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Mechanical characterization of a flexible epoxy adhesive for the design of hybrid bonded-bolted joints
Polymer Testing 79 (2019) 106048
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Material Properties
Mechanical characterization of a flexible epoxy adhesive for the design of hybrid bonded-bolted joints
T
Gyu-Hyeong Lima, Mohammad Heidari-Raranib, Kobye Bodjonaa, Karthik Prasanna Rajua, Valentin Romanova, Larry Lessarda,∗ a
Composite and Structures Laboratory, Department of Mechanical Engineering, McGill University. Macdonald Room 270, 817 Sherbrooke Street West, Montreal, Quebec, H3A 0C3, Canada b Department of Mechanical Engineering, Faculty of Engineering, University of Isfahan, 81746-73441, Isfahan, Iran
A R T I C LE I N FO
A B S T R A C T
Keywords: Flexible adhesive Hybrid joint Mechanical properties Digital image correlation
Hybrid bolted/bonded joints are less effective when designed with strong structural adhesives as insignificant load is introduced to the bolt before the bond reaches failure. Advancement in hybrid joint design requires further knowledge on the behavior of flexible adhesives, which involve significant complexities such as large inelastic deformation. This study investigates the mechanical properties of EA9361 AERO, a representative flexible epoxy adhesive, within the context of the design of hybrid bolted/bonded joints. Tensile and shear tests were performed to obtain the tensile stress/strain relation, strength, strain-to-failure, Poisson's ratio, and adhesive's responses under pure shear state. A practical methodology for strain measurement of a thin bondline of adhesive was proposed using digital image correlation (DIC). It was concluded that the nonlinear tensile stress/ strain relation of the flexible adhesive can be accurately represented with a bilinear elastic/plastic material model. The Poisson's ratio was found to significantly change throughout the strain development.
1. Introduction Structural joints are the passages by which loads flow from one component to another and are the locations of stress concentration. Therefore, proper design of joints is vital for all structural assemblies. The importance of joint design is particularly recognized in transportation applications; while joints tend to be heavily loaded, they are designed with the lightest weight possible. It is only natural that the structures of different applications constantly seek to advance their joint technology, especially for composite materials, which have the desired specific strength and stiffness properties. Joining of composite materials has conventionally employed two types of joining techniques. One is mechanical fastening, and another is adhesive bonding. Bonded joints are known, in their uses in both mechanical engineering [1,2] and civil engineering [3], to possess higher strength than bolted joints. The insignificant weight of a thin adhesive layer also makes bonded joints lighter than bolted joints. However, some aspects of bonded joints present challenges to certify them for commercial applications. Predominantly, it is the insufficient ability to detect defects [4,5]. The presence and propagation of damage, if undetected, tends to lead to catastrophic failure. These challenges have favored mechanically fastened joints to be the preferred method to join ∗
composite materials [6]. Nevertheless, the use of the mechanical fastening comes at the cost of fastener weight. A potential alternative to the two conventional techniques is the hybrid bonded/bolted joints termed HBB joints - which combines the efficiency of bonded joints and non-catastrophic failure mode of bolted joints. Effective designs of hybrid joints are of a particular interest to aerospace applications; aircrafts significantly leverage fuel economy from weight efficiency, and also strictly require fail-safe mechanism to avoid fatal accidents for passengers. Hart-Smith firstly introduced the HBB joints for joining composite materials for aerospace applications. His experiments with the singlebolted HBB joints showed that the addition of a bolt to bonded joints slows down the damage propagation following the failure in the adhesive. Nevertheless, the Hart-Smith's HBB joints showed no strength improvement compared to bonded joints [7]. Similar results were obtained by Chowdhury et al., who studied HBB joints with multiple fasteners. Chowdhury's study demonstrated that the presence of the bolts in practice could provide the HBB joints with fail-safe mechanism which bonded joints alone are not able to offer [8]. Such fail-safe feature of hybrid joints is also observed in civil engineering applications, where an addition of local reinforcement shifted the failure mechanism of beam/column bonded joints from brittle to pseudo-ductile [9].
Corresponding author. E-mail address: [email protected] (L. Lessard).
https://doi.org/10.1016/j.polymertesting.2019.106048 Received 10 April 2019; Received in revised form 17 July 2019; Accepted 16 August 2019 Available online 17 August 2019 0142-9418/ © 2019 Elsevier Ltd. All rights reserved.
Polymer Testing 79 (2019) 106048
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However, it was presented in terms of engineering stresses and strains while the adhesive reached large deformation before failure. Banea et al. [21] investigated the shear behavior of Sikaflex 552 which is primarily used as sealants rather than in structural applications. A study on the evolution of a flexible adhesive's Poisson's ratio, whose value may significantly vary during the course of large deformation, is yet to be found in literature. The aim of this study is to characterize the flexible epoxy adhesive EA9361 AERO, which serves for aerospace uses as well as other applications. Firstly, uniaxial tensile tests are performed to obtain the true stress/strain relation and to capture the Poisson's ratio evolution throughout the full strain range until failure. In addition, this test allows one to quantify mechanical properties such as yield and failure stresses. Then, shear tests follow to examine the adhesive's properties under pure shear state. The measured properties will be valuable inputs for the analysis of HBB joints, especially for the numerical modeling whose capacities to imitate the complex HBB joint mechanism have been verified [14,22,23]. Additionally, an appropriate material model for flexible epoxy adhesive is to be recommended between hyper-elastic and elastic/plastic models. The observations from the experiments are also to be incorporated into qualitative guidelines for the design of the HBB joints with flexible epoxy adhesives. Lastly, a practical technique to measure adhesive strain in a thin bond line is introduced.
Further confirming the damage tolerance of HBB joints, Fu and Mallick [10] performed fatigue testing and quantified the superior fatigue life of hybrid joints compared to bonded joints. While these studies showed the feasibility of utilizing adhesive bonding in aerospace applications, the HBB joints were still considered an inefficient design because the adhesives were taking the majority of the load through the joints. This was due to the use of conventional adhesives whose high-performance strength was correspondingly associated with the adhesive's high stiffness. The adhesive stiffness was too high for effective load sharing between the bond and the fasteners [11–13]. The realization of the unbalanced load sharing led to the use of flexible adhesives in HBB joints. Kelly [11] compared the load sharing observed in two types of HBB joints, one with stiff epoxy adhesive and another with flexible polyurethane adhesive. His experimental results showed that the bolts only carried less than 5% of the total load in the HBB joints with the stiff adhesive. By contrast, the ones with the flexible adhesive achieved bolt load sharing (bolt load/total load) over 40%. Similar experiments by Bodjona et al. [14] observed bolt load sharing as high as 38% for HBB joints with flexible epoxy adhesives. Due to the increase in bolt load sharing, the structural performance of the HBB joints was accordingly enhanced. Kelly's experiments showed that the strength of the HBB joints with flexible adhesive was greater than those of both bonded joints and bolted joints [2]. Furthermore, Lopez-Cruz et al. [1] demonstrated the higher strength of HBB joints with flexible adhesive, compared to those with stiff adhesive. The improved joint strength was due not only to the effective load sharing, but also to the ability of the flexible adhesives to relieve stress concentration in the joints' bond line [15,16]. The outstanding performance of the HBB joint with flexible adhesive has been acknowledged. Consequently, a more exhaustive understanding on flexible adhesives' properties follows in order to advance HBB joint design. For example, Bodjona's sensitivity test considers the adhesive yield stress to be the major parameter for load sharing [17], and Lopez-Cruz's experiments found the adhesive stiffness to be highly relevant to the joint strength [1]. Until now, relatively fewer investigations have been made on the characterization of flexible adhesives compared to stiff adhesives [18]. The following are the limited few pre-established characterizations found in the literature. Crocker et al. [19] characterized flexible polyurethane adhesives through uniaxial, equi-biaxial, and planar tension tests then modeled them with hyper-elasticity. Kelly [11] tested the polyurethane adhesive, Pilogrip 7400/7100, under tension and used an elastic/plastic model to perform finite element analysis. Duncan and Dean [18] characterized a rubber toughened epoxy adhesive, and numerically simulated bonded joints using a hyper-elastic model. Da Silva et al. [20] tensile tested epoxy adhesive EA9361, and produced the stress/strain curve.
2. Materials and methodology The representative material to be characterized in this study is a two-part epoxy-based adhesive EA 9361 AERO, supplied by Henkel. Two types of testes, i.e., uniaxial tensile tests and pure shear tests are performed. The details of specimen preparation and experimental tests are explained as follows. 2.1. Tensile test methodology 2.1.1. Specimen preparation A plate of EA9361 is manufactured to produce specimens with uniform thickness. For homogeneous and void-free mixing, the two parts of the adhesive are mixed inside a Thinky Mixer ARE-310 with 2200 rpm for 1 min. Afterwards, the adhesive is compression-molded by a hot press. The mold is made of 6061 aluminum alloys and the molding surface machined to a mirror finish. A silicone frame is inserted to control the plate thickness to be 3.28 ± 0.025 mm. The adhesive is cured at 82 °C for an hour, as suggested by the adhesive's data sheet [24], inside the hot press that applies a hydrostatic pressure of 2 MPa. The cured plate is cut into seven specimens and machined into the shape of Type I specimens as outlined in the ASTM D638 standard [25].
Fig. 1. Tensile test specimen preparation: (a) adhesive plate after curing, (b) cut samples, (c) machined sample, (d) samples with painted speckle pattern, (e) close-up of speckle pattern. 2
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For the same purpose of accounting for large deformation, the differential form of the Poisson's ratio is used. Poisson's ratio is obtained using Eq. (5) for which the rate of change in transverse strain with respect to longitudinal strain is computed at every increment of imagecapturing.
υ=−
∂εjj (5)
∂εii
where the indices ii and jj indicate the axial and transverse directions. 2.1.4. Material model fitting Least square fitting is performed on the overall stress/strain curve, constructed by taking the average of the results from all seven specimens, using both hyper-elastic and elastic-plastic material models. For hyper-elasticity, the generalized polynomial model is used to fit the data. This model is formulated with the strain energy density function (W) shown in Eq. (6) [26], which is an extension to the pre-established Mooney-Rivlin model [27]. Eq. (6) is expanded to a third order polynomial, seen in Eq. (7), to fit the test results. Fig. 2. Arcan fixture and coaxial shear loading.
W=
∑ ∑ Cij (I1 − 3)i (I2 − 3) j + D (J − 1)2 i
For the later strain approximation with digital image correlation (DIC) technique, the gage sections of the specimens are painted with speckles, whose size is controlled to be from 0.5 to 1 mm in diameter. The preparation of the specimen is visually summarized in Fig. 1.
+ C30 (I1 − 3)3 + D (J − 1)2
εii . Eng =
2.2. Shear test methodology 2.2.1. Test fixture and specimen preparation In this study, an Arcan fixture made of stainless steel 303, as illustrated in Fig. 2, is used for shear tests in the adhesive. This fixture is able to apply the shear load co-axially and consequently it contributes to achieve pure shear deformation in the adhesive [28]. For the pure shear tests, the V-notched specimens are used, whose notches are made at a 45° angle from the bonding surface. ASTM STP 981 validates that such V-notched geometry, used together with the Arcan fixture, is capable of applying uniform pure shear in the adhesive [28]. Two adherends made of 6061 aluminum alloys are bonded by EA9361 adhesive to form a V-notched specimen. The specimen dimensions are shown in Fig. 3. Prior to specimen manufacturing, the adherends’ bonding surfaces are treated. After an initial cleaning with dilute acetone, the bonding surfaces are applied with FreshStart, a mold cleaning chemical from Zyvax. FreshStart is able to remove not only dirt and contaminants but also the aluminum oxide layer of an aluminum surface, ensuring a complete cleaning. Then, 3 M AC-130 pre-treatment solution is applied on the bonding surface to enhance the bonding between the adhesive and the adherends. Once the surface treatment is complete, the bottom adherends are placed and fixed in the jig. While the jig is tilted, the adhesive mixed by the Thinky mixer is injected with a syringe onto the bonding surface of the specimen. The top adherends are then placed and fixed. After the lid is closed, the jig assembly is clamped. These processes are illustrated by Fig. 4 (a), (b), and (c). Lastly, the adhesive is oven-cured. The oven temperature is initially set at 50 °C for an hour. Afterwards, the temperature is elevated to 82 °C to fully cure the specimens. Fig. 5 represents curing cycle of EA9361. The initial dwell at 50 °C was necessary, since sudden temperature rise from the ambient temperature (25 °C) to 82 °C rapidly reduces the adhesive viscosity. Such sudden drop in viscosity allows the adhesive to flow through the gaps between the specimens and the jig before gelation. Although the jig and specimens were designed and machined to
σii . True =
(1)
Lf − Lo Lo
F A
ΔL Lo
(2) (3)
L εii . True = ln ⎛ ⎞ ⎝ Lo ⎠ ⎜
=
(7)
where Cij and D are empirically determined constants, and I1, I2 and I3 are the invariants of the left Cauchy-Green deformation tensor, and the J is the Jacobian which is related to I3 such that I3 = J2.
2.1.3. Post-processing The DIC technique measures the displacement fields and compute the strains in both longitudinal and transverse directions. The use of engineering stress and strain, shown by Eqs. (1) and (2), is inappropriate for flexible adhesives which undergo large deformation before failure. Therefore, the calculations provided by Eqs. (3) and (4) are used to calculate the true stress and true strain respectively. The contractual strain in the transverse direction allows the approximation of instantaneous cross-section area of the specimen, given that the same amount of strain is found in both width and thickness directions of the specimens under pure tension.
F Ao
(6)
W = C10 (I1 − 3) + C01 (I2 − 3) + C11 (I1 − 3)(I2 − 3) + C20 (I2 − 3)2
2.1.2. Experimental set-up An Insight 5 kN MTS machine measures the force exerted by the sample and the camera, a PointGrey Flea 5 MP, takes images of the speckled gage section simultaneously. The DIC technique is used to measure the displacement field. A sampling rate of 1 Hz is used for both MTS and DIC. The cross-head speed is set at 2.5 mm/min. This is half as fast as the ASTM D638 recommended speed of 5 mm/min. The test speed was set slower than the ASTM in order to reduce the adhesive's viscous response. At this fixed crosshead speed, the strain rate is initially found at 0.05/min then the rate decreases as the specimen elongates. The experiments are performed to seven specimens at an ambient temperature of 25 °C.
σii . Eng =
j
⎟
(4)
where Ao and A are the original and instantaneous cross-section areas respectively, F is applied force, Lo and Lf are the original and final lengths respectively, σ is axial stress, ε is strain in the adhesive, and ii indicates the longitudinal direction. 3
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Fig. 3. Details of the adherend and the shear specimen a) Dimensions of an adherend b) Specimen assembly.
contributed to the elevated thickness. Finally, for DIC measurements, the samples are covered with a speckle pattern using an airbrush technique. As seen in Fig. 4 (d) and (e), the both adherends of the specimen are painted. The displacements of the both specimens are to be tracked to derive the adhesive shear strain. This technique is further discussed in Section 2.2.3.2. 2.2.2. Experimental set-up As in the tensile test, the Insight 5 kN MTS measures the forces and the PointGrey Flea 5 MP captures the images at a sampling rate of 1 Hz. The crosshead displacement speed is set at 0.015 mm/min. At this fixed speed, the strain rate at the beginning of the test is 0.03/min. Five specimens are tested at room temperature of 25 °C. The methodologies employed to process the test data into stress-strain responses will be explained in Section 2.2.3. 2.2.3. Methodology validation and post-processing 2.2.3.1. Shear stress measurement. As the cross-section area subjected to shear load remains unchanged, the values of shear stress are to be processed with Eq. (8)
Fig. 4. Shear test specimen preparation: (a) curing jig, (b) specimens placed in jig, (c) jig ready for oven cure, (d) specimen with speckle pattern, (e) close-up of speckle pattern around adhesive.
τxy =
P Ao
(8)
where Ao is the initial cross section area on the adhesive layer. Accurate stress measurement is only possible if the stress distribution is uniform. Although the Arcan fixture and V-notched specimen together are known to produce uniform shear in the bond, the degree of uniformity is to be quantified through finite element modeling for further confidence on the customized set-up. The statistics are calculated from all finite elements that represent the adhesive: mean, standard deviation and the resulting coefficient of variation. The coefficient of variation is the measure used to verify the uniformity. Being sufficient for this purpose, a linear elastic finite element analysis is performed. The Arcan fixture and V-notched specimen are modeled and analyzed in MSC Nastran 2012. The number of hexahedral elements through the width, length and thickness of adhesive region are 50, 14 and 4, respectively. Therefore, there are 2800 hexahedral elements to represent the adhesive. The size of each adhesive element is 0.39 × 0.64 × 0.15 mm3. The whole FE model contains 58,000 elements in total. The input material properties are tabulated in Table 1. The nodes at the fixed end are constrained in three translational direction, (x, y, z) = (0, 0, 0); and the nodes at the moving end are constrained in all direction except for the MTS head displacement, (x, y, z) = (0, y, 0) with respect to the coordinate shown in Fig. 6(a). The magnitude of the applied shear force is adjusted to produce the average shear stress value of unity, that is P = 175.5 N acting over Ao = 19.5
Fig. 5. Two-dwell curing cycle for EA9361.
achieve an adhesive thickness of 0.5 mm, the adhesive thickness in specimens were found to be 0.6 mm ± 0.08 mm after the curing. While the adherends are fixed on the jig, some adhesives were trapped in the gap between the adherends and the jig. The trapped adhesives 4
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Δu ⎞ εxy . ARD = Arctan ⎛ ⎝ t ⎠
Table 1 Material properties. Region
Material
E [GPa]
υ
Adhesive Adherend Fixture
EA9361 Aluminum Stainless Steel
0.514 73.1 193
0.43 0.33 0.3
where t is adhesive bondline thickness of a V-notched specimen and Δu is the relative displacements of the two adherends in the direction of the shear loading as illustrated in Fig. 8(a). This technique is to be referred as the adherends relative displacement (ARD) technique further in the text. To validate the accuracy of the proposed ARD method, the strain approximation by the proposed methodology is compared with the DIC performed on the adhesive bondline. For this exercise, the tested specimen is painted both on the adhesive and on the adherends leaving the unpainted regions of the adherends at the interface, as seen in Fig. 8(b). Fig. 9 compares the estimated shear strains, one by the ARD method and another by direct DIC processing. The strain measured by the direct DIC has a scatter with a magnitude of ± 0.01, whose presence indicates the difficulty of performing DIC on a thin bondline. The discontinuous shift of strain at εxy = 0.42 corresponds to the failure of the specimen. The sudden rise in the ARD method curve at failure is due to the adherends and their connected systems returning to their undeformed state following the failure. The subsequent increase in the strain, after the specimen failed, is due to the cross-head displacing at constant speed. The sudden drop in the DIC curve is due to the adhesive returning to the stress-free state following the failure. The viscosity of the adhesive explains the following gradual decrease in εxy . Except for the small initial strain region, where experimental noise and scatter of the direct DIC method are dominant over the value of strain, the percentage difference is controlled within 5%. Therefore, the accuracy of strain approximation by ARD method is concluded to be high. The least squares technique [29] is additionally performed to quantitatively compare the obtained strain/displacement curves prior to the adhesive failure. The strain approximation by the proposed ARD methodology matches the DIC curve with the coefficient of determination of R2 = 0.994. The calculated R2 in addition to the percent difference in the strains, confirms the validity of the ARD method. Thus, despite the small thickness of the adhesive, with a proper measurement of the adherends displacement, the strain in the adhesive can be accurately approximated from the relative displacement of the adjacent adherends.
mm×9 mm = 175.5 mm2. Fig. 6(a) and (b) illustrate the finite element model and elements at adhesive. Fig. 7 shows the distribution of the shear stress, τxy , obtained from FE modeling. The distribution of τxy is plotted only along the w-direction only because the variation along the v-direction was negligible. The magnitude of other stress components were at least two orders of magnitudes lower than that of τxy , and therefore are considered insignificant. As seen in this figure, the distribution is uniform throughout the overlap except near the outer edges that are affected by the free surfaces. Based on the results from all adhesive elements, the coefficient of variation is computed to be CV = 2.5%, indicating that the degreeof-variation is acceptable. 2.2.3.2. Shear strain measurement and ARD method. Shear strain is a measure of angular deformation of a body. Only when subjected to a very small strain in which θ ≈ tan(θ), it is applicable to use the definition of engineering strain, εij . Eng = tan(θij ) . For this study on flexible adhesives, the expression for true shear strain, shown with Eq. (9), is used.
εij = θij
(10)
(9)
where ij is the plane over which shear deformation is found. The use of strain gage or extensometer is infeasible to measure strain in the thin bondline, which therefore leaves the DIC to be utilized for the strain approximation. Yet, performing DIC directly on the bondline is also associated with challenges. It is problematic to prepare speckles whose miniscule size has to be comparable with the thin adhesive thickness. Spraying together on bondline and adherends causes difficulty for DIC to distinguish them. Thus, preparing specimens compatible for DIC processing, though not impossible, is laborious and time-consuming. Alternative to performing DIC directly on the thin bondline, the relative displacement of the adherends can be used to determine the adhesive strain. The schematic is illustrated in Fig. 8(a). This technique is feasible for the case of flexible adhesive, because the modulus of the aluminum is two orders of magnitude greater than the adhesive modulus. In other words, the deformation of the aluminum adherends is insignificant compared to that of the adhesive. Given that the adherends are rigid relative to the adhesive, Eq. (10), derived from Eq. (9), is used to calculate the shear strain.
3. Results and discussion This section includes two subsections 3.1 and 3.2 which present and discuss in detail the results of tensile and shear tests, respectively. 3.1. Tensile test results All the tensile test samples failed in the gage section as desired. The
Fig. 6. Finite element modeling of uniform shear stress: (a) FE model and (b) adhesive elements. 5
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Fig. 7. Shear stress distribution obtained from FE model.
stress/strain curves obtained from the tensile tests are presented in Fig. 10. As seen, there is a very little variation between the curves. This correlation – along with identical failure modes of all samples – indicates the uniform mixing and curing of the material. The tensile modulus in the elastic region was computed in the strain range of 0 < εxx < 0.01 and its value was Eel = 514 MPa. However, the datasheet of EA9361 [24] reports a modulus of Eel = 723 MPa, which is also measured based on ASTM D638 standard. The present experiments show lower elastic modulus than the datasheet. It is because the presented study employed slower test speed than the recommended speed specified by the ASTM, as discussed previously in section 2.1.2. The modulus in the plastic regions, whose value was computed in the strain range of 0.1 < εxx < 0.2 , was Epl = 28 MPa. The values of failure stresses, σxxf , and strains, εxxf , under tension along with the permanent strain, εxxp , are shown in Table 2. The permanent strain was calculated using Eq. (4) using the initial gage lengths and the gage length of the failed specimen; after the testing the failed specimens had been left overnight to shrink to a stress-free state such that the gage length after full contraction was used for the calculation of permanent strain. The average value of σxxf is 27.5 MPa; the average εxxf is 0.53; the average εxxp is 0.086.
Fig. 9. Strain measurement validation.
development. Having an initial value, νo = 0.44, it first increases to a value as high as νmax = 0.47 and then drops to a value as low as νmin = 0.38. The range of Poisson's ratio values of 0.09 is a significant variation, considering that the possible full range of Poisson's ratio for
3.1.1. Poisson's ratio As shown in Fig. 11, the Poisson's ratio is not constant throughout the strain development but evolves over the range of tensile strain
Fig. 8. Strain measurement: (a) schematics of relative displacement measurement, (b) Special specimen used for validation. 6
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Fig. 10. True Tensile Stress vs True Tensile Strain
Fig. 12. Curve-fitting on EA9361 tensile results.
Table 2 EA9361 tensile tests: failure stress and strain, and permanent strain. Sample #
f σxx [MPa]
f εxx
p εxx
Specimen 1 Specimen 2 Specimen 3 Specimen 4 Specimen 5 Specimen 6 Specimen 7 Average ( ± SDV)
25.30 28.90 28.00 29.00 25.70 29.10 26.50 27.5 ± 1.63
0.49 0.56 0.53 0.55 0.49 0.55 0.51 0.53 ± 0.029
0.07 0.10 0.07 0.09 0.07 0.09 0.11 0.086 ± 0.016
data to an FE model, one has to identify the most appropriate material model. As explained before, two material models, i.e., hyper-elastic model and bilinear elastic-plastic models are investigated. Fig. 12 displays the curves best-fitted by the two models. The curve from the experiment found in Fig. 12 is the average of the seven specimen's results from the tensile tests. R2 values, calculated with the definition of R2 recommended by 2 = 0.99 for the elastic/plastic model and Kvålseth [29], were RBL 2 RHE = 0.99 for the hyper-elastic model. Although both models have matching R2 values, the elastic/plastic model fits better in the initial strain range (0 < ε < 0.05) which includes the elastic region and the yielding region. Since the hyper-elastic model is formulated with polynomials, the smoothness of its curve was not able to accurately imitate the sharp modulus drop at yielding, also affecting the fitting in the adjacent elastic region; for the strains found in the entire elastic region, the corresponding stress values were significantly underestimated with respect to the test results. The elastic/plastic model accurately fitted the experimental stress/strain curve throughout the full strain range that is bilinear in nature with the two distinct moduli before and after yielding. Therefore, the elastic/plastic model is recommended for the modeling and analysis of flexible epoxy adhesives in general. The qualitative observations of the tensile test data also support the use of elastic/plastic model. Although hyper-elasticity is able to model large deformations, the plastic behavior of the adhesive observed after yielding does not fit with the fully elastic behavior of a hyper-plastic material. Furthermore, the use of the bilinear relationship also simplifies the analysis of joints with flexible adhesives including the HBB joints. For instance, the simplicity of the bilinear relation led to the kinematic semi-analytical model, developed by some researchers [30–34], for the strength analysis of HBB joints. When applicable, such simplified modeling techniques could replace fully numerical simulation of HBB joints and achieve substantial reduction in computational costs.
Fig. 11. Poisson's ratio vs true tensile strain.
isotropic materials is from 0 to 0.5. The evolution of the adhesive's Poisson's ratio must be reflected in the analysis of flexible epoxy adhesives. When constrained by the adherends, the thin bondline of adhesive is subjected to stress concentration due to the Poisson's effects. Therefore, the understanding of this nature of the flexible epoxy adhesive is vital in joint design for accurate stress analysis and, hence, failure prediction of the adhesive. Involving nonlinearly behaving flexible adhesives and their interactions with substrates, such design problems are too complex for analytical solutions, leaving the numerical modeling as a feasible alternative option. However, in general, commercial finite element packages only account for a constant value of Poisson's ratio. A manual subroutine introducing the varying Poisson's ratio is recommended for more realistic simulation of structures with flexible adhesives.
3.1.3. Permanent deformation After achieving large elongation past the yielding in the loading direction, the adhesive was found with permanent deformation. However, this permanent deformation could contribute to improved bolt load sharing (bolt load/total load) and therefore be beneficial for the HBB joints with a flexible epoxy adhesive. The following exercise qualitatively demonstrates this aspect. A hybrid bolted/bonded joint illustrated in Fig. 13(a) is subjected to tensile load repeatedly. Fig. 13(b) illustrates the resulting force/displacement curves (marked with solid lines) and the bolt load sharing
(= ) curves (marked with dashed lines). For this practice, a boltFbolt Ftotal
3.1.2. Material models for flexible adhesives In order to imitate the material's response accurately as an input
hole with no clearance is assumed. It is also assumed that the adhesive's
7
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Fig. 14. True Shear Stress vs True Shear Strain.
adhesive are clearly seen on both bonding surfaces of the adherends, indicating a good adhesion. This observation ensures that the test results were free from the poor bonding at the interface. The shear failure occurred gradually with the initial crack slowly propagating along the adhesive bondline. All specimens other than Specimen 1 resulted in stress/strain curves that correlate with each other very well. Specimen 1 is considered an outlier with a defect in the adhesive. Yielding was observed at the stress value of τxyy = 8.3 MPa. After yielding, the shear modulus dropped from Gel = 174 MPa to Gpl = 25 MPa; the elastic and plastic moduli are captured in the strange range of 0 < θxy < 0.02 and 0.12 < θxy < 0.22 , respectively. The shear tests, as well as the tensile tests, demonstrate the applicability of the elastic/plastic material model to characterize the non-linear behavior of the present flexible epoxy adhesive. The failure stresses were captured at crack initiation. Any test results between crack initiation and complete specimen failure were not considered to be a material property, therefore are not presented in Fig. 14. The failure stresses τxyf and strains εxyf are summarized in Table 3. The average value for τxyf is 14.57 MPa; εxyf average value is 0.31.
Fig. 13. Hybrid joint under the tensile load (a) Single-lap HBB joints (b) Effects of permanent deformation in adhesive.
elastic and plastic moduli and the value of yield strain are not affected by yielding, yet the permanent strain is introduced. After the first loading, the joint returns to the unloaded state with a residual displacement of d′ > 0 due to permanent deformation of its adhesive. As a result, for the same magnitude of tensile load applied, the HBB joint displaces more in the second loading than in the first loading as seen in Fig. 13(b). The higher joint displacement indicates higher shear deformation in the bolt and consequently higher load through the bolt. Hence, the bolt load sharing (bolt load/total load) is improved on the second and subsequent loadings. Testing the HBB joints under repeated loading is of great future interest to further confirm this joint design practice. In practical applications, the joints may be subjected to loading in multiple directions. Yet, the behavior of yielding under multiaxial loading is currently far too complex to be sufficiently understood. Consequently, taking advantage of the permanent deformation for improved bolt load sharing has to be particular to the HBB joints that are loaded in a single direction. Examples of which include aircraft wings, helicopter blades and so on.
3.3. Characterization summary The mechanical properties measured by the two tests are summarized in Table 4. The symbols and the corresponding properties are elaborated as: Eel and Epl are the tensile moduli in elastic and plastic regions; Gel and Gpl are the shear moduli in elastic and plastic regions; ν is the Poisson's ratio; σxxyield , σxxf and εxxf are the yield stress, failure stress and strain under tension; and τxyyield , τxyf and εxyf are the yield stress, failure stress and strain under shear. 4. Conclusions
3.2. Shear test results A HBB joint is considered the next stage of innovation for joining composite materials, especially for its use in aircraft structures. Yet, the HBB joint is not fully understood largely due to the complex behavior of flexible adhesives. Even though standards exist to measure stress/strain behavior of conventional structural adhesives, insufficient efforts have been made to extend their application to flexible adhesives that display
The results of the shear test are presented in Fig. 14. Only the results for four specimens are presented as the results for the remaining one was considered an outlier because of a defect. Prior to any observations or conclusions drawn from this custom-designed test, the accuracy of the results is verified in addition to the methodology validations presented in section 2.2.3. The measured elastic shear modulus of Gel = 174 MPa (Fig. 14) is compared with the shear modulus calculated from relation G = E/2(1+ν). For the latter, the elastic tensile modulus, Eel, and the initial Poisson's ratio, νo, obtained from the tensile tests are taken. Taking the initial elastic tensile and shear moduli and the initial Poisson's ratio was essential as the relationship is only valid in the small elastic region in which the variation of the elastic properties is negligible. The calculated Gel is 178 MPa. The small difference of 2.3% between the two shear moduli verifies that the test results are accurate. All specimens failed by cohesive failure. The remains of the
Table 3 Shear failure stress and strain.
8
Specimen #
f σxy [MPa]
f εxy
Specimen 1 Specimen 2 Specimen 3 Specimen 4 Average ( ± SDV)
15.8 13.8 13.5 15.2 14.57 ± 1.1
0.36 0.27 0.26 0.33 0.31 ± 0.048
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Table 4 Material properties of EA9361. Eel [MPa]
Epl [MPa]
Gel [MPa]
Gpl [MPa]
v
yield σxx [MPa]
f σxx [MPa]
f εxx
yield τxy [MPa]
f τxy [MPa]
f εxy
514
28
174
25
0.38–0.47
10
27.5
0.53
8.3
14.6
0.31
clearly nonlinear behavior. The innovative methodologies outlined in this work represent a promising guideline for performing such tests: characterizing a thin layer of flexible adhesives was possible through applying co-axial loads with an Arcan fixture and simultaneously measuring strains by tracking relative adherends displacement. With EA9361 AERO used as a representative material, mechanical characterization was performed to quantify the tensile and shear stress/ strain relation and failure properties. The qualitative observations from the test results led to the following insights for the design and analysis of HBB joints.
adhesive joints using ultrasonic techniques, Ultrasonics 41 (2003) 521–529. [5] R.V. Kumar, M. Bhat, C. Murthy, Evaluation of kissing bond in composite adhesive lap joints using digital image correlation: preliminary studies, Int. J. Adhesion Adhes. 42 (2013) 60–68. [6] 20-107B - Composite Aircraft Structure (Advisory Circular P 4-6), Federal-AviationAdministration, 2009. [7] L.J. Hart-Smith, Bonded-bolted composite joints, J. Aircr. 22 (1985) 993–1000. [8] N. Chowdhury, W.K. Chiu, J. Wang, P. Chang, Static and fatigue testing thin riveted, bonded and hybrid carbon fiber double lap joints used in aircraft structures, Compos. Struct. 121 (2015) 315–323. [9] F. Ascione, M. Lamberti, A. Razaqpur, S. Spadea, M. Malagic, Pseudo-ductile failure of adhesively joined GFRP beam-column connections: an experimental and numerical investigation, Compos. Struct. 200 (2018) 864–873. [10] M. Fu, P. Mallick, Fatigue of hybrid (adhesive/bolted) joints in SRIM composites, Int. J. Adhesion Adhes. 21 (2001) 145–159. [11] G. Kelly, Load transfer in hybrid (bonded/bolted) composite single-lap joints, Compos. Struct. 69 (2005) 35–43. [12] J.-H. Kweon, J.-W. Jung, T.-H. Kim, J.-H. Choi, D.-H. Kim, Failure of carbon composite-to-aluminum joints with combined mechanical fastening and adhesive bonding, Compos. Struct. 75 (2006) 192–198. [13] W.S. Chan, S. Vedhagiri, Analysis of composite bonded/bolted joints used in repairing, J. Compos. Mater. 35 (2001) 1045–1061. [14] K. Bodjona, K. Raju, G.-H. Lim, L. Lessard, Load sharing in single-lap bonded/bolted composite joints. part I: model development and validation, Compos. Struct. 129 (2015) 268–275. [15] C.-T. Hoang-Ngoc, E. Paroissien, Simulation of single-lap bonded and hybrid (bolted/bonded) joints with flexible adhesive, Int. J. Adhesion Adhes. 30 (2010) 117–129. [16] A. Loureiro, L.F. Da Silva, C. Sato, M. Figueiredo, Comparison of the mechanical behaviour between stiff and flexible adhesive joints for the automotive industry, J. Adhes. 86 (2010) 765–787. [17] K. Bodjona, L. Lessard, Load sharing in single-lap bonded/bolted composite joints. Part II: global sensitivity analysis, Compos. Struct. 129 (2015) 276–283. [18] B.C. Duncan, G. Dean, Measurements and models for design with modern adhesives, Int. J. Adhesion Adhes. 23 (2003) 141–149. [19] L. Crocker, B. Duncan, R. Hughes, J. Urquhart, Hyperelastic Modelling of Flexible Adhesives, vol. 183, (1999) NPL Report No. CMMT (A). [20] L.F. da Silva, T. Rodrigues, M. Figueiredo, M. De Moura, J. Chousal, Effect of adhesive type and thickness on the lap shear strength, J. Adhes. 82 (2006) 1091–1115. [21] M.D. Banea, L.F. da Silva, Mechanical characterization of flexible adhesives, J. Adhes. 85 (2009) 261–285. [22] K.P. Raju, K. Bodjona, G.-H. Lim, L. Lessard, Improving load sharing in hybrid bonded/bolted composite joints using an interference-fit bolt, Compos. Struct. 149 (2016) 329–338. [23] N.M. Chowdhury, J. Wang, W.K. Chiu, P. Chang, Experimental and finite element studies of thin bonded and hybrid carbon fibre double lap joints used in aircraft structures, Compos. B Eng. 85 (2016) 233–242. [24] Technical Datasheet Hysol EA9361," Henkel Corporation Aerospace Group. [25] ASTM D638-14 Standard Test Method for Tensile Properties of Plastics, American Society for Testing and Materials, 2014. [26] A.F. Bower, Applied Mechanics of Solids, CRC press, 2009. [27] M. Mooney, A theory of large elastic deformation, J. Appl. Phys. 11 (1940) 582–592. [28] V. Weissberg, M. Arcan, A uniform pure shear testing specimen for adhesive characterization, Adhesively Bonded Joints: Testing, Analysis, and Design, ASTM International, 1988. [29] T.O. Kvålseth, Cautionary note about R 2, Am. Statistician 39 (1985) 279–285. [30] K. Bodjona, L. Lessard, Nonlinear static analysis of a composite bonded/bolted single-lap joint using the meshfree radial point interpolation method, Compos. Struct. 134 (2015) 1024–1035. [31] E. Paroissien, F. Lachaud, S. Schwartz, A. Da Veiga, P. Barrière, Simplified stress analysis of hybrid (bolted/bonded) joints, Int. J. Adhesion Adhes. 77 (2017) 183–197. [32] C. Bois, H. Wargnier, J.-C. Wahl, E. Le Goff, An analytical model for the strength prediction of hybrid (bolted/bonded) composite joints, Compos. Struct. 97 (2013) 252–260. [33] E. Paroissien, M. Sartor, J. Huet, Hybrid (bolted/bonded) joints applied to aeronautic parts: analytical one-dimensional models of a single-lap joint, Advances in Integrated Design and Manufacturing in Mechanical Engineering II, Springer, 2007, pp. 95–110. [34] E. Paroissien, F. Gaubert, A. Da Veiga, F. Lachaud, Elasto-plastic analysis of bonded joints with macro-elements, J. Adhes. Sci. Technol. 27 (2013) 1464–1498.
• Poisson's ratio significantly varies throughout the large range of
• •
strain, and the peak value is as high as υ = 0.47 . In a joint, a thin layer of adhesive is significantly exposed to Poisson's effect as its deformation is constrained by the adherends. Therefore, this study recommends that the evolution of Poisson's ratio is reflected in the stress analysis of the flexible adhesive, whether analytical or numerical. The elastic/plastic material model is recommended as it can accurately imitate the nonlinear stress/strain relation of flexible epoxy adhesives. Simplifying the material model to a bilinear relationship also allows the analysis of HBB joints, and other adhesively bonded structures, at a reduced computational cost. Yielding produces permanent deformation in the adhesive, which could improve the bolt load sharing, thus the structural performance of the HBB joints. The use of this benefit is applicable to the joints that are loaded in a single direction.
Data availability The raw/processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations. Acknowledgements The authors would like to thank the Consortium de Recherche et d’Innovation en Aérospatiale au Quebec (CRIAQ) and the National Research Council labs (NRC-AMTC) without whose generous support this research would not have been possible. Behnam Ashrafi, Laurin Hugo, and Steven Roy (CNRC-NRC) are also acknowledged for their support regarding the fabrication of the test specimens. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.polymertesting.2019.106048. References [1] P. Lopez-Cruz, J. Laliberté, L. Lessard, Investigation of bolted/bonded composite joint behaviour using design of experiments, Compos. Struct. 170 (2017) 192–201. [2] G. Kelly, Quasi-static strength and fatigue life of hybrid (bonded/bolted) composite single-lap joints, Compos. Struct. 72 (2006) 119–129. [3] F. Ascione, M. Lamberti, A. Razaqpur, S. Spadea, Strength and stiffness of adhesively bonded GFRP beam-column moment resisting connections, Compos. Struct. 160 (2017) 1248–1257. [4] C. Brotherhood, B. Drinkwater, S. Dixon, The detectability of kissing bonds in
9
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Material Properties
Mechanical characterization of a flexible epoxy adhesive for the design of hybrid bonded-bolted joints
T
Gyu-Hyeong Lima, Mohammad Heidari-Raranib, Kobye Bodjonaa, Karthik Prasanna Rajua, Valentin Romanova, Larry Lessarda,∗ a
Composite and Structures Laboratory, Department of Mechanical Engineering, McGill University. Macdonald Room 270, 817 Sherbrooke Street West, Montreal, Quebec, H3A 0C3, Canada b Department of Mechanical Engineering, Faculty of Engineering, University of Isfahan, 81746-73441, Isfahan, Iran
A R T I C LE I N FO
A B S T R A C T
Keywords: Flexible adhesive Hybrid joint Mechanical properties Digital image correlation
Hybrid bolted/bonded joints are less effective when designed with strong structural adhesives as insignificant load is introduced to the bolt before the bond reaches failure. Advancement in hybrid joint design requires further knowledge on the behavior of flexible adhesives, which involve significant complexities such as large inelastic deformation. This study investigates the mechanical properties of EA9361 AERO, a representative flexible epoxy adhesive, within the context of the design of hybrid bolted/bonded joints. Tensile and shear tests were performed to obtain the tensile stress/strain relation, strength, strain-to-failure, Poisson's ratio, and adhesive's responses under pure shear state. A practical methodology for strain measurement of a thin bondline of adhesive was proposed using digital image correlation (DIC). It was concluded that the nonlinear tensile stress/ strain relation of the flexible adhesive can be accurately represented with a bilinear elastic/plastic material model. The Poisson's ratio was found to significantly change throughout the strain development.
1. Introduction Structural joints are the passages by which loads flow from one component to another and are the locations of stress concentration. Therefore, proper design of joints is vital for all structural assemblies. The importance of joint design is particularly recognized in transportation applications; while joints tend to be heavily loaded, they are designed with the lightest weight possible. It is only natural that the structures of different applications constantly seek to advance their joint technology, especially for composite materials, which have the desired specific strength and stiffness properties. Joining of composite materials has conventionally employed two types of joining techniques. One is mechanical fastening, and another is adhesive bonding. Bonded joints are known, in their uses in both mechanical engineering [1,2] and civil engineering [3], to possess higher strength than bolted joints. The insignificant weight of a thin adhesive layer also makes bonded joints lighter than bolted joints. However, some aspects of bonded joints present challenges to certify them for commercial applications. Predominantly, it is the insufficient ability to detect defects [4,5]. The presence and propagation of damage, if undetected, tends to lead to catastrophic failure. These challenges have favored mechanically fastened joints to be the preferred method to join ∗
composite materials [6]. Nevertheless, the use of the mechanical fastening comes at the cost of fastener weight. A potential alternative to the two conventional techniques is the hybrid bonded/bolted joints termed HBB joints - which combines the efficiency of bonded joints and non-catastrophic failure mode of bolted joints. Effective designs of hybrid joints are of a particular interest to aerospace applications; aircrafts significantly leverage fuel economy from weight efficiency, and also strictly require fail-safe mechanism to avoid fatal accidents for passengers. Hart-Smith firstly introduced the HBB joints for joining composite materials for aerospace applications. His experiments with the singlebolted HBB joints showed that the addition of a bolt to bonded joints slows down the damage propagation following the failure in the adhesive. Nevertheless, the Hart-Smith's HBB joints showed no strength improvement compared to bonded joints [7]. Similar results were obtained by Chowdhury et al., who studied HBB joints with multiple fasteners. Chowdhury's study demonstrated that the presence of the bolts in practice could provide the HBB joints with fail-safe mechanism which bonded joints alone are not able to offer [8]. Such fail-safe feature of hybrid joints is also observed in civil engineering applications, where an addition of local reinforcement shifted the failure mechanism of beam/column bonded joints from brittle to pseudo-ductile [9].
Corresponding author. E-mail address: [email protected] (L. Lessard).
https://doi.org/10.1016/j.polymertesting.2019.106048 Received 10 April 2019; Received in revised form 17 July 2019; Accepted 16 August 2019 Available online 17 August 2019 0142-9418/ © 2019 Elsevier Ltd. All rights reserved.
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However, it was presented in terms of engineering stresses and strains while the adhesive reached large deformation before failure. Banea et al. [21] investigated the shear behavior of Sikaflex 552 which is primarily used as sealants rather than in structural applications. A study on the evolution of a flexible adhesive's Poisson's ratio, whose value may significantly vary during the course of large deformation, is yet to be found in literature. The aim of this study is to characterize the flexible epoxy adhesive EA9361 AERO, which serves for aerospace uses as well as other applications. Firstly, uniaxial tensile tests are performed to obtain the true stress/strain relation and to capture the Poisson's ratio evolution throughout the full strain range until failure. In addition, this test allows one to quantify mechanical properties such as yield and failure stresses. Then, shear tests follow to examine the adhesive's properties under pure shear state. The measured properties will be valuable inputs for the analysis of HBB joints, especially for the numerical modeling whose capacities to imitate the complex HBB joint mechanism have been verified [14,22,23]. Additionally, an appropriate material model for flexible epoxy adhesive is to be recommended between hyper-elastic and elastic/plastic models. The observations from the experiments are also to be incorporated into qualitative guidelines for the design of the HBB joints with flexible epoxy adhesives. Lastly, a practical technique to measure adhesive strain in a thin bond line is introduced.
Further confirming the damage tolerance of HBB joints, Fu and Mallick [10] performed fatigue testing and quantified the superior fatigue life of hybrid joints compared to bonded joints. While these studies showed the feasibility of utilizing adhesive bonding in aerospace applications, the HBB joints were still considered an inefficient design because the adhesives were taking the majority of the load through the joints. This was due to the use of conventional adhesives whose high-performance strength was correspondingly associated with the adhesive's high stiffness. The adhesive stiffness was too high for effective load sharing between the bond and the fasteners [11–13]. The realization of the unbalanced load sharing led to the use of flexible adhesives in HBB joints. Kelly [11] compared the load sharing observed in two types of HBB joints, one with stiff epoxy adhesive and another with flexible polyurethane adhesive. His experimental results showed that the bolts only carried less than 5% of the total load in the HBB joints with the stiff adhesive. By contrast, the ones with the flexible adhesive achieved bolt load sharing (bolt load/total load) over 40%. Similar experiments by Bodjona et al. [14] observed bolt load sharing as high as 38% for HBB joints with flexible epoxy adhesives. Due to the increase in bolt load sharing, the structural performance of the HBB joints was accordingly enhanced. Kelly's experiments showed that the strength of the HBB joints with flexible adhesive was greater than those of both bonded joints and bolted joints [2]. Furthermore, Lopez-Cruz et al. [1] demonstrated the higher strength of HBB joints with flexible adhesive, compared to those with stiff adhesive. The improved joint strength was due not only to the effective load sharing, but also to the ability of the flexible adhesives to relieve stress concentration in the joints' bond line [15,16]. The outstanding performance of the HBB joint with flexible adhesive has been acknowledged. Consequently, a more exhaustive understanding on flexible adhesives' properties follows in order to advance HBB joint design. For example, Bodjona's sensitivity test considers the adhesive yield stress to be the major parameter for load sharing [17], and Lopez-Cruz's experiments found the adhesive stiffness to be highly relevant to the joint strength [1]. Until now, relatively fewer investigations have been made on the characterization of flexible adhesives compared to stiff adhesives [18]. The following are the limited few pre-established characterizations found in the literature. Crocker et al. [19] characterized flexible polyurethane adhesives through uniaxial, equi-biaxial, and planar tension tests then modeled them with hyper-elasticity. Kelly [11] tested the polyurethane adhesive, Pilogrip 7400/7100, under tension and used an elastic/plastic model to perform finite element analysis. Duncan and Dean [18] characterized a rubber toughened epoxy adhesive, and numerically simulated bonded joints using a hyper-elastic model. Da Silva et al. [20] tensile tested epoxy adhesive EA9361, and produced the stress/strain curve.
2. Materials and methodology The representative material to be characterized in this study is a two-part epoxy-based adhesive EA 9361 AERO, supplied by Henkel. Two types of testes, i.e., uniaxial tensile tests and pure shear tests are performed. The details of specimen preparation and experimental tests are explained as follows. 2.1. Tensile test methodology 2.1.1. Specimen preparation A plate of EA9361 is manufactured to produce specimens with uniform thickness. For homogeneous and void-free mixing, the two parts of the adhesive are mixed inside a Thinky Mixer ARE-310 with 2200 rpm for 1 min. Afterwards, the adhesive is compression-molded by a hot press. The mold is made of 6061 aluminum alloys and the molding surface machined to a mirror finish. A silicone frame is inserted to control the plate thickness to be 3.28 ± 0.025 mm. The adhesive is cured at 82 °C for an hour, as suggested by the adhesive's data sheet [24], inside the hot press that applies a hydrostatic pressure of 2 MPa. The cured plate is cut into seven specimens and machined into the shape of Type I specimens as outlined in the ASTM D638 standard [25].
Fig. 1. Tensile test specimen preparation: (a) adhesive plate after curing, (b) cut samples, (c) machined sample, (d) samples with painted speckle pattern, (e) close-up of speckle pattern. 2
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For the same purpose of accounting for large deformation, the differential form of the Poisson's ratio is used. Poisson's ratio is obtained using Eq. (5) for which the rate of change in transverse strain with respect to longitudinal strain is computed at every increment of imagecapturing.
υ=−
∂εjj (5)
∂εii
where the indices ii and jj indicate the axial and transverse directions. 2.1.4. Material model fitting Least square fitting is performed on the overall stress/strain curve, constructed by taking the average of the results from all seven specimens, using both hyper-elastic and elastic-plastic material models. For hyper-elasticity, the generalized polynomial model is used to fit the data. This model is formulated with the strain energy density function (W) shown in Eq. (6) [26], which is an extension to the pre-established Mooney-Rivlin model [27]. Eq. (6) is expanded to a third order polynomial, seen in Eq. (7), to fit the test results. Fig. 2. Arcan fixture and coaxial shear loading.
W=
∑ ∑ Cij (I1 − 3)i (I2 − 3) j + D (J − 1)2 i
For the later strain approximation with digital image correlation (DIC) technique, the gage sections of the specimens are painted with speckles, whose size is controlled to be from 0.5 to 1 mm in diameter. The preparation of the specimen is visually summarized in Fig. 1.
+ C30 (I1 − 3)3 + D (J − 1)2
εii . Eng =
2.2. Shear test methodology 2.2.1. Test fixture and specimen preparation In this study, an Arcan fixture made of stainless steel 303, as illustrated in Fig. 2, is used for shear tests in the adhesive. This fixture is able to apply the shear load co-axially and consequently it contributes to achieve pure shear deformation in the adhesive [28]. For the pure shear tests, the V-notched specimens are used, whose notches are made at a 45° angle from the bonding surface. ASTM STP 981 validates that such V-notched geometry, used together with the Arcan fixture, is capable of applying uniform pure shear in the adhesive [28]. Two adherends made of 6061 aluminum alloys are bonded by EA9361 adhesive to form a V-notched specimen. The specimen dimensions are shown in Fig. 3. Prior to specimen manufacturing, the adherends’ bonding surfaces are treated. After an initial cleaning with dilute acetone, the bonding surfaces are applied with FreshStart, a mold cleaning chemical from Zyvax. FreshStart is able to remove not only dirt and contaminants but also the aluminum oxide layer of an aluminum surface, ensuring a complete cleaning. Then, 3 M AC-130 pre-treatment solution is applied on the bonding surface to enhance the bonding between the adhesive and the adherends. Once the surface treatment is complete, the bottom adherends are placed and fixed in the jig. While the jig is tilted, the adhesive mixed by the Thinky mixer is injected with a syringe onto the bonding surface of the specimen. The top adherends are then placed and fixed. After the lid is closed, the jig assembly is clamped. These processes are illustrated by Fig. 4 (a), (b), and (c). Lastly, the adhesive is oven-cured. The oven temperature is initially set at 50 °C for an hour. Afterwards, the temperature is elevated to 82 °C to fully cure the specimens. Fig. 5 represents curing cycle of EA9361. The initial dwell at 50 °C was necessary, since sudden temperature rise from the ambient temperature (25 °C) to 82 °C rapidly reduces the adhesive viscosity. Such sudden drop in viscosity allows the adhesive to flow through the gaps between the specimens and the jig before gelation. Although the jig and specimens were designed and machined to
σii . True =
(1)
Lf − Lo Lo
F A
ΔL Lo
(2) (3)
L εii . True = ln ⎛ ⎞ ⎝ Lo ⎠ ⎜
=
(7)
where Cij and D are empirically determined constants, and I1, I2 and I3 are the invariants of the left Cauchy-Green deformation tensor, and the J is the Jacobian which is related to I3 such that I3 = J2.
2.1.3. Post-processing The DIC technique measures the displacement fields and compute the strains in both longitudinal and transverse directions. The use of engineering stress and strain, shown by Eqs. (1) and (2), is inappropriate for flexible adhesives which undergo large deformation before failure. Therefore, the calculations provided by Eqs. (3) and (4) are used to calculate the true stress and true strain respectively. The contractual strain in the transverse direction allows the approximation of instantaneous cross-section area of the specimen, given that the same amount of strain is found in both width and thickness directions of the specimens under pure tension.
F Ao
(6)
W = C10 (I1 − 3) + C01 (I2 − 3) + C11 (I1 − 3)(I2 − 3) + C20 (I2 − 3)2
2.1.2. Experimental set-up An Insight 5 kN MTS machine measures the force exerted by the sample and the camera, a PointGrey Flea 5 MP, takes images of the speckled gage section simultaneously. The DIC technique is used to measure the displacement field. A sampling rate of 1 Hz is used for both MTS and DIC. The cross-head speed is set at 2.5 mm/min. This is half as fast as the ASTM D638 recommended speed of 5 mm/min. The test speed was set slower than the ASTM in order to reduce the adhesive's viscous response. At this fixed crosshead speed, the strain rate is initially found at 0.05/min then the rate decreases as the specimen elongates. The experiments are performed to seven specimens at an ambient temperature of 25 °C.
σii . Eng =
j
⎟
(4)
where Ao and A are the original and instantaneous cross-section areas respectively, F is applied force, Lo and Lf are the original and final lengths respectively, σ is axial stress, ε is strain in the adhesive, and ii indicates the longitudinal direction. 3
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Fig. 3. Details of the adherend and the shear specimen a) Dimensions of an adherend b) Specimen assembly.
contributed to the elevated thickness. Finally, for DIC measurements, the samples are covered with a speckle pattern using an airbrush technique. As seen in Fig. 4 (d) and (e), the both adherends of the specimen are painted. The displacements of the both specimens are to be tracked to derive the adhesive shear strain. This technique is further discussed in Section 2.2.3.2. 2.2.2. Experimental set-up As in the tensile test, the Insight 5 kN MTS measures the forces and the PointGrey Flea 5 MP captures the images at a sampling rate of 1 Hz. The crosshead displacement speed is set at 0.015 mm/min. At this fixed speed, the strain rate at the beginning of the test is 0.03/min. Five specimens are tested at room temperature of 25 °C. The methodologies employed to process the test data into stress-strain responses will be explained in Section 2.2.3. 2.2.3. Methodology validation and post-processing 2.2.3.1. Shear stress measurement. As the cross-section area subjected to shear load remains unchanged, the values of shear stress are to be processed with Eq. (8)
Fig. 4. Shear test specimen preparation: (a) curing jig, (b) specimens placed in jig, (c) jig ready for oven cure, (d) specimen with speckle pattern, (e) close-up of speckle pattern around adhesive.
τxy =
P Ao
(8)
where Ao is the initial cross section area on the adhesive layer. Accurate stress measurement is only possible if the stress distribution is uniform. Although the Arcan fixture and V-notched specimen together are known to produce uniform shear in the bond, the degree of uniformity is to be quantified through finite element modeling for further confidence on the customized set-up. The statistics are calculated from all finite elements that represent the adhesive: mean, standard deviation and the resulting coefficient of variation. The coefficient of variation is the measure used to verify the uniformity. Being sufficient for this purpose, a linear elastic finite element analysis is performed. The Arcan fixture and V-notched specimen are modeled and analyzed in MSC Nastran 2012. The number of hexahedral elements through the width, length and thickness of adhesive region are 50, 14 and 4, respectively. Therefore, there are 2800 hexahedral elements to represent the adhesive. The size of each adhesive element is 0.39 × 0.64 × 0.15 mm3. The whole FE model contains 58,000 elements in total. The input material properties are tabulated in Table 1. The nodes at the fixed end are constrained in three translational direction, (x, y, z) = (0, 0, 0); and the nodes at the moving end are constrained in all direction except for the MTS head displacement, (x, y, z) = (0, y, 0) with respect to the coordinate shown in Fig. 6(a). The magnitude of the applied shear force is adjusted to produce the average shear stress value of unity, that is P = 175.5 N acting over Ao = 19.5
Fig. 5. Two-dwell curing cycle for EA9361.
achieve an adhesive thickness of 0.5 mm, the adhesive thickness in specimens were found to be 0.6 mm ± 0.08 mm after the curing. While the adherends are fixed on the jig, some adhesives were trapped in the gap between the adherends and the jig. The trapped adhesives 4
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Δu ⎞ εxy . ARD = Arctan ⎛ ⎝ t ⎠
Table 1 Material properties. Region
Material
E [GPa]
υ
Adhesive Adherend Fixture
EA9361 Aluminum Stainless Steel
0.514 73.1 193
0.43 0.33 0.3
where t is adhesive bondline thickness of a V-notched specimen and Δu is the relative displacements of the two adherends in the direction of the shear loading as illustrated in Fig. 8(a). This technique is to be referred as the adherends relative displacement (ARD) technique further in the text. To validate the accuracy of the proposed ARD method, the strain approximation by the proposed methodology is compared with the DIC performed on the adhesive bondline. For this exercise, the tested specimen is painted both on the adhesive and on the adherends leaving the unpainted regions of the adherends at the interface, as seen in Fig. 8(b). Fig. 9 compares the estimated shear strains, one by the ARD method and another by direct DIC processing. The strain measured by the direct DIC has a scatter with a magnitude of ± 0.01, whose presence indicates the difficulty of performing DIC on a thin bondline. The discontinuous shift of strain at εxy = 0.42 corresponds to the failure of the specimen. The sudden rise in the ARD method curve at failure is due to the adherends and their connected systems returning to their undeformed state following the failure. The subsequent increase in the strain, after the specimen failed, is due to the cross-head displacing at constant speed. The sudden drop in the DIC curve is due to the adhesive returning to the stress-free state following the failure. The viscosity of the adhesive explains the following gradual decrease in εxy . Except for the small initial strain region, where experimental noise and scatter of the direct DIC method are dominant over the value of strain, the percentage difference is controlled within 5%. Therefore, the accuracy of strain approximation by ARD method is concluded to be high. The least squares technique [29] is additionally performed to quantitatively compare the obtained strain/displacement curves prior to the adhesive failure. The strain approximation by the proposed ARD methodology matches the DIC curve with the coefficient of determination of R2 = 0.994. The calculated R2 in addition to the percent difference in the strains, confirms the validity of the ARD method. Thus, despite the small thickness of the adhesive, with a proper measurement of the adherends displacement, the strain in the adhesive can be accurately approximated from the relative displacement of the adjacent adherends.
mm×9 mm = 175.5 mm2. Fig. 6(a) and (b) illustrate the finite element model and elements at adhesive. Fig. 7 shows the distribution of the shear stress, τxy , obtained from FE modeling. The distribution of τxy is plotted only along the w-direction only because the variation along the v-direction was negligible. The magnitude of other stress components were at least two orders of magnitudes lower than that of τxy , and therefore are considered insignificant. As seen in this figure, the distribution is uniform throughout the overlap except near the outer edges that are affected by the free surfaces. Based on the results from all adhesive elements, the coefficient of variation is computed to be CV = 2.5%, indicating that the degreeof-variation is acceptable. 2.2.3.2. Shear strain measurement and ARD method. Shear strain is a measure of angular deformation of a body. Only when subjected to a very small strain in which θ ≈ tan(θ), it is applicable to use the definition of engineering strain, εij . Eng = tan(θij ) . For this study on flexible adhesives, the expression for true shear strain, shown with Eq. (9), is used.
εij = θij
(10)
(9)
where ij is the plane over which shear deformation is found. The use of strain gage or extensometer is infeasible to measure strain in the thin bondline, which therefore leaves the DIC to be utilized for the strain approximation. Yet, performing DIC directly on the bondline is also associated with challenges. It is problematic to prepare speckles whose miniscule size has to be comparable with the thin adhesive thickness. Spraying together on bondline and adherends causes difficulty for DIC to distinguish them. Thus, preparing specimens compatible for DIC processing, though not impossible, is laborious and time-consuming. Alternative to performing DIC directly on the thin bondline, the relative displacement of the adherends can be used to determine the adhesive strain. The schematic is illustrated in Fig. 8(a). This technique is feasible for the case of flexible adhesive, because the modulus of the aluminum is two orders of magnitude greater than the adhesive modulus. In other words, the deformation of the aluminum adherends is insignificant compared to that of the adhesive. Given that the adherends are rigid relative to the adhesive, Eq. (10), derived from Eq. (9), is used to calculate the shear strain.
3. Results and discussion This section includes two subsections 3.1 and 3.2 which present and discuss in detail the results of tensile and shear tests, respectively. 3.1. Tensile test results All the tensile test samples failed in the gage section as desired. The
Fig. 6. Finite element modeling of uniform shear stress: (a) FE model and (b) adhesive elements. 5
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Fig. 7. Shear stress distribution obtained from FE model.
stress/strain curves obtained from the tensile tests are presented in Fig. 10. As seen, there is a very little variation between the curves. This correlation – along with identical failure modes of all samples – indicates the uniform mixing and curing of the material. The tensile modulus in the elastic region was computed in the strain range of 0 < εxx < 0.01 and its value was Eel = 514 MPa. However, the datasheet of EA9361 [24] reports a modulus of Eel = 723 MPa, which is also measured based on ASTM D638 standard. The present experiments show lower elastic modulus than the datasheet. It is because the presented study employed slower test speed than the recommended speed specified by the ASTM, as discussed previously in section 2.1.2. The modulus in the plastic regions, whose value was computed in the strain range of 0.1 < εxx < 0.2 , was Epl = 28 MPa. The values of failure stresses, σxxf , and strains, εxxf , under tension along with the permanent strain, εxxp , are shown in Table 2. The permanent strain was calculated using Eq. (4) using the initial gage lengths and the gage length of the failed specimen; after the testing the failed specimens had been left overnight to shrink to a stress-free state such that the gage length after full contraction was used for the calculation of permanent strain. The average value of σxxf is 27.5 MPa; the average εxxf is 0.53; the average εxxp is 0.086.
Fig. 9. Strain measurement validation.
development. Having an initial value, νo = 0.44, it first increases to a value as high as νmax = 0.47 and then drops to a value as low as νmin = 0.38. The range of Poisson's ratio values of 0.09 is a significant variation, considering that the possible full range of Poisson's ratio for
3.1.1. Poisson's ratio As shown in Fig. 11, the Poisson's ratio is not constant throughout the strain development but evolves over the range of tensile strain
Fig. 8. Strain measurement: (a) schematics of relative displacement measurement, (b) Special specimen used for validation. 6
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Fig. 10. True Tensile Stress vs True Tensile Strain
Fig. 12. Curve-fitting on EA9361 tensile results.
Table 2 EA9361 tensile tests: failure stress and strain, and permanent strain. Sample #
f σxx [MPa]
f εxx
p εxx
Specimen 1 Specimen 2 Specimen 3 Specimen 4 Specimen 5 Specimen 6 Specimen 7 Average ( ± SDV)
25.30 28.90 28.00 29.00 25.70 29.10 26.50 27.5 ± 1.63
0.49 0.56 0.53 0.55 0.49 0.55 0.51 0.53 ± 0.029
0.07 0.10 0.07 0.09 0.07 0.09 0.11 0.086 ± 0.016
data to an FE model, one has to identify the most appropriate material model. As explained before, two material models, i.e., hyper-elastic model and bilinear elastic-plastic models are investigated. Fig. 12 displays the curves best-fitted by the two models. The curve from the experiment found in Fig. 12 is the average of the seven specimen's results from the tensile tests. R2 values, calculated with the definition of R2 recommended by 2 = 0.99 for the elastic/plastic model and Kvålseth [29], were RBL 2 RHE = 0.99 for the hyper-elastic model. Although both models have matching R2 values, the elastic/plastic model fits better in the initial strain range (0 < ε < 0.05) which includes the elastic region and the yielding region. Since the hyper-elastic model is formulated with polynomials, the smoothness of its curve was not able to accurately imitate the sharp modulus drop at yielding, also affecting the fitting in the adjacent elastic region; for the strains found in the entire elastic region, the corresponding stress values were significantly underestimated with respect to the test results. The elastic/plastic model accurately fitted the experimental stress/strain curve throughout the full strain range that is bilinear in nature with the two distinct moduli before and after yielding. Therefore, the elastic/plastic model is recommended for the modeling and analysis of flexible epoxy adhesives in general. The qualitative observations of the tensile test data also support the use of elastic/plastic model. Although hyper-elasticity is able to model large deformations, the plastic behavior of the adhesive observed after yielding does not fit with the fully elastic behavior of a hyper-plastic material. Furthermore, the use of the bilinear relationship also simplifies the analysis of joints with flexible adhesives including the HBB joints. For instance, the simplicity of the bilinear relation led to the kinematic semi-analytical model, developed by some researchers [30–34], for the strength analysis of HBB joints. When applicable, such simplified modeling techniques could replace fully numerical simulation of HBB joints and achieve substantial reduction in computational costs.
Fig. 11. Poisson's ratio vs true tensile strain.
isotropic materials is from 0 to 0.5. The evolution of the adhesive's Poisson's ratio must be reflected in the analysis of flexible epoxy adhesives. When constrained by the adherends, the thin bondline of adhesive is subjected to stress concentration due to the Poisson's effects. Therefore, the understanding of this nature of the flexible epoxy adhesive is vital in joint design for accurate stress analysis and, hence, failure prediction of the adhesive. Involving nonlinearly behaving flexible adhesives and their interactions with substrates, such design problems are too complex for analytical solutions, leaving the numerical modeling as a feasible alternative option. However, in general, commercial finite element packages only account for a constant value of Poisson's ratio. A manual subroutine introducing the varying Poisson's ratio is recommended for more realistic simulation of structures with flexible adhesives.
3.1.3. Permanent deformation After achieving large elongation past the yielding in the loading direction, the adhesive was found with permanent deformation. However, this permanent deformation could contribute to improved bolt load sharing (bolt load/total load) and therefore be beneficial for the HBB joints with a flexible epoxy adhesive. The following exercise qualitatively demonstrates this aspect. A hybrid bolted/bonded joint illustrated in Fig. 13(a) is subjected to tensile load repeatedly. Fig. 13(b) illustrates the resulting force/displacement curves (marked with solid lines) and the bolt load sharing
(= ) curves (marked with dashed lines). For this practice, a boltFbolt Ftotal
3.1.2. Material models for flexible adhesives In order to imitate the material's response accurately as an input
hole with no clearance is assumed. It is also assumed that the adhesive's
7
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Fig. 14. True Shear Stress vs True Shear Strain.
adhesive are clearly seen on both bonding surfaces of the adherends, indicating a good adhesion. This observation ensures that the test results were free from the poor bonding at the interface. The shear failure occurred gradually with the initial crack slowly propagating along the adhesive bondline. All specimens other than Specimen 1 resulted in stress/strain curves that correlate with each other very well. Specimen 1 is considered an outlier with a defect in the adhesive. Yielding was observed at the stress value of τxyy = 8.3 MPa. After yielding, the shear modulus dropped from Gel = 174 MPa to Gpl = 25 MPa; the elastic and plastic moduli are captured in the strange range of 0 < θxy < 0.02 and 0.12 < θxy < 0.22 , respectively. The shear tests, as well as the tensile tests, demonstrate the applicability of the elastic/plastic material model to characterize the non-linear behavior of the present flexible epoxy adhesive. The failure stresses were captured at crack initiation. Any test results between crack initiation and complete specimen failure were not considered to be a material property, therefore are not presented in Fig. 14. The failure stresses τxyf and strains εxyf are summarized in Table 3. The average value for τxyf is 14.57 MPa; εxyf average value is 0.31.
Fig. 13. Hybrid joint under the tensile load (a) Single-lap HBB joints (b) Effects of permanent deformation in adhesive.
elastic and plastic moduli and the value of yield strain are not affected by yielding, yet the permanent strain is introduced. After the first loading, the joint returns to the unloaded state with a residual displacement of d′ > 0 due to permanent deformation of its adhesive. As a result, for the same magnitude of tensile load applied, the HBB joint displaces more in the second loading than in the first loading as seen in Fig. 13(b). The higher joint displacement indicates higher shear deformation in the bolt and consequently higher load through the bolt. Hence, the bolt load sharing (bolt load/total load) is improved on the second and subsequent loadings. Testing the HBB joints under repeated loading is of great future interest to further confirm this joint design practice. In practical applications, the joints may be subjected to loading in multiple directions. Yet, the behavior of yielding under multiaxial loading is currently far too complex to be sufficiently understood. Consequently, taking advantage of the permanent deformation for improved bolt load sharing has to be particular to the HBB joints that are loaded in a single direction. Examples of which include aircraft wings, helicopter blades and so on.
3.3. Characterization summary The mechanical properties measured by the two tests are summarized in Table 4. The symbols and the corresponding properties are elaborated as: Eel and Epl are the tensile moduli in elastic and plastic regions; Gel and Gpl are the shear moduli in elastic and plastic regions; ν is the Poisson's ratio; σxxyield , σxxf and εxxf are the yield stress, failure stress and strain under tension; and τxyyield , τxyf and εxyf are the yield stress, failure stress and strain under shear. 4. Conclusions
3.2. Shear test results A HBB joint is considered the next stage of innovation for joining composite materials, especially for its use in aircraft structures. Yet, the HBB joint is not fully understood largely due to the complex behavior of flexible adhesives. Even though standards exist to measure stress/strain behavior of conventional structural adhesives, insufficient efforts have been made to extend their application to flexible adhesives that display
The results of the shear test are presented in Fig. 14. Only the results for four specimens are presented as the results for the remaining one was considered an outlier because of a defect. Prior to any observations or conclusions drawn from this custom-designed test, the accuracy of the results is verified in addition to the methodology validations presented in section 2.2.3. The measured elastic shear modulus of Gel = 174 MPa (Fig. 14) is compared with the shear modulus calculated from relation G = E/2(1+ν). For the latter, the elastic tensile modulus, Eel, and the initial Poisson's ratio, νo, obtained from the tensile tests are taken. Taking the initial elastic tensile and shear moduli and the initial Poisson's ratio was essential as the relationship is only valid in the small elastic region in which the variation of the elastic properties is negligible. The calculated Gel is 178 MPa. The small difference of 2.3% between the two shear moduli verifies that the test results are accurate. All specimens failed by cohesive failure. The remains of the
Table 3 Shear failure stress and strain.
8
Specimen #
f σxy [MPa]
f εxy
Specimen 1 Specimen 2 Specimen 3 Specimen 4 Average ( ± SDV)
15.8 13.8 13.5 15.2 14.57 ± 1.1
0.36 0.27 0.26 0.33 0.31 ± 0.048
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Table 4 Material properties of EA9361. Eel [MPa]
Epl [MPa]
Gel [MPa]
Gpl [MPa]
v
yield σxx [MPa]
f σxx [MPa]
f εxx
yield τxy [MPa]
f τxy [MPa]
f εxy
514
28
174
25
0.38–0.47
10
27.5
0.53
8.3
14.6
0.31
clearly nonlinear behavior. The innovative methodologies outlined in this work represent a promising guideline for performing such tests: characterizing a thin layer of flexible adhesives was possible through applying co-axial loads with an Arcan fixture and simultaneously measuring strains by tracking relative adherends displacement. With EA9361 AERO used as a representative material, mechanical characterization was performed to quantify the tensile and shear stress/ strain relation and failure properties. The qualitative observations from the test results led to the following insights for the design and analysis of HBB joints.
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• Poisson's ratio significantly varies throughout the large range of
• •
strain, and the peak value is as high as υ = 0.47 . In a joint, a thin layer of adhesive is significantly exposed to Poisson's effect as its deformation is constrained by the adherends. Therefore, this study recommends that the evolution of Poisson's ratio is reflected in the stress analysis of the flexible adhesive, whether analytical or numerical. The elastic/plastic material model is recommended as it can accurately imitate the nonlinear stress/strain relation of flexible epoxy adhesives. Simplifying the material model to a bilinear relationship also allows the analysis of HBB joints, and other adhesively bonded structures, at a reduced computational cost. Yielding produces permanent deformation in the adhesive, which could improve the bolt load sharing, thus the structural performance of the HBB joints. The use of this benefit is applicable to the joints that are loaded in a single direction.
Data availability The raw/processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations. Acknowledgements The authors would like to thank the Consortium de Recherche et d’Innovation en Aérospatiale au Quebec (CRIAQ) and the National Research Council labs (NRC-AMTC) without whose generous support this research would not have been possible. Behnam Ashrafi, Laurin Hugo, and Steven Roy (CNRC-NRC) are also acknowledged for their support regarding the fabrication of the test specimens. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.polymertesting.2019.106048. References [1] P. Lopez-Cruz, J. Laliberté, L. Lessard, Investigation of bolted/bonded composite joint behaviour using design of experiments, Compos. Struct. 170 (2017) 192–201. [2] G. Kelly, Quasi-static strength and fatigue life of hybrid (bonded/bolted) composite single-lap joints, Compos. Struct. 72 (2006) 119–129. [3] F. Ascione, M. Lamberti, A. Razaqpur, S. Spadea, Strength and stiffness of adhesively bonded GFRP beam-column moment resisting connections, Compos. Struct. 160 (2017) 1248–1257. [4] C. Brotherhood, B. Drinkwater, S. Dixon, The detectability of kissing bonds in
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