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Strength and damage growth in composite bonded joints with defects
Composites Part B 100 (2016) 91e100
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Composites Part B journal homepage: www.elsevier.com/locate/compositesb
Strength and damage growth in composite bonded joints with defects F.M.F. Ribeiro a, R.D.S.G. Campilho a, b, *, R.J.C. Carbas b, c, L.F.M. da Silva c ^nica, Instituto Superior de Engenharia do Porto, Instituto Polit nio Bernardino de Almeida, Departamento de Engenharia Meca ecnico do Porto, Rua Dr. Anto 431, 4200-072 Porto, Portugal b lo FEUP, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal INEGI e Po c ^nica, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal Departamento de Engenharia Meca a
a r t i c l e i n f o
a b s t r a c t
Article history: Received 13 February 2016 Received in revised form 28 April 2016 Accepted 13 June 2016 Available online 16 June 2016
The use of adhesive joints is increasing in various industrial applications because of their advantages such as weight reduction, reduction of stress concentrations and ease of manufacture. However, one of the limitations of adhesive joints is the difficulty in predicting the joint strength due to the presence of defects in the adhesive. This paper presents an experimental and numerical study of single-lap joints (SLJ) with defects centred in the adhesive layer for different overlap lengths (LO) and adhesives. The numerical analysis by cohesive zone models (CZM) included the analysis of the peel (sy) and shear (txy) stress distributions in the adhesive layer, the CZM damage variable study and the strength prediction. The joints’ behaviour was accurately characterized by CZM and showed a distinct behaviour as a function of the defect size, depending on the adhesive. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Carbon fibre Fracture toughness Mechanical testing Cohesive zone modelling
1. Introduction The use of adhesive joints is increasing in various industrial applications such as aeronautical, automotive and civil engineering [1e4] because of their advantages such as weight reduction, reduction of stress concentrations and ease of manufacture. One of the limitations of adhesive joints is the difficulty in predicting the joint strength due to the presence of defects in the adhesive. Defects are typically generated by the fabrication procedure, inadequate joint preparation, kissing bonds, micro-cracking, air bubbles, foreign bodies, grease, dirt or degradation due to the environment (e.g. humidity), reducing the joint quality and influencing the joint strength [1]. Actually, at the sites of these defects the loads are not transmitted between the structure’s components, and have to be transferred by the neighbouring portions of the adhesives, where stresses locally increase, thus reducing the joint strength [5]. An important issue is the understanding of the joint behaviour when these defects are present in a structural joint, and the knowledge of how a joint designed without taking into account these defects will behave when these defects appear. Thus, accurate tools must exist such that these effects are fully understood and a clear assessment
^nica, Instituto Su* Corresponding author. Departamento de Engenharia Meca cnico do Porto, Rua Dr. Anto nio perior de Engenharia do Porto, Instituto Polite Bernardino de Almeida, 431, 4200-072 Porto, Portugal. E-mail address: [email protected] (R.D.S.G. Campilho). http://dx.doi.org/10.1016/j.compositesb.2016.06.060 1359-8368/© 2016 Elsevier Ltd. All rights reserved.
can be made on whether a joint with a given defect can continue to operate or it must be repaired or replaced. Different experimental studies are available regarding joints with bondline defects [6e8]. Heslehurst [9] experimentally addressed the influence of debonds and weak bonds on the strength and durability of adhesivelybonded repairs, considering holography interferometry to spot the defect sites. This technique was effective in detecting the defects by variation of the fringe patterns near the zone with defect. Yang et al. [10] proposed an experimental non-destructive procedure based on vibration damping and frequency measurement to locate defects in adhesively-bonded joints between composite adherends. Llopart P et al. [11] used ultrasonic C-scan and X-ray imaging to inspect full adhesive spread to the bonding area of the joint. Tserpes et al. [12] also considered ultrasonic C-scan to detect defects in the adhesive layer of noncrimp fabric double-lap joints, and digital macrographs enabled concluding that the specimens failed in the adhesive by shear (debonding) and fracture of the composite boundary layer. The initial theoretical works regarding bonded joint bondline defects were based on the shear lag model, i.e., in which the adherends are purely axially loaded and the adhesive is solely under shear stresses. This is only applicable to joints in which no or only negligible bending exists [13e16]. In an early analytical study on the effect of bonding defects by Wang et al. [17], it was concluded that the strength of a SLJ bonded with a brittle two-part epoxy adhesive is ruled by the overlap ends. Thus, a bondline defect
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in an intermediate region of the joint does not alter significantly the strength. In a different work by the same authors [18], a ductile adhesive was used (low-density polyethylene) and, under these conditions, the sustained load by the joint is dictated by the bonded area without defect rather than by the overlap ends, because ductile adhesives have the ability to undergo plasticization before failure, which occurs with a more uniform state of stress in the bondline. Olia and Rossettos [19] proposed an analytical closedform analysis for SLJ with symmetrical and centred defects loaded in tension and/or bending, applicable to both isotropic and orthotropic adherends. It was concluded that sy and txy stresses are virtually unaffected by the void if it is sufficiently far from the overlap ends, while if the void is near to the overlap ends it will result in a significant effect on stresses, up to 25%. Berry and d’Almeida [7] considered the maximum load variations in composite SLJ by introducing circular centred defects in the adhesive layer, by analysing sy and txy stresses using a closed-form model. Whilst the average txy stress was not affected by the defect, the joint compliance highly increased with the defects. Chadegani and Batra [20] considered the first-order shear deformation theory to compute nodal displacements and stresses in bonded joints with interfacial cracks and defects, simplifying the analysis to linear elastic for the adherends and adhesive. A good agreement was found by comparing with the Finite Element Method (FEM). In contrast with theoretical techniques, numerical techniques are typically easier to work with and the associated simplifying assumptions many times mandatory to attain a solution are straightforward to deal with. The experimental and stress analysis (by the FEM) study of Pereira and de Morais [21] showed that the inclusion of defects at the overlap edges had little effect on the effective joint strength (averaged to the bonded area) for an adhesive with some degree of ductility. Ribeiro et al. [22] used the FEM to analyse the stress distributions in SLJ with different defect types and showed that defects at one of the adhesive layer’s edges were particularly harmful to the joints’ strength, oppositely to using centred defects in the adhesive layer, since the overlap ends remain the main zone for load transfer. You et al. [23] addressed by experimentation and the FEM adhesively-bonded double-lap joints with different gap lengths and different positions in the bondline (including centred defects). It was concluded that short length defects centred in the adhesive layer’s length do not significantly affect the joints’ strength because of the small disruption to stress distributions, oppositely to large size defects. Chow and Woo [24] used the FEM to assess the size and distribution effects of internal defects in bonded joints, revealing the major influence of these defects on txy stresses and maximum load (Pm) sustained by the joints. Karachalios et al. [5] studied the impact of rectangular and circular defects at the middle of the overlap on the strength of SLJ loaded in tension and four-point bending, considering different adhesives (brittle and ductile) and adherends (steel adherends: low strength/high ductility and high strength). Under tension and with a ductile adhesive, the joints’ strength depends on the type of steel: (1) high strength steel adherends lead to a practically linear reduction of Pm with the reduction of the effective bonded area and (2) for mild steel or medium carbon adherends small dimension defects have virtually no influence, while large-area defects significantly reduce the strength. Considering the brittle adhesive the behaviour is different: (1) for non-yielding adherends (highstrength steel) the strength reduction is not proportional to the defect size, which shows that the overlap ends rule the joints’ behaviour and (2) for yielding adherends the strength is dependent on overlap end-plasticization, which triggers premature failure by crack onset due to excessive strains. Under bending, it was found that the overlap ends govern failure in joints bonded with a ductile adhesive and high-strength steel adherends. CZM is particularly
recommended for bonded joints, since it clearly accounts for the coupling between tension and shear that occurs in the mixed-mode fracture of adhesive layers [25]. Several studies regarding the suitability of this technique and failure criteria/law types are available in the literature [26e28]. Serrano [29] used CZM modelling to simulate the effect of geometrical imperfections on the strength of bonded joints with different configurations between wood members. The softening laws in tension in shear developed for the adhesive layer included both the influence of the bulk adhesive and respective interfaces with the wood adherends. It was found that the sensitivity to geometrical imperfections in the tested joint configurations highly depends on the adhesive type. Ascione [30] used the CZM technique to test different CZM models to predict the strength of composite double-lap joints with defects, namely the models of Hutchinson & Suo, Xu & Needleman, and Camacho & Ortiz. It was found that the two latter models are more conservative than the model of Hutchinson & Suo. Xu and Wei [31] numerically studied the tensile strength of bonded joints with three types of defects: local debonding, weak bonding and voids. Local debonding and weak bonding were addressed by CZM implemented in user-defined sub-routines to account for the effect of the defect size and location. In the models for the void analyses, the Gurson-Tvergaard-Needleman model was used, enabling to account for the void size. Overall, the joints’ strength diminished by increasing the defect size, and the fracture properties of the weak adhesive revealed a major influence on the strength results when the weakly-bonded area is large. This paper presents an experimental and numerical study of SLJ with defects centred in the adhesive layer for different values of LO. The adhesives used were the brittle Araldite® AV138 and the ductile Sikaforce® 7752. The experimental part consisted of tensile testing different SLJ allowing to obtain the load-displacement (P-d) curves. The numerical analysis by CZM included the analysis of peel (sy) and shear (txy) stress distributions in the adhesive layer, the CZM damage variable study during the failure process and the CZM evaluation to predict the joint strength. The main innovations of the proposed work over the previously mentioned studies are related to the use of CZM for an integrated damage analysis/strength prediction and the assessment of the joints’ behaviour under different geometric (LO) and material conditions (adhesive type), which will enable selecting the best adhesive depending on the defect size and value of LO. 2. Experimental work 2.1. Materials characterization The composite adherends were fabricated from unidirectional carbon-epoxy pre-preg (SEAL® Texipreg HS 160 RM; Legnano, Italy) with 0.15 mm thickness by hand-lay-up of 20 unidirectional plies and curing in a hot-plates press for 1 h at 130 C and pressure of 2 bar. Table 1 provides the elastic-orthotropic properties of a unidirectional lamina for identical curing conditions [32]. The strong and brittle epoxy Araldite® AV138 and the less strong but ductile polyurethane Sikaforce® 7752 were evaluated. These adhesives were characterized in previous works regarding the Young’s (E) and
Table 1 Elastic orthotropic properties of a unidirectional carbon-epoxy ply aligned in the fibres direction (x-direction; y and z are the transverse and through-thickness directions, respectively) [32]. Ex ¼ 1.09E þ 05 MPa Ey ¼ 8819 MPa Ez ¼ 8819 MPa
nxy ¼ 0.342 nxz ¼ 0.342 nyz ¼ 0.380
Gxy ¼ 4315 MPa Gxz ¼ 4315 MPa Gyz ¼ 3200 MPa
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shear modulus (G), failure strengths in tension and shear (corresponding to the CZM cohesive strengths in tension (t0n) and shear (t0s )) and values of fracture toughness in tension (Gcn) and shear (Gcs) [26,33]. The tensile data was estimated by bulk tests to dogbone shape specimens, while the relevant shear properties were obtained from Thick Adherend Shear Tests (TAST). For more details see Ref. [34]. Gcn and Gcs for the AV138 were previously derived by inverse techniques [33]. For the 7752, Gcn was determined by Double-Cantilever Beam (DCB) tests and Gcs by End-Notched Flexure (ENF) tests [35]. Table 2 summarizes all collected mechanical and fracture properties (Table 3 presents the cohesive parameters used in the numerical models, derived from the data of Table 2). 2.2. Joint dimensions, fabrication and testing The geometry and dimensions of the SLJ are described in Fig. 1. The joint dimensions are: plate thickness tP ¼ 3 mm, adhesive thickness tA ¼ 0.2 mm, LO ¼ 25 and 50 mm, and length between grips LT ¼ 170 mm. For both LO values, centred defects in the bondline were evaluated with 25, 50 and 75% of LO (Fig. 2). The composite plates were fabricated as described in Section 2.1 and cut into specimens in a diamond disc cutter. Initially the adherends were manually abraded at the bonding surfaces with fine mesh sandpaper. The specimens were subsequently placed in a steel mould to ensure the proper alignment, and 25 mm thick Teflon® strips were wrapped around the adherends, secured with adhesive tape, and property positioned before pouring the adhesive with a spatula. Concurrently, calibrated spacers were used to provide the chosen tA value, which had a nearly perfect quadrilateral crosssection and were properly coated with demoulding agent to guarantee an easy extraction. After applying this process to all specimens in the mould, it is closed and curing takes place at room temperature for one week. Finally, tabs were glued at the specimens’ edges for a correct alignment in the testing machine. Tensile testing was undertaken in an Instron® 3367 (Norwood, MA, USA) electro-mechanical testing machine with a load cell of 30 kN, at room temperature and velocity of 0.5 mm/min. Five specimens were tested for each LO/adhesive type combination. 3. Numerical work 3.1. Modelling conditions The joints were modelled in Abaqus® with geometrical nonlinearities to account for the rotational effects induced by the load eccentricities [36]. The two-dimensional models were meshed with 4-node plane-strain elements (CPE4 from Abaqus®) for the
Table 2 Properties of the adhesives Araldite® AV138 and Sikaforce® 7752 [26,33,35]. Property
AV138
7752
Young’s modulus, E [GPa] Poisson’s ratio, n Tensile yield stress, se [MPa] Tensile failure strength, sf [MPa] Tensile failure strain, εf [%] Shear modulus, G [GPa] Shear yield stress, te [MPa] Shear failure strength, tf [MPa] Shear failure strain, gf [%] Toughness in tension, Gcn [N/mm] Toughness in shear, Gcs [N/mm]
4.89 ± 0.81 0.35a 36.49 ± 2.47 39.45 ± 3.18 1.21 ± 0.10 1.56 ± 0.01 25.1 ± 0.33 30.2 ± 0.40 7.8 ± 0.7 0.20b 0.38b
0.49 ± 0.09 0.30a 3.24 ± 0.48 11.48 ± 0.25 19.18 ± 1.40 0.19 ± 0.01 5.16 ± 1.14 10.17 ± 0.64 54.82 ± 6.38 2.36 ± 0.17 5.41 ± 0.47
a b
Manufacturer’s data. Estimated in Ref. [33].
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Table 3 Cohesive parameters of the adhesives Araldite® AV138 and Sikaforce® 7752 for CZM modelling. Property
AV138
7752
E [GPa] G [GPa] t0n [MPa] t0s [MPa] Gcn [N/mm] Gcs [N/mm]
4.89 1.56 39.45 30.2 0.20 0.38
0.49 0.19 11.48 10.17 2.36 5.41
adherends and COH2D4 4-node cohesive elements for the adhesive [37]. The adherends were modelled as elastic-orthotropic due to the absence of plastic effects [38], using the properties of Table 1. The stress analysis in the bondline was performed by continuumbased finite elements throughout, while in the damage variable and strength analyses CZM elements were considered in the adhesive layer. Another difference between these analyses is the mesh refinement, since the stress analysis is considerably more refined such that the stress gradients at the overlap and defect edges are accurately captured. The continuum elements’ size at the overlap edges is 0.02 0.02 mm for all LO values, although the number of elements across the overlap varied with LO. This promotes a higher precision of calculated strains and stresses at these areas with high stress variations. The mesh for the damage variable and strength analyses is coarser but without compromising the validity of the obtained results. The CZM elements’ size at the overlap edges was 0.2 0.2 mm for all LO values, again with a varying number of elements across the overlap depending on LO. Size grading effects were used throughout the models: in the vertical direction towards the adhesive layer and horizontally towards the adhesive layers’ edges, such that a higher refinement is present at these regions [39,40]. Fig. 3 gives an example of mesh detail at the overlap for the stress and strength (CZM) analyses for a non-defective joint with LO ¼ 25 mm. For the defective joints the models are identical, with the particularity that the horizontal mesh grading effects are such that they are oriented towards both the overlap edges and the defect edges within the bondline, to account for eventual stress concentration regions at these sites. The continuum modelling approach was used for damage growth in the adhesive layer, i.e., considering a single row of CZM elements through-thickness in the adhesive layer [41] and employing the triangular CZM described next in Section 3.2. The boundary conditions consisted of clamping one of the model edges, and applying a vertical restraint and tensile displacement at the other edge. 3.2. CZM model CZM are based on a relationship between stresses and relative displacements connecting homologous nodes of the cohesive elements (Fig. 4), to simulate the elastic behaviour up to a peak load and subsequent softening, to model the gradual degradation of material properties up to complete failure [42]. The areas under the traction-separation laws in each mode of loading (tension and shear) are equalled to Gcn or Gcs. Under pure mode, damage propagation occurs at a specific integration point when the stresses are released in the respective traction-separation law. Under mixed mode, energetic criteria are often used to combine tension and shear [43]. The traction-separation law assumes an initial linear elastic behaviour followed by linear evolution of damage. The elastic behaviour of the cohesive elements up to the tipping tractions is defined by an elastic constitutive matrix relating stresses and strains across the interface, containing E and G as main parameters. Damage initiation under mixed-mode can be specified by
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Fig. 1. Geometry and dimensions of the single-lap joints: LO ¼ 25 (a) and 50 mm (b).
Fig. 2. Layout of the defects in the joints: LO ¼ 25 (a) and 50 mm (b).
Fig. 3. Mesh detail at the overlap for the stress and strength (CZM) analyses for a non-defective joint with LO ¼ 25 mm.
different criteria. In this work, the quadratic nominal stress criterion was considered for the initiation of damage. After the peak value in Fig. 4 is attained (t0m), the material stiffness is degraded. Complete separation is predicted by a linear power law form of the required energies for failure in the pure modes. For full details of this model, the reader can refer to reference [44].
4. Results and discussion 4.1. Stress analysis during the elastic behaviour
Fig. 4. Traction-separation law with linear softening law available in ABAQUS®.
sy and txy stresses at the adhesive layer’s mid-thickness are considered during the elastic regime of loading. sy and txy stresses are normalized over the average shear stress (tavg) for the respective LO value and joint without defect. A similar normalization
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procedure was performed for LO (x/LO), where x is the distance from the left edge of the adhesive layer. The plot range is then given by 0 x/LO 1. In this study, only figures for LO ¼ 25 mm are presented, although the discussion is extended to both LO values. Fig. 5 shows the txy/tavg stress distributions for the joints bonded with the AV138 (a) and the 7752 (b) without and with defect (LO ¼ 25 mm). In all cases, txy stresses are lower at the inner part of the adhesive layer, peaking at the overlap ends [45,46]. This behaviour is due to differential deformation of the adherends [47]. For the AV138 (Fig. 5 a), the increase of the % defective area increases the normalized peak values of txy (with a minimum variation up to a % defective area of 50%). By increasing the defect size, peak txy stresses at the inner discontinuities (adjacent to the defect) approach the peak value at the overlap ends. txy stress gradients increase with LO (the maximum values of txy/tavg, for the joints with 75% defect, increased from z5 to z7 from LO ¼ 25 to 50 mm), due to the increasing gradient of longitudinal deformation in the adherends for large overlaps [41]. For the 7752 (Fig. 5 b), the overall behaviour is identical to that of the AV138, although with lower gradients due to the lower adhesive stiffness (the maximum value of txy/tavg, for LO ¼ 50 mm and 75% defect, decreased from z7.0 to z4.2). For higher LO values, there is a slight increase in txy/ tavg near the adhesive ends, as previously described for the joints bonded with the AV138. Fig. 6 depicts the sy/tavg stress distributions for the joints bonded with the AV138 (a) and the 7752 (a) for LO ¼ 25 mm. All stress plots show sy peel regions at the overlap ends and compressive zones in-between. This effect is related to the adherends’ rotation under loading, which causes separation at the overlap ends and compression in-between [37]. For the AV138 (Fig. 6 a), sy stress gradients increase with the % defective area, although negligibly up to 50%. sy compressive stresses near the defect increase with the % defective area. Higher LO values (50 mm) promote higher magnitude sy peak stresses near the singularities of the joint (for 75% defect, the maximum value of sy/tavg increased from z8.5 to z11.3 by changing LO ¼ 25 to 50 mm). sy compressive stresses in the inner part of the adhesive layer become less significant. The 7752 (Fig. 6 b) results in smaller normalised sy peak stresses compared to the AV138 due to its more compliant nature (the value maximum value of sy/tavg, for 75% defect, decreased from z11.3 to z4.8). With the increase in the % defective area, sy compressive stresses within the adhesive quickly approach the tensile value. Larger LO values promote higher sy peel peak stresses at the overlap ends (the maximum value of sy/tavg increased from z3.1 to z4.8 by varying LO from 25 to 50 mm). As discussed for the AV138, sy compressive stresses at the inner part of the adhesive layer become less significant. Fig. 7 summarizes the peak normalized txy (a) and sy stresses (b)
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at the overlap edges as a function of the defective area (%) considering both tested adhesives and LO values. For both LO values and all defect sizes, the joints bonded with the AV138 revealed higher peak txy/tavg and sy/tavg stresses than with the 7752 because of the higher E. On the other hand, the joints with LO ¼ 50 mm always showed higher peaks of txy/tavg (because of more significant differential deformation effects) and sy/tavg (on account of high joint rotations due to the higher loads). This should be responsible for a reduced Pm improvement for the joints bonded with the AV138 and LO ¼ 50 mm over LO ¼ 25 mm, since this brittle adhesive cannot undergo plasticization when the peak stresses are attained. On the contrary, the 7752 is not prone to be significantly affected by the increase of peak stresses due to its highly ductile nature. The evolution of txy/tavg and sy/tavg with the % defective area reinforces the previous statement that a relevant increase only occurs between 50 and 75%. In view of this, the joints with the AV138 would not be affected by a large amount by defects up to 50%, since brittle adhesives’ failure is governed by peak stresses. Oppositely, Pm for the joints with the 7752 should not be affected by peak stresses but by the bonded area, since this adhesive is highly ductile. 4.2. Damage growth analysis The analysis of the damage parameter or SDEG (stiffness degradation) of the CZM elements provides a detailed perception of the failure process during loading. This variable gives the stiffness degradation of the mixed mode CZM law (Fig. 4) and varies between SDEG ¼ 0 (undamaged material) and SDEG ¼ 1 (complete failure). The figures presented here only relate to LO ¼ 25 mm, although a descriptive comparison is made with LO ¼ 50 mm. Fig. 8 shows the damage variable in the adhesive layer at the instant Pm is attained for the joints with LO ¼ 25 mm and the AV138 (a) and 7752 (b). The damage state for the AV138 (Fig. 8 a) shows that increasing the % defect reduces the damaged portion at Pm, which is related to the increase of stress gradients towards the overlap ends (Fig. 5 (a) for txy and Fig. 6 (a) for sy stresses) leading to concentration of damage in smaller areas. Higher LO values, i.e., 50 mm, result in an identical behaviour, although with a lesser difference between curves because of aggravated stress gradients for all joint configurations. The 7752 (Fig. 8) promotes a more uniform spread of the variable damage throughout the bonding zone. For example, for the non-defective joints, SDEG ranges between z0.08 in the middle overlap to z0.47 at the overlap ends. Increasing the % defective area, the SDEG values at Pm decrease because of reduction of stress gradients resulting from the smaller bonded areas (Fig. 5 (b) for txy and Fig. 6 (b) for sy stresses). The joints with LO ¼ 50 mm showed in general higher SDEG values at Pm at the overlap ends (SDEG z 0.63
Fig. 5. Normalized txy stress distributions at the adhesive mid-thickness as a function of the defective area (%) for the joints bonded with the Araldite® AV138 (a) and Sikaforce® 7752 (b).
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Fig. 6. Normalized sy stress distributions at the adhesive mid-thickness as a function of the defective area (%) for the joints bonded with the Araldite® AV138 (a) and Sikaforce® 7752 (b).
Fig. 7. Peak normalized txy (a) and sy stresses (b) at the overlap edges as a function of the defective area (%) for the joints bonded with the Araldite® AV138 and Sikaforce® 7752 and LO ¼ 25 and 50 mm.
Fig. 8. Damage variable in the adhesive layer at the instant Pm is attained for the joints with LO ¼ 25 mm and the adhesive Araldite® AV138 (a) and Sikaforce® 7752 (b).
for the non-defective joint) because of the higher stress gradients. Fig. 9 represents the evolution of SDEG in the adhesive with d/ dPm (%) for the joints bonded with the AV138 and no defect (a) and 75% defect (b), in which d is the current displacement and dPm is the displacement at Pm (d/dPm ¼ 100% regards Pm). Increasing ratios of d/dPm are compared, from damage initiation till failure. Joints with 25% and 50% defective area have an intermediate behaviour between the joints reported here. Disregarding the % defect, in all joints bonded with the AV138 the SDEG value varies between 0 and 1 in a reduced extent, which results in a very small damage zone, while most of the bonded length does not significantly contribute to the joints’ strength. Complete failure occurs very rapidly for all joint configurations (between d/dPm ¼ 100% and 103.6% for
LO ¼ 25 mm and without defect and between 100% and 100.6% for LO ¼ 25 mm and with 75% defective joint). In the joints with LO ¼ 50 mm, d/dPm at complete joint failure is smaller (between d/ dPm ¼ 100% and 101.8% for LO ¼ 25 mm and without defect and 100% and 100.4% for LO ¼ 25 mm and with 75% defective joint) because of the higher stress variations in the bondline [37]. Fig. 10 is a similar analysis to Fig. 9 but with the 7752. Because of the adhesive’s ductility, the SDEG variation is much more gradual. The damage process initiates at the overlap ends and grows towards the inner overlap till failure. The smoother stress distributions, compared to the AV138, and the ductility of this adhesive justify the high values of d/dPm at failure (for example 437.5% for the nondefective joint with LO ¼ 25 mm). Equally to the reported for the
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Fig. 9. Evolution of the damage variable in the adhesive layer with d/dPm (%) for the joints bonded with the Araldite® AV138 and no defect (a) and 75% defect (b).
Fig. 10. Evolution of the damage variable in the adhesive layer with d/dPm (%) for the joints bonded with the Sikaforce® 7752 and no defect (a) and 75% defect (b).
brittle adhesive, increasing LO to 50 mm reduces this value (d/ dPm ¼ 308.8% for the non-defective joint), due to the larger stress gradients. Although not showed here, the damage variable has higher gradients for LO ¼ 50 mm than for 25 mm, because of higher variations in the stress distributions. On the other hand, for this adhesive d/dPm at complete failure increases with the % defective area (for example, for LO ¼ 25 mm, d/dPm at failure increases from 437.5% e non-defective joint e up to 996.2% e 75% defective joint), because of the allowable plasticization with this adhesive. 4.3. Failure modes All experimental and numerical failures for both adhesives were fully cohesive in the adhesive layer. Fig. 11 shows as an example representative failure surfaces for each joint configuration with the 7752 (LO ¼ 25 mm). Fig. 12 depicts the damage variable at Pm for the non-defective (a) and 75% defect (b) joint bonded with the AV138
and LO ¼ 25 mm, showing the small amount of softening that this adhesive sustains prior to failure (and diminishing with the % defective area). On the other hand, for the 7752, the entire or almost all the bonded region is under softening at Pm, reinforcing the idea that the joints bonded with this adhesive fail under conditions proximal to global yielding. 4.4. Load-displacement (P-d) curves Two examples are presented regarding the general correlation between the experimental and numerical P-d curves obtained in this work (Fig. 13): non-defective joints bonded with the AV138 and LO ¼ 25 mm (a), and 75% defect joints bonded with the 7752 and LO ¼ 50 mm (b). The general correlation was quite acceptable for all joints with the AV138 in which regards to the initial stiffness, Pm and dPm, although in few of the experiments some slip of the specimens occurred. The CZM results for the 7752 consistently
Fig. 11. Representative experimental failure for each joint configuration bonded with the Sikaforce® 7752 (LO ¼ 25 mm).
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Fig. 12. Damage variable at Pm for the non-defective (a) and 75% defect (b) joint bonded with the Sikaforce® 7752 and LO ¼ 25 mm.
Fig. 13. Experimental and numerical (CZM) P-d curves for the non-defective joints bonded with the Araldite® AV138 and LO ¼ 25 mm (a) and for the 75% defect joints bonded with the Sikaforce® 7752 and LO ¼ 50 mm (b).
under predicted the experiments, although the difference is not too significant, as it is visible in the example of Fig. 13 (b). This difference in Pm will be discussed in more detail in the following Section. Apart from Pm, also the P-d curves’ shape and correspondingly dPm
vary by a significant amount. However, this deviation results from numerical limitations associated to using a triangular CZM shape to model a very compliant and ductile adhesive. Under these conditions, the predicted P-d curve closely follows the assumed CZM law
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shape, instead of having an abrupt failure as it occurs in the experiments. 4.5. Joint strength Fig. 14 provides a comparison between the experimental and numerical values of Pm for all joint configurations and the AV138 (a) and 7752 (b). A distinct behaviour between adhesives is found regarding the influence of the defect size. Actually, Pm for the AV138 is only significantly affected by large defect sizes (75% defect). As a result, up to this dimension, the overall joint’s behaviour is not meaningfully affected by centred defects in the bondline. This behaviour is linked to the variation of sy and txy peak stresses at the crack onset regions, i.e., the overlap edges, with the defect dimensions. In fact, only for 75% defective area do txy (Fig. 5 (a) and Fig. 7 (a)) and sy peak stresses (Fig. 6 (a) and Fig. 7 (b)) change by a relevant amount. Thus, because of the adhesive’s brittleness and resulting lack of plasticization ability, these peak stress govern the failure process of the joints. Corroborating this assumption, in the SDEG analysis it was initially found that, at Pm, the joints bonded with the AV138 concentrated the damage in a small region at the overlap edges and with an abrupt variation (Fig. 8 a). Moreover, complete failure is attained for a very small value of d/dPm over 100%, because of the absence of plasticization [37]. Regarding the joints’ behaviour with the increase of % defective area, the value of d/dPm at failure diminished significantly for 75% defect (Fig. 9) because of the increase of stress concentrations and inability of the AV138 to accommodate these peak stresses. These issues reinforce the brittle nature of the failure process. The 7752 results in a completely different behaviour, since Pm decreases almost linearly and proportionally with the increase in the % defect. This behaviour results from a combination of two factors: (1) more uniform distribution of txy (Fig. 5 (b) and Fig. 7 (a)) and sy stresses (Fig. 6 (b) and Fig. 7 (b)) on account of the adhesive’s flexibility and (2) plasticization capability, causing levelling of stresses at the bonded portions of the bondline. Thus, the Pm values directly reflect the reduction of the bonded area by increasing the % defective area. In the damage analysis it was shown that this adhesive enables spreading the damage through a large portion of the joint at Pm, reinforcing the failure occurring by global yielding (Fig. 8 b). Moreover, increasing values of d/dPm at failure were found with growing % defects (Fig. 10), which is indicative of a marked degree of plasticization. The effect of increasing LO from 25 to 50 mm is also dependent on the type of adhesive. The Pm values for the joints bonded with the AV138 increased between 33.0% (non-defective joint) and 67.8% (75% defective area), while for the joints bonded with the 7752 the improvement was between 88.1% (non-defective joint) and 100.1% (75% defective area). The AV138 has a smaller Pm improvement
99
with LO because of the increase of stress concentrations at the overlap ends for higher LO values (Fig. 7), which are not accommodated by the adhesive’s brittleness [44]. On the other hand, the ductile nature of the 7752 enables it to undergo global yielding in the adhesive layer, resulting in almost duplicating or even exceeding Pm by doubling LO [37]. Although not shown here, the damage variable analysis revealed damage spreading in a more confined region for the joints bonded with the AV138 when increasing LO from 25 to 50 mm, which is consistent with the aforementioned small % Pm improvement. On the other hand, for the joints bonded with the 7752, damage extended across the entire bonded region. In view of the exposed behaviours, by comparing the two adhesives, for the non-defective joints Pm is higher for the 7752 than the AV138 by 14.1% (LO ¼ 25 mm) and 61.3% (LO ¼ 50 mm). Despite the higher strength of the AV138, the 7752 has a higher ductility, which is prevalent in these joints. Moreover, this difference is bigger for LO ¼ 50 mm since this adhesive is little affected by the peak stresses that limit the strength of the AV138 for big overlaps. On the other hand, with the increase of % defective area, the AV138 gradually gains advantage over the 7752 (up to 34.8% for LO ¼ 25 mm and 22.3% for LO ¼ 50 mm, in both cases for 75% defect). This is caused by the almost linear Pm reduction for the 7752 with the % defect (failure near to global yielding conditions), while the AV138 at Pm concentrates stresses at the overlap ends, thus not being so much affected by the centred defects (especially up to 50% defective area). The CZM predictions showed different results between the joints bonded with the AV138 and the 7752. The maximum percentile deviations between the simulations and the experimental values for each adhesive were 7.2% for the AV138 (nondefective joints with LO ¼ 50 mm) and 25.7% for the 7752 (75% defect joints with LO ¼ 50 mm). Fairly accurate results were obtained for the AV138 by using a triangular CZM law to model the adhesive layer because of its brittleness, which is accurately modelled by a CZM law that undergoes softening in the constitutive response when Pm is attained [26]. For the 7752 the CZM results consistently under predicted the experiments for all tested geometries. This behaviour originated from the high ductility of the adhesive, which is not adequately modelled by a triangular CZM law [37]. In fact, for adhesives that experience a large ductility as it is the case of the 7752, the transmitted stresses across the adhesive are kept at high levels after the adhesive’s tensile yield stress (se) is attained first at the overlap edges. Moreover, at Pm, a significant part of the overlap is exceeding se (Fig. 8 (a) and Fig. 10). However, by using a triangular CZM law (Fig. 4), stress softening occurs after attaining t0m, which invariably results in a Pm under prediction [26]. In this case, the simulations only provide an approximate idea of Pm and how it evolves with the % increase of the defect. To obtain more accurate results, trapezoidal CZM laws could be considered instead,
Fig. 14. Experimental/numerical comparison of Pm values as a function of the defective area (%) for the Araldite® AV138 (a) and Sikaforce® 7752 (b).
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since these account for the adhesive’s plasticization without softening [36]. 5. Concluding remarks This work aimed at studying the effect of % defective area, value of LO and adhesive type on the tensile strength of SLJ. The obtained results were highly dependent on the adhesive type. The AV138, by being brittle and stiff, revealed high stress concentrations and inability to undergo plasticization after the limiting stresses are attained. Oppositely, the 7752 is more flexible, which resulted in smaller stress gradients. Moreover, its ductility enabled failure conditions close to global yielding and corresponding higher Pm values for the non-defective joints. Higher LO values increase the difference between the two adhesives (especially for the nondefective joints). The presence of centred defects in the adhesive layer has a bigger effect for the joints bonded with the 7752 than the AV138 (average experimental Pm reduction from the nondefective to the 75% defective joints of 51.8% for the AV138 and of 72.4% for the 7752). Actually, the joints bonded with the 7752 fail under global yielding conditions, such that Pm decreases practically linearly with the reduction of bonded area. On the other hand, the joints bonded with the AV138 have a brittle failure as soon as the limiting adhesive stresses are reached at the overlap ends. Thus, the presence of a defect centred in the adhesive layer (typically lightly loaded) is not so preponderant for the joints’ strength. These effects were described in detail in light of stress and damage variable analyses. The CZM predictive technique was accurate in predicting the strength of the joints bonded with the AV138 (maximum difference to the experiments of 7.2%), although under predicting Pm for the joints bonded with the 7752 (maximum deviation of 25.7%). Actually, due to the high ductility of this adhesive, the trapezoidal CZM laws would provide a better approximation. As design guidelines, the obtained results indicate that, for both small and large overlaps, non-defective joints work better with ductile and lower strength adhesives, while joints with large % of defects have higher Pm values with stronger although brittle adhesives. References [1] Mancusi G, Ascione F. Performance at collapse of adhesive bonding. Compos Struct 2013;96:256e61. [2] Dai J, Ueda T, Sato Y. Development of the nonlinear bond stresseslip model of fiber reinforced plastics sheeteconcrete interfaces with a simple Method. J Compos Constr 2005;9(1):52e62. [3] Higgins A. Adhesive bonding of aircraft structures. Int J Adhes Adhes 2000;20(5):367e76. [4] Jia Z, Yuan G, Ma H-L, Hui D, Lau K-T. Tensile properties of a polymer-based adhesive at low temperature with different strain rates. Compos Part B 2016;87:227e32. [5] Karachalios EF, Adams RD, da Silva LFM. Strength of single lap joints with artificial defects. Int J Adhes Adhes 2013;45:69e76. [6] Engerer JD, Sancaktar E. The effects of partial bonding in load carrying capacity of single lap joints. Int J Adhes Adhes 2011;31(5):373e9. [7] Berry NG, d’Almeida JRM. The influence of circular centered defects on the performance of carboneepoxy single lap joints. Polym Test 2002;21(4): 373e9. [8] Park J-H, Choi J-H, Kweon J-H. Evaluating the strengths of thick aluminum-toaluminum joints with different adhesive lengths and thicknesses. Compos Struct 2010;92(9):2226e35. [9] Heslehurst RB. Observations in the structural response of adhesive bondline defects. Int J Adhes Adhes 1999;19(2e3):133e54. [10] Yang S, Gu L, Gibson RF. Nondestructive detection of weak joints in adhesively bonded composite structures. Compos Struct 2001;51(1):63e71. [11] Llopart P LI, Tserpes KI, Labeas GN. Experimental and numerical investigation of the influence of imperfect bonding on the strength of NCF double-lap shear joints. Compos Struct 2010;92(7):1673e82. [12] Tserpes KI, Pantelakis S, Kappatos V. The effect of imperfect bonding on the pull-out behavior of non-crimp fabric Pi-shaped joints. Comput Mater Sci 2011;50(4):1372e80. [13] Hart-Smith LJ. Further developments in the design and analysis of adhesivebonded structural joints. ASTM STP 1981;749:3e31.
[14] Kan HP, Ratwani M. Stress analysis of stepped-lap joints with bondline flaws. J Aircr 1983;20(10):848e52. [15] Rossettos JN, Lin P, Nayeb-Hashemi H. Comparison of the effects of debonds and voids in adhesive joints. J Eng Mater Tech 1994;116(4):533e8. [16] Rossettos JN, Zang E. On the peak shear stresses in adhesive joints with voids. J Appl Mech 1993;60(2):559e60. [17] Wang TT, Ryan FW, Schonhorn H. Effect of bonding defects on shear strength in tension of lap joints having brittle adhesives. J Appl Polym Sci 1972;16(8): 1901e9. [18] Schonhorn H, Ryan FW, Wang TT. Effects of symmetrical bonding defects on tensile shear strength of lap joints having ductile adhesives. J Appl Polym Sci 1971;15(5):1069e78. [19] Olia M, Rossettos JN. Analysis of adhesively bonded joints with gaps subjected to bending. Int J Solids Struct 1996;33(18):2681e93. [20] Chadegani A, Batra RC. Analysis of adhesive-bonded single-lap joint with an interfacial crack and a void. Int J Adhes Adhes 2011;31(6):455e65. [21] Pereira AB, de Morais AB. Strength of adhesively bonded stainless steel joints. Int J Adhes Adhes 2003;23(4):315e22. [22] Ribeiro FL, Borges L, d’Almeida JRM. Numerical stress analysis of carbon-fibrereinforced epoxy composite single-lap joints. Int J Adhes Adhes 2011;31(5): 331e7. [23] You M, Yan Z-M, Zheng X-L, Yu H-Z, Li Z. A numerical and experimental study of gap length on adhesively bonded aluminum double-lap joint. Int J Adhes Adhes 2007;27(8):696e702. [24] Chow CL, Woo CW. On flaw size and distribution in lap joints. Theor Appl Fract Mec 1985;4(1):75e82. [25] Nunes SLS, Campilho RDSG, da Silva FJG, de Sousa CCRG, Fernandes TAB, Banea MD, et al. Comparative failure assessment of single and double-lap joints with varying adhesive systems. J Adhes 2016;92:610e34. [26] Campilho RDSG, Banea MD, Neto JABP, da Silva LFM. Modelling adhesive joints with cohesive zone models: effect of the cohesive law shape of the adhesive layer. Int J Adhes Adhes 2013;44:48e56. [27] Ascione F, Mancusi G. Axial/bending coupled analysis for FRP adhesive lap joints. Mech Adv Mater Struct 2010;17(2):85e98. [28] Ascione F, Mancusi G. Failure criteria for FRP adhesive lap joints: a comparative analysis. Mech Adv Mater Struct 2010;17(2):157e64. [29] Serrano E. A numerical study of the shear-strength-predicting capabilities of test specimens for woodeadhesive bonds. Int J Adhes Adhes 2004;24(1): 23e35. [30] Ascione F. The influence of adhesion defects on the collapse of FRP adhesive joints. Compos Part B 2016;87:291e8. [31] Xu W, Wei Y. Strength analysis of metallic bonded joints containing defects. Comput Mater Sci 2012;53(1):444e50. [32] Ribeiro TEA, Campilho RDSG, da Silva LFM, Goglio L. Damage analysis of compositeealuminium adhesively-bonded single-lap joints. Compos Struct 2016;136:25e33. [33] Campilho RDSG, Banea MD, Pinto AMG, da Silva LFM, de Jesus AMP. Strength prediction of single- and double-lap joints by standard and extended finite element modelling. Int J Adhes Adhes 2011;31(5):363e72. [34] Campilho RDSG, Pinto AMG, Banea MD, Silva RF, da Silva LFM. Strength improvement of adhesively-bonded joints using a reverse-bent geometry. J Adhes Sci Technol 2011;25(18):2351e68. [35] Faneco TMS, Campilho RDSG, da Silva FJG, Lopes RM. Strength and fracture characterization of a novel polyurethane adhesive for the automotive industry. J Test Eval 2016. http://dx.doi.org/10.1520/JTE20150335. [36] Azevedo JCS, Campilho RDSG, da Silva JFG, Faneco TMS, Lopes RM. Cohesive law estimation of adhesive joints in mode II condition. Theor Appl Fract Mec 2015;80:143e54. [37] Fernandes TAB, Campilho RDSG, Banea MD, da Silva LFM. Adhesive selection for single lap bonded joints: experimentation and advanced techniques for strength prediction. J Adhes 2015;91(10e11):841e62. [38] Chowdhury NM, Wang J, Chiu WK, Chang P. Experimental and finite element studies of thin bonded and hybrid carbon fibre double lap joints used in aircraft structures. Compos Part B 2016;85:233e42. [39] Marques GP, Campilho RDSG, da Silva FJG, Moreira RDF. Adhesive selection for hybrid spot-welded/bonded single-lap joints: experimentation and numerical analysis. Compos Part B 2016;84:248e57. [40] Li G, Li C. Assessment of debond simulation and cohesive zone length in a bonded composite joint. Compos Part B 2015;69:359e68. [41] Neto JABP, Campilho RDSG, da Silva LFM. Parametric study of adhesive joints with composites. Int J Adhes Adhes 2012;37(0):96e101. lizy-Villacoublay, editor. Dassault Syst [42] Abaqus. Documentation. In: Ve emes; 2013. [43] Moreira RDF, Campilho RDSG. Strength improvement of adhesively-bonded scarf repairs in aluminium structures with external reinforcements. Eng Struct 2015;101:99e110. [44] Campilho RDSG, Banea MD, Neto JABP, da Silva LFM. Modelling of single-lap joints using cohesive zone models: effect of the cohesive parameters on the output of the simulations. J Adhes 2012;88(4e6):513e33. [45] Vable M, Reddy Maddi J. Boundary element analysis of adhesively bonded joints. Int J Adhes Adhes 2006;26(3):133e44. [46] Luo Q, Tong L. Fully-coupled nonlinear analysis of single lap adhesive joints. Int J Solids Struct 2007;44(7e8):2349e70. [47] Volkersen O. Die nietkraftoerteilung in zubeanspruchten nietverbindungen konstanten loschonquerschnitten. Luftfahrtforschung 1938;15:41e7.
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Composites Part B journal homepage: www.elsevier.com/locate/compositesb
Strength and damage growth in composite bonded joints with defects F.M.F. Ribeiro a, R.D.S.G. Campilho a, b, *, R.J.C. Carbas b, c, L.F.M. da Silva c ^nica, Instituto Superior de Engenharia do Porto, Instituto Polit nio Bernardino de Almeida, Departamento de Engenharia Meca ecnico do Porto, Rua Dr. Anto 431, 4200-072 Porto, Portugal b lo FEUP, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal INEGI e Po c ^nica, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal Departamento de Engenharia Meca a
a r t i c l e i n f o
a b s t r a c t
Article history: Received 13 February 2016 Received in revised form 28 April 2016 Accepted 13 June 2016 Available online 16 June 2016
The use of adhesive joints is increasing in various industrial applications because of their advantages such as weight reduction, reduction of stress concentrations and ease of manufacture. However, one of the limitations of adhesive joints is the difficulty in predicting the joint strength due to the presence of defects in the adhesive. This paper presents an experimental and numerical study of single-lap joints (SLJ) with defects centred in the adhesive layer for different overlap lengths (LO) and adhesives. The numerical analysis by cohesive zone models (CZM) included the analysis of the peel (sy) and shear (txy) stress distributions in the adhesive layer, the CZM damage variable study and the strength prediction. The joints’ behaviour was accurately characterized by CZM and showed a distinct behaviour as a function of the defect size, depending on the adhesive. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Carbon fibre Fracture toughness Mechanical testing Cohesive zone modelling
1. Introduction The use of adhesive joints is increasing in various industrial applications such as aeronautical, automotive and civil engineering [1e4] because of their advantages such as weight reduction, reduction of stress concentrations and ease of manufacture. One of the limitations of adhesive joints is the difficulty in predicting the joint strength due to the presence of defects in the adhesive. Defects are typically generated by the fabrication procedure, inadequate joint preparation, kissing bonds, micro-cracking, air bubbles, foreign bodies, grease, dirt or degradation due to the environment (e.g. humidity), reducing the joint quality and influencing the joint strength [1]. Actually, at the sites of these defects the loads are not transmitted between the structure’s components, and have to be transferred by the neighbouring portions of the adhesives, where stresses locally increase, thus reducing the joint strength [5]. An important issue is the understanding of the joint behaviour when these defects are present in a structural joint, and the knowledge of how a joint designed without taking into account these defects will behave when these defects appear. Thus, accurate tools must exist such that these effects are fully understood and a clear assessment
^nica, Instituto Su* Corresponding author. Departamento de Engenharia Meca cnico do Porto, Rua Dr. Anto nio perior de Engenharia do Porto, Instituto Polite Bernardino de Almeida, 431, 4200-072 Porto, Portugal. E-mail address: [email protected] (R.D.S.G. Campilho). http://dx.doi.org/10.1016/j.compositesb.2016.06.060 1359-8368/© 2016 Elsevier Ltd. All rights reserved.
can be made on whether a joint with a given defect can continue to operate or it must be repaired or replaced. Different experimental studies are available regarding joints with bondline defects [6e8]. Heslehurst [9] experimentally addressed the influence of debonds and weak bonds on the strength and durability of adhesivelybonded repairs, considering holography interferometry to spot the defect sites. This technique was effective in detecting the defects by variation of the fringe patterns near the zone with defect. Yang et al. [10] proposed an experimental non-destructive procedure based on vibration damping and frequency measurement to locate defects in adhesively-bonded joints between composite adherends. Llopart P et al. [11] used ultrasonic C-scan and X-ray imaging to inspect full adhesive spread to the bonding area of the joint. Tserpes et al. [12] also considered ultrasonic C-scan to detect defects in the adhesive layer of noncrimp fabric double-lap joints, and digital macrographs enabled concluding that the specimens failed in the adhesive by shear (debonding) and fracture of the composite boundary layer. The initial theoretical works regarding bonded joint bondline defects were based on the shear lag model, i.e., in which the adherends are purely axially loaded and the adhesive is solely under shear stresses. This is only applicable to joints in which no or only negligible bending exists [13e16]. In an early analytical study on the effect of bonding defects by Wang et al. [17], it was concluded that the strength of a SLJ bonded with a brittle two-part epoxy adhesive is ruled by the overlap ends. Thus, a bondline defect
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in an intermediate region of the joint does not alter significantly the strength. In a different work by the same authors [18], a ductile adhesive was used (low-density polyethylene) and, under these conditions, the sustained load by the joint is dictated by the bonded area without defect rather than by the overlap ends, because ductile adhesives have the ability to undergo plasticization before failure, which occurs with a more uniform state of stress in the bondline. Olia and Rossettos [19] proposed an analytical closedform analysis for SLJ with symmetrical and centred defects loaded in tension and/or bending, applicable to both isotropic and orthotropic adherends. It was concluded that sy and txy stresses are virtually unaffected by the void if it is sufficiently far from the overlap ends, while if the void is near to the overlap ends it will result in a significant effect on stresses, up to 25%. Berry and d’Almeida [7] considered the maximum load variations in composite SLJ by introducing circular centred defects in the adhesive layer, by analysing sy and txy stresses using a closed-form model. Whilst the average txy stress was not affected by the defect, the joint compliance highly increased with the defects. Chadegani and Batra [20] considered the first-order shear deformation theory to compute nodal displacements and stresses in bonded joints with interfacial cracks and defects, simplifying the analysis to linear elastic for the adherends and adhesive. A good agreement was found by comparing with the Finite Element Method (FEM). In contrast with theoretical techniques, numerical techniques are typically easier to work with and the associated simplifying assumptions many times mandatory to attain a solution are straightforward to deal with. The experimental and stress analysis (by the FEM) study of Pereira and de Morais [21] showed that the inclusion of defects at the overlap edges had little effect on the effective joint strength (averaged to the bonded area) for an adhesive with some degree of ductility. Ribeiro et al. [22] used the FEM to analyse the stress distributions in SLJ with different defect types and showed that defects at one of the adhesive layer’s edges were particularly harmful to the joints’ strength, oppositely to using centred defects in the adhesive layer, since the overlap ends remain the main zone for load transfer. You et al. [23] addressed by experimentation and the FEM adhesively-bonded double-lap joints with different gap lengths and different positions in the bondline (including centred defects). It was concluded that short length defects centred in the adhesive layer’s length do not significantly affect the joints’ strength because of the small disruption to stress distributions, oppositely to large size defects. Chow and Woo [24] used the FEM to assess the size and distribution effects of internal defects in bonded joints, revealing the major influence of these defects on txy stresses and maximum load (Pm) sustained by the joints. Karachalios et al. [5] studied the impact of rectangular and circular defects at the middle of the overlap on the strength of SLJ loaded in tension and four-point bending, considering different adhesives (brittle and ductile) and adherends (steel adherends: low strength/high ductility and high strength). Under tension and with a ductile adhesive, the joints’ strength depends on the type of steel: (1) high strength steel adherends lead to a practically linear reduction of Pm with the reduction of the effective bonded area and (2) for mild steel or medium carbon adherends small dimension defects have virtually no influence, while large-area defects significantly reduce the strength. Considering the brittle adhesive the behaviour is different: (1) for non-yielding adherends (highstrength steel) the strength reduction is not proportional to the defect size, which shows that the overlap ends rule the joints’ behaviour and (2) for yielding adherends the strength is dependent on overlap end-plasticization, which triggers premature failure by crack onset due to excessive strains. Under bending, it was found that the overlap ends govern failure in joints bonded with a ductile adhesive and high-strength steel adherends. CZM is particularly
recommended for bonded joints, since it clearly accounts for the coupling between tension and shear that occurs in the mixed-mode fracture of adhesive layers [25]. Several studies regarding the suitability of this technique and failure criteria/law types are available in the literature [26e28]. Serrano [29] used CZM modelling to simulate the effect of geometrical imperfections on the strength of bonded joints with different configurations between wood members. The softening laws in tension in shear developed for the adhesive layer included both the influence of the bulk adhesive and respective interfaces with the wood adherends. It was found that the sensitivity to geometrical imperfections in the tested joint configurations highly depends on the adhesive type. Ascione [30] used the CZM technique to test different CZM models to predict the strength of composite double-lap joints with defects, namely the models of Hutchinson & Suo, Xu & Needleman, and Camacho & Ortiz. It was found that the two latter models are more conservative than the model of Hutchinson & Suo. Xu and Wei [31] numerically studied the tensile strength of bonded joints with three types of defects: local debonding, weak bonding and voids. Local debonding and weak bonding were addressed by CZM implemented in user-defined sub-routines to account for the effect of the defect size and location. In the models for the void analyses, the Gurson-Tvergaard-Needleman model was used, enabling to account for the void size. Overall, the joints’ strength diminished by increasing the defect size, and the fracture properties of the weak adhesive revealed a major influence on the strength results when the weakly-bonded area is large. This paper presents an experimental and numerical study of SLJ with defects centred in the adhesive layer for different values of LO. The adhesives used were the brittle Araldite® AV138 and the ductile Sikaforce® 7752. The experimental part consisted of tensile testing different SLJ allowing to obtain the load-displacement (P-d) curves. The numerical analysis by CZM included the analysis of peel (sy) and shear (txy) stress distributions in the adhesive layer, the CZM damage variable study during the failure process and the CZM evaluation to predict the joint strength. The main innovations of the proposed work over the previously mentioned studies are related to the use of CZM for an integrated damage analysis/strength prediction and the assessment of the joints’ behaviour under different geometric (LO) and material conditions (adhesive type), which will enable selecting the best adhesive depending on the defect size and value of LO. 2. Experimental work 2.1. Materials characterization The composite adherends were fabricated from unidirectional carbon-epoxy pre-preg (SEAL® Texipreg HS 160 RM; Legnano, Italy) with 0.15 mm thickness by hand-lay-up of 20 unidirectional plies and curing in a hot-plates press for 1 h at 130 C and pressure of 2 bar. Table 1 provides the elastic-orthotropic properties of a unidirectional lamina for identical curing conditions [32]. The strong and brittle epoxy Araldite® AV138 and the less strong but ductile polyurethane Sikaforce® 7752 were evaluated. These adhesives were characterized in previous works regarding the Young’s (E) and
Table 1 Elastic orthotropic properties of a unidirectional carbon-epoxy ply aligned in the fibres direction (x-direction; y and z are the transverse and through-thickness directions, respectively) [32]. Ex ¼ 1.09E þ 05 MPa Ey ¼ 8819 MPa Ez ¼ 8819 MPa
nxy ¼ 0.342 nxz ¼ 0.342 nyz ¼ 0.380
Gxy ¼ 4315 MPa Gxz ¼ 4315 MPa Gyz ¼ 3200 MPa
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shear modulus (G), failure strengths in tension and shear (corresponding to the CZM cohesive strengths in tension (t0n) and shear (t0s )) and values of fracture toughness in tension (Gcn) and shear (Gcs) [26,33]. The tensile data was estimated by bulk tests to dogbone shape specimens, while the relevant shear properties were obtained from Thick Adherend Shear Tests (TAST). For more details see Ref. [34]. Gcn and Gcs for the AV138 were previously derived by inverse techniques [33]. For the 7752, Gcn was determined by Double-Cantilever Beam (DCB) tests and Gcs by End-Notched Flexure (ENF) tests [35]. Table 2 summarizes all collected mechanical and fracture properties (Table 3 presents the cohesive parameters used in the numerical models, derived from the data of Table 2). 2.2. Joint dimensions, fabrication and testing The geometry and dimensions of the SLJ are described in Fig. 1. The joint dimensions are: plate thickness tP ¼ 3 mm, adhesive thickness tA ¼ 0.2 mm, LO ¼ 25 and 50 mm, and length between grips LT ¼ 170 mm. For both LO values, centred defects in the bondline were evaluated with 25, 50 and 75% of LO (Fig. 2). The composite plates were fabricated as described in Section 2.1 and cut into specimens in a diamond disc cutter. Initially the adherends were manually abraded at the bonding surfaces with fine mesh sandpaper. The specimens were subsequently placed in a steel mould to ensure the proper alignment, and 25 mm thick Teflon® strips were wrapped around the adherends, secured with adhesive tape, and property positioned before pouring the adhesive with a spatula. Concurrently, calibrated spacers were used to provide the chosen tA value, which had a nearly perfect quadrilateral crosssection and were properly coated with demoulding agent to guarantee an easy extraction. After applying this process to all specimens in the mould, it is closed and curing takes place at room temperature for one week. Finally, tabs were glued at the specimens’ edges for a correct alignment in the testing machine. Tensile testing was undertaken in an Instron® 3367 (Norwood, MA, USA) electro-mechanical testing machine with a load cell of 30 kN, at room temperature and velocity of 0.5 mm/min. Five specimens were tested for each LO/adhesive type combination. 3. Numerical work 3.1. Modelling conditions The joints were modelled in Abaqus® with geometrical nonlinearities to account for the rotational effects induced by the load eccentricities [36]. The two-dimensional models were meshed with 4-node plane-strain elements (CPE4 from Abaqus®) for the
Table 2 Properties of the adhesives Araldite® AV138 and Sikaforce® 7752 [26,33,35]. Property
AV138
7752
Young’s modulus, E [GPa] Poisson’s ratio, n Tensile yield stress, se [MPa] Tensile failure strength, sf [MPa] Tensile failure strain, εf [%] Shear modulus, G [GPa] Shear yield stress, te [MPa] Shear failure strength, tf [MPa] Shear failure strain, gf [%] Toughness in tension, Gcn [N/mm] Toughness in shear, Gcs [N/mm]
4.89 ± 0.81 0.35a 36.49 ± 2.47 39.45 ± 3.18 1.21 ± 0.10 1.56 ± 0.01 25.1 ± 0.33 30.2 ± 0.40 7.8 ± 0.7 0.20b 0.38b
0.49 ± 0.09 0.30a 3.24 ± 0.48 11.48 ± 0.25 19.18 ± 1.40 0.19 ± 0.01 5.16 ± 1.14 10.17 ± 0.64 54.82 ± 6.38 2.36 ± 0.17 5.41 ± 0.47
a b
Manufacturer’s data. Estimated in Ref. [33].
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Table 3 Cohesive parameters of the adhesives Araldite® AV138 and Sikaforce® 7752 for CZM modelling. Property
AV138
7752
E [GPa] G [GPa] t0n [MPa] t0s [MPa] Gcn [N/mm] Gcs [N/mm]
4.89 1.56 39.45 30.2 0.20 0.38
0.49 0.19 11.48 10.17 2.36 5.41
adherends and COH2D4 4-node cohesive elements for the adhesive [37]. The adherends were modelled as elastic-orthotropic due to the absence of plastic effects [38], using the properties of Table 1. The stress analysis in the bondline was performed by continuumbased finite elements throughout, while in the damage variable and strength analyses CZM elements were considered in the adhesive layer. Another difference between these analyses is the mesh refinement, since the stress analysis is considerably more refined such that the stress gradients at the overlap and defect edges are accurately captured. The continuum elements’ size at the overlap edges is 0.02 0.02 mm for all LO values, although the number of elements across the overlap varied with LO. This promotes a higher precision of calculated strains and stresses at these areas with high stress variations. The mesh for the damage variable and strength analyses is coarser but without compromising the validity of the obtained results. The CZM elements’ size at the overlap edges was 0.2 0.2 mm for all LO values, again with a varying number of elements across the overlap depending on LO. Size grading effects were used throughout the models: in the vertical direction towards the adhesive layer and horizontally towards the adhesive layers’ edges, such that a higher refinement is present at these regions [39,40]. Fig. 3 gives an example of mesh detail at the overlap for the stress and strength (CZM) analyses for a non-defective joint with LO ¼ 25 mm. For the defective joints the models are identical, with the particularity that the horizontal mesh grading effects are such that they are oriented towards both the overlap edges and the defect edges within the bondline, to account for eventual stress concentration regions at these sites. The continuum modelling approach was used for damage growth in the adhesive layer, i.e., considering a single row of CZM elements through-thickness in the adhesive layer [41] and employing the triangular CZM described next in Section 3.2. The boundary conditions consisted of clamping one of the model edges, and applying a vertical restraint and tensile displacement at the other edge. 3.2. CZM model CZM are based on a relationship between stresses and relative displacements connecting homologous nodes of the cohesive elements (Fig. 4), to simulate the elastic behaviour up to a peak load and subsequent softening, to model the gradual degradation of material properties up to complete failure [42]. The areas under the traction-separation laws in each mode of loading (tension and shear) are equalled to Gcn or Gcs. Under pure mode, damage propagation occurs at a specific integration point when the stresses are released in the respective traction-separation law. Under mixed mode, energetic criteria are often used to combine tension and shear [43]. The traction-separation law assumes an initial linear elastic behaviour followed by linear evolution of damage. The elastic behaviour of the cohesive elements up to the tipping tractions is defined by an elastic constitutive matrix relating stresses and strains across the interface, containing E and G as main parameters. Damage initiation under mixed-mode can be specified by
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Fig. 1. Geometry and dimensions of the single-lap joints: LO ¼ 25 (a) and 50 mm (b).
Fig. 2. Layout of the defects in the joints: LO ¼ 25 (a) and 50 mm (b).
Fig. 3. Mesh detail at the overlap for the stress and strength (CZM) analyses for a non-defective joint with LO ¼ 25 mm.
different criteria. In this work, the quadratic nominal stress criterion was considered for the initiation of damage. After the peak value in Fig. 4 is attained (t0m), the material stiffness is degraded. Complete separation is predicted by a linear power law form of the required energies for failure in the pure modes. For full details of this model, the reader can refer to reference [44].
4. Results and discussion 4.1. Stress analysis during the elastic behaviour
Fig. 4. Traction-separation law with linear softening law available in ABAQUS®.
sy and txy stresses at the adhesive layer’s mid-thickness are considered during the elastic regime of loading. sy and txy stresses are normalized over the average shear stress (tavg) for the respective LO value and joint without defect. A similar normalization
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procedure was performed for LO (x/LO), where x is the distance from the left edge of the adhesive layer. The plot range is then given by 0 x/LO 1. In this study, only figures for LO ¼ 25 mm are presented, although the discussion is extended to both LO values. Fig. 5 shows the txy/tavg stress distributions for the joints bonded with the AV138 (a) and the 7752 (b) without and with defect (LO ¼ 25 mm). In all cases, txy stresses are lower at the inner part of the adhesive layer, peaking at the overlap ends [45,46]. This behaviour is due to differential deformation of the adherends [47]. For the AV138 (Fig. 5 a), the increase of the % defective area increases the normalized peak values of txy (with a minimum variation up to a % defective area of 50%). By increasing the defect size, peak txy stresses at the inner discontinuities (adjacent to the defect) approach the peak value at the overlap ends. txy stress gradients increase with LO (the maximum values of txy/tavg, for the joints with 75% defect, increased from z5 to z7 from LO ¼ 25 to 50 mm), due to the increasing gradient of longitudinal deformation in the adherends for large overlaps [41]. For the 7752 (Fig. 5 b), the overall behaviour is identical to that of the AV138, although with lower gradients due to the lower adhesive stiffness (the maximum value of txy/tavg, for LO ¼ 50 mm and 75% defect, decreased from z7.0 to z4.2). For higher LO values, there is a slight increase in txy/ tavg near the adhesive ends, as previously described for the joints bonded with the AV138. Fig. 6 depicts the sy/tavg stress distributions for the joints bonded with the AV138 (a) and the 7752 (a) for LO ¼ 25 mm. All stress plots show sy peel regions at the overlap ends and compressive zones in-between. This effect is related to the adherends’ rotation under loading, which causes separation at the overlap ends and compression in-between [37]. For the AV138 (Fig. 6 a), sy stress gradients increase with the % defective area, although negligibly up to 50%. sy compressive stresses near the defect increase with the % defective area. Higher LO values (50 mm) promote higher magnitude sy peak stresses near the singularities of the joint (for 75% defect, the maximum value of sy/tavg increased from z8.5 to z11.3 by changing LO ¼ 25 to 50 mm). sy compressive stresses in the inner part of the adhesive layer become less significant. The 7752 (Fig. 6 b) results in smaller normalised sy peak stresses compared to the AV138 due to its more compliant nature (the value maximum value of sy/tavg, for 75% defect, decreased from z11.3 to z4.8). With the increase in the % defective area, sy compressive stresses within the adhesive quickly approach the tensile value. Larger LO values promote higher sy peel peak stresses at the overlap ends (the maximum value of sy/tavg increased from z3.1 to z4.8 by varying LO from 25 to 50 mm). As discussed for the AV138, sy compressive stresses at the inner part of the adhesive layer become less significant. Fig. 7 summarizes the peak normalized txy (a) and sy stresses (b)
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at the overlap edges as a function of the defective area (%) considering both tested adhesives and LO values. For both LO values and all defect sizes, the joints bonded with the AV138 revealed higher peak txy/tavg and sy/tavg stresses than with the 7752 because of the higher E. On the other hand, the joints with LO ¼ 50 mm always showed higher peaks of txy/tavg (because of more significant differential deformation effects) and sy/tavg (on account of high joint rotations due to the higher loads). This should be responsible for a reduced Pm improvement for the joints bonded with the AV138 and LO ¼ 50 mm over LO ¼ 25 mm, since this brittle adhesive cannot undergo plasticization when the peak stresses are attained. On the contrary, the 7752 is not prone to be significantly affected by the increase of peak stresses due to its highly ductile nature. The evolution of txy/tavg and sy/tavg with the % defective area reinforces the previous statement that a relevant increase only occurs between 50 and 75%. In view of this, the joints with the AV138 would not be affected by a large amount by defects up to 50%, since brittle adhesives’ failure is governed by peak stresses. Oppositely, Pm for the joints with the 7752 should not be affected by peak stresses but by the bonded area, since this adhesive is highly ductile. 4.2. Damage growth analysis The analysis of the damage parameter or SDEG (stiffness degradation) of the CZM elements provides a detailed perception of the failure process during loading. This variable gives the stiffness degradation of the mixed mode CZM law (Fig. 4) and varies between SDEG ¼ 0 (undamaged material) and SDEG ¼ 1 (complete failure). The figures presented here only relate to LO ¼ 25 mm, although a descriptive comparison is made with LO ¼ 50 mm. Fig. 8 shows the damage variable in the adhesive layer at the instant Pm is attained for the joints with LO ¼ 25 mm and the AV138 (a) and 7752 (b). The damage state for the AV138 (Fig. 8 a) shows that increasing the % defect reduces the damaged portion at Pm, which is related to the increase of stress gradients towards the overlap ends (Fig. 5 (a) for txy and Fig. 6 (a) for sy stresses) leading to concentration of damage in smaller areas. Higher LO values, i.e., 50 mm, result in an identical behaviour, although with a lesser difference between curves because of aggravated stress gradients for all joint configurations. The 7752 (Fig. 8) promotes a more uniform spread of the variable damage throughout the bonding zone. For example, for the non-defective joints, SDEG ranges between z0.08 in the middle overlap to z0.47 at the overlap ends. Increasing the % defective area, the SDEG values at Pm decrease because of reduction of stress gradients resulting from the smaller bonded areas (Fig. 5 (b) for txy and Fig. 6 (b) for sy stresses). The joints with LO ¼ 50 mm showed in general higher SDEG values at Pm at the overlap ends (SDEG z 0.63
Fig. 5. Normalized txy stress distributions at the adhesive mid-thickness as a function of the defective area (%) for the joints bonded with the Araldite® AV138 (a) and Sikaforce® 7752 (b).
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Fig. 6. Normalized sy stress distributions at the adhesive mid-thickness as a function of the defective area (%) for the joints bonded with the Araldite® AV138 (a) and Sikaforce® 7752 (b).
Fig. 7. Peak normalized txy (a) and sy stresses (b) at the overlap edges as a function of the defective area (%) for the joints bonded with the Araldite® AV138 and Sikaforce® 7752 and LO ¼ 25 and 50 mm.
Fig. 8. Damage variable in the adhesive layer at the instant Pm is attained for the joints with LO ¼ 25 mm and the adhesive Araldite® AV138 (a) and Sikaforce® 7752 (b).
for the non-defective joint) because of the higher stress gradients. Fig. 9 represents the evolution of SDEG in the adhesive with d/ dPm (%) for the joints bonded with the AV138 and no defect (a) and 75% defect (b), in which d is the current displacement and dPm is the displacement at Pm (d/dPm ¼ 100% regards Pm). Increasing ratios of d/dPm are compared, from damage initiation till failure. Joints with 25% and 50% defective area have an intermediate behaviour between the joints reported here. Disregarding the % defect, in all joints bonded with the AV138 the SDEG value varies between 0 and 1 in a reduced extent, which results in a very small damage zone, while most of the bonded length does not significantly contribute to the joints’ strength. Complete failure occurs very rapidly for all joint configurations (between d/dPm ¼ 100% and 103.6% for
LO ¼ 25 mm and without defect and between 100% and 100.6% for LO ¼ 25 mm and with 75% defective joint). In the joints with LO ¼ 50 mm, d/dPm at complete joint failure is smaller (between d/ dPm ¼ 100% and 101.8% for LO ¼ 25 mm and without defect and 100% and 100.4% for LO ¼ 25 mm and with 75% defective joint) because of the higher stress variations in the bondline [37]. Fig. 10 is a similar analysis to Fig. 9 but with the 7752. Because of the adhesive’s ductility, the SDEG variation is much more gradual. The damage process initiates at the overlap ends and grows towards the inner overlap till failure. The smoother stress distributions, compared to the AV138, and the ductility of this adhesive justify the high values of d/dPm at failure (for example 437.5% for the nondefective joint with LO ¼ 25 mm). Equally to the reported for the
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Fig. 9. Evolution of the damage variable in the adhesive layer with d/dPm (%) for the joints bonded with the Araldite® AV138 and no defect (a) and 75% defect (b).
Fig. 10. Evolution of the damage variable in the adhesive layer with d/dPm (%) for the joints bonded with the Sikaforce® 7752 and no defect (a) and 75% defect (b).
brittle adhesive, increasing LO to 50 mm reduces this value (d/ dPm ¼ 308.8% for the non-defective joint), due to the larger stress gradients. Although not showed here, the damage variable has higher gradients for LO ¼ 50 mm than for 25 mm, because of higher variations in the stress distributions. On the other hand, for this adhesive d/dPm at complete failure increases with the % defective area (for example, for LO ¼ 25 mm, d/dPm at failure increases from 437.5% e non-defective joint e up to 996.2% e 75% defective joint), because of the allowable plasticization with this adhesive. 4.3. Failure modes All experimental and numerical failures for both adhesives were fully cohesive in the adhesive layer. Fig. 11 shows as an example representative failure surfaces for each joint configuration with the 7752 (LO ¼ 25 mm). Fig. 12 depicts the damage variable at Pm for the non-defective (a) and 75% defect (b) joint bonded with the AV138
and LO ¼ 25 mm, showing the small amount of softening that this adhesive sustains prior to failure (and diminishing with the % defective area). On the other hand, for the 7752, the entire or almost all the bonded region is under softening at Pm, reinforcing the idea that the joints bonded with this adhesive fail under conditions proximal to global yielding. 4.4. Load-displacement (P-d) curves Two examples are presented regarding the general correlation between the experimental and numerical P-d curves obtained in this work (Fig. 13): non-defective joints bonded with the AV138 and LO ¼ 25 mm (a), and 75% defect joints bonded with the 7752 and LO ¼ 50 mm (b). The general correlation was quite acceptable for all joints with the AV138 in which regards to the initial stiffness, Pm and dPm, although in few of the experiments some slip of the specimens occurred. The CZM results for the 7752 consistently
Fig. 11. Representative experimental failure for each joint configuration bonded with the Sikaforce® 7752 (LO ¼ 25 mm).
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Fig. 12. Damage variable at Pm for the non-defective (a) and 75% defect (b) joint bonded with the Sikaforce® 7752 and LO ¼ 25 mm.
Fig. 13. Experimental and numerical (CZM) P-d curves for the non-defective joints bonded with the Araldite® AV138 and LO ¼ 25 mm (a) and for the 75% defect joints bonded with the Sikaforce® 7752 and LO ¼ 50 mm (b).
under predicted the experiments, although the difference is not too significant, as it is visible in the example of Fig. 13 (b). This difference in Pm will be discussed in more detail in the following Section. Apart from Pm, also the P-d curves’ shape and correspondingly dPm
vary by a significant amount. However, this deviation results from numerical limitations associated to using a triangular CZM shape to model a very compliant and ductile adhesive. Under these conditions, the predicted P-d curve closely follows the assumed CZM law
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shape, instead of having an abrupt failure as it occurs in the experiments. 4.5. Joint strength Fig. 14 provides a comparison between the experimental and numerical values of Pm for all joint configurations and the AV138 (a) and 7752 (b). A distinct behaviour between adhesives is found regarding the influence of the defect size. Actually, Pm for the AV138 is only significantly affected by large defect sizes (75% defect). As a result, up to this dimension, the overall joint’s behaviour is not meaningfully affected by centred defects in the bondline. This behaviour is linked to the variation of sy and txy peak stresses at the crack onset regions, i.e., the overlap edges, with the defect dimensions. In fact, only for 75% defective area do txy (Fig. 5 (a) and Fig. 7 (a)) and sy peak stresses (Fig. 6 (a) and Fig. 7 (b)) change by a relevant amount. Thus, because of the adhesive’s brittleness and resulting lack of plasticization ability, these peak stress govern the failure process of the joints. Corroborating this assumption, in the SDEG analysis it was initially found that, at Pm, the joints bonded with the AV138 concentrated the damage in a small region at the overlap edges and with an abrupt variation (Fig. 8 a). Moreover, complete failure is attained for a very small value of d/dPm over 100%, because of the absence of plasticization [37]. Regarding the joints’ behaviour with the increase of % defective area, the value of d/dPm at failure diminished significantly for 75% defect (Fig. 9) because of the increase of stress concentrations and inability of the AV138 to accommodate these peak stresses. These issues reinforce the brittle nature of the failure process. The 7752 results in a completely different behaviour, since Pm decreases almost linearly and proportionally with the increase in the % defect. This behaviour results from a combination of two factors: (1) more uniform distribution of txy (Fig. 5 (b) and Fig. 7 (a)) and sy stresses (Fig. 6 (b) and Fig. 7 (b)) on account of the adhesive’s flexibility and (2) plasticization capability, causing levelling of stresses at the bonded portions of the bondline. Thus, the Pm values directly reflect the reduction of the bonded area by increasing the % defective area. In the damage analysis it was shown that this adhesive enables spreading the damage through a large portion of the joint at Pm, reinforcing the failure occurring by global yielding (Fig. 8 b). Moreover, increasing values of d/dPm at failure were found with growing % defects (Fig. 10), which is indicative of a marked degree of plasticization. The effect of increasing LO from 25 to 50 mm is also dependent on the type of adhesive. The Pm values for the joints bonded with the AV138 increased between 33.0% (non-defective joint) and 67.8% (75% defective area), while for the joints bonded with the 7752 the improvement was between 88.1% (non-defective joint) and 100.1% (75% defective area). The AV138 has a smaller Pm improvement
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with LO because of the increase of stress concentrations at the overlap ends for higher LO values (Fig. 7), which are not accommodated by the adhesive’s brittleness [44]. On the other hand, the ductile nature of the 7752 enables it to undergo global yielding in the adhesive layer, resulting in almost duplicating or even exceeding Pm by doubling LO [37]. Although not shown here, the damage variable analysis revealed damage spreading in a more confined region for the joints bonded with the AV138 when increasing LO from 25 to 50 mm, which is consistent with the aforementioned small % Pm improvement. On the other hand, for the joints bonded with the 7752, damage extended across the entire bonded region. In view of the exposed behaviours, by comparing the two adhesives, for the non-defective joints Pm is higher for the 7752 than the AV138 by 14.1% (LO ¼ 25 mm) and 61.3% (LO ¼ 50 mm). Despite the higher strength of the AV138, the 7752 has a higher ductility, which is prevalent in these joints. Moreover, this difference is bigger for LO ¼ 50 mm since this adhesive is little affected by the peak stresses that limit the strength of the AV138 for big overlaps. On the other hand, with the increase of % defective area, the AV138 gradually gains advantage over the 7752 (up to 34.8% for LO ¼ 25 mm and 22.3% for LO ¼ 50 mm, in both cases for 75% defect). This is caused by the almost linear Pm reduction for the 7752 with the % defect (failure near to global yielding conditions), while the AV138 at Pm concentrates stresses at the overlap ends, thus not being so much affected by the centred defects (especially up to 50% defective area). The CZM predictions showed different results between the joints bonded with the AV138 and the 7752. The maximum percentile deviations between the simulations and the experimental values for each adhesive were 7.2% for the AV138 (nondefective joints with LO ¼ 50 mm) and 25.7% for the 7752 (75% defect joints with LO ¼ 50 mm). Fairly accurate results were obtained for the AV138 by using a triangular CZM law to model the adhesive layer because of its brittleness, which is accurately modelled by a CZM law that undergoes softening in the constitutive response when Pm is attained [26]. For the 7752 the CZM results consistently under predicted the experiments for all tested geometries. This behaviour originated from the high ductility of the adhesive, which is not adequately modelled by a triangular CZM law [37]. In fact, for adhesives that experience a large ductility as it is the case of the 7752, the transmitted stresses across the adhesive are kept at high levels after the adhesive’s tensile yield stress (se) is attained first at the overlap edges. Moreover, at Pm, a significant part of the overlap is exceeding se (Fig. 8 (a) and Fig. 10). However, by using a triangular CZM law (Fig. 4), stress softening occurs after attaining t0m, which invariably results in a Pm under prediction [26]. In this case, the simulations only provide an approximate idea of Pm and how it evolves with the % increase of the defect. To obtain more accurate results, trapezoidal CZM laws could be considered instead,
Fig. 14. Experimental/numerical comparison of Pm values as a function of the defective area (%) for the Araldite® AV138 (a) and Sikaforce® 7752 (b).
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since these account for the adhesive’s plasticization without softening [36]. 5. Concluding remarks This work aimed at studying the effect of % defective area, value of LO and adhesive type on the tensile strength of SLJ. The obtained results were highly dependent on the adhesive type. The AV138, by being brittle and stiff, revealed high stress concentrations and inability to undergo plasticization after the limiting stresses are attained. Oppositely, the 7752 is more flexible, which resulted in smaller stress gradients. Moreover, its ductility enabled failure conditions close to global yielding and corresponding higher Pm values for the non-defective joints. Higher LO values increase the difference between the two adhesives (especially for the nondefective joints). The presence of centred defects in the adhesive layer has a bigger effect for the joints bonded with the 7752 than the AV138 (average experimental Pm reduction from the nondefective to the 75% defective joints of 51.8% for the AV138 and of 72.4% for the 7752). Actually, the joints bonded with the 7752 fail under global yielding conditions, such that Pm decreases practically linearly with the reduction of bonded area. On the other hand, the joints bonded with the AV138 have a brittle failure as soon as the limiting adhesive stresses are reached at the overlap ends. Thus, the presence of a defect centred in the adhesive layer (typically lightly loaded) is not so preponderant for the joints’ strength. These effects were described in detail in light of stress and damage variable analyses. The CZM predictive technique was accurate in predicting the strength of the joints bonded with the AV138 (maximum difference to the experiments of 7.2%), although under predicting Pm for the joints bonded with the 7752 (maximum deviation of 25.7%). Actually, due to the high ductility of this adhesive, the trapezoidal CZM laws would provide a better approximation. As design guidelines, the obtained results indicate that, for both small and large overlaps, non-defective joints work better with ductile and lower strength adhesives, while joints with large % of defects have higher Pm values with stronger although brittle adhesives. References [1] Mancusi G, Ascione F. Performance at collapse of adhesive bonding. Compos Struct 2013;96:256e61. [2] Dai J, Ueda T, Sato Y. Development of the nonlinear bond stresseslip model of fiber reinforced plastics sheeteconcrete interfaces with a simple Method. J Compos Constr 2005;9(1):52e62. [3] Higgins A. Adhesive bonding of aircraft structures. Int J Adhes Adhes 2000;20(5):367e76. [4] Jia Z, Yuan G, Ma H-L, Hui D, Lau K-T. Tensile properties of a polymer-based adhesive at low temperature with different strain rates. Compos Part B 2016;87:227e32. [5] Karachalios EF, Adams RD, da Silva LFM. Strength of single lap joints with artificial defects. Int J Adhes Adhes 2013;45:69e76. [6] Engerer JD, Sancaktar E. The effects of partial bonding in load carrying capacity of single lap joints. Int J Adhes Adhes 2011;31(5):373e9. [7] Berry NG, d’Almeida JRM. The influence of circular centered defects on the performance of carboneepoxy single lap joints. Polym Test 2002;21(4): 373e9. [8] Park J-H, Choi J-H, Kweon J-H. Evaluating the strengths of thick aluminum-toaluminum joints with different adhesive lengths and thicknesses. Compos Struct 2010;92(9):2226e35. [9] Heslehurst RB. Observations in the structural response of adhesive bondline defects. Int J Adhes Adhes 1999;19(2e3):133e54. [10] Yang S, Gu L, Gibson RF. Nondestructive detection of weak joints in adhesively bonded composite structures. Compos Struct 2001;51(1):63e71. [11] Llopart P LI, Tserpes KI, Labeas GN. Experimental and numerical investigation of the influence of imperfect bonding on the strength of NCF double-lap shear joints. Compos Struct 2010;92(7):1673e82. [12] Tserpes KI, Pantelakis S, Kappatos V. The effect of imperfect bonding on the pull-out behavior of non-crimp fabric Pi-shaped joints. Comput Mater Sci 2011;50(4):1372e80. [13] Hart-Smith LJ. Further developments in the design and analysis of adhesivebonded structural joints. ASTM STP 1981;749:3e31.
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