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Numerical prediction on the tensile residual strength of repaired CFRP under different geometric changes
ARTICLE IN PRESS International Journal of Adhesion & Adhesives 29 (2009) 195– 205
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Numerical prediction on the tensile residual strength of repaired CFRP under different geometric changes R.D.S.G. Campilho a, M.F.S.F. de Moura a,, J.J.M.S. Domingues b a b
ˆnica e Gesta ˜o Industrial, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal Departamento de Engenharia Meca ˆnica, Instituto Superior de Engenharia do Porto, Rua Dr. Anto ´nio Bernardino de Almeida, 431, 4200-072 Porto, Portugal Departamento de Engenharia Meca
a r t i c l e in fo
abstract
Article history: Accepted 15 March 2008 Available online 27 May 2008
This work presents a two-dimensional numerical analysis to assess the influence of several geometric changes on the tensile residual strength of repaired CFRP composite plates. The model was validated by comparison with previously published experimental results. Single- and double-lap repair techniques were evaluated. The geometric changes include chamfering the patch outer face, thickening the adhesive near the overlap outer edge, filling the plates gap with adhesive (plug filling), using fillets of different shapes and dimensions at the patch ends, chamfering the outer and inner plate edges, and combinations of these changes. This work shows that, with the correct joint configuration, the residual strength can be increased by 27% for single-lap joints and 12% for double-lap joints. & 2008 Elsevier Ltd. All rights reserved.
Keywords: A. Adhesive joints B. Strength C. Laminates C. Finite element analysis M. Repair
1. Introduction Nowadays, fibre reinforced composite materials are widely used. Low strength composites are employed on home and recreational applications. High strength composites, including carbon-fibre reinforced composites (CFRP), present excellent strength and stiffness to weight ratios. Their main applications are directed to structural industries such as aeronautical, automotive and others where high performance materials are necessary and affordable. However, these materials are prone to suffer damage, specifically delamination between plies, due to, for example, low velocity impact which can easily occur in a structure’s lifetime. This phenomenon can highly reduce the strength of these structures which, associated to the recycling difficulties and replacement costs, makes repairing very advantageous. Adhesively-bonded patched repairs, analysed in this work, are also very attractive due to their high efficiency, more uniform stress distribution and superior fatigue behaviour, when compared to fastened joints. This kind of repair can also be easily applied, especially when considering the single- or double-lap repair techniques. Basically the procedure consists of removing the damaged material and bonding one (single-lap repair) or two patches (double-lap repair). Generally, and more specifically with unidirectional composites, a full strength recovery after repair cannot be observed. It is then important to increase the repairs efficiency. Several techniques can be used to increase the residual
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E-mail address: [email protected] (M.F.S.F. de Moura). 0143-7496/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijadhadh.2008.03.005
strength of the repaired structures, such as geometric changes of the plates/patches or adhesive. Several studies were already conducted on this subject. Bogdanovich and Kizhakkethara [1] performed a numerical study concerning the effect of a fillet on peel and shear stresses in the adhesive layer, for a single-lap composite joint. A sub-modelling technique was employed using plane stress two-dimensional continuum finite elements. The authors concluded that the fillet significantly diminishes peak peel and shear stresses near the fillet. Tsai and Morton [2] presented a similar study, validating the numerical analysis with experimental results. Shear strains near the fillet were obtained with the Moire´ method. It was concluded that a fillet reduces the shear strain and peak peel and shear stresses near the fillet, increasing the joint strength. Rispler et al. [3] used a numerical optimization iterative method to determine the optimal fillet shape. In each iteration of the optimization process, the low stressed fillet elements were removed in order to optimize its shape. The optimal solution (a 451 flat fillet) was achieved when all fillet representative elements were stressed by at least 20% of the structure maximum stress. In this case, 50% and 40% reductions on peak peel stresses in the adhesive and plate were obtained, respectively. Hu and Soutis [4] presented a numerical analysis of double-lap joints under a compressive load, concluding that localized stresses act at the end zones of the overlap. Results showed that peak shear strains can be markedly reduced increasing the adhesive thickness at the patch edges. Therefore, a joint with patches tapered from inside was hypothetically considered to reduce stress concentrations in the adhesive layer and consequently to increase the joint strength. No experimental analyses were performed to corroborate this fact.
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The optimal taper slope proposed in this work is 1/10. Ganesh and Choo [5] carried out a numerical study on single-lap joints under a tensile load in which material grading, i.e., Young’s modulus, of the plates at the overlap region was used to reduce stress concentrations. A 20% reduction on peak shear stresses in the adhesive layer, increasing load transfer at its central region, was obtained. Peel stresses were not affected, while load oriented axial stresses slightly increased. Since these last were much lower in magnitude, when comparing with shear stresses, this technique proved its usefulness. No strength comparison was performed with the traditional geometry. Boss et al. [6] carried out an analysis similar to [5], considering different plate chamfer shapes in order to improve the joint strength. Peak shear stresses at the adhesive layer edges were reduced with both solutions, i.e., modulus grading and chamfering. Peel stresses were reduced only by the chamfering technique. A´vila and Bueno [7] studied a E-glass/epoxy composite wavy-lap joint and its influence on the joint tensile strength. This geometry consisted on a sinusoidal plates shape at the overlap region, instead of the traditional flat one (Fig. 1). A numerical and experimental work was accomplished. The authors concluded that this modification increased approximately 40% the joint strength, which was justified by the flattening of the shear and peel stress distributions in the adhesive layer along the bond length. Kim et al. [8] accomplished an experimental study on unidirectional carbon–epoxy composite single-lap joints under a tensile load, in which different joint configurations were considered: specimens with and without a flat fillet, and co-cured specimens with and without adhesive layer. In the co-cured specimens, joints manufacturing included simultaneous curing of the entire assembly. The highest failure strength was obtained for the co-cured specimens without adhesive layer. Fillets also proved to increase the joint strength. Potter et al. [9] and Guild et al. [10] performed a two-phase study, experimental and numerical, respectively, about crack propagation in double-lap bonded composite joints with geometric changes in the adhesive and plates (fillets and plate tapering) and incorporating modification layers inside the adhesive. Preventing crack propagation from the adhesive to the laminates was the main objective. This objective was accomplished using modifying layers inside the adhesive. These layers were placed in the adhesive at its mid-thickness along the entire bond length, including the tapering and fillet regions. KaptonTM films (Fig. 2) proved to be the most performing, as they could deflect cracks when they reached the modifying layer, preventing crack propagation to the plates. Plate tapering alone was also considered, resulting in an interlaminar failure of the joint and strength reductions of approximately 30%, comparing with the filleted joints. The authors concluded that adhesive filleting is very important in controlling both failure load and failure mode.
The objective of this work is to predict numerically the influence of geometric changes on the tensile residual strength of repaired CFRP composite plates. This work is justified by the necessity to maximize the strength of repaired joints, thus increasing their efficiency. Single- and double-lap repair techniques were considered. A two-dimensional analysis was performed. The geometric changes included chamfering the patch outer face, adhesive thickening near the outer edge of the overlap, filling the plates gap with adhesive (plug filling), using fillets of different shapes and dimensions at the patch ends, chamfering of the outer and inner plate edges, and combinations of these changes. The numerical analysis used the ABAQUSs software and special developed interface finite elements including a cohesive mixed-mode damage model based on the indirect use of Fracture Mechanics. The objective was to study the influence of the different geometrical configurations on the repair residual strength. Prior to the numerical work, the proposed numerical model will be validated using experimental results of Quaresimin and Ricotta [11].
2. Cohesive damage model A cohesive mixed-mode damage model based on interface finite elements was considered to simulate damage onset and propagation [12–14]. A triangular constitutive relationship between stresses (r) and relative displacements (d, r) is established (Fig. 3). The subscripts ‘‘o’’ and ‘‘u’’ refer to onset and ultimate relative displacement, respectively, and the subscript ‘‘m’’ corresponds to mixed-mode. The model requires the knowledge of the local strengths (su,i, i ¼ I, II) and the critical strain energies release rates (Gic, i ¼ I, II). The constitutive relationship before damage onset is r ¼ Edr
(1)
where E is a stiffness diagonal matrix containing the stiffness parameters ei (i ¼ I, II). These values must be quite high (106 N/mm3) in order to avoid physically unacceptable interpenetrations. The softening relationship can be written as r ¼ ðI DÞEdr
(2)
i
u,i
Pure mode model
Gic
um,i
i = I, II
Mixed-mode model Fig. 1. Wavy-lap joint geometry [7]. Dimensions in mm.
Gi
i = I, II um,i
om,i Fig. 2. Schematic representation of the KaptonTM film position [9,10].
i u,i
o,i
Fig. 3. The triangular softening law for pure mode and mixed mode.
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where I is the identity matrix and D is a diagonal matrix containing, on the position corresponding to mode i (i ¼ I, II) the damage parameter. In general, bonded joints are subjected to mixed-mode loading. Therefore, a formulation for interface finite elements should include a mixed-mode damage model (Fig. 3). Damage onset is predicted using a quadratic stress criterion
sI su;I
2
sII 2 ¼1 su;II sII ¼ su;II þ
Fig. 4. Geometry and boundary conditions of the single-lap joint.
if sI 40
(3)
if sI p0
where si (i ¼ I, II) represent the stresses in each mode. Considering Eq. (1), the first Eq. (3) can be rewritten as a function of the relative displacements dom;I 2 dom;II 2 þ ¼1 do;I do;II
(4)
where dom,i (i ¼ I, II) are the relative displacements in each mode corresponding to damage initiation. Crack propagation was simulated by the linear energetic criterion GI GII þ ¼1 GIc GIIc
(5)
The area under the minor triangle of Fig. 3 represents the energy released in each mode, while the bigger triangle area corresponds to the respective critical fracture energy. When Eq. (5) is satisfied damage propagation occurs and stresses are completely released, with the exception of normal compressive ones. Using the proposed criteria (Eqs. (4) and (5)), it is possible to define the equivalent mixed-mode displacements dom and dum, thus establishing the damage parameters in the softening region dm ¼
du;m ðdm do;m Þ dm ðdu;m do;m Þ
(6)
A detailed description of the model is presented in [13].
3. Model validation Experimental results of Quaresimin and Ricotta [11], concerning the tensile strength of CFRP single-lap joints with and without a 451 flat fillet at the overlap edges, were used to validate the numerical model presented in this work. The joint is constituted by autoclave-mounted laminates (Seals Texipreg CC206, T300 twill 2 2 carbon-fibre fabric/ET442 toughened epoxy matrix), bonded with the epoxy adhesive 3MTM 9323. A [0]6 lay-up was considered for the laminates. The laminates, adhesive and interface elements properties used in the numerical models are presented in Table 1. Due to insufficient available data on the materials properties, an inverse method was used in order to obtain the critical strain energies release rates (Gic) of the adhesive, assuming GIIc ¼ 2GIc. This method consisted on fitting the numerical and experimental failure loads for the square edge joint. The obtained adhesive properties are used in the filleted joint model to predict the respective strength improvement of this geometry, comparing with the square edge one. The joint geometry with the 451 flat fillet, including the boundary Table 1 Laminates, adhesive and interface elements mechanical properties Plates [11]
Adhesive [11]
Interface elements
E1 ¼ 58050 MPa E2 ¼ 58050 MPa G12 ¼ 3300 MPa n12 ¼ 0.06
E ¼ 2870 MPa n ¼ 0.37
GIc ¼ 0.6 N/mm GIIc ¼ 1.2 N/mm su,I ¼ 80 MPa su,II ¼ 47 MPa
Fig. 5. Interface finite elements loci in the joint.
conditions used to simulate the experiments, is presented in Fig. 4. Fig. 5 details the model including the 451 flat fillet at the overlap region, highlighting the interface finite elements loci. Several sites were considered, accounting for the different failure modes possible to occur. Three possible damage initiation locations (1, 2 and 3 in Fig. 5) and growth planes (lines 4, 5 and 6 in Fig. 5) were considered. In addition, extra interface elements were placed at both overlap edges, allowing for all failure onset/ propagation path combinations. Lines 4, 5 and 6 correspond to the lower adherend/adhesive interface, middle of the adhesive and adhesive/upper adherend interface, respectively. The model without the fillet (with square edges) includes interface elements only at lines 4, 5 and 6. Considering the filleted joint, damage initiation occurred experimentally within the fillets at a 451 angle, propagating to the adherend/adhesive interfaces (see indication in Fig. 5). The square edges joint experienced failure at the adherend/adhesive interface. Numerically, these failure modes were accurately reproduced. Fig. 6 shows the failure path predicted numerically for the filleted joint. Damage onset occurred within the adhesive fillet (location 2 in Fig. 5), propagating to the adherend/adhesive interfaces until complete separation of the laminates. Table 2 presents the failure loads for both geometries and the percentile strength improvement of the numerical analysis and the experimental results. Approximate 16% and 18% strength improvements were achieved using the fillet with the numerical and experimental analyses, respectively. These results show that the proposed numerical model reproduces accurately the behaviour of these joints.
4. Numerical analysis The following work consists on a two-dimensional numerical analysis of single- and double-lap repaired joints (Fig. 7) with different geometric changes. These geometries represent the repair of rectangular plates bonded with rectangular patches [15–19], or they can be considered as an approximation of a threedimensional repair [4,20]. In the second case, a composite plate is deemed to have suffered damage at an intermediate section. The damaged material is removed drilling a circular hole and one (single-lap) or two (double-lap) circular patches are bonded, concentric with the hole. It must be stressed that in this case some three-dimensional effects are not captured by the numerical models. Furthermore, the repair may still sustain loads after patch debonding [4]. A non-linear material and geometrical analysis was
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Fig. 6. Numerical failure path for the filleted joint.
Table 2 Comparison between numerical and experimental failure loads Failure load (N)
Experimental [11] Numerical
Without fillet
With fillet
Strength improvement (%)
13,777 13,714
16,192 15,860
17.5 15.6
Fig. 8. Numerical models simulating the single-lap (a) and double-lap (b) joints.
Fig. 7. Single-lap (a) and double-lap (b) joints.
performed, using plane strain rectangular eight-node finite elements. Interface finite elements were used to simulate crack onset and growth. The numerical idealizations of the single- and double-lap joints are presented in Fig. 8. Both geometries were modelled with symmetry conditions at the middle of the joint (line A in Fig. 8), thus considering only half the joint length. Additionally, double-lap joints were modelled using symmetry conditions at the plates mid-thickness (line B in Fig. 8). Boundary conditions included vertical restraining and an applied displacement at the joint edges (d in Fig. 8). At this stage, the authors establish the inner edge of the overlap (IEO) and outer edge of the overlap (OEO). Carbon–epoxy composite plates and patches were used. The mechanical properties of a unidirectional lamina are presented in Table 3 [13]. A ductile adhesive (Araldites 420) was used, whose elastic properties are se ¼ 8.325 MPa, E ¼ 1850 MPa and n ¼ 0.3. The respective stress–strain curve, obtained experimentally with tensile bulk tests [21], is presented in Fig. 9. The adhesive data was included in the numerical models for the
continuum elements representing the adhesive. The objective of using a ductile adhesive is to promote plastic yielding at the overlap edges (stress concentration regions), thus avoiding premature damage initiation at these regions, which would occur using a brittle adhesive. Therefore, the obtained results may only be valid for similar adhesives. General dimensions of the joints are presented in Table 4. (02,902)S and (04) lay-ups were considered for the plates and patches, respectively. The influence of different lay-ups on joint strength will be analysed further in this work. The following properties were used for the interface finite elements: GIc ¼ 0.3 N/mm, GIIc ¼ 0.6 N/mm, su,I ¼ su,II ¼ 40 MPa [13]. The location of the interface finite elements is shown in Fig. 10 (dashed lines) for the standard joint, without geometric changes. These elements were placed at the adhesive/patch and adhesive/ plate interfaces, at the middle of the adhesive thickness and, inside the plates, between differently orientated plies and between the two 01 plies closest to the adhesive layer. Additional interface elements were used according to the different geometric changes. The objective was to assess numerically the influence of the geometric changes on the tensile joint strength, as well as to evaluate the influence of crack onset location and growth path on this phenomenon. The joint strength (sC) is the ratio between the peak load and the plate cross-sectional area. Throughout this paper the joint strength (sC) is normalized to the strength of a joint with no geometric changes (s0).
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Table 3 CFRP unidirectional lamina mechanical properties CFRP unidirectional lamina mechanical properties E1 ¼ 1.09E+05 MPa E2 ¼ 8819 MPa E3 ¼ 8819 MPa
n12 ¼ 0.342 n13 ¼ 0.342 n23 ¼ 0.380
G12 ¼ 4315 MPa G13 ¼ 4315 MPa G23 ¼ 3200 MPa
50
the joint strength (0.25%), comparing to a standard joint. Bigger patch chamfers gradually decrease the joint strength. This behaviour is justified by the crack initiation locus. In fact, damage onset in these joints occurs at the IEO [13,21]. This modification at the OEO decreases load transfer at this region and increases stress concentrations at the IEO [21], gradually reducing the joint strength with the chamfer dimensions, although by a small amount. 4.1.2. Adhesive thickening To decrease peak peel stresses at the OEO, the adhesive thickness was increased at that region. Hu and Soutis [4] numerically proved that the peak shear strains at the end of the overlap diminish using this procedure. Fig. 12 represents a singlelap joint with a 0.4 mm adhesive thickening at the OEO. Only the 0.1 mm thickening rendered a slight increase of the joint strength (0.64%). Larger thickenings gradually decrease the joint strength. This geometric modification has a similar effect on the joint behaviour as the previous one, i.e., the softening introduced at the OEO decreases peel and shear stresses at that region, decreasing the load transfer and increasing stress concentrations at the IEO [23,24], which reduce the joint strength.
40
[MPa]
199
30 20 10 0 0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Fig. 9. Stress–strain curve of the adhesive Araldites 420.
Table 4 Plates, patches and adhesive dimensions Plates
Patches
Adhesive
Length: L ¼ 50 mm, width: b ¼ 15 mm Thickness: tP ¼ 1 mm
Thickness: tH ¼ 0.5 mm Overlap length: LC ¼ 10 mm
Thickness: tA ¼ 0.1 mm
Plates gap: e ¼ 5 mm
Fig. 10. Interface finite elements loci in the repaired joint.
4.1. Single-lap joints 4.1.1. Patch chamfer The objective of this modification is to decrease the peak peel stresses observed at the OEO [13,15], assessing the influence of this modification on the joint strength. Kaye and Heller [22] stressed that patch tapering spreads the load transfer more evenly between the plates and patches. A 1/10 slope was considered [4]. Patch thickness reductions of 0.1, 0.2, 0.3 and 0.4 mm were tested. Fig. 11 represents the single-lap joint standard configuration (a) and with a 0.4 mm patch thickness reduction (b). This nomenclature and slope are used throughout this work in all chamfers. No advantage exists in using this kind of modification, since only with a 0.1 mm patch chamfer it was observed a slight increase on
4.1.3. Plug filling with adhesive It is also possible to fill with adhesive the plates gap (e in Fig. 7), in order to increase the load transfer between the two plates. Soutis et al. [20] verified that the compressive strength of double-lap repairs increases plugging the specimen’s hole. The geometry is shown in Fig. 13 for the single-lap joint. Additional interface finite elements were placed at the plug/plate and plug/ patch interfaces. This change caused a 7% reduction on the joint strength, justified by the crack onset location, at the plate/plug interface, which, due to its instantaneous propagation nature, induced premature crack growth along the adhesive layer. Crack onset and growth process is presented in Fig. 14. To clarify this behaviour, the influence of the Young’s modulus of the plug adhesive on joint strength was evaluated. Fig. 15 presents the normalized joint strength for different values of plug adhesive Young’s modulus, ranging from 70 to +70% of the adhesive layer modulus. It is necessary to reduce by 70% the Young’s modulus of the plug adhesive to avoid a plug/plate interface failure prior to the adhesive layer failure, and a consequent strength reduction relatively to the standard geometry. Lower values of E for the plug were discarded, since the load transfer between the plug and the plates becomes minimal. 4.1.4. Fillets Using fillets at the patch ends (Fig. 16) was also investigated. This technique is widely considered to increase joint strength [1,2,23]. Additional interface finite elements were placed at the fillet/plate and fillet/patch interfaces. Geometry 1 represents the standard configuration; geometry 5 represents a flat fillet comprising all the patch thickness. Fig. 17 illustrates the joint strength as a function of the fillet geometry. An approximate 4% strength improvement was achieved using the geometry 5. A quadrangular fillet was considered (Fig. 18a), as well as a combination of a flat fillet with adhesive thickening (Fig. 18b–d). However, with these configurations a maximum increase of 3.5% on joint strength was achieved. 4.1.5. Plate chamfer Plate chamfering at the IEO was also evaluated. Plate outer chamfering (near the patch) and plate inner chamfering were considered. Boss et al. [6] analysed several types of plates geometrical grading and verified that both peak peel and shear
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Fig. 11. Single-lap joint standard configuration (a) and with a 0.4 mm patch outer chamfer (b).
Fig. 12. Single-lap joint with a 0.4 mm adhesive thickening.
Fig. 13. Single-lap joint with a plug filling (shaded region).
Fig. 14. Crack onset and growth for the plug filled repaired joint.
102 100
C/0 [%]
98 96 94 92 90 -80
-60
-40
-20
0 ΔE [%]
20
40
60
80
Fig. 15. Joint strength as function of the plug adhesive Young’s modulus (single-lap joint).
stresses were reduced at the plate edge, increasing the joint strength. In this work 0.1, 0.2 and 0.3 mm plate thickness reductions were considered for the patch outer chamfering (Fig. 19). Strength improvements of 0, 2.3 and 1% were obtained, respectively. Different inner chamfering dimensions were also evaluated (plate thickness reductions ranging from 0.1 to 0.7 mm), considering simultaneously a 0.2 mm outer chamfer (the most
efficient one). Fig. 20 represents 0.1, 0.4 and 0.7 mm inner chamfer joint geometries. Fig. 21 presents the joint strength as a function of the inner chamfer dimensions. A 23% strength improvement was obtained using a 0.6 mm plate inner chamfer combined with a 0.2 mm plate outer chamfer. This behaviour is justified by the significant plate stiffness reduction at the IEO, diminishing peel stresses at this region and delaying damage onset and growth. Fig. 22 illustrates this situation, comparing the chamfered joint with a standard one, under the same applied displacement. It is stressed that this particular result is valid only for the plate lay-up under analysis. In fact, it was observed that using the optimal inner and outer chamfering geometries, the plate section at the IEO is almost constituted by 901 plies, i.e., the 01 plies are removed by the considered chamfer geometries (Fig. 22). This modification renders the joint flexible enough to significantly reduce stress concentrations at this region, and consequently to increase the joint strength. The influence of the plate and patch lay-ups will be analysed in a subsequent section. 4.1.6. Geometry changes combination The most representative geometric changes were combined to maximize the joint strength (geometry 5 flat fillet, Fig. 16, which leads to a 4% strength improvement, and plate outer and inner chamfering with the optimal dimensions, which lead to a 23% strength improvement). Combining these two geometric changes (Fig. 23), a 26.8% strength improvement is obtained.
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201
Fig. 16. Single-lap joint with different fillet geometries.
104 adhesive thickening region in double-lap joints [22,25,26]. This occurrence decreases load transfer at the OEO, overloading the joint at the IEO, which justifies the observed behaviour.
C/0 [%]
102
100
98 1
2
3 Fillet geometry
4
5
Fig. 17. Joint strength as function of the fillet geometry (single-lap joint).
4.2. Double-lap joints 4.2.1. Patch chamfer For all double-lap joint analyses, the geometries were similar to the single-lap joint ones (using symmetry conditions, Fig. 8). No significant increase on the joint strength was obtained. Patch chamfers of 0.3 and 0.4 mm lead to 0.18% and 0.20% strength improvements, respectively, while the smaller ones do not present influence on the joint strength. Kaye and Heller [22] used an optimization procedure on double-lap joints to define the optimal patch chamfer geometry allowing reducing Von Mises equivalent stresses along the bond length. A preliminary study using a linear chamfer, similar to Fig. 11, led to a significant reduction of Von Mises stresses near the chamfer. Potter et al. [9] pointed a similar behaviour. Actually, this modification gradually decreases load transfer near the chamfer with its dimensions, whilst increasing stress concentrations at the crack initiation region (IEO), justifying the obtained results.
4.2.2. Adhesive thickening No strength improvement was observed thickening the adhesive at the OEO (only a 0.26% strength improvement was obtained with a 0.1 mm thickening). Besides, thickening the adhesive above 0.2 mm decreases the joint strength of a significant amount (a 0.4 mm adhesive thickening causes an approximate 3% joint strength reduction). It is known that this procedure reduces considerably stress concentrations near the
4.2.3. Plug filling with adhesive Using the double-lap repair procedure, plug filling highly increases the joint strength. With similar adhesive layer and plug mechanical properties, a 9% strength improvement was achieved. This disagrees with the results obtained for the single-lap joint, and is justified by the reduced bending in the double-lap joints, compared to the single-lap ones. Consequently, filling the plug with adhesive simply increases the load transfer between the two plates, without inconvenient. The influence of the plug adhesive Young’s modulus on the joint strength, considering the same range for DE as in single-lap joints, was evaluated (Fig. 24). It was observed that the joint strength is highly influenced by this parameter. In fact, changing this parameter never diminishes the joint strength relatively to a standard joint, in contrast to what occurs in the single-lap joints (Fig. 15). A smaller Young’s modulus for the plug adhesive leads to a reduced load transfer between the plug and the plate, and subsequently a minor increase on the joint strength. Using plug adhesives stiffer than the adhesive layer leads to a gradual decreasing of the joint strength. In fact, the plug adhesive/plate vertical interface begins to crack before crack growth at the adhesive layer, diminishing its influence on the joint strength. If the plug adhesive is too stiff (DEX50%), the joint strength remains unchanged, comparing to the standard joint, because the plug adhesive/plate vertical interface fails completely before damage onset in the adhesive layer. The correct choice of this parameter was DE ¼ 20%, corresponding to a strength improvement of 10%. This situation corresponds to the maximum value of E for the plug adhesive assuring that the plug adhesive/ plate crack occurs after the plate/patch debonding. 4.2.4. Fillets The same fillet geometries were evaluated (Figs. 16 and 18). Fig. 25 shows the normalized strength as a function of the geometry. The results are similar to single-lap ones, i.e., a 4% strength improvement was obtained using a geometry 5 flat fillet. The quadrangular fillet and combination of the geometry 5 flat fillet with adhesive thickening lead to strength improvements smaller than 0.4%. 4.2.5. Geometry changes combination Using the geometry 5 flat fillet and an optimized plug adhesive filling leads to a 11.9% strength improvement.
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Fig. 18. Single-lap joint with a quadrangular fillet (a) and combinations with fillet/adhesive thickening (b–d).
Fig. 19. Single-lap joint with a plate outer chamfering of 0.1 mm (a), 0.2 mm (b) and 0.3 mm (c).
Fig. 20. Single-lap joint with a plate inner chamfering of 0.1 mm (a), 0.4 mm (b) and 0.7 mm (c).
5. Influence of the plate and patch lay-ups on the joint strength The influence of the plate and patch lay-ups on the joint strength is analysed, for the single- and double-strap optimal solutions. For the single-strap geometry the plate lay-up has a
particular significance, since as mentioned earlier, the plate stiffness has a major influence on the joint strength. A more realistic approximation to the three-dimensional repair is obtained considering different patch lay-ups, allowing repairing the lost strength in the 901 direction. Table 5 represents a summary of the strength improvement relatively to the standard
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112
108 C/0 [%]
joint and maximum strength displacement (dC, Fig. 7) obtained with different plate and patch lay-up combinations. With the single-lap repair technique, combinations including 01 plies near the adhesive (1, 2 and 3) show a significant strength improvement (ranging from 21.8% to 26.8%), which depends on the plate and patch stiffness at the crack initiation region (IEO). Generally, increasing the plate stiffness decreases the joint strength, which is justified by the increase of stress concentrations caused by a less significant plate bending. Combination 4 leads to a 13.9% strength reduction, which is justified by the plate and patch bending stiffness reduction. This occurrence leads to a highly localized patch bending and a higher plate bending, which overload the adhesive at a very restricted region, thus diminishing the joint strength. Fig. 26 clarifies this behaviour, showing combinations 1 and 4 under a similar displacement (d in Fig. 7). Analysing the double-lap results, a significant difference is noticed between combination 1 and the remaining ones. Using lay-up combinations 2, 3 and 4, the vertical plug/plate interface fails prior to failure in the adhesive layer, thus not influencing the joint
203
104
100
96 -80
-60
-40
-20
0 E [%]
20
40
60
80
Fig. 24. Joint strength as function of the plug adhesive Young’s modulus (doublelap joint).
104 128
C/0 [%]
102
C/0 [%]
120
112
100
104 98 1
2
96 0
0.1
0.2 0.3 0.4 0.5 Plate thickness reduction [mm]
0.6
3 Fillet geometry
4
5
0.7 Fig. 25. Joint strength as function of the fillet geometry (double-lap joint).
Fig. 21. Joint strength as function of the plate inner chamfer dimensions (singlelap joint).
Fig. 22. Crack onset and growth for the standard joint (a) and the plate chamfered joint (b).
Fig. 23. Single-lap joint combining a flat fillet with plate chamfering.
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6. Influence of the plates gap (e) The following study assesses the influence of the plates gap (e, Fig. 7), which also simulates the hole diameter in the simplified analysis of the three-dimensional repair, on the strength of the single- and double-lap optimal solutions. This study arises from the need of considering different gaps, representative of varying damaged region dimensions, according to the characteristics of the damage imposed to the structure. Gaps of 0.5, 2.5, 5, 10, 15, 20 and 30 mm were evaluated. Fig. 27 shows the strength improvement and maximum strength displacement (dC, Fig. 7) as functions of the plates gap (e) for the single-lap (SL) and double-lap (DL) optimal solutions. A strength reduction is observed for the smaller plates gaps, for both single- and double-lap repair configurations. In the single-lap joint, this behaviour is justified by the significant increase of the peak shear stresses at the IEO for the smallest values of e. In the double-lap joint the observed strength reduction is caused by the smaller plug dimensions, which diminishes its compliance. This occurrence leads to a premature plate/plug vertical interface failure, prior to failure in the adhesive layer. In both configurations, a plateau is achieved for higher values of e. The maximum strength displacement gradually increases with the plates gap, because the joint length increases accordingly.
Table 5 Influence of lay-ups on the joint strength improvement and maximum strength displacement Combination
1
2
3
4
Plate lay-up Patch lay-up Single-lap
(02,902)S (04) 26.8% 0.389 mm 11.9% 0.330 mm
(02,902)S (02,902) 25.9% 0.436 mm 4.2% 0.383 mm
(08) (04) 21.8% 0.268 mm 4.5% 0.221 mm
(902,02)S (902,02) 13.9% 0.312 mm 4.2% 0.386 mm
Double-lap
7. Concluding remarks This work aimed to predict numerically the influence of geometric changes on the tensile strength of CFRP repairs. A numerical study was performed, using the ABAQUSs software and special developed interface elements. Interface elements allow locating crack onset and growth path for the different geometries. Prior to the numerical work description, a validation with the experimental results of Quaresimin and Ricotta [11] was accomplished. A good agreement was found with the numerical predictions of failure path and load. For the single-lap joint, a significant strength improvement (26.8%) was achieved filleting the patch ends and chamfering the outer and inner edges of the plates. Patch chamfering, adhesive thickening at the patch ends and plug filling, proved to reduce the strength of these joints. Using the double-lap repair technique, a significant strength improvement was observed using a flat fillet at the patch ends and plug filling the plates gap. Combining of these two leads to a 11.9% strength improvement. It was also proved that, using lower Young’s modulus for the plug adhesive, an increase on joint strength was obtained. Although the results presented in this paper may depend on materials properties, lay-ups and geometric parameters, it can be concluded that the models provide design guidelines in order to increase the residual strength of composite repairs.
130
0.6
125
0.5
120
0.4
115
0.3
110
0.2
105
C/0, SL
C/0, DL
C, SL
C, DL
C [mm]
strength. The strength improvement of approximately 4% is caused exclusively by the fillet. The maximum strength displacement (dC, Fig. 7) for all combinations presented in Table 5 is inversely proportional to the global plate and patch stiffness, which corresponds to the expected behaviour.
C/0 [%]
204
0.1 0
100 0
5
10
15 20 e [mm]
25
30
Fig. 27. Joint strength and maximum strength displacement as functions of the plates gap (e).
Fig. 26. Crack onset and growth for the combination one lay-up (a) and combination four lay-up (b) optimal solutions.
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Acknowledgements The authors thank the Portuguese Foundation for Science and Technology for supporting the work here presented, through the research project POCI/EME/56567/2004 and the individual grant SFRH/BD/30305/2006. References [1] Bogdanovich AE, Kizhakkethara I. Three-dimensional finite element analysis of double-lap composite adhesive bonded joint using submodeling approach. Compos Pt B 1999;30:537–51. [2] Tsai MY, Morton J. The effect of a spew fillet on adhesive stress distributions in laminated composite single-lap joints. Compos Struct 1995;32:123–31. [3] Rispler AR, Tong L, Steven GP, Wisnom MR. Shape optimization of adhesive fillets. Int J Adhes Adhes 2000;20:221–31. [4] Hu FZ, Soutis C. Strength prediction of patch repaired CFRP laminates loaded in compression. Compos Sci Technol 2000;60:1103–14. [5] Ganesh VK, Choo TS. Modulus graded composite adherends for single-lap bonded joints. J Compos Mater 2002;36(14):1757–67. [6] Boss JN, Ganesh VK, Lim CT. Modulus grading versus geometrical grading of composite adherends in single-lap bonded joints. Compos Struct 2003;62:113–21. [7] A´vila AF, Bueno PO. An experimental and numerical study on adhesive joints for composites. Compos Struct 2004;64:531–7. [8] Kim KS, Yoo JS, Yi YM, Kim CG. Failure mode and strength of uni-directional composite single-lap bonded joints with different bonding methods. Compos Struct 2006;72(4):477–85. [9] Potter KD, Guild FJ, Harvey MR, Wisnom MR, Adams RD. Understanding and control of adhesive crack propagation in bonded joints between carbon fibre composite adherends I experimental. Int J Adhes Adhes 2001;21:435–43. [10] Guild FJ, Potter KD, Heinrich J, Adams RD, Wisnom MR. Understanding and control of adhesive crack propagation in bonded joints between carbon fibre composite adherends, II: Finite element analysis. Int J Adhes Adhes 2001;21:445–53. [11] Quaresimin M, Ricotta M. Fatigue behaviour and damage evolution of singlelap bonded joints in composite material. Compos Sci Technol 2006;66: 176–87.
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[12] de Moura MFSF, Gonc- alves JPM, Marques AT, de Castro PMST. Prediction of compressive strength of carbon–epoxy laminates containing delamination by using a mixed-mode damage model. Compos Struct 2000;50:151–7. [13] Campilho RDSG, de Moura MFSF, Domingues JJMS. Modelling single and double-lap repairs on composite materials. Compos Sci Technol 2005;65:1948–58. [14] Campilho RDSG, de Moura MFSF, Domingues JJMS. Stress and failure analyses of scarf repaired CFRP laminates using a cohesive damage model. J Adhes Sci Technol 2007;21(9):855–970. [15] Mortensen F, Thomsen OT. Analysis of adhesive bonded joints: a unified approach. Compos Sci Technol 2002;62:1011–31. [16] da Silva LFM, Adams RD, Gibbs M. Manufacture of adhesive joints and bulk specimens with high-temperature adhesives. Int J Adhes Adhes 2004; 24:69–83. [17] Reis P, Antunes F, Ferreira JAM. Influence of superposition length on mechanical resistance of single-lap adhesive joints. Compos Struct 2005; 67(1):125–33. [18] de Moura MFSF, Daniaud R, Magalha˜es AG. Simulation of mechanical behaviour of composite bonded joints containing strip defects. Int J Adhes Adhes 2006;26:464–73. [19] Oterkus E, Barut A, Madenci E, Smeltzer III SS, Ambur DR. Bonded lap joints of composite laminates with tapered edges. Int J Solids Struct 2006;43:1459–89. [20] Soutis C, Duan DM, Goutas P. Compressive behaviour of CFRP laminates repaired with adhesively bonded external patches. Compos Struct 1999;45: 289–301. [21] Campilho RDSG. Modelac-a˜o da Execuc-a˜o de Reparac- o˜es em Materiais Compo´sitos. M.Sc. thesis. Porto, Portugal: Department of Mechanical Engineering and Industrial Management, Enginnering Faculty; 2005. [22] Kaye RH, Heller M. Through-thickness shape optimisation of bonded repairs and lap-joints. Int J Adhes Adhes 2002;22:7–21. [23] Hildebrand M. Non-linear analysis and optimization of adhesively bonded single-lap joints between fibre-reinforced plastics and metals. Int J Adhes Adhes 1994;14(4):261–7. [24] Belingardi G, Goglio L, Tarditi A. Investigating the effect of spew and chamfer size on the stresses in metal/plastics adhesive joints. Int J Adhes Adhes 2002;22:273–82. [25] Adams RD, Atkins RW, Harris JA, Kinloch AJ. Stress analysis and failure properties of carbon-fibre-reinforced-plastic/steel double-lap joints. J Adhes 1986;20:29–53. [26] da Silva LFM, Adams RD. Techniques to reduce peel stresses in adhesive joints with composites. Int J Adhes Adhes 2007;27:227–35.
Contents lists available at ScienceDirect
International Journal of Adhesion & Adhesives journal homepage: www.elsevier.com/locate/ijadhadh
Numerical prediction on the tensile residual strength of repaired CFRP under different geometric changes R.D.S.G. Campilho a, M.F.S.F. de Moura a,, J.J.M.S. Domingues b a b
ˆnica e Gesta ˜o Industrial, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal Departamento de Engenharia Meca ˆnica, Instituto Superior de Engenharia do Porto, Rua Dr. Anto ´nio Bernardino de Almeida, 431, 4200-072 Porto, Portugal Departamento de Engenharia Meca
a r t i c l e in fo
abstract
Article history: Accepted 15 March 2008 Available online 27 May 2008
This work presents a two-dimensional numerical analysis to assess the influence of several geometric changes on the tensile residual strength of repaired CFRP composite plates. The model was validated by comparison with previously published experimental results. Single- and double-lap repair techniques were evaluated. The geometric changes include chamfering the patch outer face, thickening the adhesive near the overlap outer edge, filling the plates gap with adhesive (plug filling), using fillets of different shapes and dimensions at the patch ends, chamfering the outer and inner plate edges, and combinations of these changes. This work shows that, with the correct joint configuration, the residual strength can be increased by 27% for single-lap joints and 12% for double-lap joints. & 2008 Elsevier Ltd. All rights reserved.
Keywords: A. Adhesive joints B. Strength C. Laminates C. Finite element analysis M. Repair
1. Introduction Nowadays, fibre reinforced composite materials are widely used. Low strength composites are employed on home and recreational applications. High strength composites, including carbon-fibre reinforced composites (CFRP), present excellent strength and stiffness to weight ratios. Their main applications are directed to structural industries such as aeronautical, automotive and others where high performance materials are necessary and affordable. However, these materials are prone to suffer damage, specifically delamination between plies, due to, for example, low velocity impact which can easily occur in a structure’s lifetime. This phenomenon can highly reduce the strength of these structures which, associated to the recycling difficulties and replacement costs, makes repairing very advantageous. Adhesively-bonded patched repairs, analysed in this work, are also very attractive due to their high efficiency, more uniform stress distribution and superior fatigue behaviour, when compared to fastened joints. This kind of repair can also be easily applied, especially when considering the single- or double-lap repair techniques. Basically the procedure consists of removing the damaged material and bonding one (single-lap repair) or two patches (double-lap repair). Generally, and more specifically with unidirectional composites, a full strength recovery after repair cannot be observed. It is then important to increase the repairs efficiency. Several techniques can be used to increase the residual
Corresponding author. Tel.: +351 225081727; fax: +351 225081584.
E-mail address: [email protected] (M.F.S.F. de Moura). 0143-7496/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijadhadh.2008.03.005
strength of the repaired structures, such as geometric changes of the plates/patches or adhesive. Several studies were already conducted on this subject. Bogdanovich and Kizhakkethara [1] performed a numerical study concerning the effect of a fillet on peel and shear stresses in the adhesive layer, for a single-lap composite joint. A sub-modelling technique was employed using plane stress two-dimensional continuum finite elements. The authors concluded that the fillet significantly diminishes peak peel and shear stresses near the fillet. Tsai and Morton [2] presented a similar study, validating the numerical analysis with experimental results. Shear strains near the fillet were obtained with the Moire´ method. It was concluded that a fillet reduces the shear strain and peak peel and shear stresses near the fillet, increasing the joint strength. Rispler et al. [3] used a numerical optimization iterative method to determine the optimal fillet shape. In each iteration of the optimization process, the low stressed fillet elements were removed in order to optimize its shape. The optimal solution (a 451 flat fillet) was achieved when all fillet representative elements were stressed by at least 20% of the structure maximum stress. In this case, 50% and 40% reductions on peak peel stresses in the adhesive and plate were obtained, respectively. Hu and Soutis [4] presented a numerical analysis of double-lap joints under a compressive load, concluding that localized stresses act at the end zones of the overlap. Results showed that peak shear strains can be markedly reduced increasing the adhesive thickness at the patch edges. Therefore, a joint with patches tapered from inside was hypothetically considered to reduce stress concentrations in the adhesive layer and consequently to increase the joint strength. No experimental analyses were performed to corroborate this fact.
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The optimal taper slope proposed in this work is 1/10. Ganesh and Choo [5] carried out a numerical study on single-lap joints under a tensile load in which material grading, i.e., Young’s modulus, of the plates at the overlap region was used to reduce stress concentrations. A 20% reduction on peak shear stresses in the adhesive layer, increasing load transfer at its central region, was obtained. Peel stresses were not affected, while load oriented axial stresses slightly increased. Since these last were much lower in magnitude, when comparing with shear stresses, this technique proved its usefulness. No strength comparison was performed with the traditional geometry. Boss et al. [6] carried out an analysis similar to [5], considering different plate chamfer shapes in order to improve the joint strength. Peak shear stresses at the adhesive layer edges were reduced with both solutions, i.e., modulus grading and chamfering. Peel stresses were reduced only by the chamfering technique. A´vila and Bueno [7] studied a E-glass/epoxy composite wavy-lap joint and its influence on the joint tensile strength. This geometry consisted on a sinusoidal plates shape at the overlap region, instead of the traditional flat one (Fig. 1). A numerical and experimental work was accomplished. The authors concluded that this modification increased approximately 40% the joint strength, which was justified by the flattening of the shear and peel stress distributions in the adhesive layer along the bond length. Kim et al. [8] accomplished an experimental study on unidirectional carbon–epoxy composite single-lap joints under a tensile load, in which different joint configurations were considered: specimens with and without a flat fillet, and co-cured specimens with and without adhesive layer. In the co-cured specimens, joints manufacturing included simultaneous curing of the entire assembly. The highest failure strength was obtained for the co-cured specimens without adhesive layer. Fillets also proved to increase the joint strength. Potter et al. [9] and Guild et al. [10] performed a two-phase study, experimental and numerical, respectively, about crack propagation in double-lap bonded composite joints with geometric changes in the adhesive and plates (fillets and plate tapering) and incorporating modification layers inside the adhesive. Preventing crack propagation from the adhesive to the laminates was the main objective. This objective was accomplished using modifying layers inside the adhesive. These layers were placed in the adhesive at its mid-thickness along the entire bond length, including the tapering and fillet regions. KaptonTM films (Fig. 2) proved to be the most performing, as they could deflect cracks when they reached the modifying layer, preventing crack propagation to the plates. Plate tapering alone was also considered, resulting in an interlaminar failure of the joint and strength reductions of approximately 30%, comparing with the filleted joints. The authors concluded that adhesive filleting is very important in controlling both failure load and failure mode.
The objective of this work is to predict numerically the influence of geometric changes on the tensile residual strength of repaired CFRP composite plates. This work is justified by the necessity to maximize the strength of repaired joints, thus increasing their efficiency. Single- and double-lap repair techniques were considered. A two-dimensional analysis was performed. The geometric changes included chamfering the patch outer face, adhesive thickening near the outer edge of the overlap, filling the plates gap with adhesive (plug filling), using fillets of different shapes and dimensions at the patch ends, chamfering of the outer and inner plate edges, and combinations of these changes. The numerical analysis used the ABAQUSs software and special developed interface finite elements including a cohesive mixed-mode damage model based on the indirect use of Fracture Mechanics. The objective was to study the influence of the different geometrical configurations on the repair residual strength. Prior to the numerical work, the proposed numerical model will be validated using experimental results of Quaresimin and Ricotta [11].
2. Cohesive damage model A cohesive mixed-mode damage model based on interface finite elements was considered to simulate damage onset and propagation [12–14]. A triangular constitutive relationship between stresses (r) and relative displacements (d, r) is established (Fig. 3). The subscripts ‘‘o’’ and ‘‘u’’ refer to onset and ultimate relative displacement, respectively, and the subscript ‘‘m’’ corresponds to mixed-mode. The model requires the knowledge of the local strengths (su,i, i ¼ I, II) and the critical strain energies release rates (Gic, i ¼ I, II). The constitutive relationship before damage onset is r ¼ Edr
(1)
where E is a stiffness diagonal matrix containing the stiffness parameters ei (i ¼ I, II). These values must be quite high (106 N/mm3) in order to avoid physically unacceptable interpenetrations. The softening relationship can be written as r ¼ ðI DÞEdr
(2)
i
u,i
Pure mode model
Gic
um,i
i = I, II
Mixed-mode model Fig. 1. Wavy-lap joint geometry [7]. Dimensions in mm.
Gi
i = I, II um,i
om,i Fig. 2. Schematic representation of the KaptonTM film position [9,10].
i u,i
o,i
Fig. 3. The triangular softening law for pure mode and mixed mode.
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197
where I is the identity matrix and D is a diagonal matrix containing, on the position corresponding to mode i (i ¼ I, II) the damage parameter. In general, bonded joints are subjected to mixed-mode loading. Therefore, a formulation for interface finite elements should include a mixed-mode damage model (Fig. 3). Damage onset is predicted using a quadratic stress criterion
sI su;I
2
sII 2 ¼1 su;II sII ¼ su;II þ
Fig. 4. Geometry and boundary conditions of the single-lap joint.
if sI 40
(3)
if sI p0
where si (i ¼ I, II) represent the stresses in each mode. Considering Eq. (1), the first Eq. (3) can be rewritten as a function of the relative displacements dom;I 2 dom;II 2 þ ¼1 do;I do;II
(4)
where dom,i (i ¼ I, II) are the relative displacements in each mode corresponding to damage initiation. Crack propagation was simulated by the linear energetic criterion GI GII þ ¼1 GIc GIIc
(5)
The area under the minor triangle of Fig. 3 represents the energy released in each mode, while the bigger triangle area corresponds to the respective critical fracture energy. When Eq. (5) is satisfied damage propagation occurs and stresses are completely released, with the exception of normal compressive ones. Using the proposed criteria (Eqs. (4) and (5)), it is possible to define the equivalent mixed-mode displacements dom and dum, thus establishing the damage parameters in the softening region dm ¼
du;m ðdm do;m Þ dm ðdu;m do;m Þ
(6)
A detailed description of the model is presented in [13].
3. Model validation Experimental results of Quaresimin and Ricotta [11], concerning the tensile strength of CFRP single-lap joints with and without a 451 flat fillet at the overlap edges, were used to validate the numerical model presented in this work. The joint is constituted by autoclave-mounted laminates (Seals Texipreg CC206, T300 twill 2 2 carbon-fibre fabric/ET442 toughened epoxy matrix), bonded with the epoxy adhesive 3MTM 9323. A [0]6 lay-up was considered for the laminates. The laminates, adhesive and interface elements properties used in the numerical models are presented in Table 1. Due to insufficient available data on the materials properties, an inverse method was used in order to obtain the critical strain energies release rates (Gic) of the adhesive, assuming GIIc ¼ 2GIc. This method consisted on fitting the numerical and experimental failure loads for the square edge joint. The obtained adhesive properties are used in the filleted joint model to predict the respective strength improvement of this geometry, comparing with the square edge one. The joint geometry with the 451 flat fillet, including the boundary Table 1 Laminates, adhesive and interface elements mechanical properties Plates [11]
Adhesive [11]
Interface elements
E1 ¼ 58050 MPa E2 ¼ 58050 MPa G12 ¼ 3300 MPa n12 ¼ 0.06
E ¼ 2870 MPa n ¼ 0.37
GIc ¼ 0.6 N/mm GIIc ¼ 1.2 N/mm su,I ¼ 80 MPa su,II ¼ 47 MPa
Fig. 5. Interface finite elements loci in the joint.
conditions used to simulate the experiments, is presented in Fig. 4. Fig. 5 details the model including the 451 flat fillet at the overlap region, highlighting the interface finite elements loci. Several sites were considered, accounting for the different failure modes possible to occur. Three possible damage initiation locations (1, 2 and 3 in Fig. 5) and growth planes (lines 4, 5 and 6 in Fig. 5) were considered. In addition, extra interface elements were placed at both overlap edges, allowing for all failure onset/ propagation path combinations. Lines 4, 5 and 6 correspond to the lower adherend/adhesive interface, middle of the adhesive and adhesive/upper adherend interface, respectively. The model without the fillet (with square edges) includes interface elements only at lines 4, 5 and 6. Considering the filleted joint, damage initiation occurred experimentally within the fillets at a 451 angle, propagating to the adherend/adhesive interfaces (see indication in Fig. 5). The square edges joint experienced failure at the adherend/adhesive interface. Numerically, these failure modes were accurately reproduced. Fig. 6 shows the failure path predicted numerically for the filleted joint. Damage onset occurred within the adhesive fillet (location 2 in Fig. 5), propagating to the adherend/adhesive interfaces until complete separation of the laminates. Table 2 presents the failure loads for both geometries and the percentile strength improvement of the numerical analysis and the experimental results. Approximate 16% and 18% strength improvements were achieved using the fillet with the numerical and experimental analyses, respectively. These results show that the proposed numerical model reproduces accurately the behaviour of these joints.
4. Numerical analysis The following work consists on a two-dimensional numerical analysis of single- and double-lap repaired joints (Fig. 7) with different geometric changes. These geometries represent the repair of rectangular plates bonded with rectangular patches [15–19], or they can be considered as an approximation of a threedimensional repair [4,20]. In the second case, a composite plate is deemed to have suffered damage at an intermediate section. The damaged material is removed drilling a circular hole and one (single-lap) or two (double-lap) circular patches are bonded, concentric with the hole. It must be stressed that in this case some three-dimensional effects are not captured by the numerical models. Furthermore, the repair may still sustain loads after patch debonding [4]. A non-linear material and geometrical analysis was
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Fig. 6. Numerical failure path for the filleted joint.
Table 2 Comparison between numerical and experimental failure loads Failure load (N)
Experimental [11] Numerical
Without fillet
With fillet
Strength improvement (%)
13,777 13,714
16,192 15,860
17.5 15.6
Fig. 8. Numerical models simulating the single-lap (a) and double-lap (b) joints.
Fig. 7. Single-lap (a) and double-lap (b) joints.
performed, using plane strain rectangular eight-node finite elements. Interface finite elements were used to simulate crack onset and growth. The numerical idealizations of the single- and double-lap joints are presented in Fig. 8. Both geometries were modelled with symmetry conditions at the middle of the joint (line A in Fig. 8), thus considering only half the joint length. Additionally, double-lap joints were modelled using symmetry conditions at the plates mid-thickness (line B in Fig. 8). Boundary conditions included vertical restraining and an applied displacement at the joint edges (d in Fig. 8). At this stage, the authors establish the inner edge of the overlap (IEO) and outer edge of the overlap (OEO). Carbon–epoxy composite plates and patches were used. The mechanical properties of a unidirectional lamina are presented in Table 3 [13]. A ductile adhesive (Araldites 420) was used, whose elastic properties are se ¼ 8.325 MPa, E ¼ 1850 MPa and n ¼ 0.3. The respective stress–strain curve, obtained experimentally with tensile bulk tests [21], is presented in Fig. 9. The adhesive data was included in the numerical models for the
continuum elements representing the adhesive. The objective of using a ductile adhesive is to promote plastic yielding at the overlap edges (stress concentration regions), thus avoiding premature damage initiation at these regions, which would occur using a brittle adhesive. Therefore, the obtained results may only be valid for similar adhesives. General dimensions of the joints are presented in Table 4. (02,902)S and (04) lay-ups were considered for the plates and patches, respectively. The influence of different lay-ups on joint strength will be analysed further in this work. The following properties were used for the interface finite elements: GIc ¼ 0.3 N/mm, GIIc ¼ 0.6 N/mm, su,I ¼ su,II ¼ 40 MPa [13]. The location of the interface finite elements is shown in Fig. 10 (dashed lines) for the standard joint, without geometric changes. These elements were placed at the adhesive/patch and adhesive/ plate interfaces, at the middle of the adhesive thickness and, inside the plates, between differently orientated plies and between the two 01 plies closest to the adhesive layer. Additional interface elements were used according to the different geometric changes. The objective was to assess numerically the influence of the geometric changes on the tensile joint strength, as well as to evaluate the influence of crack onset location and growth path on this phenomenon. The joint strength (sC) is the ratio between the peak load and the plate cross-sectional area. Throughout this paper the joint strength (sC) is normalized to the strength of a joint with no geometric changes (s0).
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Table 3 CFRP unidirectional lamina mechanical properties CFRP unidirectional lamina mechanical properties E1 ¼ 1.09E+05 MPa E2 ¼ 8819 MPa E3 ¼ 8819 MPa
n12 ¼ 0.342 n13 ¼ 0.342 n23 ¼ 0.380
G12 ¼ 4315 MPa G13 ¼ 4315 MPa G23 ¼ 3200 MPa
50
the joint strength (0.25%), comparing to a standard joint. Bigger patch chamfers gradually decrease the joint strength. This behaviour is justified by the crack initiation locus. In fact, damage onset in these joints occurs at the IEO [13,21]. This modification at the OEO decreases load transfer at this region and increases stress concentrations at the IEO [21], gradually reducing the joint strength with the chamfer dimensions, although by a small amount. 4.1.2. Adhesive thickening To decrease peak peel stresses at the OEO, the adhesive thickness was increased at that region. Hu and Soutis [4] numerically proved that the peak shear strains at the end of the overlap diminish using this procedure. Fig. 12 represents a singlelap joint with a 0.4 mm adhesive thickening at the OEO. Only the 0.1 mm thickening rendered a slight increase of the joint strength (0.64%). Larger thickenings gradually decrease the joint strength. This geometric modification has a similar effect on the joint behaviour as the previous one, i.e., the softening introduced at the OEO decreases peel and shear stresses at that region, decreasing the load transfer and increasing stress concentrations at the IEO [23,24], which reduce the joint strength.
40
[MPa]
199
30 20 10 0 0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Fig. 9. Stress–strain curve of the adhesive Araldites 420.
Table 4 Plates, patches and adhesive dimensions Plates
Patches
Adhesive
Length: L ¼ 50 mm, width: b ¼ 15 mm Thickness: tP ¼ 1 mm
Thickness: tH ¼ 0.5 mm Overlap length: LC ¼ 10 mm
Thickness: tA ¼ 0.1 mm
Plates gap: e ¼ 5 mm
Fig. 10. Interface finite elements loci in the repaired joint.
4.1. Single-lap joints 4.1.1. Patch chamfer The objective of this modification is to decrease the peak peel stresses observed at the OEO [13,15], assessing the influence of this modification on the joint strength. Kaye and Heller [22] stressed that patch tapering spreads the load transfer more evenly between the plates and patches. A 1/10 slope was considered [4]. Patch thickness reductions of 0.1, 0.2, 0.3 and 0.4 mm were tested. Fig. 11 represents the single-lap joint standard configuration (a) and with a 0.4 mm patch thickness reduction (b). This nomenclature and slope are used throughout this work in all chamfers. No advantage exists in using this kind of modification, since only with a 0.1 mm patch chamfer it was observed a slight increase on
4.1.3. Plug filling with adhesive It is also possible to fill with adhesive the plates gap (e in Fig. 7), in order to increase the load transfer between the two plates. Soutis et al. [20] verified that the compressive strength of double-lap repairs increases plugging the specimen’s hole. The geometry is shown in Fig. 13 for the single-lap joint. Additional interface finite elements were placed at the plug/plate and plug/ patch interfaces. This change caused a 7% reduction on the joint strength, justified by the crack onset location, at the plate/plug interface, which, due to its instantaneous propagation nature, induced premature crack growth along the adhesive layer. Crack onset and growth process is presented in Fig. 14. To clarify this behaviour, the influence of the Young’s modulus of the plug adhesive on joint strength was evaluated. Fig. 15 presents the normalized joint strength for different values of plug adhesive Young’s modulus, ranging from 70 to +70% of the adhesive layer modulus. It is necessary to reduce by 70% the Young’s modulus of the plug adhesive to avoid a plug/plate interface failure prior to the adhesive layer failure, and a consequent strength reduction relatively to the standard geometry. Lower values of E for the plug were discarded, since the load transfer between the plug and the plates becomes minimal. 4.1.4. Fillets Using fillets at the patch ends (Fig. 16) was also investigated. This technique is widely considered to increase joint strength [1,2,23]. Additional interface finite elements were placed at the fillet/plate and fillet/patch interfaces. Geometry 1 represents the standard configuration; geometry 5 represents a flat fillet comprising all the patch thickness. Fig. 17 illustrates the joint strength as a function of the fillet geometry. An approximate 4% strength improvement was achieved using the geometry 5. A quadrangular fillet was considered (Fig. 18a), as well as a combination of a flat fillet with adhesive thickening (Fig. 18b–d). However, with these configurations a maximum increase of 3.5% on joint strength was achieved. 4.1.5. Plate chamfer Plate chamfering at the IEO was also evaluated. Plate outer chamfering (near the patch) and plate inner chamfering were considered. Boss et al. [6] analysed several types of plates geometrical grading and verified that both peak peel and shear
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Fig. 11. Single-lap joint standard configuration (a) and with a 0.4 mm patch outer chamfer (b).
Fig. 12. Single-lap joint with a 0.4 mm adhesive thickening.
Fig. 13. Single-lap joint with a plug filling (shaded region).
Fig. 14. Crack onset and growth for the plug filled repaired joint.
102 100
C/0 [%]
98 96 94 92 90 -80
-60
-40
-20
0 ΔE [%]
20
40
60
80
Fig. 15. Joint strength as function of the plug adhesive Young’s modulus (single-lap joint).
stresses were reduced at the plate edge, increasing the joint strength. In this work 0.1, 0.2 and 0.3 mm plate thickness reductions were considered for the patch outer chamfering (Fig. 19). Strength improvements of 0, 2.3 and 1% were obtained, respectively. Different inner chamfering dimensions were also evaluated (plate thickness reductions ranging from 0.1 to 0.7 mm), considering simultaneously a 0.2 mm outer chamfer (the most
efficient one). Fig. 20 represents 0.1, 0.4 and 0.7 mm inner chamfer joint geometries. Fig. 21 presents the joint strength as a function of the inner chamfer dimensions. A 23% strength improvement was obtained using a 0.6 mm plate inner chamfer combined with a 0.2 mm plate outer chamfer. This behaviour is justified by the significant plate stiffness reduction at the IEO, diminishing peel stresses at this region and delaying damage onset and growth. Fig. 22 illustrates this situation, comparing the chamfered joint with a standard one, under the same applied displacement. It is stressed that this particular result is valid only for the plate lay-up under analysis. In fact, it was observed that using the optimal inner and outer chamfering geometries, the plate section at the IEO is almost constituted by 901 plies, i.e., the 01 plies are removed by the considered chamfer geometries (Fig. 22). This modification renders the joint flexible enough to significantly reduce stress concentrations at this region, and consequently to increase the joint strength. The influence of the plate and patch lay-ups will be analysed in a subsequent section. 4.1.6. Geometry changes combination The most representative geometric changes were combined to maximize the joint strength (geometry 5 flat fillet, Fig. 16, which leads to a 4% strength improvement, and plate outer and inner chamfering with the optimal dimensions, which lead to a 23% strength improvement). Combining these two geometric changes (Fig. 23), a 26.8% strength improvement is obtained.
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201
Fig. 16. Single-lap joint with different fillet geometries.
104 adhesive thickening region in double-lap joints [22,25,26]. This occurrence decreases load transfer at the OEO, overloading the joint at the IEO, which justifies the observed behaviour.
C/0 [%]
102
100
98 1
2
3 Fillet geometry
4
5
Fig. 17. Joint strength as function of the fillet geometry (single-lap joint).
4.2. Double-lap joints 4.2.1. Patch chamfer For all double-lap joint analyses, the geometries were similar to the single-lap joint ones (using symmetry conditions, Fig. 8). No significant increase on the joint strength was obtained. Patch chamfers of 0.3 and 0.4 mm lead to 0.18% and 0.20% strength improvements, respectively, while the smaller ones do not present influence on the joint strength. Kaye and Heller [22] used an optimization procedure on double-lap joints to define the optimal patch chamfer geometry allowing reducing Von Mises equivalent stresses along the bond length. A preliminary study using a linear chamfer, similar to Fig. 11, led to a significant reduction of Von Mises stresses near the chamfer. Potter et al. [9] pointed a similar behaviour. Actually, this modification gradually decreases load transfer near the chamfer with its dimensions, whilst increasing stress concentrations at the crack initiation region (IEO), justifying the obtained results.
4.2.2. Adhesive thickening No strength improvement was observed thickening the adhesive at the OEO (only a 0.26% strength improvement was obtained with a 0.1 mm thickening). Besides, thickening the adhesive above 0.2 mm decreases the joint strength of a significant amount (a 0.4 mm adhesive thickening causes an approximate 3% joint strength reduction). It is known that this procedure reduces considerably stress concentrations near the
4.2.3. Plug filling with adhesive Using the double-lap repair procedure, plug filling highly increases the joint strength. With similar adhesive layer and plug mechanical properties, a 9% strength improvement was achieved. This disagrees with the results obtained for the single-lap joint, and is justified by the reduced bending in the double-lap joints, compared to the single-lap ones. Consequently, filling the plug with adhesive simply increases the load transfer between the two plates, without inconvenient. The influence of the plug adhesive Young’s modulus on the joint strength, considering the same range for DE as in single-lap joints, was evaluated (Fig. 24). It was observed that the joint strength is highly influenced by this parameter. In fact, changing this parameter never diminishes the joint strength relatively to a standard joint, in contrast to what occurs in the single-lap joints (Fig. 15). A smaller Young’s modulus for the plug adhesive leads to a reduced load transfer between the plug and the plate, and subsequently a minor increase on the joint strength. Using plug adhesives stiffer than the adhesive layer leads to a gradual decreasing of the joint strength. In fact, the plug adhesive/plate vertical interface begins to crack before crack growth at the adhesive layer, diminishing its influence on the joint strength. If the plug adhesive is too stiff (DEX50%), the joint strength remains unchanged, comparing to the standard joint, because the plug adhesive/plate vertical interface fails completely before damage onset in the adhesive layer. The correct choice of this parameter was DE ¼ 20%, corresponding to a strength improvement of 10%. This situation corresponds to the maximum value of E for the plug adhesive assuring that the plug adhesive/ plate crack occurs after the plate/patch debonding. 4.2.4. Fillets The same fillet geometries were evaluated (Figs. 16 and 18). Fig. 25 shows the normalized strength as a function of the geometry. The results are similar to single-lap ones, i.e., a 4% strength improvement was obtained using a geometry 5 flat fillet. The quadrangular fillet and combination of the geometry 5 flat fillet with adhesive thickening lead to strength improvements smaller than 0.4%. 4.2.5. Geometry changes combination Using the geometry 5 flat fillet and an optimized plug adhesive filling leads to a 11.9% strength improvement.
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Fig. 18. Single-lap joint with a quadrangular fillet (a) and combinations with fillet/adhesive thickening (b–d).
Fig. 19. Single-lap joint with a plate outer chamfering of 0.1 mm (a), 0.2 mm (b) and 0.3 mm (c).
Fig. 20. Single-lap joint with a plate inner chamfering of 0.1 mm (a), 0.4 mm (b) and 0.7 mm (c).
5. Influence of the plate and patch lay-ups on the joint strength The influence of the plate and patch lay-ups on the joint strength is analysed, for the single- and double-strap optimal solutions. For the single-strap geometry the plate lay-up has a
particular significance, since as mentioned earlier, the plate stiffness has a major influence on the joint strength. A more realistic approximation to the three-dimensional repair is obtained considering different patch lay-ups, allowing repairing the lost strength in the 901 direction. Table 5 represents a summary of the strength improvement relatively to the standard
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112
108 C/0 [%]
joint and maximum strength displacement (dC, Fig. 7) obtained with different plate and patch lay-up combinations. With the single-lap repair technique, combinations including 01 plies near the adhesive (1, 2 and 3) show a significant strength improvement (ranging from 21.8% to 26.8%), which depends on the plate and patch stiffness at the crack initiation region (IEO). Generally, increasing the plate stiffness decreases the joint strength, which is justified by the increase of stress concentrations caused by a less significant plate bending. Combination 4 leads to a 13.9% strength reduction, which is justified by the plate and patch bending stiffness reduction. This occurrence leads to a highly localized patch bending and a higher plate bending, which overload the adhesive at a very restricted region, thus diminishing the joint strength. Fig. 26 clarifies this behaviour, showing combinations 1 and 4 under a similar displacement (d in Fig. 7). Analysing the double-lap results, a significant difference is noticed between combination 1 and the remaining ones. Using lay-up combinations 2, 3 and 4, the vertical plug/plate interface fails prior to failure in the adhesive layer, thus not influencing the joint
203
104
100
96 -80
-60
-40
-20
0 E [%]
20
40
60
80
Fig. 24. Joint strength as function of the plug adhesive Young’s modulus (doublelap joint).
104 128
C/0 [%]
102
C/0 [%]
120
112
100
104 98 1
2
96 0
0.1
0.2 0.3 0.4 0.5 Plate thickness reduction [mm]
0.6
3 Fillet geometry
4
5
0.7 Fig. 25. Joint strength as function of the fillet geometry (double-lap joint).
Fig. 21. Joint strength as function of the plate inner chamfer dimensions (singlelap joint).
Fig. 22. Crack onset and growth for the standard joint (a) and the plate chamfered joint (b).
Fig. 23. Single-lap joint combining a flat fillet with plate chamfering.
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6. Influence of the plates gap (e) The following study assesses the influence of the plates gap (e, Fig. 7), which also simulates the hole diameter in the simplified analysis of the three-dimensional repair, on the strength of the single- and double-lap optimal solutions. This study arises from the need of considering different gaps, representative of varying damaged region dimensions, according to the characteristics of the damage imposed to the structure. Gaps of 0.5, 2.5, 5, 10, 15, 20 and 30 mm were evaluated. Fig. 27 shows the strength improvement and maximum strength displacement (dC, Fig. 7) as functions of the plates gap (e) for the single-lap (SL) and double-lap (DL) optimal solutions. A strength reduction is observed for the smaller plates gaps, for both single- and double-lap repair configurations. In the single-lap joint, this behaviour is justified by the significant increase of the peak shear stresses at the IEO for the smallest values of e. In the double-lap joint the observed strength reduction is caused by the smaller plug dimensions, which diminishes its compliance. This occurrence leads to a premature plate/plug vertical interface failure, prior to failure in the adhesive layer. In both configurations, a plateau is achieved for higher values of e. The maximum strength displacement gradually increases with the plates gap, because the joint length increases accordingly.
Table 5 Influence of lay-ups on the joint strength improvement and maximum strength displacement Combination
1
2
3
4
Plate lay-up Patch lay-up Single-lap
(02,902)S (04) 26.8% 0.389 mm 11.9% 0.330 mm
(02,902)S (02,902) 25.9% 0.436 mm 4.2% 0.383 mm
(08) (04) 21.8% 0.268 mm 4.5% 0.221 mm
(902,02)S (902,02) 13.9% 0.312 mm 4.2% 0.386 mm
Double-lap
7. Concluding remarks This work aimed to predict numerically the influence of geometric changes on the tensile strength of CFRP repairs. A numerical study was performed, using the ABAQUSs software and special developed interface elements. Interface elements allow locating crack onset and growth path for the different geometries. Prior to the numerical work description, a validation with the experimental results of Quaresimin and Ricotta [11] was accomplished. A good agreement was found with the numerical predictions of failure path and load. For the single-lap joint, a significant strength improvement (26.8%) was achieved filleting the patch ends and chamfering the outer and inner edges of the plates. Patch chamfering, adhesive thickening at the patch ends and plug filling, proved to reduce the strength of these joints. Using the double-lap repair technique, a significant strength improvement was observed using a flat fillet at the patch ends and plug filling the plates gap. Combining of these two leads to a 11.9% strength improvement. It was also proved that, using lower Young’s modulus for the plug adhesive, an increase on joint strength was obtained. Although the results presented in this paper may depend on materials properties, lay-ups and geometric parameters, it can be concluded that the models provide design guidelines in order to increase the residual strength of composite repairs.
130
0.6
125
0.5
120
0.4
115
0.3
110
0.2
105
C/0, SL
C/0, DL
C, SL
C, DL
C [mm]
strength. The strength improvement of approximately 4% is caused exclusively by the fillet. The maximum strength displacement (dC, Fig. 7) for all combinations presented in Table 5 is inversely proportional to the global plate and patch stiffness, which corresponds to the expected behaviour.
C/0 [%]
204
0.1 0
100 0
5
10
15 20 e [mm]
25
30
Fig. 27. Joint strength and maximum strength displacement as functions of the plates gap (e).
Fig. 26. Crack onset and growth for the combination one lay-up (a) and combination four lay-up (b) optimal solutions.
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Acknowledgements The authors thank the Portuguese Foundation for Science and Technology for supporting the work here presented, through the research project POCI/EME/56567/2004 and the individual grant SFRH/BD/30305/2006. References [1] Bogdanovich AE, Kizhakkethara I. Three-dimensional finite element analysis of double-lap composite adhesive bonded joint using submodeling approach. Compos Pt B 1999;30:537–51. [2] Tsai MY, Morton J. The effect of a spew fillet on adhesive stress distributions in laminated composite single-lap joints. Compos Struct 1995;32:123–31. [3] Rispler AR, Tong L, Steven GP, Wisnom MR. Shape optimization of adhesive fillets. Int J Adhes Adhes 2000;20:221–31. [4] Hu FZ, Soutis C. Strength prediction of patch repaired CFRP laminates loaded in compression. Compos Sci Technol 2000;60:1103–14. [5] Ganesh VK, Choo TS. Modulus graded composite adherends for single-lap bonded joints. J Compos Mater 2002;36(14):1757–67. [6] Boss JN, Ganesh VK, Lim CT. Modulus grading versus geometrical grading of composite adherends in single-lap bonded joints. Compos Struct 2003;62:113–21. [7] A´vila AF, Bueno PO. An experimental and numerical study on adhesive joints for composites. Compos Struct 2004;64:531–7. [8] Kim KS, Yoo JS, Yi YM, Kim CG. Failure mode and strength of uni-directional composite single-lap bonded joints with different bonding methods. Compos Struct 2006;72(4):477–85. [9] Potter KD, Guild FJ, Harvey MR, Wisnom MR, Adams RD. Understanding and control of adhesive crack propagation in bonded joints between carbon fibre composite adherends I experimental. Int J Adhes Adhes 2001;21:435–43. [10] Guild FJ, Potter KD, Heinrich J, Adams RD, Wisnom MR. Understanding and control of adhesive crack propagation in bonded joints between carbon fibre composite adherends, II: Finite element analysis. Int J Adhes Adhes 2001;21:445–53. [11] Quaresimin M, Ricotta M. Fatigue behaviour and damage evolution of singlelap bonded joints in composite material. Compos Sci Technol 2006;66: 176–87.
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