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Abstract—The aim of this work is to analyze by the finite
element method using three dimensional finite element analysis code ABAQUS the effect of the geometry of the edge adhesive and adherend on reducing peel stresses, von mises, and the shear stress in the adhesive layer, several forms were considered namely bead of adhesive, internal and external beveling of the plate and the combination of an adhesive bead and beveling of the plate, the results show clearly that the change form of the edges of the adhesive and the adherend decreases considerably the value of the stresses in the adhesive layer.
Keywords— bead of adhesive, beveling of plate, elastoplastic behavior, single lap joint.
I. INTRODUCTION
N adhesive bonded joint is a structure composed of two adhérends joined by an adhesive. Adams and Wake [1]
define the adhesive as "a polymer material which, when applied to surfaces, can join together and resist separation" and adherents as members of a structure which are joined together by an adhesive. Dans les structures collées, les efforts sont transmis d'un substrat à un autre à travers les couches d'adhésifs dans la surface de recouvrement, c'est-à-dire que l'adhésif joue le rôle de moyen de transfert des efforts. La différence majeure entre les structures assemblées par collage et celles assemblées par fixation mécanique est la surface de contact. Qui dans le cas du collage est beaucoup plus large que dans le cas des fixations mécaniques. Les concentrations des contraintes sont donc minimisées et leur distribution devient plus uniforme dans la région de recouvrement.
Kouider. MADANI, Djillali Liabes University, mechanical engineering departement Bp, 89 cité ben M'hidi,Sidi bel abbes, 22000, Algeria, (phone:00213779101093; fax:0021348544100; e-mail: [email protected]).
Mohamed MOKHTARI, Djillali Liabes University, mechanical engineering departement Bp, 89 cité ben M'hidi,Sidi bel abbes, 22000, Algeria (e-mail: [email protected]).
Mohamed BELHOUARI, Djillali Liabes University, mechanical engineering departement Bp, 89 cité ben M'hidi,Sidi bel abbes, 22000, Algeria (e-mail:[email protected]).
Mohamed EL HANNANI, Djillali Liabes University, mechanical engineering departement Bp, 89 cité ben M'hidi,Sidi bel abbes, 22000, Algeria (e-mail:[email protected]).
Configurations of a single lap joint have been studied for about more than sixty years and many analytical and numerical models have been developed. Volkerson [2] proposed a first approach to analyze this type of structure. He considered only shear strain in the adhesive and axial deformations in adhérends. Demarkles [3] improved the model including shear deformation of adhérends. These analyzes do not include the bending moment produced by the eccentric path of the load. The effect of the bending moment resulting in efforts normal to the plane of the adhesive, called efforts coats, which are important at the edges of the joint. Goland and Reissner [4] were the first to include the effect of the eccentric path of the load by applying moments to the joint edges. These moments were calculated taking into account the geometry, material properties and the applied load The rapid development of computers makes use of the most attractive and practicable digital techniques. Numerical methods can be used to analyze models with any geometry and loading conditions. They are best suited to the analysis of structures made of different materials.
Numerical methods can be applied to solve the equations that represent the structural behavior. Bigwood and Crocombe [5] have used the finite difference method to resolve the equation for the peeling forces and shear stresses in the adhesive layer. they have included non-linear effects in the previous work and developed a elasto-plastic analysis in the adhesive bonded joints, using the same approach, another method of discretization is to divide the structure in small portions and to make the model of each of these parts and then assemble these small portions to model the entire structure. The finite element method is widely used in the technology and its application to the determination of stresses in structures assembled by adhesive has a great advantage. Wooley and Carver [6] made one of the first finite element analysis of an assembly single lap. They used elements in the state of plane stress and the results were comparable to those solutions Goland and Reissner [4] Wooley and Carver [6] showed stress concentrations at the edges of the lap joint. Cooper and Sawyer [7] performed a two-dimensional finite element of a single lap joint by using non-linear plane stress elements analysis. They modeled the adhesive layer using five rows of
Effect of Modifying the Edges of the Adherends and the Adhesive on the Stress Distribution over
the Width and Length of Recovery, Case of a Single Lap Joint
MADANI. Kouider, MOKHTARI. Mohamed, BELHOUARI. Mohamed, and HANNANI Mohamed
A
International Journal of Mining, Metallurgy & Mechanical Engineering (IJMMME) Volume 1, Issue 4 (2013) ISSN 2320-4052; EISSN 2320-4060
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elements. Adams and Peppiatt [8] used a two-dimensional finite element model. They found that a layer of adhesive with effusion causes stress concentrations lower than adhesive layer with a square edge, Harris and Adams [9] have developed a method of nonlinear finite element and included the response elastoplastic components and adhere the adhesive. The quadrilateral plane stress elements were used for this analysis. They performed this analysis to a single standard covering assembly and a single lap joint with nets at the edges of the joint. Breaking conditions were considered using the Von Mises criterion for adhérends and adhesive. The main objective of this chapter is to analyze by the finite element method the effect of the geometry of the joint edge of adhesive and adherend on reducing peel stresses, von mises, as well as shear stresses in the adhesive layer, several forms have been proposed. For each model we studied the stress distribution in the adhesive according to different bevel angles of the plate and the bead of adhesive.
II. GEOMETRIC MODEL AND MATERIALS PRESENTATION
The essential properties of the materials used in this study were obtained after tensile tests performed in the laboratory LASIE (laboratoire des sciences pour ingénieur et environnement, la rochelle) namely 2024-T3 aluminum and adhesive ADEKIT A140. These materials are used in many applications, among which we cite as a priority Aeronautics and Aerospace (Figure 1 and 2).
A. Mechanical properties of 2024-T3 The 2024-T3 alloy has good mechanical properties
according to its stress-strain curve shown in Figure1.
Fig. 1 traction curve for aluminum (stress / strain) [10].
TABLE I MAIN TENSILE MECHANICAL PROPERTIES OF THE ALUMINUM ALLOY.
The results of the tensile test performed on the adhesive
ADEKIT A140 is shown in Figure 2.
Fig.2 Traction curve for the Adekit A140 adhesive (stress/strain)[10].
The geometry of the model used in this study is shown in
Figure 3.
Fig.3 Geometric model of the single lap joint.
The boundary conditions used are: - Fixed Side of the specimen (embedding). u1 = u2 = 0 and u ` 0 3 0 ` R1, R2 ` 0, R3 ` 0 - Mobile Side of the specimen. u1 ` 0, u2 = u 3 = 0 and R1 ` 0, 0 ` R2, R3 ` 0 and à =
40Mpa The modifications onto the free edges of the plate and the
adhesive are shown in Figure 4. a) b) c)
Fig.4 Representation of angles for different geometric models. a) of the beveling plate, b) the bead of adhesive, c) internal beveling and
adhesif bead bead.
III. ANALYSIS RESULTS
A. Influence of beveling the plate
Adams [11] showed that changing the edge shape of the
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plate can reduce the bending moment for that we proposed to modify the geometry of the free edge of the plate while varying the bevel angle by considering a è angle which has the value è = 30 °, è = 40 °, è = 60 °.
Fig.5 Introduction of the first geometric model [beveling]. We can see clearly from The modeling of geometrical
model (Figure 5), a fine mesh is introduced at the edge of the plate in order to obtain accurate results because in this location the stresses are high.
Figure 6 shows the variation of the von Mises equivalent stress according to a length (figure 6a) and the width of overlap (figure 6b) for different angles of beveling of the aluminum plate at the interface adhesive / adherend.
The Von Mises stress distribution is identical regardless of the different bevel angle.
Along the length of recovery, the smaller stresses values are noted for a bevel angle for è = 40 ° for this angle also..
Along the width of the adhesive joint, the increase in the angle of folding clearly reduce Von Mises stresses both in the middle and the edge of the adhesive.
Fig. 6 Equivalent Stress distribution along the length and the width of overlap.
The peeling stress is shown in Figure 7. One notices that the symmetry of the stress distribution is presented. the peeling Stresses decrease with increasing of the bevel angle of the plate, this is due to the reduction of the thickness at the edge so a minimal of bending moment.
Fig. 7 peeling stress distribution along the length and the width of
overlap
Figure 8 shows the variation of the shear stresses according
to the length and width of the adhesive joint. one notices according to the length of recovery the increase
in bevel angle actually reduce the value of the shear stress and the distribution is not symmetric. Along the width, the increase of the angle of beveling clearly reduces the values of shear stress.
Fig. 8 Distribution of the shear stresses according to the length and the width of overlap
B. Influence of the bead of adhesive
The influence of adhesive bead has been widely studied by Adams and Peppiatt [12]. The authors showed that it reduced the overstress peak at the edge of the joint, because of the existence of significant tensile stresses, and it is a privileged place of initiation of rupture. Experimentally, the correlation with the numerical studies were conducted by Tsai and Morton [13]. Where they represented through the moiré fringes of the adhesive strain fields, through which they noticed that although the changes, the strains variation are less abrupt when a bead of adhesive is present.
Belingardi et al [14] have recommended to make sure that the bead of adhesive covers the entire side of the adherend. The study adopts an assumed a right bead of adhesive, and the optimal determined angle is 45 degrees.
In the work of Lang and Mallick [15], the authors are interested in all possible forms of adhesive bead. The elliptical shape is determined as optimal and it is noted that the presence of the adhesive bead decreases more the peeling stresses that the shear stresses.
Figure 9 shows the mesh of the assembly, it clearly notes the modification edge of the adhesive with different angles of the bead. A fine mesh was introduced to the free edge in order to obtain accurate results.
a) b) Fig.9 representation of the bead of adhesive: a) mesh b) the edge
of the adhesive. The Figure 10 represent the distribution of equivalent,
peeling and shear stresses along the length of the adhesive
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joint at the interface adhesive / adherend. a) b) c)
Fig.10 distribution of a) Von Mises, b) peeling and shear stresses along the length of recovery
It is noteworthy in Figure 10a that the equivalent stresses
are very sensitive to the angle bead parameter, more the angle increases more stress decreases.
Also the bead of adhesive reduces considerably the Von Mises stresses. Furthermore, the increase in the angle of the bead of adhesive leads to a decrease stress in free and non-free edge of the adhesive joint. The stress absorption by plastic deformation of the adhesive takes place with the increase of the angle of the bead of the adhesive giving rise to a considerable elongation.
The figure 10b and c represents the peeling and shear
stresses distribution according to the length of the adhesive for different angles of the bead of adhesive. The bead of the adhesive reduces the peeling and shear stress along the joint. At the free edge of the adhesive, the influence of the angle of the bead is not important in reducing the peeling stress however there is a considerable reduction in shear stress.
At the non-free edge, the modification of the bead of adhesive leads to a significant reduction of the two stresses.
Fig.11 representation free edge and no free of the adhesive
It is important to know the stress levels along the width of recovery, but it limited only to the edge of recovery. the increasing of the angle è of the bead of adhesive minimizes bonding area, there are two points for measuring the stresses: the free edge of the plate along the width and the no free edge (figure 11).
a) b) c)
Fig.12 distribution of ; a) Von mises, b) Peeling and c) shear stress along the adhesive width at the no-free edge.
For the equivalent stresses (Figure 12a), one notices that the increase of angle of the bead clearly reduces the Von Mises
International Journal of Mining, Metallurgy & Mechanical Engineering (IJMMME) Volume 1, Issue 4 (2013) ISSN 2320-4052; EISSN 2320-4060
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along the width of recovery. The distribution of the peeling and shear stresses (figure 12
b and c) is identical with a different values, a minimum at the edge and a maximum in the middle of the adhesive layer, the increasing of the angle of the bead of adhesive have reduced stresses at the edge and in the middle of the adhesive according to its length and its width.
C. Influence of internal beveling the plate with the adhesive bead
Beveling at the ends of the adherents may seem attractive, because a decrease in the thickness at this level reduces the bending moment around the joint thus leading to a decrease of peeling overstress.
Indeed, Hart Smith [16] and Adams [17] shows that a bead of adhesive around the joint improves further the mechanical strength of the assembly that the beveling of the supports, but the combination of an inner bevel with a bead leads to a maximum strength of the assembly.
Fig. 13 Representation of free and non-free edges for a model with internal beveling plate and the adhesive bead.
The figure 13 shows the mesh of the assembly in the presence of a bead of adhesive and the beveling of the substrate.
A fine mesh was introduced to the two edges of the plate and adhesive to have accurate results. The two geometric changes of the edge of the plate and the adhesive at the same time have presented a significant effect at the cover edge, the variation of the angle of the beveling automatically leads a variation of the angle of the bead of the adhesive. The figure 14a shows the distribution of equivalent stresses at the interface adhesive / adherend along the length of recovery, it should be noted that the internal beveling of the plate gives more bonding surface and when the angle of internal beveling decreases the angle of adhesive bead increases which gives minimum equivalent stresses at the edge of the adhesive. For this combination of a bevel plate and an adhesive bead, it is better to take a è = 30 ° angle to the bead of adhesive and è = 60 ° angle of beveling of the plate because this combination provides Von mises stresses lower than the other angles in this study.
The same remarks are noted for peeling and shear stress distribution. The value of the stresses is reduced in the presence of an adhesive bead and the beveling plate, and more the angle of the bead increases the peeling stresses decrease.
These geometric changes take effect only for reducing the peeling stresses which remain low in comparison with those of
equivalent stresses and shear (Figure 14b).The same effects are noted for the shear stresses (Figure 14c), where the increase in the angle of the bead increases the value of shear stress. However, the shear stresses are high values at the sensitive point denoted (A) in Figure 14c, where one notices overstress shear peaks. you are using Word, use either the Microsoft Equation Editor or the MathType add-on (http://www.mathtype.com) for equations in your paper (Insert | Object | Create New | Microsoft Equation or MathType Equation). “Float over text” should not be selected.
a) b) c)
Fig.14: Distribution of a) Von mises, b) peeling and c) shear stresses along the length of recovery.
Figure 15a shows the distribution of equivalent stresses along the width of recovery at the no-free edges, we can clearly see that the stresses increase with the increase of the bead angle but remain as even lower than those found in the case of an single lap joint without modification. and the same remarks are noted for the peeling stresses and shear stresses
free edge
no-free edge
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( figure 15b and c). a) b) c)
Fig. 15 distribution of a) Von mises, b) peeling and c) shear stresses along the adhesive width.
IV. CONCLUSION
After evaluation of the stress fields at the level of all different geometric adhesive and the cover plates at the ends, and in order to achieve our objective to reduce the stress concentration at these responsive areas to creation of cracks, we combined the effect of the different geometries in Table II-5 to allow comparison of these effects.
Table II-5 summarizes the gain reduction of the various stresses under the effect of the various changes made to the free edge of the adherents and the adhesive. All these modifications give rise to a more or less considerable reduction of the stresses. The value of these stresses varies with the type of modification. The best shape is one that consists of internal beveling plate with an bead of adhesive
TABLE II
COMPARISON OF THE REDUCTION IN THE VALUE OF THE STRESSES FOR
THE VARIOUS SHAPES OF THE EDGE OF THE PLATE AND THE ADHESIVE.
REFERENCES [1] R. D. Adams, and W. C. Wake, Structural Adhesive Joints in
Engineering. Elsevier applied science 1984. [2] O. Volkersen Die nictkraftvertcilung in zugbeanspruchten niet
verbingen mit Konstanten Luftfahrtforschung 1938, pp15-41. [3] L.R. Demarkles, Investigation on the use of rubber analogue in the
study of the stress distribution in riveted and cemented joint, NASA, 1955, TN N° 3413.
[4] M, Goland E. J Reissner Appl Mech Tranc Am Soc Mech Eng 1944;66:.
[5] D. A. Bigwood, and A. D Crocombe,. ‘Non-linear adhesive bonded joint design analysis.’ Int. J. Adhesion and Adhesives 1990, vol 10, pp 31-41,
[6] G. R. Wooley, D. R. Carver, Stress concentration factors for bonded lap joints. J. Aircraft, octobre 1971, p. 817.
[7] P.A Cooper, JW.Sawyer, A critical examination of stresses in an elastic single lap joint. Report no. TP-1507, NASA, 1979.
[8] R.D.Adams, N.A.Peppiatt, Effect of Poisson’s ratio strains in adherends on stresses of an idealized lap joint, Journal of Adhesion, 1973, Vol. 8, N° 2, pp. 134-139.
[9] J.A Harris., R.D. Adams Strength prediction of bonded single lap joints by non linear finite elements, International Journal of Adhesive, 1984, Vol. 4, N° 2, pp. 65-78.
[10] K. Madani, S. Touzain, X. Feaugas, S. Cohendouz, M. Ratwani, experimental and numerical study of repair techniques for panels with geometrical discontinuities, Original Research Article. 2010, Volume 48, Issue 1, pp83-93,
[11] R.D.Adams,S.H.,Chambers, P.H.A. DelStrother, and N.A. Peppiatt, Rubber model for adhesive lap joints. The journal of strain analysis for engineering design, 1973, 8(1):52–57.
[12] R. D. Adams, and N.A Peppiatt, Effect of poisson’s ratio strains in adherends on stresses of an idealized lap joint. The journal of strain analysis for engineering design 1977, 8(2) :134–139.
[13] M. Y. Tsai, and J. Morton, The effect of a spew fillet on adhesive stress distributions in laminated composite single-lap joints. Composite Structures, 1995, 32 :123–131.
[14] G. Belingardi, L. Goglio, and A. Tarditi, Investigating the effect of spew and chamfer size on the stresses in metal/plastics adhesive joints. International Journal of Adhesion and Adhesives, 2002, 22 :273–282.
[15] T. P. Lang, and P. K. Mallick,. Effect of spew geometry on stresses in single lap adhesive, 1998.
[16] Hart-Smith, L. J.. Adhesive-bonded double lap joints. Langley contract report NASACR-112235,NASA, 1973.
[17] R. D. Adams and W. C. Wake, Structural Adhesive Joints in Engineering. Elsevier applied science ,1984.
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