Structure, Elsevier, Amsterdam, 2002. [3] L.R.F. Rose, A cracked plate repaired by bonded reinforcements, Int. J. Fract. 18 (1982) 135–144. [4] C.T. Sun, G. Klug, C. Arendt, Analysis of cracked aluminum plates repaired with bonded composite patches, AIAA 34 (1996) 369–374. [5] A.M. Kumar, S.A. Hakeem, Optimum design of symmetric composite patch repair to central cracked cracked metallic sheet, Compos. Struct. 49 (2000) 285–292. [6] P.C. Pandey, S. Kumar, Adhesively-bonded patch repair with composites, Def. Sci. J. 60 (2010) 320–329. [7] A.R. Maligno, C. Soutis, V.V. Silberschmidt, An advanced numerical tool to study fatigue crack propagation in aluminium paltes repaired with a composite patch, Eng. Fract. Mech. 99 (2013) 62–78. [8] H. Fekirini, B. Bachir Bouiadjra, M. Belhouari, B. Boutabout, B. Serier, Numerical analysis of the performances of bonded composite repair with two adhesive band in aircraft structures, Compos. Struct. 82 (2008) 84–89. [9] B. Bachir Bouiadjra, M. Belhouari, B. Serier, Computation of the stress intensity factor for repaired crack with bonded composite patch in mode I and mixed mode, Compos. Struct. 56 (2002) 401–406. [10] C.N. Duong, C.H. Wang, Composite Repair Theory and Design, Elsevier Science Ltd., 2007 [11] G.P. Zou, K. Shahin, F. Taheri, An analytical solution for the analysis of symmetric composite adhesively bonded joints, Compos. Struct. 65 (2004) 499–510. [12] H. Hosseini-Toudeshky, Effects of composite patches on fatigue crack propagation of single-side repaired aluminum panels, Compos. Struct. 76 (2006) 243–251. [13] D.C. Hart, E.P. Udinski, M. Hayden, X. Liu, Fatigue performance and analysis of composite patch repaired cracked aluminum plates, Composite_1_Hart, 2014. [14] F. Benyahia, L. Aminallah, Albedah, B. Bachir Bouiadjra, T. Achour, Experimental and numerical analysis of bonded composite patch repair in aluminum alloy 7075 T6, Mater. Des. 73 (2015) 67–73. [15] K.-H. Chung, W.-H. Yang, A study on the fatigue crack growth behavior of thick aluminum panels repaired with a composite patch, Compos. Struct. 60 (2003) 1–7. [16] Q.Y. Wang, R.M. Pidaparti, Static characteristic and fatigue behavior of composite repaired aluminum plates, Compos. Struct. 56 (2) (2002) 151–155. [17] S. Mall, D.S. Conley, Modeling and validation of composite patch repair to cracked thick and thin mentallic panels, Compos. Part A 40 (2009) 1331–1339. [18] J.J. Schubbe, S. Mall, Fatigue behavior in thick aluminum panels with a composite repair, AIAA 98 (1997) 2434–2443. [19] S.W. Wen, J.Y. Xiao, Y.R. Wang, Accelerated ageing behavior of aluminum plate with composite patches under salt fog effect, Compos. Part B 44 (2013) 266–273. [20] E. Ergun, S. Tasgetiren, M. Topcu, Stress intensity factor estimation of repaired aluminum plate with bonded composite patch by combined genetic algorithms and FEM under temperature effects, Indian J. Eng. Mater. Sci. 19 (2012) 17–23.
Contents lists available at ScienceDirect
Materials and Design journal homepage: www.elsevier.com/locate/jmad
Fatigue behavior of thick center cracked aluminum plates repaired by two-sided composite patching Hao Jian-Bin ⁎, Li Xu-Dong, Mu Zhi-Tao Naval Aeronautical Engineering Academy Qingdao Branch, Qingdao, 266000, Peoples Republic of China
a r t i c l e
i n f o
Article history: Received 21 January 2015 Received in revised form 1 September 2015 Accepted 2 September 2015 Available online 6 September 2015 Keywords: Fatigue behavior Thick center cracked plate Two-sided composite patches
a b s t r a c t Experimental investigations on the fatigue behavior of thick center cracked aluminum plates (10 mm) bonded with two-sided composite patches were conducted. Fatigue tests indicated that fatigue life of two-sided repaired specimens is 31 times greater than that of unrepaired specimens. The stress intensity factors (SIF) were calculated by using three-dimensional finite element method (FEM), which provide foundations to the prediction of fatigue life of two-sided repaired specimens based on Paris' law. Predictions are in good agreement with the experimental results. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction According to the standard of GB/T3880-1997, plates with the thickness of greater than 5 mm can be regarded as thick plates, which are often used as the bearing structures in the aircraft. Unavoidably, the bearing structures will also experience various forms of damages in the service life, and there are many defected plates had to be repaired and replaced every year. Adhesively-bonded composite patch repair over cracked or corrosion-damaged metallic aircraft structures has shown great promise for extending life of aging structures [1–6]. Due to the existence of the bonded patches, the stress concentration of the damaged areas is greatly improved [7–9]. Compared with the traditional mechanical repair methods, adhesively-bonded composite patch repair does not only minimize the weight increase but also improves the reliability of the structure since it can prevent introducing the new drilling hole in the damaged areas [10–12]. Fatigue characteristic of structures is one of the most important mechanical properties. To investigate the fatigue behavior of the repaired structures, many researchers have performed experimental tests and numerical analysis. D.C. Hart et al. [13] conducted fatigue tests of the patched plates at different applied stress levels, and they found that the benefit of the composite patch repair system increased with the levels of applied stress. F. Benyahia et al. [14] investigated the fatigue life of 7075 T6 aluminum alloy repaired with composite patch, and in their study, they found that the stress intensity factors (SIF) at the crack tip had a significantly decrease because of the presence of the patch. Ki-Hyun Chung and Won-Ho Yang [15] investigated the effect ⁎ Corresponding author. E-mail address: [email protected] (H. Jian-Bin).
http://dx.doi.org/10.1016/j.matdes.2015.09.011 0264-1275/© 2015 Elsevier Ltd. All rights reserved.
of composite patch lengths on the fatigue crack growth behavior in Al 6061-T6 panels with one-sided fiber reinforced composite patches. The results had shown that the sizes of composite patch could affect the fatigue life. Q.Y. Wang and R.M. Pidaparti [16] investigated the effect of different patch-ply on the fatigue life and SIF of one-sided patched plates. An experimental investigation was also conducted by S. Mall and D.S. Conley [17] to characterize the fatigue crack growth behavior in pre-cracked aluminum specimens of two thicknesses (1 and 6.35 mm) with asymmetrically bonded patches. Repairs were found to provide four and ten times improvement in the fatigue life of thick and thin panels over the unrepaired cases, respectively. Schubbe and Mall [18] measured the fatigue crack growth rates of the unpatched and patched faces in the pre-cracked 6.35 mm thick specimens, which were repaired asymmetrically with composite patches. Two-sided repair patching is usually used to increase the durability of damaged structures, especially when the thickness of the damaged plate is very large. In the present study, fatigue life and fatigue crack growth rates of 10 mm thick aluminum panels repaired with twosided bonded patches were evaluated. The SIF values of the patched plates were obtained by using 3-D finite element method (FEM) and the fatigue life prediction of two-sided repaired plates was investigated.
2. Experiments 2.1. Materials and specimens Aluminum plates ware made of LY12CZ. The composite patch was T300/E51 carbon-epoxy prepreg tape. The J150 Nitrile Modified Epoxy Resin adhesive (cured at 80 °C–120 °C, peel strength is 4.2 kN/m at room temperature) was used to bond the patches to the aluminum
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H. Jian-Bin et al. / Materials and Design 88 (2015) 331–335
Table 1 Material properties. Young's modulus (GPa)
Al-plate Adhesive Patch
Shear modulus (GPa)
Poisson's ratio
E1
E2
E3
G12
G13
G23
γ12
γ13
γ23
73.8 2.9 134
– – 10.3
– – 10.3
– – 5.5
– – 5.5
– – 3.2
0.33 0.33 0.33
– – 0.33
– – 0.33
Fig. 3. The stress intensity factor (SIF) against different crack lengths in thickness direction.
Fig. 1. The geometry of two-sided repaired specimen.
plates. Material properties of aluminum plate, composite patch and adhesive are shown in Table 1. The plates were machined with the dimensions of 350 mm in length and 100 mm in width from the 10 mm thick LY12CZ aluminum sheets. A crack with the length of 20 mm was manually fabricated at the center of the plate by wire cutting as shown in Fig. 1. The surface of the aluminum plate was treated by phosphoric acid anodizing method to increase the adhesion force of the bonded surface [19]. The rectangular composite patches laminated of [0/45/− 45/90]4 with fibers oriented along the loading direction were bonded on two sides of the aluminum plate. The thickness of each ply for the carbon/epoxy patch was 0.1 mm. The average thickness of adhesive was 0.15 mm. The patches and adhesive were co-cured. The prepreg of composites was bonded to the aluminum plates layer by layer with hand-lay-up
Fig. 4. The average SIF values against different crack lengths.
process. The repaired areas of specimens were vacuum bagged and cured at 80 °C for 4 h and 120 °C for 2 h, and the pressure was kept at 0.1 MPa. The cure cycle involved a single ramp of heating at a rate of 3 °C/min and cooling down at a rate of 4 °C/min.
2.2. Experimental setup Fatigue tests of two-sided repaired and unrepaired specimens were carried out according to GB/T 6398-2000 and GB/T 3075-
Fig. 2. Finite element mesh of the repaired plate and near crack mesh refinement.
H. Jian-Bin et al. / Materials and Design 88 (2015) 331–335
333
Fig. 5. Distribution of the Von-Mises stresses (MPa) in cracked aluminum plate of unrepaired structures.
2008, respectively. Each group had five specimens, and a total number of ten specimens were tested. The fatigue tester used is MTS-810 tester with 50 ton capacity. All fatigue tests were operated at 10 Hz with sinusoidal wave form, the stress load ratio of 0.1 and the maximum stress of 150 MPa. The crack lengths of unrepaired specimens were measured by digital camera while the crack lengths of twosided repaired specimens were measured periodically during the fatigue test through nondestructive inspection technique (NDT) by stopping test and removing the specimen from the fatigue test machine. 3. Finite element analyses In the view point of Linear Elastic Fracture Mechanics (LEFM), fatigue crack is driven by SIF. To investigate the fatigue behavior, 3-D finite element analysis was performed to calculate the SIF of the patched plates. Emin Ergun et al. [20] calculated SIF using 3-D finite element
displacement correlation technique. In the present paper, SIF was obtained by using the fracture mechanics module post-processing program of the ABAQUS ver.6.10. Typical geometries and dimensions used in this study were shown as Fig. 1. The uniaxial load of 150 MPa was applied. In order to simplify the calculation, only one quarter of the patched plate was established due to symmetry. In the finite element analysis, twenty-node brick elements were employed to model the aluminum plate, eight-node 3-D cohesive elements were used to model the adhesive, and layered eight-node shell elements were employed to model the laminate composite patch. The plate had two elements in the thickness direction, the adhesive and the patch had one element through the thickness. The tie constraints were used in the contact surfaces. The global seed size was 2 mm. The mesh was refined for the regions close to the crack tip with an element dimension of 0.1 mm. Fig. 2 presents the overall mesh of the repaired plate and the mesh refinement in crack tip areas.
Fig. 6. Distribution of the Von-Mises stresses (MPa) in cracked aluminum plate of two-sided repaired structures.
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H. Jian-Bin et al. / Materials and Design 88 (2015) 331–335
Fig. 7. Fatigue behavior of unrepaired plate and two-sided repaired plate.
Fig. 9. The SIF range ΔK against the crack length a.
4. Results and discussions 4.1. Numerical results Fig. 3 shows SIF variation in thickness direction against different crack lengths for two-sided repaired plates, where a is half of the crack length, W is half of the test section width, tplate is half of the thickness of the aluminum plate, K is SIF, tplate = 0, and tplate = 5 represents the location near the repaired surface and the center of the plate respectively. From the FEM model, it is found that in thickness direction of two-sided repaired plates, SIF reaches the maximum value at the center and the minimum value at the bonded surface, which is similar to SIF distribution of the unrepaired plates but totally different from that of the single-sided repaired plates. Sun CT et al. [4] showed that if the SIF value at the thickness did not vary much, the average SIF could be used to characterize the crack growth behavior. As can be seen in Fig. 3, the difference between SIF at the middle point of thickness and that at the surface is well within 10%. So the average SIF Kaver was used to characterize the crack growth behavior for the present twosided repaired plates. Fig. 4 shows the plot of the average SIF of two-sided repaired and unrepaired plates against different crack lengths. It can be noted that the crack tip SIF of two-sided repaired plates decreases significantly. And this decrease trend increases as the crack length grows, which agrees with the numerical results of Ki-Hyun Chung and Won-Ho Yang [15]. (When a/W = 0.25, SIF for unrepaired plate is 789 MPa·mm0.5 while the value for two-sided repaired plate is 559 MPa·mm0.5, and a 1.41 times decrease is achieved. When a/W = 0.875, SIF for unrepaired plate is 2739 MPa·mm0.5 while the value for two-sided plate is 786 MPa·mm0.5, and a 3.55 times decrease is achieved.)
Fig. 8. The failure figures of two-sided repaired specimens.
Figs. 5 and 6 present the distribution of Von-Mises stresses in cracked aluminum plate of unrepaired structure and two-sided repaired structure respectively. The crack length is taken to be 20 mm. From Fig. 6, it can be found that because of the stress transfer between the repaired plate and the patches mainly occurs in the patched side of the plate, the stress at the crack tip in the patched side of the plate is much smaller than that in the center of the plate, which accounts for SIF variation in thickness direction of the aluminum plate. Comparing the crack tip stresses distribution between Figs. 5 and 6, it can be also observed that with the help of the patches, the stress at the crack tip in two-sided repaired cracked aluminum plate is much smaller than that in the unrepaired structure, which accounts for the significant SIF difference between the repaired structures and unrepaired structures. 4.2. Fatigue tests results As shown in Fig. 7, the unrepaired plates and the two-sided repaired plates failed at an average of 4961 and 112,000 cycles, respectively. Fatigue life of the pre-cracked specimens with two-sided bonded composite patches is thirty-one times larger than that of unrepaired cracked specimen. Benyahia F et al. [14] showed that the fatigue life of cracked plates was increased fifteen times by one-sided composite patching. Sun CT et al. [4] claimed that the fatigue life of asymmetry patched plate increased about six times longer than un-patched plate. Q.Y. Wang and R.M. Pidaparti [16] showed that a life extension factor between five and fourteen could be obtained for the cracked specimens with different bonded patch plies by one-sided composite repair. From the above literatures, it is known that the increase ratio in the
Fig. 10. Comparisons of finite element results with experimental data for the fatigue life of unrepaired and two-sided repaired plates.
H. Jian-Bin et al. / Materials and Design 88 (2015) 331–335
fatigue life number of cycles brought by two-sided composite repair is about two to three times as the value obtained by one-sided composite repair, which indicates two-sided composite repair is more efficiency in improving the lifespan of aged aircraft structure. Fig. 8 presents the fractured figures of repaired specimens. It can be seen that the fatigue crack propagated along the direction perpendicular to the remote loading direction. The total crack extension length is equal to the full specimen width. In the tests process, it is also found that there was no obvious debond between the plates and the composite patches until the crack extend to the edge of the specimen width. As the plates failed, the patches failed simultaneously because of the delamination and debond. 4.3. Fatigue life prediction
References
ð2Þ
Based on the finite element analysis results of the SIF range ΔK and experimental constants C and m, the predictions of the fatigue life of two-sided repaired plates were calculated by the following integration equation: Z N¼
afinal
a0
da C ðΔK Þm
The authors would like to thank the projects (Grant No: 11272173) supported by NSFC.
ð1Þ
where N is the number of cycles, ΔK is the SIF range, C and m are material constants. By conducting fatigue tests on pre-cracked aluminum plates, the material constants of the present specimen were obtained as C = 6.3496 × 10−12, m = 3.72972. In the study, the Paris law's material constants of the two-sided repaired plate were assumed to be the same as the unrepaired plate. The SIF range Δ K of the two-sided repaired plate was calculated by the finite element analysis, and the results are shown in Fig. 9. The relationship between the SIF range ΔK and the crack length a can be presented by the following equation using quadratic polynomial fitting method: ΔK ¼ −6:67042 104 a2 þ 7:5189a þ 438:773:
(1)Numerical results showed that similar to unrepaired cracked plate, the crack tip SIF for two-sided repaired plate is the maximum at the center and minimum at the bonded surface in thickness direction, with a difference of less than 10%. Compared with unrepaired plates, the SIF in two-sided repaired plates is significantly reduced by the patches. And this decrease trend increases as the crack length grows. (2)The experimental results showed that the fatigue life of aluminum plates was increased by thirty-one times with two-sided bonded patches compared to unrepaired plates. (3)Based on Paris' law and the SIF, the fatigue life prediction of twosided repaired plates are in good agreement with the experimental observations.
Acknowledgments
Due to simplicity, Paris law is usually used to predict the fatigue life, which can be expressed as Eq. (1) da ¼ C ðΔKÞm dN
335
ð3Þ
where a0, afinal are the initial and final crack lengths, respectively (which is 10 mm and 40 mm in the paper). Fig. 10 is the plot of the comparisons of the fatigue life between experimental results and finite element results for all the patched configurations. As can be seen from the figure, the difference between the prediction and the experimental results of fatigue life for two-sided repaired plates is 6.66%, which shows the present method is valuable to give precise prediction of two-sided repaired structures. 5. Conclusions In this study, the performances of non-patched and two-sided bonded composite repair of cracked aluminum plates had been observed by conducting experimental and numerical investigations.
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