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MP 110521

adhesive crack and then quickly becomes a cohesive failure.

Different approaches were recently em-ployed to predict the mechanical behaviour of bonded assemblies. In the early stages of bonded structures analyses, theoretical studies were popular [14-16], which em-ployed simplifying assumptions in the structures geometry, materials behaviour, loading, and boundary conditions, to for-mulate efficient closed-form elasticity solu-tions for the local fields in the adhesive re-gion. The main advantage of analytical modelling is that the structure can be ana-lysed quickly, although with lot of embed-ded simplifications [17].

In the computer age, FEM codes to simu-late the mechanical behaviour of structures were rapidly implemented, providing a more accurate insight on this subject. In the FEM, each component of the adhesive joint is treated as a continuum and the anal-ysis of large displacements, such as those seen in the single lap joints, is also availa-ble. Accounting for the materials plasticity was also made easier, since FEM codes ac-tually incorporate several complex material laws. One of the first FEM works on bonded

bonded joint. Due to differential straining in the substrates, adhesively-bonded joints inevitably experience stress concentra-tions, especially in the adhesive layer near the ends of overlap where the load transfer takes place. Among the many factors af-fecting the strength of a bonded joint, the stresses in both adhesive layer and sub-strates are probably most crucial for de-signing of bonded joints [6-8].

Structural designers are interested in the strength evaluation under service con-ditions. A reliable prediction of stresses at locations where a high risk of crack initia-tion exists is thus a necessary step in de-signing mechanical structures. Simplified models [9-11] and solid finite element cal-culations [12, 13] showed that in adhesive joint, both shear and normal stresses reach their maximum value in the vicinity of the bond edges. These stress concentrations often lead to the joint failure. In an adhe-sive joint, three kinds of failure are possi-ble. The first is adhesive failure, which °Ccurs at the adherend/adhesive in-terface. The second is cohesive failure, which °Ccurs in the adhesive. The last kind of failure is mixed: it starts out as an

Adhesive bonding technology is widely used today in almost all the industries fields of the world and this is mainly due to its high strength–weight ratio, low cost and high efficiency [1].

The potential use of adhesive joints as fasteners in machine and structure compo-nents has been increasing gradually. Adhe-sive joints supersede, especially in long-time periods, conventional joining methods such as bolting, riveting, soldering and welding from day to day in aviation, space, automotive, substructure, medicine, elec-tronic packaging, sport, building and ma-rine industrials, for which the security of the joints is needed [2-4].

Adams and Harris [5] have studied the influence of the geometry of the ends of the overlap of adhesively bonded joints on the stresses. They showed that rounding the corners removes the mechanical singular-ity point and these roundings have consid-erable effect on the magnitude of the stress reduction.

The reduction of transverse shear and normal stress concentrations along the edges of adhesive bondlines is important in order to prevent premature failure of the

In this paper, the mechanical behavior of the Double Lap Joints (DLJs) bonded with adhesive was analyzed. The stress-strain behaviors were investigated along the overlap length and adherend thickness in DLJs subjected by tensile loads. The stress analyses were performed via Finite Element Method (FEM). The FEM calculations were performed with ANSYS (12.0.1). Experimental results were compared with the FEM results and were found quite reasonable. The results show that the failure loads were increased with an increase in adherend thickness. The stress-strains were changed depending on adherend thickness and overlap length. Both FEM stress analyses and experimental results revealed that failure occurred around at the edge zones of the overlap length due to the effect of shear stresses, while the failure at the edges of the adhesive layer originated from the peel strain in tensile.

Hamit Adin and Şemsettin Temiz, Batman, Turkey

Experimental and Numerical Strength Analysis of Double Lap Joints Subjected to Tensile Loads

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assemblies dates back to the 1970s when Wooley and Carver [18] conducted a stress analysis on single-lap joints.

On the strength prediction of bonded as-semblies, two different lines of analyses were developed over the years: the strength of materials and fracture mechanics-based methods. The strength of materials ap-proach is based on the evaluation of allow-able stresses [19, 20] or strains [21, 22], by theoretical formulations or the FEM. The assemblies strength can be predicted by comparing the respective equivalent stresses or strains at the critical regions, obtained by stress or strain-based criteria, with the properties of the structure con-stituents [23-25].

The purpose of this research is to investi-gate strength of joint along different the overlap lengths in double lap joints (DLJs) subjected by tensile load. A hard adhesive was used as adhesive. The mechanical be-haviors of DLJs were analyzed, both experi-mentally and numerically. The numerical analysis of stress-strain in the DLJs was per-formed via Finite Element Method (FEM). FEM was carried out to predict failure loads, to assist the geometric design and to identify effective ratios of properties to maximize joint strength. The joint strengths were esti-mated using the obtained interface stress-strain distributions. The FEM results were also compared with experimental results.

Experimental

The determination of mechanical proper-ties of adhesive. In the study, the 2214 regular produced by 3M was chosen as ad-hesive and AA2024-T3 alloy was utilized as adherend which widely used in the air-craft industry. To determine mechanical properties of adhesive bulk specimen method was performed. The bulk speci-mens used in this study were prepared as described in Ref. [26].

The stress–strain (σ – ε) behaviors of the adhesive was determined by bulk speci-mens tested under specified the conditions. The experiments of bulk specimen were performed using video extensometer, Shi-madzu (Shimadzu Corporation, Tokyo, Ja-pan) (100 kN) machine at room tempera-ture and relative humidity 50 % ± 5. During tensile tests, the crosshead speeds were maintained at 1 mm/min. Four specimens were tested. Typical tensile stress–strain curves for the adhesives and adherend are shown in Figure 1. It can be seen in Figure 1.a that the maximum stress of the adhe-sive is measured as 72 MPa.

Production of DLJs. DLJs were made of AA2024-T3 alloy bonded using 2214 regu-lar type adhesive. The dimensions of adher-end are shown in Table 1. The thicknesses of adhesive and outer adherend (cover plate) were chosen as 0.25 mm and 1.6 mm, re-spectively. In addition, the width of adher-end was chosen as 25 mm. The other dimen-sions of the DLJs are shown in Figure 2. Since effects of thickness and overlap length

were examined, the same element dimen-sion was used in all models as often as prac-ticable (see in Table 1 and Figure 3a). The upper and lower cover plates have the same dimensions and materials. The thickness of upper and lower patches was 1.6 mm.

Four different adherend thickness and overlap length were used. The DLJs were manufactured as four different specimens for each condition of adherend thicknesses

Hin

wei

s Ta

ble

2 fe

hlt!

Figure 2. Double Lap Joints (DLJs) configuration under tensile loading: (a) geometry and loading (all dimensions in mm); b) Mesh details and boundary conditions

Adherend thickness (mm) Overlap length (mm) Adherend width (mm) Adhesive thickness (mm)

3.2 24.8 25 0.25

4.8 26.8 25 0.25

6.4 28.8 25 0.25

8.0 30.8 25 0.25

Table 1. Geometrical parameters of the DLJs used in experimental and numerical studies (all dimensions in mm)

Figure 1. Tensile stress–strain behaviors of adhesive and adherend: (a) SBT 9244 adhesive; (b) AA2024-T3 alloy [26]

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and overlap lengths. The mechanical prop-erties of adherend and adhesive are given in Tables 1. Before bonding, the adherend surfaces were degreased with acetone, etched with H2SO4 + Na2Cr2O7.2H2O for 30 minutes at 60-65 °C, washed in running tap water and dried in an oven for 30 min-utes at 60 °C. Then, the adhesive was pre-pared. It was applied at the joint surface and the adherend were clamped for curing as cure of adhesives were waited.

The tensile load was applied in the x di-rection. DLJs experiments were performed under the same conditions with bulk speci-men experiments as mentioned above.

Finite Element Modeling of the DLJs. In this step, Finite Element Method (FEM) was employed in order to analyze the behaviors of stress and strain of the DLJs. The FEM cal-culations were the ANSYS (Academic Teach-ing Advanced, Ver. 12.0.1) software [27]. Additionally, the stress-strain analysis was obtained according to von Mises yield crite-rion. Because, Gali et al. [28] showed that the von Misses yield criterion was suitable to model the stress-strain behavior of the adhesives used in the joint. By means of this criterion, the stress-strain distributions in the adhesive layer were calculated.

Loading, boundary conditions and mesh conditions were presented in Figure 3. In this study, Plane 82 elements were used. The elements are composed of eight differ-ent nodes with two degrees of freedom. Baylor and Sancaktar [29] showed that if the mesh density along the transverse di-rection of the overlap was greater than 3 elements per mm, then the variation in maximum principal stress and von Mises stress with mesh density would be effec-tively removed. It was also shown that for an adhesive thickness of 0.2 mm, 25 ele-ments per mm in the peel direction would result in the uncoupling of these stresses with mesh density.

The mesh density can effect the strain predictions in the adhesive layer. A smaller element size will generally give a higher strain. For this reason, the size of elements in the mesh was reduced until a stable strain value had been achieved. Eventually, 25 elements through the adhesive thick-ness (0.25 mm) were used in the models, as shown in Figure 3b. The adherend thick-ness was meshed with 100 layers. The cover plate thickness (1.6 mm) was meshed with 12 layers. So, the smallest element sizes were used as 0.01 mm in the adhe-sives and 0.133 mm in the adherends. The total number of nodes and elements were chosen 26889 and 8810, respectively.

Results and discussion

Experimental results. Four different spec-imens were tested in experiments for each condition of adherend thickness and over-lap length. The specimens were carefully and closely observed to understand failure mechanism during the tensile experi-ments. All failures of the joints were cata-strophic failure and occurred at the inter-face without breaking the adherends. The average values of failure loads were pre-sented in Table 3. It is clearly seen from table that the lowest failure load was deter-mined at t = 3.2 mm for each specimen.

The FEM calculations. To find out the failure loads of the specimens in the FEM calculations, ultimate strength of adhe-sives (σ*) were used. The equivalent stress

(σeqv) was calculated using the von Mises failure criterion and it was assumed that the failure occurred when the equivalent stress calculated at any point of adhesive layer reached the ultimate strength of ad-hesive. In addition, the effects of thickness and overlap length at the interfaces of ad-herends were examined.

As the maximum von Mises stress val-ues at adhesive interface approach to these values, then they were multiplied by the frontal area of specimens (t × b = thickness of specimen × breadth of specimen) from which the failure loads were obtained, as shown in Table 3.

When the results that calculated from FEM approach near to the maximum stress of bulk specimen, the adhesive interfaces were turned on. Paths were defined

Figure 3. Comparison of failure loads for DLJs; (a) The effects of different adherend thicknesses (L = 24.8 mm); (b) The effects of different overlap lengths (h = 4.8 mm)

AA2024-T3 (Adherend) 2214 (Adhesive)

E (MPa) 71875 5171

ν 0.33 0.35

σ* (MPa) 482 72

ε*(mm/mm) 0.159 0.02

E, Young’s modulus; ν, Poisson’s ratio; σ*, ultimate strength; ε* Ultimate strain.

Table 2. Material proper-ties of the adherend and adhesives [26]

Adherend thickness (mm)

Overlap length (mm)

FEM Failure Load (FFEM) (kN)

Experimental Failure Load (FEXP) (kN) FR (FFEM/FEXP)

3.2 24.8 5.771 5.398 1.069

4.8 24.8 8.705 8.436 1.032

6.4 24.8 11.637 11.027 1.055

8.0 24.8 14.608 14.273 1.023

4.8 24.8 8.705 8.436 1.032

4.8 26.8 8.733 8.455 1.033

4.8 28.8 8.747 8.475 1.032

4.8 30.8 8.762 8.491 1.032

Table 3. Comparison of failure loads obtained from FEM and experimental for different adherend thickness and overlap length

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through the lines A-B and C-D. After that, path values were separately found for each adhesives and specimen. The stress and strain values (σx, σy, τxy, σeqv, εx, εy, γxy, εeqv) were selected for each specimen and their results were found. The figures were drawn using Matlap.

Effect of the adherend thickness and overlap length on failure load. The failure loads of experimental and FEM calculation were shown in Table 3. As it can be seen from the above mentioned tables, the fail-ure loads from the FEM calculations and the experimentally measured values seem to be quite close to each other. In addition, it was found that the FEM results of stress were well consistent with the experimental results. In the last columns of the tables, the convergence ratios were found by di-viding the experimental loads (FEXP) with failure loads (FFEM) found by the FEM calcu-lations. In general, the values of FR were found to be very close to 1. As a result, the values of experimental results were con-sistent with the values of FEM calculations. Additionally, FR ratios were found between 1.023 and 1.069.

The effects of adherend thickness and overlap length in failure loads were showed in Figure 3. It can be seen from Figure 3a that when the adherend thicknesses were increased, the failure loads were increased. The adherend thicknesses were played a significant role in failure initiation and loads. So, these results have been consist-ent with Ref. [26]. The adhesion area of the butt region increased gradually with an in-crease in adherend thickness, therefore, the failure load increased.

The effect of overlap lengths on the fail-ure load for the DSJs with 2214 adhesive are given in Figure 3b.10. It can be seen in both FEM and experimental results that the increase in overlap length was in-creased less than Figure 3a in the load car-ried by the DSJs. In addition, the failure loads were maximum when the adherend thickness and overlap length was around t = 8 mm, L = 30.8 mm, respectively. So, it was shown that this dimensions were af-fected the performance of the DLJs.

Stress and strain distribution results. The stress and strain distributions of DSJs subjected to a tensile load are given in the following figures. For the stress strain dis-tributions between adherend and cover plate, adhesive-cover plate interface along line A-B were selected and for the stress and strain distributions in the butt region, the mid-line of adhesive along line C-D was selected as given in Figure 2a.

Figure 5. Stress distributions along the C-D bond-line on the adhesive side of the DLJs for different adherend thickness (L: 24.8 mm): (a) Sx (σx) stress distributions; (b) Sy (σy) stress distributions; (c) Sxy (τxy) stress distributions; (d) Seqv (σeqv) von-Mises stress distributions

a) b)

c) d)

Figure 4. Stress distributions along the A-B bond-line on the adhesive side of the DLJs for different adherend thickness (L: 24.8 mm): (a) Sx (σx) stress distributions; (b) Sy (σy) stress distributions; (c) Sxy (τxy) stress distributions; (d) Seqv (σeqv) von-Mises stress distributions

a) b)

c) d)

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Effect of the adherend thickness on stress distribution. The stress distribu-tions along the line A-B for different adher-end thickness obtained from FEM analyses is presented in Figure 4. The longitudinal stress (σx) and peel stress (σy) distribu-tions along the bond-line A-B for different adherend thickness are given in Figure 4a and b, respectively. The σx and σy stresses were maximum at the edges of x/L (point A and B). The stresses increased when close to points A and B. In addition, σx and σy increased with increasing of adherend thickness. Note that both the σx and σy stresses were symmetric along the hori-zontal centerlines of the adhesive.

The shear stress (τxy) and equivalent stress (σeqv) distributions along the bond-line A-B for different adherend thickness are depicted in Figure 4c and d, respec-tively. The τxy was maximum at point A, whereas it was minimum at point B. The σeqv was symmetric and maximum at point A and B. The σeqv stress also in-creased when the adherend thickness in-creased.

Contrary to Figure 4a and 4b, the adher-end thickness had a considerable effect on τxy stress distributions, and τxy stress de-creased when the adherend thickness in-creased. Except for t : 3.2 mm adherend thickness the τxy was symmetric. σx, σy and σeqv were also maximum at point A and B point. They were more uniform at the end of the overlap length. The comparison indi-cates close agreement for the stress distri-bution of σx, σy and σeqv as shown in Figure 4a, 4b and 4d, respectively. Both the peel-ing and shear stresses were increased with increasing of adherend thickness. Due to these stresses, failures were initiated at A and B points.

The stress distributions along the line C-D for different adherend thickness ob-tained from FEM analyses is showed in Fig-ure 5. The σx, σy and σeqv stress distribu-tions along the bond-line C-D for different adherend thickness are illustrated in Fig-ure 5a, 5b and 5d, respectively. The σx, σy and σeqv stresses were minimum at the edges of x/L (point A and B) but the stresses were higher close to middle point of x/L. The values of σx, σy and σeqv increased with increasing of adherend thickness. The nor-mal and equivalent stresses were high for thick adherend and those stresses in-creased with an increase in adherend thickness. The reason of this is that when the adherend thickness gets thinner, the adhesive in the butt region is exposed to more strain in the loading direction and

Figure 7. Stress distributions along the C-D bond-line on the adhesive side of the DLJs for different overlap length (h: 4.8 mm): (a) Sx (σx) stress distributions; (b) Sy (σy) stress distributions; (c) Sxy (τxy) stress distributions; (d) Seqv (σeqv) von-Mises stress distributions

a) b)

c) d)

Figure 6. Stress distributions along the A-B bond-line on the adhesive side of the DLJs for different overlap length (h: 4.8 mm): (a) Sx (σx) stress distributions; (b) Sy (σy) stress distributions; (c) Sxy (τxy) stress distributions; (d) Seqv (σeqv) von-Mises stress distributions

a) b)

c) d)

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this causes an increase in the normal and equivalent stresses.

The shear stress (τxy) distributions along the bond-line C-D for different adherend thickness are showed in Figure 5c. The τxy was maximum at point C, whereas it was minimum at point D. Contrary to Figure 5a, 5b and 5c; the τxy shear stress also de-creases when the adherend thickness in-creases. The σx, σy, τxy and σeqv stresses were also symmetric along the horizontal centerlines of the x/L. Except for τxy distri-bution the σx, σy and σeqv were more uni-formly along the bond-line C-D.

Effect of the overlap length on stress distribution. In Figure 6, as a result of the FEM, normal (σx and σy), shear (τxy) and equivalent (σeqv) stress distributions ob-tained from the adhesive layers A-B bond-line throughout at t = 4.8 mm adherend thickness have been given. This figure clarified that maximum values of all stress located at the edges of x/L. It was observed in Figure 6a that maximum and minimum values of σx occurred in the edges. As over-lap length were increased, the values of σxincreased as well. But, when overlap length were increased, the σeqv decreased. The peeling stresses (σy) along the A-B bond-line were determined by means of Figure 6b. Maximum and minimum values of the peeling stress were determined in edges and in the middle of x/L. Similar to the σy components in the middle of the ad-hesive layer, the σy at the interface was al-most constant across the x/L, but increased near the edges. The peel stresses at the edges of the overlap were very important because of cause initiation and propagation of failure in this region. This argument is consistent with Hart-Smith’s argument [1].

Figure 6c showed that the overlap length had a considerable effect on τxy stress dis-tributions, and the stresses of τxy were de-creased when the overlap length was in-creased until the middle of x/L. But, τxy, after this point was decreased. As seen can be in Figure 6d, σeqv stress distribution has almost the same characteristics with σy peeling stress distribution. Maximum and minimum values of the equivalent stress were obtained in edges and middle of x/L. In addition, it should be noted that σx, σy, τxy and σeqv distributions were symmetric along the horizontal and vertical center-lines axis of x/L.

The longitudinal (σx) stress, peel (σx) stress and equivalent (σeqv) stress distribu-tions along the bond-line C-D for different overlap lengths are given in Figure 7a, b and d, respectively. In these figures, the

Figure 9. Strain distributions along the C-D bond-line on the adhesive side of the DLJs for different adhesive thickness (L: 24.8 mm): (a) Ex (εx) strain distributions; (b) Ey (εy) strain distributions; (c) Exy (γxy) strain distributions; (d) Eeqv (εeqv) von-Mises strain distributions

a) b)

c) d)

Figure 8. Strain distributions along the A-B bond-line on the adhesive side of the DLJs for different adhesive thickness (L: 24.8 mm): (a) Ex (εx) strain distributions; (b) Ey (εy) strain distributions; (c) Exy (γxy) strain distributions; (d) Eeqv (εeqv) von-Mises strain distributions

a) b)

c) d)

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stress distributions σx, σy, and σeqv are similar to each other qualitatively. The σx, σy and σeqv stresses were maximum at the ends of the overlap length (point A and point B). The stresses points far from A and B were low. It can be seen from Figure 7a and d that the values σx and σeqv were de-creased with increase of the overlap length. That’s way the load carried by the bond-line decreases depending on decreased in overlap length. Consequently, the load was carried more by the butt region in short overlap length and, therefore, this situation accelerated an increase in the longitudinal and peel stresses. In addition, the overlap length longitudinal (σx) stress had no sig-nificant effect of on stress distributions as value along the C-D bond-line.

The shear (τxy) stress distribution along line C-D on the adhesive different overlap lengths is given in Figure 7c. Contrary to σx, σy and σeqv stresses, the overlap length had a considerable effect on τxy stress dis-tribution, and τxy stresses until the middle of x/L were decreased when the overlap length was increased. Then, τxy was in-creased. τxy was also maximum at point A and minimum near B point. The joint dis-tributes the shear stress (τxy) from the ends of the overlap towards the centre more uni-formly than the longitudinal (σx), peel (σy) and von Mises equivalent (σeqv) stresses.

Effect of the adherend thickness on strain distribution. The strain distributions along the line A-B for different adherend thickness are presented in Figure 8. The εx, εy, γxy and εeqv distributions along the bond-line A-B for different adherend thickness are given in Figure 8a, b, c and d, respec-tively. Similar to Figure 8b and d that, the εy and εeqv strains were maximum at the ends of the overlap (point A and B). The strain of εy was decreased with increase of the adher-end thickness along A-B line. Contrarily, the equivalent strains (εeqv) were increased. The εx strain was maximum at the end of the x/L, and was decreased when near point A and B. Figure 8c showed that the overlap length had a considerable effect on γxy strain distributions, and the values of γxy were decreased when the overlap length was increased until the middle of x/L. But, γxy after this point they were decreased. Maximum and minimum values of the shear strain were obtained in edges and middle of x/L. In addition, notes that εx, εy, γxy and εeqv distributions were symmetric along the ver-tical centerline axis of x/L.

The εx, εy, γxy and εeqv distributions along the bond-line C-D for different adherend thickness are shown in Figure 9a, b, c and

d, respectively. Figure 9a and d are similar. A comparison of the εx peeling strain and the εeqv equivalent strain evaluated along the C-D these strains were increased with increase of the adherend thickness. Maxi-mum and minimum values of the εx and εeqv strains were obtained in edges of x/L whereas, the εy peeling strain distribution was minimum in edges. The peeling strain distribution along C-D was also decreased with an increased in adherend thickness. The shear strain (γxy) distribution along the bond-line C-D for different adherend thick-ness is illustrated in Figure 9c. The γxy was maximum at point C, whereas it was mini-mum at point D. Contrary to Figure 9a, 9b and 9d, the γxy shear strain was increased in the middle point of C-D bond-line and then it was decreased when the adherend thickness increases. The values of γxy away from C were approached to zero. It can be seen from Figure 9 that εx, εy, γxy and εeqv distributions were symmetric along the vertical centerline axis of x/L.

Effects of the overlap length on strain distribution. The strain distributions along the line A-B for different overlap length are illustrated in Figure 10. Figure 8 and Fig-ure 10 are similar except for Figure 8c and

10c. The εx, εy, γxy and εeqv distributions along the bond-line A-B for different over-lap length are given in Figure 10a, b, c and d, respectively. The εy and εeqv strains were maximum at the ends of the overlap (point A and B). The strain of εy was decreased with increase of the adherend thickness along A-B line. Contrarily, the equivalent strains (εeqv) were increased. The εx strain was maximum in the middle of the x/L, and was decreased when far from point A and B. Figure 8c showed that the overlap length had a considerable effects on γxy strain dis-tributions, and the values of γxy were de-creased when the overlap length was in-creased until the middle of x/L. But, after this point γxy was decreased. Maximum and minimum values of the shear strain were obtained in edges and middle of x/L. It can be seen from Figure 10a, b and d that the strains were increased when the over-lap length was increased. In addition, note that the εx, εy and εeqv strain distributions were symmetric along the vertical center-line axis of x/L.

The εx, εy, γxy and εeqv distributions along the bond-line C-D for different overlap length are shown in Figure 11a, b, c and d, respectively. Figure 11a and d are similar.

Figure 10. Strain distributions along the A-B bond-line on the adhesive side of the DLJs for different overlap length (h: 4.8 mm): (a) Ex (εx) strain distributions; (b) Ey (εy) strain distributions; (c) Exy (γxy) strain distributions; (d) Eeqv (εeqv) von-Mises strain distributions

a) b)

c) d)

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A comparison of the εx peeling strain and the εeqv equivalent strain were evaluated along the C-D. These strains were de-creased again with increase of the overlap length. Maximum and minimum values of the εx and εeqv strains were obtained at edges of x/L whereas, the εy peeling strain distribution was minimum at edges. It is observed from Figure 11b that the peeling strain distribution along C-D was also in-creased with increase in overlap length. The shear strain (γxy) distribution along the bond-line C-D for different overlap length is illustrated in Figure 11c. The γxy was maxi-mum at point C, whereas it was minimum at point D. Contrary to Figure 11a, 11b and 11d, the γxy shear strain was increased in the middle point of C-D bond-line and then was decreased when the overlap length in-creased. The values of γxy away from C were approached to zero. Figure 11 b and c showed that the overlap length had no sig-nificant effect on strains distributions as value along the C-D bond-line. It can be seen from Figure 11 that εx, εy, γxy and εeqv distributions were symmetric along the vertical centerline axis of x/L.

As seen from Figure 9 and Figure 11, while all strains in the DLJs were close to

each other, εx alone was considerably. All of the strains were maximum at the ends of the overlap length except for γxy shear strain.

When the magnitude of the equivalent stresses is considered, it is clearly that the equivalent stresses have very important influence on the initiation and the propaga-tion of failure at the edges of DLJs. Conse-quently, failure initiation was probably oc-curred on the edges of overlap (the line A-B) at the interface of adhesives. Then, the failure at ends promotes to the centre of overlap before joining each other.

Conclusions

This work is about the effects of the adherend thickness and overlap length on DLJs sub-jected to static tensile loadings. In the calcu-lations Finite Element Method (FEM) was used. The following results were obtained:• Comparing the failure loads estimated

by the analysis of FEM with the failure loads obtained by tensile test, it was seen that they were in a considerable harmony with each other.

• The failure loads were increased with an increase in adherend thickness. The ef-fect of overlap lengths on the failure loads

was less than adherend thickness. The load carried was increased with an in-crease in adherend thickness due to the increased adhesion area. In addition, the failure loads were maximum when the adherend thickness and overlap length was around t = 8 mm, L = 30.8 mm, re-spectively. Namely, the dimensions were affected the performance of the DLJs.

• The stress-strains were changed depend-ing on the adherend thickness and over-lap length. When adherend thickness was increased, the values of normal, peel and equivalent stress-strains were in-creased. These stresses along A-B bond-line were also higher in the ends of the interface. The effect of the adhesive thickness on stress-strain along A-B was higher than that of along C-D bond-line.

• The equivalent stress and strain has very important influence on the initia-tion and the propagation of failure at the edges of DLJs. Equivalent stress and strain transferee from the end to the center of the DLJs with increasing of both adherend thickness and overlap length. This is the reason for increase in the strength of joints. In addition, the ef-fect of equivalent strain increases with increasing of adherend thickness and overlap length. Eventually, failure initia-tion occurred on the edges of overlap at the interface of adhesives.

• The joint distributes the shear stress-strain from the ends of the overlap to-wards the centre more uniformly than the longitudinal, peel and equivalent stresses. The normal and equivalent stresses are high for thick adherend and those stresses increase with an increase in adherend thickness. The reason of this is that when the adherend thickness gets thinner, the adhesive in the butt region is exposed to more strain in the loading direction and this causes an increase in the normal and equivalent stresses.

• The peel stresses at the edges of the over-lap length was very important because of causes initiation and propagation of fail-ure in this region. Both FEM stress analy-ses and experimental results presented that failure occurred around at the edges zone of the overlap length due to the ef-fect of shear stresses, while the failure at the edges of the adhesive layer originated from the peel strain in tensile.

• The stress and strain distributions were symmetric along the horizontal and ver-tical centerlines axis of x/L. They are more uniformly at the end of the overlap length.

Figure 11. Strain distributions along the C-D bond-line on the adhesive side of the DLJs for different overlap length (h: 4.8 mm): (a) Ex (εx) strain distributions; (b) Ey (εy) strain distributions; (c) Exy (γxy) strain distributions; (d) Eeqv (εeqv) von-Mises strain distributions

a) b)

c) d)

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References

 1 L. J. Hart-Smith: R. D. Adams (Ed.), Aerospace, Adhesive bonding, Cambridge England: Wood-head Publishing Ltd., (2005), pp. 489-494

 2 M. K. Apalak, R. Davies R.: Analysis and de-sign of adhesively bonded corner joints, Int. J. Adhesion Adhesives, 13 (1993), pp. 219-235

 3 M. D. Aydın: Experimental and theoretical investigation of mechanical properties of the adhesive bonded single lap joint, Ph.D. Thesis, Mechanical Engineering, Atatürk University, Erzurum, Turkey (2003)

 4 M. D. Aydın, Ş. Temiz, A. Özel: Machine and Engineer 536 (2004), pp.18-24

 5 R. D. Adams, J. A. Harris: The influence of local geometry on the strength of adhesive joints, Int. J. Adhesion Adhesives 7 (1987), pp. 69-80

 6 L. J. Hart-Smith: Adhesive-bonded Single-lap Joints, NASA Technical Report CR-112236. NASA, Houston, TX (1973)

 7 R. D. Adams, J. Comyn, W. C. Wake: Structural Adhesive Joints in Engineering. Elsevier, Amsterdam, ISBN 0-412-70920 (1997)

 8 A. J. Kinloch: Adhesion and Adhesives, Science and Technology, Chapman and Hall, London, (1993)

 9 O. Volkersen: Die Nietkraftverteilung in zugbeanspruchten Nietverbindungen mit konstanten Laschenquerschnitten, Luftfahrt-forschung 15 (1938), pp. 41-47

10 F. Delale, F. Erdogan, M. N. Aydinoglu: Stresses in Adhesively Bonded Joints: A Closed Form Solution, J. Composite Materials 15 (1981), pp. 249-259

11 P. A. Gustafson, A. Bizard, A. Waas: Dimen-sionless parameters in symmetric double lap joints: An orthotropic solution for thermome-chanical loading, Int. Journal Solids Structure 44 (2007), pp. 5774-5795

12 R. D. Adams, W. C. Wake: Structural adhesive joints in engineering. Elsevier Applied Sci-ence, London and New York, 1984

13 K. Shahin, F. Taheri: Analysis of Deformations and Stresses in Balanced and unbalanced Adhesively Bonded Single-Strap Joints. Int. J. of Composite Structure 81 (2007), pp. 511-524

14 M. Goland, E. Reissner: The stresses in ce-mented joints. Journal of Applied Mechanics 66 (1944), pp. 17-27

15 F. Szépe: Strength of adhesive-bonded lap joints with respect to change of temperature and fatigue. Experimental Mechanics 6 (1966), pp. 280-286

16 J. Pirvics: Two dimensional displacement–stress distributions in adhesive bonded com-posite structures. The Journal of Adhesion 6 (1974), pp. 207-228

17 S. K. Panigrahi, B. Pradhan: Three dimensional failure analysis and damage propagation behav-ior of adhesively bonded single lap joints in lam-inated FRP composites, Journal of Reinforced Plastics and Composites 26 (2007), pp. 183-201

18 G. R. Wooley, D. R. Carver: Stress concentration factors for bonded lap joint, Journal of Aircraft 8 (1971), pp. 817-820

19 J. A. Harris, R. D. Adams: Strength prediction of bonded single-lap joints by non-linear finite element methods. International Journal of Adhesion & Adhesives 4 (1984), pp. 65-78

20 D. A. Bigwood, A. D. Crocombe: Non-linear ad-hesive bonded joint design analyses, Interna-tional Journal of Adhesion and Adhesives 10 (1990), pp. 31-41

21 A. D. Crocombe, R. D. Adams: An elastoplastic investigation of the peel test, The Journal of Adhesion 13 (1982), pp. 241-267

22 S. J. Lee, G. L. Lee: Development of a failure model for the adhesively bonded tubular single lap joint, The Journal of Adhesion 406 (1992), pp. 1-14

23 Z. Q. Qian, A. R. Akisanya: An investigation of the stress singularity near the free edge of scarf joints, European Journal of Mechanics A/Solids 18 (1999), pp. 443-463

24 E. Dragoni, P. Mauri: Intrinsic static strength of friction interfaces augmented with anaero-bic adhesives, International Journal of Adhe-sion and Adhesives 20 (2000), pp. 315-321

25 S. Feih, H. R. Shercliff: Adhesive and composite failure prediction of single L joint structures under tensile loading, International Journal of Adhesion & Adhesives 25 (2005), pp. 47-59

26 Ş. Temiz: Application of bi-adhesive in double-strap joints subjected to bending moment, J. Adhesion Sci. Technol. 20 (2006), pp. 1547-1560

27 ANSYS, The general purpose finite element software, Swanson Analysis Systems, Houston, TX

28 S. Gali, G. Dolev, O. Ishai: An effective stress/ strain concept in the mechanical characteriza-

tion of structural adhesive bonding, Int. J. of Adhesion and Adhesives 1 (1981), pp. 135-140

29 J. S. Baylor, E. Sancaktar: Reliability, Stress Analysis and Failure Prevention Issues in Emerging Technologies and Materials 87 (1995), ASME-DE, pp. 41-48

The Authors of This Contribution

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Abstract

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