- Email: [email protected]
Design rationale of weld-bonded joints
ARTICLE IN PRESS
International Journal of Adhesion & Adhesives 24 (2004) 367–377
Design rationale of weld-bonded joints S.M. Darwish*, A. Al-Samhan Mechanical Engineering Department, King Saud University, Industrial Engineering Program, P.O. Box 800, Riyadh 11421, Saudi Arabia Accepted 11 April 2003
Abstract The aim of the present work is to study the most influential parameters governing the strength of weld-bonded joints. The thickness and elastic modulus of adhesive, the stress concentration factor and the adherent materials, were all considered and their effectiveness evaluated. The present work demonstrated that for rationale design of weld-bonded joints, adhesives with the less Young’s modulus available should be coupled with maximum permissible gap thickness. r 2003 Elsevier Ltd. All rights reserved.
1. Introduction Weld-bonding is essentially the spot-resistance welding of parts that subsequently have their overlapping areas adhesive-bonded. Weld-bonded joints were first developed and used in USSR in planes of the type AN24. The approach was a ‘‘flow-in’’ method, whereby parts were welded together first, then the adhesive was made to flow into the joint. A low-viscosity adhesive is used which penetrates the overlap joint by capillary action and is subsequently cured. The technique used in the United States is the weld-through method, whereby the adhesive is applied to the parts to be joined, spot welded and subsequently cured. In comparison with mechanical fasteners, weld bonding offers the following benefits [1–12]: * * * * * *
High static strength Improved fatigue strength Elimination of sealing operations High corrosion resistance Elimination of the shop noise associated with riveting Reduced manufacturing costs and adaptability to mechanization.
The degree of acceptance of weld-bond applications has been increasing, as the process has been understood and its mechanical properties developed [13]. Since little *Corresponding author. Fax: +966-1-467-4254. E-mail address: [email protected] (S.M. Darwish). 0143-7496/03/$ - see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0143-7496(03)00065-4
attention has been paid in the past to the analysis of weld-bonded joints, the present work was aimed at considering the most important factors governing the strength of weld-bonded joints. The stress concentration effect of a resistance spot weld between two sheets of metal is known to be dependent upon the geometric dimensions and the plane periphery crack imposed by the interfaces of the welded plates. This paper investigates the stress distribution through the adhesive layer, as well as around a single elliptical spot weld by using the finite element approach. An elliptical blunt notch is applied to approximate the notch effect around the periphery of the nugget [1]. The finite element technique was used for the analysis of the present work as it avoids the approximations of the closed-form solutions by neglecting the strain energy of certain stresses within the joint, so enabling more accurate results to be obtained [13,14].
2. Finite element modeling and boundary conditions A general-purpose structural finite element program [15] with preprocessing and post-processing was used for the solution of the problem at hand. Fig. 1 shows the configuration and dimensions (B.S.5350) of the considered joint. The finite element model considered along with constraints and loading conditions are shown in Fig. 2. The material properties of the strips and adhesive materials are listed in Table 1.
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Fig. 1. Dimensions and configuration of spot-weld specimen (B.S.5350).
Fig. 2. Finite-element model for weld-bonded joint.
Table 1 Material properties of adherents and adhesive material Material
Young’s modulus (N/ mm2)
Poisson’s ratio
Shear modulus (GPa)
Steel Aluminum Adhesive
2.0 105 0.6 105 2.5 103
0.3 0.33 0.38
78.1 28.1 0.905
The mesh of this finite element model was generated using the GID preprocessing program [15]. To improve accuracy, fine mesh is used in zones where rapid variations in stress are anticipated, rather than in the zone of constant stress. A difficulty encountered in proceeding with the finite element model is the determination of the shape of the notch around the periphery of the nugget between the sheets. As
mentioned, the curvature of the crack tip will severely affect the stress distribution and stress concentration factor. In order to simplify the configuration, an elliptical blunt notch shown in Fig. 2 is assumed to approximate the apex of the periphery crack, where a and b are the lengths of the semi-major and the semiminor axes of the elliptical blunt notch [1], respectively. The FE computation was carried out using Calsef FE program [15], which is an internal module inside the GID program. GID [15] is widely used for preprocessing FE meshes and FE results visualization in a number of linear and non-linear problems in structural engineering mechanics, using the finite element method. In Calsef [15], the principal of minimum potential energy (the force method) is used and the set of equations to be solved is: ½kfbg ¼ ff g; where [k] is the stiffness matrix, {b} the vector of nodal
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369
Fig. 3. Post processing output of deformed and undeformed FE meshes for weld-bonded FE model.
displacement and {f } the vector of nodal loads. The element used throughout the modeling process was three-node linear triangular element and the following assumptions and boundary conditions were considered throughout the idealization process:
* *
The problem is two-dimensional. The adhesive layer is isotropic, i.e. stresses on the micro-scale, such as those caused by flaws in the adhesive, were neglected.
The points as well as the applied load (position and value) were kept constant to enable fair comparison between the data to be made. The applied load was taken to be the relatively small value of 500 N, as the displacement and accordingly the stresses are assumed proportional to the load in Calsef program. Fig. 3 shows the deformed mesh overlaid on the un-deformed mesh for the comparison given for weld-bond FE model.
3. Effect of elastic modulus of adhesive on the stress distribution within weld-bonded layer The predicted normal stresses, sx through the weldbonded layer associated with adhesives having different elastic Young moduli (1.25, 2.5, and 3.75 MPa, respectively) are shown in Fig. 4. From the figure it can be noticed that the normal stresses concentrated at the far ends of the nugget do not change with the variation in the elastic modulus. The normal stresses concentrated at the free ends of the joint seemed to be changing with the change in elastic modulus, such that increasing the elastic modulus of adhesive increases the normal stresses concentrated at the far end of the joint. The same trend is repeated with the normal stress, sy ; as shown in Fig. 5. Fig. 6 shows the shear stress, txy associated with various elastic modulus of adhesives considered. The stresses at the free ends of the joint follow the same trend, however, the trend is reversed at the two far ends of the nugget, where the highly concentrated stresses are associated with the adhesive having the lowest elastic modulus. Figs. 7 and 8 show the major and minor stresses associated with the adhesives having different elastic moduli. From the figures it can be observed that the
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Normal stress σx per unit load (mm-2)
0.600 Adhessive-1 (Young's Modulus =1.25E3 MPa) Adhessive-2 (Young's Modulus =2.5E3 MPa) Adhessive-3 (Young's Modulus =3.75E3 MPa)
0.500
0.400
0.300
0.200 0.157 0.149 0.103
0.100
0.000 0.0
5.0
10.0
15.0
20.0
25.0
Distance along overlap area (mm)
-0.100
Fig. 4. Normal stress sx associated with adhesives having different elastic Young’s moduli.
0.400 0.350 Adhessive-1 (Young's Modulus=1.25E3 MPa) Adhessive-2 (Young's Modulus=2.5E3 MPa) Adhessive-3 (Young's Modulus=3.75E3 MPa)
Normal stress σy per unit load (mm-2)
0.300
0.329 0.313
0.250 0.219 0.200 0.150 0.100 0.050 0.000 0.0
5.0
10.0
15.0
20.0
25.0
-0.050 Distance along overlap area (mm) -0.100
Fig. 5. Normal stress sy associated with adhesives having different elastic Young’s moduli.
principal stresses (major and minor) concentrated at the free ends of the joint increases with the increase of the elastic modulus of adhesive, in the case of adhesive 2 (the elastic modulus of adhesive two is twice that of adhesive 1). However, when the elastic modulus was increased to be 3.75 MPa (adhesive 3), the increase in normal stress seemed to be insignificant.
4. Effect of stress concentration on the stress distribution within weld-bonded joints Figs. 9–11 show the normal, shear and principal stresses developed in weld-bonded joints, having different gap thicknesses. The major principal stress, s1 for a weld-bonded joint having different gap thicknesses is
shown in Fig. 12, while the minor principal stress, s2 is shown in Fig. 13. A geometric stress concentration factor K is defined as K ¼ s1 =tave ; where s1 is the maximum principal stress, tave the nominal stress (=P/A), P the axial load, A the crosssectional area of the nugget (=pD2 =4) and D the diameter of the electrode. It is worth mentioning that the stress concentration factor was decreased from 18.5 to 14.25, when the gap thickness was increased from 0.08 to 0.1 mm, and from 14.25 to 13.5, when the gap thickness was increased from 0.1 to 0.12 mm, respectively.
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0.300
Adhessive-1 (Young's Modulus= 1.25E3 MPa) Adhessive-2 (Young's Modulus= 2.5E3 MPa) Adhessive-3 (Young's Modulus= 3.75E3 MPa)
Shear stress τxy per unit load (mm-2)
0.250
0.25626 0.245
0.200 0.177 0.150
0.100
0.050
0.000 0.0
5.0
10.0
15.0
20.0
25.0
Distance along overlap area (mm)
Fig. 6. Shear stress txy associated with adhesives having different elastic Young’s moduli.
Major principal stress σ1 per unit load (mm-2)
0.700
Adhessive-1 (Young's Modulus = 1.25E3 MPa) Adhessive-2 (Young's Modulus = 2.5E3 MPa) Adhessive-3 (Young's Modulus = 3.75E3 MPa)
0.600
0.596 0.568
0.500
0.400
0.400
0.300
0.200
0.100
0.000 0.0 -0.100
5.0
10.0
15.0
20.0
25.0
Distance along overlap area (mm)
Fig. 7. Major principal stress s1 associated with adhesives having different elastic Young’s moduli.
5. Effect of adherents type on the stresses developed The predicted normal stresses, sx through the weldbonded layer associated with different adherents, are shown in Fig 14. From the figure it can be noticed that the normal stresses concentrated at the far ends of the weld nugget do not change with the change of adherents material. However, the normal stresses concentrated at the free ends of the joint within the adhesive layer, seemed to be changing tremendously with the change in adherents material, such that increasing the elastic modulus of adherents decreases the normal stresses concentrated at the far end of the joint. The same trend
is noticed with the normal stress, sy only at the free ends of the joints (see Fig. 15). Fig. 16 shows the shear stresses, txy associated with different adherents, where the stresses at the free ends follow the same trend. Figs. 17 and 18 show the major and minor principal stresses, s2 and s2 associated with weld-bonded joints having different adherent materials. From the figures it can be observed that the principal stresses, s2 and s2 are concentrated at the free ends of the joint such that increasing the elastic modulus of adhered material decreases the principal stresses concentrated at the far end of the joint substantially. For instance, the major principal stress within the adhesive layer increased by
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Distance along overlap area (mm) 0.0
5.0
10.0
15.0
20.0
25.0
0
Minor principal stress σ2 per unit load (mm-2)
-0.02 -0.04 -0.06 -0.078
-0.08 -0.1
-0.106 -0.110 -0.12 -0.14 Adhessive-1 (Young's Modulus= 1.25E3 MPa) Adhessive-2 (Young's Modulus= 2.5E3 MPa) Adhessive-3 (Young's Modulus= 3.75E3 MPa)
-0.16 -0.18
Fig. 8. Minor principal stress s2 associated with adhesives having different elastic Young’s moduli.
0.600
0.500
Normal stress σx per unit load (mm-2)
0.08 mm gap thickness 0.1 mm gap thickness 0.400
0.12 mm gap thickness
0.300
0.200 0.153 0.150 0.139
0.100
0.000 0.00
5.00
10.00
15.00
20.00
25.00
Distance along overlap area mm -0.100
Fig. 9. Normal stress (sx ) developed in weld-bond joints, having different gap thicknesses
400%, when the steel adherents were replaced with aluminum ones. The combined effect of the Young’s modulus of adhesive and the gap thickness is demonstrated in Figs. 19 and 20. These figures show the major and minor principal stresses, s1 and s2 associated with weldbonded joints having the maximum gap thickness of 0.12 mm coupled with adhesive of 3.75 103 Young’s modulus and 1.25 103 Young’s modulus, respectively. Also, the gap thickness of 0.08 mm was coupled once with adhesive having 3.75 103 Young’s modulus and then with 1.25 103 Young’s modulus adhesive.
From Fig. 19, it can be seen that with adhesive having Young’s modulus of adhesive of 3.75 103 MPa the maximum principal stress was decreased from 0.612 to 0.379 (mm2), when gap thickness was increased from 0.08 to 0.12 mm. With adhesive having 1.25 103 MPa Young’s modulus, the maximum principal stress was decreased from 0.406 to 0.335 (mm2), when the gap thickness was increased from 0.08 to 0.12 mm. The same results are observed with minor principal stress, s2 shown in Fig. 20. From the above discussion it can be concluded that for rational design of weld-bonded joints, an adhesive having the lowest Young’s modulus
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0.350 0.08 mm gap thickness 0.1 mm gap thickness 0.12 mm gap thickness
Normal stress σy per unit load (mm-2)
0.300
0.313 0.273 0.262
0.250
0.200 0.150
0.100 0.050 0.000 0.00
5.00
-0.050
10.00
15.00
20.00
25.00
Distance along overlap area mm
-0.100
Fig. 10. Normal stress (sy ) developed in weld-bond joints, having different gap thicknesses. 0.300
0.08 mm gap thickness 0.1 mm gap thickness 0.12 mm gap thickness
Shear stress τxy per unit load (mm-2)
0.250
0.245 0.219 0.203
0.200
0.150
0.100
0.050
0.000 0.00
5.00
10.00
15.00
20.00
25.00
Distance along overlap area mm
Fig. 11. Shear stress (txy ) developed in weld-bond joints, having different gap thicknesses
Major principal stress σ1 per unit load (mm-2)
0.600
0.500
0.583 0.08 mm gap thickness 0.1 mm gap thickness 0.12 mm gap thickness
0.499 0.474
0.400
0.300
0.200
0.100
0.000 0.00
5.00
10.00
15.00
20.00
25.00
Distance along overlap area mm -0.100
Fig. 12. Major principal stress (s) developed in weld-bond joints, having different gap thicknesses.
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Distance along overlap area mm 0.00 0.000
5.00
10.00
15.00
20.00
25.00
Minor principal stress σ2 per unit load (mm-2)
-0.020 -0.040 -0.060 -0.080
-0.083
-0.100
-0.099 -0.106
-0.120 -0.140
0.08 mm gap thickness 0.1 mm gap thickness 0.12 mm gap thickness
-0.160 -0.180
Fig. 13. Minor principal stress (s2 ) associated with weld-bonded joints, having different gap thicknesses.
Fig. 14. Normal stress (sx ) associated with weld-bonded joints of different adherents, for gap thickness of 0.08 mm.
should be coupled with maximum possible gap thickness.
6. Conclusions 1. Increasing the elastic modulus of adherents increases the strength of weld-bonded joints. 2. The principal stresses concentrated at the far ends of weld-bonded joints increase with the increase in
the elastic modulus of adhesives up to a certain limit after which the increase in the principal stress is negligible. 3. Increasing the gap thickness up to a certain limit increases the maximum stresses concentrated at the far end of the joint significantly after which the increase in the principal stress is insignificant. 4. For rational design of weld-bonded joints, adhesives with less Young’s modulus are recommended with maximum possible gap thickness.
ARTICLE IN PRESS S.M. Darwish, A. Al-Samhan / International Journal of Adhesion & Adhesives 24 (2004) 367–377
Fig. 15. Normal stress (sy ) associated with weld-bonded joints of different adherents, for gap thickness of 0.08 mm.
Fig. 16. Shear stress (txy ) associated with weld-bonded joints of different adherents, for gap thickness of 0.08 mm.
Fig. 17. Major principal stress (s1 ) associated with weld-bonded joints of different adherents, for gap thickness of 0.08 mm.
375
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Fig. 18. Minor principal stress (s2 ) associated with weld-bonded joints of different adherents, for gap thickness of 0.08 mm.
Fig. 19. Major principal stress s1 associated with different Young’s modulus and various adhesive gap thicknesses.
Fig. 20. Major principal stress s2 associated with different Young’s modulus and various adhesive gap thicknesses.
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Acknowledgements The authors are grateful to the Research Center of King Saud University for supporting this work (grant no. 9/422).
References [1] Kuang JH, Liu A-H. A study of the stress concentration factor on spot welds. Weld J (Weld Res Suppl) 1990;468–474-s. [2] Darwish SM, Al-Dekhial SD. Statistical models for spot welding of commercial aluminum sheets. Int J Mach Tools Manuf 1999;39:1589–610. [3] Darwish SM, Al-Dekhial SD. Micro-hardness of spot welded (B.S. 1050) commercial aluminum as correlated with welding variables and strength attributes. Int J Mater Process Technol 1999;91:43–51. [4] Darwish SM, Soliman MS, Al-Fahead. Characteristics and variables of spot welding and weld bonding bimaterials. Int J Mater Manuf Process 1997;12(1):59–67. [5] Darwish SM, Soliman MS, Al-Fahead. Manufacturing and characteristics of brass damping sheets. Int J Mater Process Technol 1998;79:66–71. [6] Beneteau D. Resistance spot welding of aluminum. Weld J, USA, 1992. p. 129.
377
[7] Gould JE. An examination of nugget development during spot welding using both experimental and analytical techniques. Weld J (Weld Res Suppl) 1987;66:1–10. [8] Tasl GL, Jammal OA, Parpritan JC, Dikinson DW. Modeling of resistance spot welding nugget growth. Weld J (Weld Res Suppl) 1992;10:47–54. [9] Darwish S, Ghanya A. Critical assessment of weld-bonded technologies. J Mater Process Technol 2000;221–9. [10] Heidi B, El-Sebakhy I, Malik D. Weld bonding of structural adhesives for body stiffening. Worldwide Passenger Car Conf., USA, 1992. [11] Masashi K, et al. Fatigue strength of adhesive bonded box section beams with a longitudinal partition under torsion. Trans Jpn Soc Mech Eng A 1993;569:87–93. [12] Wang PC, Chishholm, Banas G, Lawrence VL. The role of failure mode, resistance spot weld and adhesive on the fatigue behavior of weld-bonded aluminum. Weld J 1995;41–7. [13] Schwartz MM. Metals joining manual book. New York: McgrawHill; 1979. p. 1–32. [14] Darwish SM, Ghanya A. Development of spot-welded low carbon steel damping sheets. 7th Cairo University International MDP Conference, vol. 1. Oxford: Pergamon Press; 2000. p. 477–88. [15] GID software copy writes of International Center For Numerical Methods In Engineering (CIMNE)- Edificio C-1, Campus Norte UPC, 08034 Barcelona-Spain.
International Journal of Adhesion & Adhesives 24 (2004) 367–377
Design rationale of weld-bonded joints S.M. Darwish*, A. Al-Samhan Mechanical Engineering Department, King Saud University, Industrial Engineering Program, P.O. Box 800, Riyadh 11421, Saudi Arabia Accepted 11 April 2003
Abstract The aim of the present work is to study the most influential parameters governing the strength of weld-bonded joints. The thickness and elastic modulus of adhesive, the stress concentration factor and the adherent materials, were all considered and their effectiveness evaluated. The present work demonstrated that for rationale design of weld-bonded joints, adhesives with the less Young’s modulus available should be coupled with maximum permissible gap thickness. r 2003 Elsevier Ltd. All rights reserved.
1. Introduction Weld-bonding is essentially the spot-resistance welding of parts that subsequently have their overlapping areas adhesive-bonded. Weld-bonded joints were first developed and used in USSR in planes of the type AN24. The approach was a ‘‘flow-in’’ method, whereby parts were welded together first, then the adhesive was made to flow into the joint. A low-viscosity adhesive is used which penetrates the overlap joint by capillary action and is subsequently cured. The technique used in the United States is the weld-through method, whereby the adhesive is applied to the parts to be joined, spot welded and subsequently cured. In comparison with mechanical fasteners, weld bonding offers the following benefits [1–12]: * * * * * *
High static strength Improved fatigue strength Elimination of sealing operations High corrosion resistance Elimination of the shop noise associated with riveting Reduced manufacturing costs and adaptability to mechanization.
The degree of acceptance of weld-bond applications has been increasing, as the process has been understood and its mechanical properties developed [13]. Since little *Corresponding author. Fax: +966-1-467-4254. E-mail address: [email protected] (S.M. Darwish). 0143-7496/03/$ - see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0143-7496(03)00065-4
attention has been paid in the past to the analysis of weld-bonded joints, the present work was aimed at considering the most important factors governing the strength of weld-bonded joints. The stress concentration effect of a resistance spot weld between two sheets of metal is known to be dependent upon the geometric dimensions and the plane periphery crack imposed by the interfaces of the welded plates. This paper investigates the stress distribution through the adhesive layer, as well as around a single elliptical spot weld by using the finite element approach. An elliptical blunt notch is applied to approximate the notch effect around the periphery of the nugget [1]. The finite element technique was used for the analysis of the present work as it avoids the approximations of the closed-form solutions by neglecting the strain energy of certain stresses within the joint, so enabling more accurate results to be obtained [13,14].
2. Finite element modeling and boundary conditions A general-purpose structural finite element program [15] with preprocessing and post-processing was used for the solution of the problem at hand. Fig. 1 shows the configuration and dimensions (B.S.5350) of the considered joint. The finite element model considered along with constraints and loading conditions are shown in Fig. 2. The material properties of the strips and adhesive materials are listed in Table 1.
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Fig. 1. Dimensions and configuration of spot-weld specimen (B.S.5350).
Fig. 2. Finite-element model for weld-bonded joint.
Table 1 Material properties of adherents and adhesive material Material
Young’s modulus (N/ mm2)
Poisson’s ratio
Shear modulus (GPa)
Steel Aluminum Adhesive
2.0 105 0.6 105 2.5 103
0.3 0.33 0.38
78.1 28.1 0.905
The mesh of this finite element model was generated using the GID preprocessing program [15]. To improve accuracy, fine mesh is used in zones where rapid variations in stress are anticipated, rather than in the zone of constant stress. A difficulty encountered in proceeding with the finite element model is the determination of the shape of the notch around the periphery of the nugget between the sheets. As
mentioned, the curvature of the crack tip will severely affect the stress distribution and stress concentration factor. In order to simplify the configuration, an elliptical blunt notch shown in Fig. 2 is assumed to approximate the apex of the periphery crack, where a and b are the lengths of the semi-major and the semiminor axes of the elliptical blunt notch [1], respectively. The FE computation was carried out using Calsef FE program [15], which is an internal module inside the GID program. GID [15] is widely used for preprocessing FE meshes and FE results visualization in a number of linear and non-linear problems in structural engineering mechanics, using the finite element method. In Calsef [15], the principal of minimum potential energy (the force method) is used and the set of equations to be solved is: ½kfbg ¼ ff g; where [k] is the stiffness matrix, {b} the vector of nodal
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Fig. 3. Post processing output of deformed and undeformed FE meshes for weld-bonded FE model.
displacement and {f } the vector of nodal loads. The element used throughout the modeling process was three-node linear triangular element and the following assumptions and boundary conditions were considered throughout the idealization process:
* *
The problem is two-dimensional. The adhesive layer is isotropic, i.e. stresses on the micro-scale, such as those caused by flaws in the adhesive, were neglected.
The points as well as the applied load (position and value) were kept constant to enable fair comparison between the data to be made. The applied load was taken to be the relatively small value of 500 N, as the displacement and accordingly the stresses are assumed proportional to the load in Calsef program. Fig. 3 shows the deformed mesh overlaid on the un-deformed mesh for the comparison given for weld-bond FE model.
3. Effect of elastic modulus of adhesive on the stress distribution within weld-bonded layer The predicted normal stresses, sx through the weldbonded layer associated with adhesives having different elastic Young moduli (1.25, 2.5, and 3.75 MPa, respectively) are shown in Fig. 4. From the figure it can be noticed that the normal stresses concentrated at the far ends of the nugget do not change with the variation in the elastic modulus. The normal stresses concentrated at the free ends of the joint seemed to be changing with the change in elastic modulus, such that increasing the elastic modulus of adhesive increases the normal stresses concentrated at the far end of the joint. The same trend is repeated with the normal stress, sy ; as shown in Fig. 5. Fig. 6 shows the shear stress, txy associated with various elastic modulus of adhesives considered. The stresses at the free ends of the joint follow the same trend, however, the trend is reversed at the two far ends of the nugget, where the highly concentrated stresses are associated with the adhesive having the lowest elastic modulus. Figs. 7 and 8 show the major and minor stresses associated with the adhesives having different elastic moduli. From the figures it can be observed that the
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Normal stress σx per unit load (mm-2)
0.600 Adhessive-1 (Young's Modulus =1.25E3 MPa) Adhessive-2 (Young's Modulus =2.5E3 MPa) Adhessive-3 (Young's Modulus =3.75E3 MPa)
0.500
0.400
0.300
0.200 0.157 0.149 0.103
0.100
0.000 0.0
5.0
10.0
15.0
20.0
25.0
Distance along overlap area (mm)
-0.100
Fig. 4. Normal stress sx associated with adhesives having different elastic Young’s moduli.
0.400 0.350 Adhessive-1 (Young's Modulus=1.25E3 MPa) Adhessive-2 (Young's Modulus=2.5E3 MPa) Adhessive-3 (Young's Modulus=3.75E3 MPa)
Normal stress σy per unit load (mm-2)
0.300
0.329 0.313
0.250 0.219 0.200 0.150 0.100 0.050 0.000 0.0
5.0
10.0
15.0
20.0
25.0
-0.050 Distance along overlap area (mm) -0.100
Fig. 5. Normal stress sy associated with adhesives having different elastic Young’s moduli.
principal stresses (major and minor) concentrated at the free ends of the joint increases with the increase of the elastic modulus of adhesive, in the case of adhesive 2 (the elastic modulus of adhesive two is twice that of adhesive 1). However, when the elastic modulus was increased to be 3.75 MPa (adhesive 3), the increase in normal stress seemed to be insignificant.
4. Effect of stress concentration on the stress distribution within weld-bonded joints Figs. 9–11 show the normal, shear and principal stresses developed in weld-bonded joints, having different gap thicknesses. The major principal stress, s1 for a weld-bonded joint having different gap thicknesses is
shown in Fig. 12, while the minor principal stress, s2 is shown in Fig. 13. A geometric stress concentration factor K is defined as K ¼ s1 =tave ; where s1 is the maximum principal stress, tave the nominal stress (=P/A), P the axial load, A the crosssectional area of the nugget (=pD2 =4) and D the diameter of the electrode. It is worth mentioning that the stress concentration factor was decreased from 18.5 to 14.25, when the gap thickness was increased from 0.08 to 0.1 mm, and from 14.25 to 13.5, when the gap thickness was increased from 0.1 to 0.12 mm, respectively.
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371
0.300
Adhessive-1 (Young's Modulus= 1.25E3 MPa) Adhessive-2 (Young's Modulus= 2.5E3 MPa) Adhessive-3 (Young's Modulus= 3.75E3 MPa)
Shear stress τxy per unit load (mm-2)
0.250
0.25626 0.245
0.200 0.177 0.150
0.100
0.050
0.000 0.0
5.0
10.0
15.0
20.0
25.0
Distance along overlap area (mm)
Fig. 6. Shear stress txy associated with adhesives having different elastic Young’s moduli.
Major principal stress σ1 per unit load (mm-2)
0.700
Adhessive-1 (Young's Modulus = 1.25E3 MPa) Adhessive-2 (Young's Modulus = 2.5E3 MPa) Adhessive-3 (Young's Modulus = 3.75E3 MPa)
0.600
0.596 0.568
0.500
0.400
0.400
0.300
0.200
0.100
0.000 0.0 -0.100
5.0
10.0
15.0
20.0
25.0
Distance along overlap area (mm)
Fig. 7. Major principal stress s1 associated with adhesives having different elastic Young’s moduli.
5. Effect of adherents type on the stresses developed The predicted normal stresses, sx through the weldbonded layer associated with different adherents, are shown in Fig 14. From the figure it can be noticed that the normal stresses concentrated at the far ends of the weld nugget do not change with the change of adherents material. However, the normal stresses concentrated at the free ends of the joint within the adhesive layer, seemed to be changing tremendously with the change in adherents material, such that increasing the elastic modulus of adherents decreases the normal stresses concentrated at the far end of the joint. The same trend
is noticed with the normal stress, sy only at the free ends of the joints (see Fig. 15). Fig. 16 shows the shear stresses, txy associated with different adherents, where the stresses at the free ends follow the same trend. Figs. 17 and 18 show the major and minor principal stresses, s2 and s2 associated with weld-bonded joints having different adherent materials. From the figures it can be observed that the principal stresses, s2 and s2 are concentrated at the free ends of the joint such that increasing the elastic modulus of adhered material decreases the principal stresses concentrated at the far end of the joint substantially. For instance, the major principal stress within the adhesive layer increased by
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Distance along overlap area (mm) 0.0
5.0
10.0
15.0
20.0
25.0
0
Minor principal stress σ2 per unit load (mm-2)
-0.02 -0.04 -0.06 -0.078
-0.08 -0.1
-0.106 -0.110 -0.12 -0.14 Adhessive-1 (Young's Modulus= 1.25E3 MPa) Adhessive-2 (Young's Modulus= 2.5E3 MPa) Adhessive-3 (Young's Modulus= 3.75E3 MPa)
-0.16 -0.18
Fig. 8. Minor principal stress s2 associated with adhesives having different elastic Young’s moduli.
0.600
0.500
Normal stress σx per unit load (mm-2)
0.08 mm gap thickness 0.1 mm gap thickness 0.400
0.12 mm gap thickness
0.300
0.200 0.153 0.150 0.139
0.100
0.000 0.00
5.00
10.00
15.00
20.00
25.00
Distance along overlap area mm -0.100
Fig. 9. Normal stress (sx ) developed in weld-bond joints, having different gap thicknesses
400%, when the steel adherents were replaced with aluminum ones. The combined effect of the Young’s modulus of adhesive and the gap thickness is demonstrated in Figs. 19 and 20. These figures show the major and minor principal stresses, s1 and s2 associated with weldbonded joints having the maximum gap thickness of 0.12 mm coupled with adhesive of 3.75 103 Young’s modulus and 1.25 103 Young’s modulus, respectively. Also, the gap thickness of 0.08 mm was coupled once with adhesive having 3.75 103 Young’s modulus and then with 1.25 103 Young’s modulus adhesive.
From Fig. 19, it can be seen that with adhesive having Young’s modulus of adhesive of 3.75 103 MPa the maximum principal stress was decreased from 0.612 to 0.379 (mm2), when gap thickness was increased from 0.08 to 0.12 mm. With adhesive having 1.25 103 MPa Young’s modulus, the maximum principal stress was decreased from 0.406 to 0.335 (mm2), when the gap thickness was increased from 0.08 to 0.12 mm. The same results are observed with minor principal stress, s2 shown in Fig. 20. From the above discussion it can be concluded that for rational design of weld-bonded joints, an adhesive having the lowest Young’s modulus
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0.350 0.08 mm gap thickness 0.1 mm gap thickness 0.12 mm gap thickness
Normal stress σy per unit load (mm-2)
0.300
0.313 0.273 0.262
0.250
0.200 0.150
0.100 0.050 0.000 0.00
5.00
-0.050
10.00
15.00
20.00
25.00
Distance along overlap area mm
-0.100
Fig. 10. Normal stress (sy ) developed in weld-bond joints, having different gap thicknesses. 0.300
0.08 mm gap thickness 0.1 mm gap thickness 0.12 mm gap thickness
Shear stress τxy per unit load (mm-2)
0.250
0.245 0.219 0.203
0.200
0.150
0.100
0.050
0.000 0.00
5.00
10.00
15.00
20.00
25.00
Distance along overlap area mm
Fig. 11. Shear stress (txy ) developed in weld-bond joints, having different gap thicknesses
Major principal stress σ1 per unit load (mm-2)
0.600
0.500
0.583 0.08 mm gap thickness 0.1 mm gap thickness 0.12 mm gap thickness
0.499 0.474
0.400
0.300
0.200
0.100
0.000 0.00
5.00
10.00
15.00
20.00
25.00
Distance along overlap area mm -0.100
Fig. 12. Major principal stress (s) developed in weld-bond joints, having different gap thicknesses.
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Distance along overlap area mm 0.00 0.000
5.00
10.00
15.00
20.00
25.00
Minor principal stress σ2 per unit load (mm-2)
-0.020 -0.040 -0.060 -0.080
-0.083
-0.100
-0.099 -0.106
-0.120 -0.140
0.08 mm gap thickness 0.1 mm gap thickness 0.12 mm gap thickness
-0.160 -0.180
Fig. 13. Minor principal stress (s2 ) associated with weld-bonded joints, having different gap thicknesses.
Fig. 14. Normal stress (sx ) associated with weld-bonded joints of different adherents, for gap thickness of 0.08 mm.
should be coupled with maximum possible gap thickness.
6. Conclusions 1. Increasing the elastic modulus of adherents increases the strength of weld-bonded joints. 2. The principal stresses concentrated at the far ends of weld-bonded joints increase with the increase in
the elastic modulus of adhesives up to a certain limit after which the increase in the principal stress is negligible. 3. Increasing the gap thickness up to a certain limit increases the maximum stresses concentrated at the far end of the joint significantly after which the increase in the principal stress is insignificant. 4. For rational design of weld-bonded joints, adhesives with less Young’s modulus are recommended with maximum possible gap thickness.
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Fig. 15. Normal stress (sy ) associated with weld-bonded joints of different adherents, for gap thickness of 0.08 mm.
Fig. 16. Shear stress (txy ) associated with weld-bonded joints of different adherents, for gap thickness of 0.08 mm.
Fig. 17. Major principal stress (s1 ) associated with weld-bonded joints of different adherents, for gap thickness of 0.08 mm.
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Fig. 18. Minor principal stress (s2 ) associated with weld-bonded joints of different adherents, for gap thickness of 0.08 mm.
Fig. 19. Major principal stress s1 associated with different Young’s modulus and various adhesive gap thicknesses.
Fig. 20. Major principal stress s2 associated with different Young’s modulus and various adhesive gap thicknesses.
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Acknowledgements The authors are grateful to the Research Center of King Saud University for supporting this work (grant no. 9/422).
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