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Analysis of the plastic zone size ahead of repaired cracks with bonded composite patch of metallic aircraft structures
Computational Materials Science 46 (2009) 950–954
Contents lists available at ScienceDirect
Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Analysis of the plastic zone size ahead of repaired cracks with bonded composite patch of metallic aircraft structures W. Oudad a, B. Bachir Bouiadjra a,*, M. Belhouari a, S. Touzain b, X. Feaugas b a b
LMPM, Department of Mechanical Engineering, University of Sidi Bel Abbes, BP 89, Cité Ben M’hidi, 27000 Sidi Bel Abbes, Algeria Laboratoire d’Etude des Matériaux en Milieux Agressifs (L.E.M.M.A), LaRochelle University, LaRochelle, France
a r t i c l e
i n f o
Article history: Received 29 March 2009 Received in revised form 23 April 2009 Accepted 28 April 2009 Available online 26 May 2009 Keywords: Composite repair Adhesive Crack Plastic zone Patch Finite element method
a b s t r a c t In this study, the three-dimensional and non-linear finite element method is used to estimate the performance of the bonded composite repair of metallic aircraft structures by analyzing the plastic zone size ahead of repaired cracks. Several calculations have been realized to extract the plasticized elements around the crack tip of repaired crack. The obtained results show that the presence of the composite patch reduces considerably the size of the plastic zone ahead of the crack. The effects of the adhesive properties and the patch thickness on the plastic zone size ahead of repaired cracks were analyzed. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction A considerable amount of research has been conducted on extending the service life of cracked engineering structures with the emphasis on the life extension of aging aircraft structures using various repair techniques. The underlining aim of any repair technique is the efficient transfer of load to the reinforcement from the cracked structure such that the driving force for crack propagation is reduced [1–3]. The goal is to restore the damage tolerance and residual strength of the structure close to its initial state. The overall effect is the reduction in the crack growth rate resulting in an extension in the service life of the structure. In order to accomplish the requirement of efficient load transfer in the repaired structure, two techniques have been and are more widely employed for repairs in the aerospace industry. And these techniques have led researchers to investigate the effectiveness of crack repairs: – Mechanically fastened repairs which employ either bolts or rivets as fasteners to secure a metallic reinforcement to the cracked structure. The fasteners introduce additional stress concentration due to the need to drill holes, and also the applied metallic reinforcement causes a discontinuity in the local geometry resulting in additional stress concentration around the boundary * Corresponding author. E-mail address: [email protected] (B. Bachir Bouiadjra). 0927-0256/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2009.04.041
of the repair area. Therefore, although the mechanically fastened repair may helps to increase the service life of the structure, the additional stress concentrations generate further damage in the structure which provides the ideal environment for new cracks. – The development in the area of advanced composites with their high specific strength, high specific stiffness and excellent thermal characteristics and adhesives has made it possible to bond reinforcing patches to cracked metallic plates. The process, referred to as ‘‘crack patching’’ does not generate high stress concentrations by avoiding drilling of holes and providing better stress distribution in the repair area. The crack patching technology has been proven to be an effective method for restoring the residual strength and damage tolerance of cracked structures [4–8]. For the case of adhesively bonded patch repair, researchers have investigated the effectiveness of composite patch repairs by the linear elastic fracture mechanics and nonlinear fracture mechanics (elastic–plastic). Although majority of studies conducted on patch repair technology are analyzes by linear elastic fracture mechanics, a few of the mentioned studies were also investigated with near fracture mechanics [9]. In the present work, the non-linear three-dimensional finite element method is used to compute the contour and the size of the plastic zone ahead of repaired cracks with bonded composite patch. The effects of the adhesive properties and the patch thickness on the plastic zone size were highlighted.
951
W. Oudad et al. / Computational Materials Science 46 (2009) 950–954
500
2. Geometrical model
450 400 350 stress (Mpa)
The basic geometry of the cracked structure considered in this study is shown in Fig. 1. Consider a rectangular elastic–plastic aluminum 2024-T3 plate with the following dimensions: height Hp = 254 mm, width Wp = 254 mm, thickness ep = 4.76 mm, with a central crack of length 2a repaired with boron–epoxy patch of dimensions: Hr = 75 mm, Wr = 130 mm and er = 2.28 mm, the plies in the patch had unidirectional lay-up where the fibers were oriented along the specimen length direction (parallel to the direction of load), bonded by 0.2 mm thick film FM 73 adhesive (ea) (Fig. 1). The plate is subjected to a remote uniaxial tensile load of r = 150 MPa. The mechanical properties of the different materials are given in Table 1, The stress–strain curve of aluminum 2024T3 is presented in Fig. 2.
300 250 200 150 100 50 0
0
0.05
0.1
0.15
stain
3. Finite element modeling
Fig. 2. Stress–strain curves for aluminum 2024-T3.
The analysis involved a three-dimensional finite element method by using a commercially available finite element code ABAQUS. The finite element model consisted of three subsections to model the cracked plate, the adhesive, and the composite patch. Due to symmetry, only one quarter of the repaired plate was considered. The plate had four layers of elements in the thickness direction, the adhesive had only one layer of elements through thickness and the patch had two layers of elements through thickness. The mesh was refined near the crack tip area with an element dimension of 0.067 mm using at least fifteen such fine elements in the front and back of the crack tip. Fig. 3 shows the overall mesh of the specimen and mesh refinement in the crack tip region.
Fig. 3. Typical mesh model of the repaired structure and near the crack tip.
The procedure used in the finite element analysis involved the following step: the tensile stress was applied to the gripped specimen. General static ‘‘STEP’’-option was used for analysis with ABAQUS. Automatic increment of step was used with maximum number of increments of 100. Minimum increment size was 10 5. Maximum increment size was 1. Nevertheless, the ABAQUS solver code could override matrix solver choice according to the ‘‘STEP’’-option. The Von-Mises criterion is used to determine whether the stress in the materials causes plastic flow. Incremental plasticity theory is introduced to model the material non-linearity. The Newton–Raphson iterative method is used as approach for resolving non-linear finite element equations. Fig. 1. Geometrical model.
4. Analysis and results Table 1 Elastic properties of different materials. Aluminium alloy T3
Boron/epoxy
Adhesive (FM-73)
E1 (GPa) E2 (GPa) E3 (GPa)
72
2.55
m12 m13 m23
0.33
200 19.6 19.6 0.3 0.28 0.28 7.2 5.5 5.5
G12 (GPa) G13 (GPa) G23 (GPa)
0.32
This study has been made in order to analyze the size of the plastic zone ahead of repaired crack with bonded composite patch in aluminum alloy 2024-T3. Calculations have been realized to extract the plasticized elements around the crack tip of repaired crack. 4.1. Effect of the crack length on the plastic zone size In order to estimate the performances of the patch repair, the shapes of the plastic zone for repaired and un-repaired cracks were computed for crack length a = 30 mm. The obtained results show
952
W. Oudad et al. / Computational Materials Science 46 (2009) 950–954
that the reduction of the plastic zone by the patch repair is about 10 times. This is due to the fact that there is transfer of stresses between the cracked plate and the composite patch throughout the adhesive layer. It is also obtained that the ratio between the plastic zone radius and the crack length for case with repair is very small (about 0.015), what unable us to conclude that the concepts of linear fracture mechanics such as stress intensity factor or energy release rate can be applied. Fig. 4 presents the contour of the plastic zone ahead of repaired crack for different crack lengths. It can be seen that the size of the plastic zone is slightly affected by the variation of the crack length. There is a weak reduction of the plastic zone size as the crack length decreases. This is due to the fact that the absorption of the stresses by the patch do not permit a great extension of the plastic zone as the crack length increases. There is an analogy with the variation of the stress intensity factor for repaired crack if the concepts of linear fracture mechanics are applied. Indeed, the stress intensity factor exhibits an asymptotic behavior as the crack length increases [4,5,7]. These results are confirmed in Fig. 5. This last figure presents the variation of the plastic zone radius (rp) as a function of the crack length. It can be noted, that the plastic radius remains
approximately constant as the crack length increases excepted when the crack length approaches the patch width (a > 55 mm). In these cases, the crack tip approaches the unrepaired region of the plate, the stresses at the crack front increase and consequently the plastic zone size increases. 4.2. Effect of the adhesive properties It is known that the adhesive properties play a very important role in the repair process with bonded composite patch. The adhesive layer transfers the stresses from the damaged plate toward the composite patch. The maximum of stresses are transferred from the crack region. In this paragraph the effects of the adhesive young modulus and that of the adhesive thickness on the plastic zone ahead of repaired crack are analyzed. 4.2.1. Effect of the adhesive Young modulus (Ea) It s known that adhesive with better qualities are characterized by weak values of Young modulus in order to attenuate the stress intensity in the adhesive layer. In the case of bonded composite 0.8
0.30 0.25
0.7
a = 5 mm a = 30 mm a = 55 mm
0.6 0.5 Y (mm)
0.20 Y (mm)
Ea = 1000 MPa Ea = 2000 MPa Ea = 3000 MPa Ea = 4000 MPa
0.15 0.10
0.4 0.3 0.2
0.05
0.1
0.00
0.0 - 0.2
-0.04
0.00
0.04
0.08
0.12
0.16
0.0
0.1 0.2 X (mm)
0.3
0.4
0.5
crack tip
X(mm)
crack tip
-0.1
0.20
Fig. 6. Contour of the plastic zone for different adhesive Young Modulus.
Fig. 4. Contour of the plastic zone for different crack length.
0.5 0.9
0.4
0.8 0.7 rp (mm)
rp (mm)
0.3
0.2
0.6 0.5 0.4
0.1
0.3
0.0
0
10
20
30
40
a (mm) Fig. 5. Plastic zone radius vs crack length.
50
60
1000
1500
2000
2500
3000
3500
Ea (MPa) Fig. 7. Plastic zone radius vs adhesive Young modulus.
4000
953
W. Oudad et al. / Computational Materials Science 46 (2009) 950–954
0.7
0.245 0.210
0.140 0.105
0.5
rp (mm)
0.175 Y (mm)
0.6
ea =0.10mm ea =0.16mm ea =0.18mm ea =0.24mm ea =0.30mm ea =0.38mm
0.070
0.3 0.2
0.035 0.000
0.4
0.1
-0.050-0.025 0.000 0.025 0.050 0.075 0.100 0.125 0.150 X (mm)
crack tip
0.0
0
er = 1mm er = 3mm er = 6mm
0.5
Y (mm)
3
4 5 er (mm)
6
7
8
9
the adhesive thickness decreases. The repair performances increase when the quantity of the adhesive is weak. However, and by analogy with what announced in the precedent paragraph, a weak adhesive thickness involves higher intensities of the adhesive stresses, what can increases the risk of e failure of the adhesion. The adhesive thickness must also be optimized.
0.7
4.3. Effect of the patch thickness (er)
0.4
This effect is illustrated in Fig. 9 by the plot of the contour the plastic zone ahead of the crack front for various values of the patch thickness (er). It can be noted, that the increase of the patch thickness involves the reduction of the plastic zone size, what can improved the repair performances. However and according to Fig. 10, one cane deduce that it is not necessary to increase indefinitely the patch thickness because it effect on the plastic zone radius remains constant when the value of er exceeds 3 mm.
0.3 0.2 0.1 0.0
2
Fig. 10. Plastic zone radius vs patch thickness.
Fig. 8. Contour of the plastic zone for different adhesive thicknesses.
0.6
1
-0.08
crack tip
0.00
0.08
0.16
0.24
0.32
0.40
0.48
X (mm)
Fig. 9. Contour of the plastic zone for different patch thicknesses.
repair, the role of the adhesive is to transmit a maximum of stresses. Theoretically, it is beneficial for the repair process to use adhesive with high Young modulus. In Fig. 6 the plot of the contour of plastic zone ahead of the tip of repaired crack for different values of the adhesive Young modulus confirms what was advanced previously. Indeed, the plastic zone size decreases as the adhesive young modulus increases. It means that the repair performances can be improved by choosing higher values of the adhesive Young modulus. However, according to Fig. 7, where is presented the variation of the radius of the plastic zone as a function of the adhesive Young modulus, one can note that that the effect of Ea on the plastic zone size is stabilized as the adhesive young modulus is greater then 2500 MPa. On the other hand, an increase of the adhesive Young modulus involves the rise of the stresses in the adhesive layer, what can increase the risk of failure of the adhesive layer. Consequently the choice of the adhesive for crack repair must be optimized. 4.2.2. Effect of the adhesive thickness (ea) Fig. 8 presents the effect of the adhesive thickness on the plastic zone contour. It can be seen that the plastic zone size decreases as
5. Conclusions This study was carried out in order to estimate the performance of the bonded composite repair of metallic aircraft structures by analyzing the plastic zone size of ahead of repaired cracks. The obtained results allow us to deduce the following conclusions: – The presence of the composite patch reduces considerably the size of the plastic zone ahead of the crack. This reduction is very important so that the concepts of linear fracture mechanics for repaired cracks. – The effect of the crack length on the plastic zone size ahead of repaired cracks is not significant because the stress absorption by the patch increases as the crack growth. – The adhesive properties must be optimized in order to increase the repair performance and to avoid the adhesive failure between the repaired structure and the composite patch. – The patch must be thicker but not indefinitely with an aim to increase the repair performances.
References [1] A.A. Baker, Compos. Struct. 74 (1999) 431–443. [2] T. Ting, R. Jones, W.K. Chiu, I.H. Marshall, J.M. Greer, Compos. Struct. 47 (1999) 737–743.
954 [3] [4] [5] [6]
W. Oudad et al. / Computational Materials Science 46 (2009) 950–954 J.J. Schubbe, S. Mall, Compos. Struct. 45 (1999) 185–193. B.B. Bachir, M. Belhouari, B. Serier, Compos. Struct. 56 (2002) 401–406. W.H. Chen, S.H. Yang, Finite Elem. Anal. Des. 21 (1995) 21–44. A. Megueni, B.B. Bachir, B. Boutabout, Compos. Struct. 59 (2003) 415–418.
[7] T. Achour, B.B. Bachir, B. Serier, Comput. Mater. Sci. 28 (2003) 41–48. [8] B. Bachir Bouiadjra, H. Fekirini, B. Serier, M. Benguediab, Comput. Mater. Sci. 38 (2007) 824–829. [9] A.O Randolph, M.F. Clifford, J. Reinf. Plast. Compos. 4 (2002) 311–332.
Contents lists available at ScienceDirect
Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Analysis of the plastic zone size ahead of repaired cracks with bonded composite patch of metallic aircraft structures W. Oudad a, B. Bachir Bouiadjra a,*, M. Belhouari a, S. Touzain b, X. Feaugas b a b
LMPM, Department of Mechanical Engineering, University of Sidi Bel Abbes, BP 89, Cité Ben M’hidi, 27000 Sidi Bel Abbes, Algeria Laboratoire d’Etude des Matériaux en Milieux Agressifs (L.E.M.M.A), LaRochelle University, LaRochelle, France
a r t i c l e
i n f o
Article history: Received 29 March 2009 Received in revised form 23 April 2009 Accepted 28 April 2009 Available online 26 May 2009 Keywords: Composite repair Adhesive Crack Plastic zone Patch Finite element method
a b s t r a c t In this study, the three-dimensional and non-linear finite element method is used to estimate the performance of the bonded composite repair of metallic aircraft structures by analyzing the plastic zone size ahead of repaired cracks. Several calculations have been realized to extract the plasticized elements around the crack tip of repaired crack. The obtained results show that the presence of the composite patch reduces considerably the size of the plastic zone ahead of the crack. The effects of the adhesive properties and the patch thickness on the plastic zone size ahead of repaired cracks were analyzed. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction A considerable amount of research has been conducted on extending the service life of cracked engineering structures with the emphasis on the life extension of aging aircraft structures using various repair techniques. The underlining aim of any repair technique is the efficient transfer of load to the reinforcement from the cracked structure such that the driving force for crack propagation is reduced [1–3]. The goal is to restore the damage tolerance and residual strength of the structure close to its initial state. The overall effect is the reduction in the crack growth rate resulting in an extension in the service life of the structure. In order to accomplish the requirement of efficient load transfer in the repaired structure, two techniques have been and are more widely employed for repairs in the aerospace industry. And these techniques have led researchers to investigate the effectiveness of crack repairs: – Mechanically fastened repairs which employ either bolts or rivets as fasteners to secure a metallic reinforcement to the cracked structure. The fasteners introduce additional stress concentration due to the need to drill holes, and also the applied metallic reinforcement causes a discontinuity in the local geometry resulting in additional stress concentration around the boundary * Corresponding author. E-mail address: [email protected] (B. Bachir Bouiadjra). 0927-0256/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2009.04.041
of the repair area. Therefore, although the mechanically fastened repair may helps to increase the service life of the structure, the additional stress concentrations generate further damage in the structure which provides the ideal environment for new cracks. – The development in the area of advanced composites with their high specific strength, high specific stiffness and excellent thermal characteristics and adhesives has made it possible to bond reinforcing patches to cracked metallic plates. The process, referred to as ‘‘crack patching’’ does not generate high stress concentrations by avoiding drilling of holes and providing better stress distribution in the repair area. The crack patching technology has been proven to be an effective method for restoring the residual strength and damage tolerance of cracked structures [4–8]. For the case of adhesively bonded patch repair, researchers have investigated the effectiveness of composite patch repairs by the linear elastic fracture mechanics and nonlinear fracture mechanics (elastic–plastic). Although majority of studies conducted on patch repair technology are analyzes by linear elastic fracture mechanics, a few of the mentioned studies were also investigated with near fracture mechanics [9]. In the present work, the non-linear three-dimensional finite element method is used to compute the contour and the size of the plastic zone ahead of repaired cracks with bonded composite patch. The effects of the adhesive properties and the patch thickness on the plastic zone size were highlighted.
951
W. Oudad et al. / Computational Materials Science 46 (2009) 950–954
500
2. Geometrical model
450 400 350 stress (Mpa)
The basic geometry of the cracked structure considered in this study is shown in Fig. 1. Consider a rectangular elastic–plastic aluminum 2024-T3 plate with the following dimensions: height Hp = 254 mm, width Wp = 254 mm, thickness ep = 4.76 mm, with a central crack of length 2a repaired with boron–epoxy patch of dimensions: Hr = 75 mm, Wr = 130 mm and er = 2.28 mm, the plies in the patch had unidirectional lay-up where the fibers were oriented along the specimen length direction (parallel to the direction of load), bonded by 0.2 mm thick film FM 73 adhesive (ea) (Fig. 1). The plate is subjected to a remote uniaxial tensile load of r = 150 MPa. The mechanical properties of the different materials are given in Table 1, The stress–strain curve of aluminum 2024T3 is presented in Fig. 2.
300 250 200 150 100 50 0
0
0.05
0.1
0.15
stain
3. Finite element modeling
Fig. 2. Stress–strain curves for aluminum 2024-T3.
The analysis involved a three-dimensional finite element method by using a commercially available finite element code ABAQUS. The finite element model consisted of three subsections to model the cracked plate, the adhesive, and the composite patch. Due to symmetry, only one quarter of the repaired plate was considered. The plate had four layers of elements in the thickness direction, the adhesive had only one layer of elements through thickness and the patch had two layers of elements through thickness. The mesh was refined near the crack tip area with an element dimension of 0.067 mm using at least fifteen such fine elements in the front and back of the crack tip. Fig. 3 shows the overall mesh of the specimen and mesh refinement in the crack tip region.
Fig. 3. Typical mesh model of the repaired structure and near the crack tip.
The procedure used in the finite element analysis involved the following step: the tensile stress was applied to the gripped specimen. General static ‘‘STEP’’-option was used for analysis with ABAQUS. Automatic increment of step was used with maximum number of increments of 100. Minimum increment size was 10 5. Maximum increment size was 1. Nevertheless, the ABAQUS solver code could override matrix solver choice according to the ‘‘STEP’’-option. The Von-Mises criterion is used to determine whether the stress in the materials causes plastic flow. Incremental plasticity theory is introduced to model the material non-linearity. The Newton–Raphson iterative method is used as approach for resolving non-linear finite element equations. Fig. 1. Geometrical model.
4. Analysis and results Table 1 Elastic properties of different materials. Aluminium alloy T3
Boron/epoxy
Adhesive (FM-73)
E1 (GPa) E2 (GPa) E3 (GPa)
72
2.55
m12 m13 m23
0.33
200 19.6 19.6 0.3 0.28 0.28 7.2 5.5 5.5
G12 (GPa) G13 (GPa) G23 (GPa)
0.32
This study has been made in order to analyze the size of the plastic zone ahead of repaired crack with bonded composite patch in aluminum alloy 2024-T3. Calculations have been realized to extract the plasticized elements around the crack tip of repaired crack. 4.1. Effect of the crack length on the plastic zone size In order to estimate the performances of the patch repair, the shapes of the plastic zone for repaired and un-repaired cracks were computed for crack length a = 30 mm. The obtained results show
952
W. Oudad et al. / Computational Materials Science 46 (2009) 950–954
that the reduction of the plastic zone by the patch repair is about 10 times. This is due to the fact that there is transfer of stresses between the cracked plate and the composite patch throughout the adhesive layer. It is also obtained that the ratio between the plastic zone radius and the crack length for case with repair is very small (about 0.015), what unable us to conclude that the concepts of linear fracture mechanics such as stress intensity factor or energy release rate can be applied. Fig. 4 presents the contour of the plastic zone ahead of repaired crack for different crack lengths. It can be seen that the size of the plastic zone is slightly affected by the variation of the crack length. There is a weak reduction of the plastic zone size as the crack length decreases. This is due to the fact that the absorption of the stresses by the patch do not permit a great extension of the plastic zone as the crack length increases. There is an analogy with the variation of the stress intensity factor for repaired crack if the concepts of linear fracture mechanics are applied. Indeed, the stress intensity factor exhibits an asymptotic behavior as the crack length increases [4,5,7]. These results are confirmed in Fig. 5. This last figure presents the variation of the plastic zone radius (rp) as a function of the crack length. It can be noted, that the plastic radius remains
approximately constant as the crack length increases excepted when the crack length approaches the patch width (a > 55 mm). In these cases, the crack tip approaches the unrepaired region of the plate, the stresses at the crack front increase and consequently the plastic zone size increases. 4.2. Effect of the adhesive properties It is known that the adhesive properties play a very important role in the repair process with bonded composite patch. The adhesive layer transfers the stresses from the damaged plate toward the composite patch. The maximum of stresses are transferred from the crack region. In this paragraph the effects of the adhesive young modulus and that of the adhesive thickness on the plastic zone ahead of repaired crack are analyzed. 4.2.1. Effect of the adhesive Young modulus (Ea) It s known that adhesive with better qualities are characterized by weak values of Young modulus in order to attenuate the stress intensity in the adhesive layer. In the case of bonded composite 0.8
0.30 0.25
0.7
a = 5 mm a = 30 mm a = 55 mm
0.6 0.5 Y (mm)
0.20 Y (mm)
Ea = 1000 MPa Ea = 2000 MPa Ea = 3000 MPa Ea = 4000 MPa
0.15 0.10
0.4 0.3 0.2
0.05
0.1
0.00
0.0 - 0.2
-0.04
0.00
0.04
0.08
0.12
0.16
0.0
0.1 0.2 X (mm)
0.3
0.4
0.5
crack tip
X(mm)
crack tip
-0.1
0.20
Fig. 6. Contour of the plastic zone for different adhesive Young Modulus.
Fig. 4. Contour of the plastic zone for different crack length.
0.5 0.9
0.4
0.8 0.7 rp (mm)
rp (mm)
0.3
0.2
0.6 0.5 0.4
0.1
0.3
0.0
0
10
20
30
40
a (mm) Fig. 5. Plastic zone radius vs crack length.
50
60
1000
1500
2000
2500
3000
3500
Ea (MPa) Fig. 7. Plastic zone radius vs adhesive Young modulus.
4000
953
W. Oudad et al. / Computational Materials Science 46 (2009) 950–954
0.7
0.245 0.210
0.140 0.105
0.5
rp (mm)
0.175 Y (mm)
0.6
ea =0.10mm ea =0.16mm ea =0.18mm ea =0.24mm ea =0.30mm ea =0.38mm
0.070
0.3 0.2
0.035 0.000
0.4
0.1
-0.050-0.025 0.000 0.025 0.050 0.075 0.100 0.125 0.150 X (mm)
crack tip
0.0
0
er = 1mm er = 3mm er = 6mm
0.5
Y (mm)
3
4 5 er (mm)
6
7
8
9
the adhesive thickness decreases. The repair performances increase when the quantity of the adhesive is weak. However, and by analogy with what announced in the precedent paragraph, a weak adhesive thickness involves higher intensities of the adhesive stresses, what can increases the risk of e failure of the adhesion. The adhesive thickness must also be optimized.
0.7
4.3. Effect of the patch thickness (er)
0.4
This effect is illustrated in Fig. 9 by the plot of the contour the plastic zone ahead of the crack front for various values of the patch thickness (er). It can be noted, that the increase of the patch thickness involves the reduction of the plastic zone size, what can improved the repair performances. However and according to Fig. 10, one cane deduce that it is not necessary to increase indefinitely the patch thickness because it effect on the plastic zone radius remains constant when the value of er exceeds 3 mm.
0.3 0.2 0.1 0.0
2
Fig. 10. Plastic zone radius vs patch thickness.
Fig. 8. Contour of the plastic zone for different adhesive thicknesses.
0.6
1
-0.08
crack tip
0.00
0.08
0.16
0.24
0.32
0.40
0.48
X (mm)
Fig. 9. Contour of the plastic zone for different patch thicknesses.
repair, the role of the adhesive is to transmit a maximum of stresses. Theoretically, it is beneficial for the repair process to use adhesive with high Young modulus. In Fig. 6 the plot of the contour of plastic zone ahead of the tip of repaired crack for different values of the adhesive Young modulus confirms what was advanced previously. Indeed, the plastic zone size decreases as the adhesive young modulus increases. It means that the repair performances can be improved by choosing higher values of the adhesive Young modulus. However, according to Fig. 7, where is presented the variation of the radius of the plastic zone as a function of the adhesive Young modulus, one can note that that the effect of Ea on the plastic zone size is stabilized as the adhesive young modulus is greater then 2500 MPa. On the other hand, an increase of the adhesive Young modulus involves the rise of the stresses in the adhesive layer, what can increase the risk of failure of the adhesive layer. Consequently the choice of the adhesive for crack repair must be optimized. 4.2.2. Effect of the adhesive thickness (ea) Fig. 8 presents the effect of the adhesive thickness on the plastic zone contour. It can be seen that the plastic zone size decreases as
5. Conclusions This study was carried out in order to estimate the performance of the bonded composite repair of metallic aircraft structures by analyzing the plastic zone size of ahead of repaired cracks. The obtained results allow us to deduce the following conclusions: – The presence of the composite patch reduces considerably the size of the plastic zone ahead of the crack. This reduction is very important so that the concepts of linear fracture mechanics for repaired cracks. – The effect of the crack length on the plastic zone size ahead of repaired cracks is not significant because the stress absorption by the patch increases as the crack growth. – The adhesive properties must be optimized in order to increase the repair performance and to avoid the adhesive failure between the repaired structure and the composite patch. – The patch must be thicker but not indefinitely with an aim to increase the repair performances.
References [1] A.A. Baker, Compos. Struct. 74 (1999) 431–443. [2] T. Ting, R. Jones, W.K. Chiu, I.H. Marshall, J.M. Greer, Compos. Struct. 47 (1999) 737–743.
954 [3] [4] [5] [6]
W. Oudad et al. / Computational Materials Science 46 (2009) 950–954 J.J. Schubbe, S. Mall, Compos. Struct. 45 (1999) 185–193. B.B. Bachir, M. Belhouari, B. Serier, Compos. Struct. 56 (2002) 401–406. W.H. Chen, S.H. Yang, Finite Elem. Anal. Des. 21 (1995) 21–44. A. Megueni, B.B. Bachir, B. Boutabout, Compos. Struct. 59 (2003) 415–418.
[7] T. Achour, B.B. Bachir, B. Serier, Comput. Mater. Sci. 28 (2003) 41–48. [8] B. Bachir Bouiadjra, H. Fekirini, B. Serier, M. Benguediab, Comput. Mater. Sci. 38 (2007) 824–829. [9] A.O Randolph, M.F. Clifford, J. Reinf. Plast. Compos. 4 (2002) 311–332.