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Numerical and experimental study on failure behavior of steel-aluminium mechanical clinched joints under multiple test conditions
International Journal of Lightweight Materials and Manufacture xxx (xxxx) xxx
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Original Article
Numerical and experimental study on failure behavior of steelaluminium mechanical clinched joints under multiple test conditions Yanli Song a, b, c, *, Lulu Yang a, b, Genpeng Zhu c, Lin Hua a, b, c, Runze Liu a, b a
Hubei Key Laboratory of Advanced Technology for Automotive Components, Wuhan University of Technology, Wuhan, 430070, China Hubei Collaborative Innovation Center for Automotive Components Technology, Wuhan University of Technology, Wuhan, 430070, China c School of Automotive Engineering, Wuhan University of Technology, Wuhan, 430070, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 13 October 2018 Received in revised form 20 November 2018 Accepted 20 December 2018 Available online xxx
In this work, the numerical and experimental study was performed to explore the mechanical properties and failure behavior of steel-aluminium mechanical clinched joints under multiple test conditions. The stress distribution of the clinched joints and the failure mode were analyzed using finite element analysis software ABAQUS. The Gurson-Tvergaard-Needleman (GTN) model was used to simulate damage and failure of the joints. The experimental tests were conducted for the verification. It was found that the clinched joints under shear condition had a peak force of 4354N, which was much higher than that of the peel (624N) and cross tensile (1046N) conditions, while the peak load displacement and failure displacement have the opposite law. The failure mode of shear condition was neck fracture, while that of tensile and peel conditions were both pulling out failure. The finite element simulation results were in good agreement with the experimental ones and the failure mode was consistent. The Gurson-tvergaardNeedleman (GTN) model can accurately predict the mechanical properties and failure mode of clinched joints. © 2018 The Authors. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/).
Keywords: Steel-aluminium mechanical clinching Mechanical properties Damage model Finite element simulation
1. Introduction In recent years, lightweight of automobiles has become a high demand worldwide due to the environmental pollution and energy shortage [1]. And the demand for coupling performances with reductions of cost, weight, fuel consumption, air pollution and the improvement of safety is stronger and stronger [2]. Since aluminium alloy has the advantages of low density, excellent lightweight performance, good collision energy absorption and so on, the proportion of aluminium alloy in the body in white (BIW) has been increased year by year. Therefore, the traditional steel body has been gradually developed into a steel-aluminium composite body. For example, the dosage of steel and aluminium alloy in Audi TT/TTS Coupe body is 35.8% and 62.6% respectively. Accordingly, the connection between the steel and aluminium alloy sheets becomes an issue.
* Corresponding author. Hubei Key Laboratory of Advanced Technology for Automotive Components, Wuhan University of Technology, Wuhan, 430070, China. Fax: þ86 27 8716 8391. E-mail address: [email protected] (Y. Song).
Mechanical clinching is a mechanical joining process where the sheet metal parts are joined together by an interlock formed through local plastic deformation without cutting or the use of any external elements such as a fastener or rivet [3]. It is an efficient, reliable and low-cost connection method, especially suitable for the connection of steel and aluminium [4]. The quality of the clinched joint is influenced by the sheet type, sheet thickness and die parameters [5]. A desired joint can be obtained by designing clinching tools based on the analytical model used to predict the strength of the joint [6]. Recent years, mechanical clinching has attracted wide attention of scholars. Most concerned the effect of die parameters on the strength of clinched joint. Lambiase and Di Ilio [7] optimized the geometric parameters of clinching dies for the steel sheet joints by artificial neural network and genetic algorithm. Abe et al. [8] developed a mechanical clinching method using counter pressure of a rubber ring to join the galvanized ultra-high strength steel sheets with low ductility. Chen et al. [9] reduced the height and improved the strength of clinched joints under shear and cross-tensile conditions by compressing the joints for Al6061 sheets. Kam et al. [10] studied the effect of the eccentricity
https://doi.org/10.1016/j.ijlmm.2018.12.005 2588-8404/© 2018 The Authors. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Please cite this article as: Y. Song et al., Numerical and experimental study on failure behavior of steel-aluminium mechanical clinched joints under multiple test conditions, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2018.12.005
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of the dies on the clinched joint strength for coated mild steel sheets. Eshtayeh and Hrairi [11] introduced the implementation of the Taguchi-based Grey optimization of the mechanical clinching with fixed dies for AA7075 and mild steel and derived the optimal process parameters combination that leads to a high strength connection. Lambiase [12] investigated the influence of clinching tool design on the cross section of a clinched joint in joining low carbon steel sheets by the clinching process with extensible dies. Liu [13] studied the forming law of mechanical clinching and obtained the influence of die parameters on the joining quality. Other studies focused on the properties and failure of the mechanical clinching. Abe et al. [14] experimentally studied the effects of the shape and size of dies on the metal flow and forming defects of the clinched joints for high strength steel and aluminium alloy sheets. Pirondi and Moroni [15] studied the failure behavior of clinch-bonded and rivet-bonded joints using the finite element method (FEM). Zhou et al. [16] established a finite element simplified model of body collision, and studied the failure model of mechanical clinching. Calabrese et al. [17] studied the effect of corrosion phenomena in critical environmental conditions on the mechanical performance of steel-aluminium clinched joints by ageing in salt spray environment. Mori et al. [18] compared the static and fatigue strength of mechanical clinched and self-pierced joints with a resistance spot welded joint and found that the former two joints have superior fatigue resistance. Abe et al. [4] compared the static and fatigue strengths of the clinched joints with those of the resistance spot welded joints. It was found that the shear and cross tensile strength of the clinched joints were lower than those of the resistance spot welded joints, while the fatigue strength the opposite results. In this paper, the finite element (FE) simulation of the clinched steel-aluminium joints was built with the Gurson-TvergaardNeedleman (GTN) damage model to simulate the mechanical properties and failure behavior under shear, peel and cross tensile conditions. The experimental tests were conducted for the verification.
3. Finite element simulation 3.1. Damage model As is known, when a joint is subjected to a tensile or shear force, it may fail and lead to fracture of the material. Therefore, a reasonable material damage or failure model should be chosen in the FE simulation of the clinched joints. The ductile damage model is a phenomenological model for predicting the onset of damage from the perspective of mechanics [19]. The modified Rousselier model can describe the failure process and evolution mechanism. It is used to predict the shear-dominated fracture and stress distribution on the clinched joint [20]. The modified Gurson model can explain the macroscopic phenomena by describing the mesoscopic behavior of the clinched joint during the clinching process. It allows for the numerical simulation of the elasticeplastic behavior until fracture and describes the localization and fracture in sheardominated stress states with low triaxiality. A distinct advantage of this model is the exact implementation of void growth behavior [21]. The Gurson-Tvergaard-Needleman (GTN) model has a clear process mechanism and is close to the actual damage of materials. It has been proven to predict the damage caused by the aggregation and growth of cavity of the internal voids of the metal and thus accurately simulate the failure of the mechanical clinching [15]. It has good performance in prediction of fracture location and parameters in fracture as equivalent plastic strain and displacement [22]. As it has a quantitative damage value of volume fraction, it is a mature and widely used theory of damage mechanics. In this work, we chose the GTN model as an alternative to simulate the damage and failure behavior of the clinched joints. From the perspective of microscopic void failure mechanism, the failure process of ductile materials involves void nucleation, void growth and void coalescence. The yield condition for porous materials proposed by Gurson is given by the following equation [15,22]:
2. Material properties In this work, the materials were dual-phase high strength steel DP590 sheet and aluminium alloy AA6061-T6 sheet which were commonly used in car bodies, and their thicknesses were 1.6 mm and 1.5 mm respectively. The uniaxial tensile mechanical properties of the two materials were tested according to the national standard GB/T 228-2002 metal tensile test method. The samples of the uniaxial tensile tests are shown in Fig. 1. To reduce the measurement error, the uniaxial tensile test was conducted three times for each material. The engineering stress-strain curves were transformed into the true stress-strain curves (Fig. 2) using for the finite element simulation through the following equations:
ðl εtrue ¼
dl l ¼ ln ¼ lnð1 þ εnom Þ l l0
strue ¼
F F ¼ ¼ snom ð1 þ εnom Þ A A0 l0
l
Where εnom and εtrue stand for the engineering strain and true strain respectively; snom and strue for engineering stress and true stress. The mechanical properties of the materials are shown in Table 1.
2 seq 2 3 sm 1 q3 f * ¼ 0 þ 2q1 f * cosh q2 2 s0 s0 2
F¼ f* ¼
d¼ (2)
(3)
Where F stands for the plastic potential; s0 is the yield stress; seq is the Von Mises equivalent stress and sm is the hydrostatic component of the stress state. When f ¼ 0, the material is homogeneous without damage, and formula (3) degenerates into the traditional Mises yield surface. The proposed model makes it possible for the void damage to describe the deformation behavior of the material. Needleman and Tvergaard [23] improved the model on the basis of the Gurson model and proposed the modified yield condition:
(1)
l0
seq 2 3 sm 1 f2 ¼ 0 þ 2fcosh 2 s0 s0 2
F¼
1 q1
f fC þ dðf fC Þ f
fF fC
if f < fC otherwise
(4)
(5)
(6)
Where q1 , q2 , q3 are the parameters considering the interaction of the voids; f * is an effective porosity; fC is the critical value of porosity ratio at the onset of void coalescence; fF is the failure value of void volume fraction. The evolution equation of the void volume fracture consists of two terms resulting from the growth rate of existing voids f_g and the nucleation rate of new voids f_n :
Please cite this article as: Y. Song et al., Numerical and experimental study on failure behavior of steel-aluminium mechanical clinched joints under multiple test conditions, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2018.12.005
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Fig. 1. Uniaxial tensile test samples.
SN ; fN ; fF ; fC ) need to be input into the definition of material in finite element analyze software. In general, q1 ¼ 1.5; q2 ¼ 1; q3 ¼ q12 ¼ 2.25; 3N ¼ 0.3; SN ¼ 0.1, so there are only three crucial parameters (fN ; fF ; fC ) need to be determined. In this work, the orthogonal simulations were conducted with GTN model to compare with the uniaxial tensile test results, thus the best parameters were determined. A 3-factor-3-level orthogonal design was carried out, the levels of the parameters are shown in Table 2. The uniaxial tensile simulation model were established in ABAQUS according to the samples described in part 2 and the element type was set to C3D8R. The uniaxial tensile simulation and test results of AA6061-T6 and DP590 are shown in Figs. 3 and 4. By comparing the load-displacement results of simulation and uniaxial tensile test, the simulation results have good agreement with the test results, and the fracture form was consistent. The best parameters were determined as: fN1 ¼ 0.0012; fF1 ¼ 0.04; fC1 ¼ 0.005 (AA6061T6); fN2 ¼ 0.008; fF2 ¼ 0.25; fC2 ¼ 0.05 (DP590). It can be seen from Figs. 3 (b) and Fig.4 (b) that the simulations without GTN damage model were inaccurate because of no fractures.
Fig. 2. True stress-true strain curves of steel and aluminium alloy.
f_ ¼ f_g þ f_n 8 > > > < > > > :
(7)
3.2. Simulation of mechanical properties and failure behavior
(8)
In order to test the mechanical properties of the joints. Threedimensional models of the steel-aluminium mechanical clinched joints under three conditions, i.e., shear, peel and cross tensile, were established respectively in the software ABAQUS. The dimensions
"
f_g ¼ ð1 f Þ_εpkk
# fN 1 εp εN 2 P _ ε_ fn ¼ pffiffiffiffiffiffi exp 2 SN SN 2 p
p
Where ε_ kk is the plastic strain rate; fN is the volume fraction of void nucleating particles; εN is the mean strain for nucleation; SN is the standard deviation of εN ; εp is the von Mises plastic strain; and ε_ P is the von Mises plastic strain rate. In order to accurately predict the damage and failure behavior of the clinched joint, the parameters in GTN model (q1 ; q2 ; q3 ; εN ;
Table 2 Levels of orthogonal experiment. level
fN (AA6061-T6/DP590)
fF (AA6061-T6/DP590)
fC (AA6061-T6/DP590)
1 2 3
0.0012/0.0008 0.006/0.008 0.03/0.08
0.04/0.25 0.12/0.40 0.36/0.60
0.005/0.015 0.015/0.05 0.045/0.1
Table 1 Mechanical properties of materials used in finite element simulation. Materials
Elastic modulus E (GPa)
Poisson's ratio v
Yield strength ds (MPa)
Tensile strength db (MPa)
Elongation
Densityr (g.cm3)
d P590 AA6061-T6
210 69
0.3 0.33
385 278
786 375
0.31 0.15
7.8 2.7
Please cite this article as: Y. Song et al., Numerical and experimental study on failure behavior of steel-aluminium mechanical clinched joints under multiple test conditions, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2018.12.005
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Fig. 3. Comparison of simulation and test results of AA6061-T6.
Fig. 4. Comparison of simulation and test results of DP590.
and geometric parameters of the three kinds of joints are shown in Fig. 5aec, respectively. In each joint, the upper sheet was dual-phase steel DP590 with thickness of 1.6 mm, while the lower one was AA6061-T6 with thickness of 1.5 mm. In order to take into account the simulation
accuracy and efficiency, the mesh size in the joints was 0.3 mm, while those in the other areas were 3 mm. The friction coefficient between the two sheets was set to 0.35 [13]. The three-dimensional finite element models and boundary conditions are shown in Fig. 6. 4. Experimental tests The experiments of mechanical properties of the joints were carried out. The test samples were made by press riveter LX8-500C (Fig. 7a) according to Fig. 5. The punch and die of the clinching equipment were shown in Fig. 8 (a). Through several times’ clinching, it was found that the clinching samples had a good repeatability, see Fig. 8 (b). The cross-sectional shape of the joint sample was obtained to compare with the simulation one, as shown in Fig. 9. It was found that the simulation result was in good agreement with the experimental one. To reduce the experimental error, three samples were prepared in each test and numbered as follows: the shear samples were
Fig. 5. Sample size of mechanical clinching.
Fig. 6. Three-dimensional finite element models.
Please cite this article as: Y. Song et al., Numerical and experimental study on failure behavior of steel-aluminium mechanical clinched joints under multiple test conditions, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2018.12.005
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Fig. 9. Comparison of the cross section shapes of joined sample and simulation one.
5.2. Mechanical properties of the joints
Fig. 7. Experimental equipment.
numbered as L01, L02 and L03, the peel samples were numbered as S01, S02 and S03, and the cross tensile samples were numbered as C01, C02 and C03 (Fig. 10). Then, the samples were tested on the microcomputer controlled electronic universal testing machine CMT6104 (Fig. 7b). In the tests, the ends of the aluminium alloy sheets were fixed, while the steel sheets were stretched by the testing machine. The tensile speed was 2 mm/min. 5. Results and discussion 5.1. Failure modes Figss. 11e13 show the FE simulation and experimental test results of the failed samples under three conditions. It can be found that failure mode is neck fracture in shear condition, while that is pulling out in peel and cross tensile conditions, and the FE simulation results of the failure modes are in good agreement with the experimental ones. The cross section shapes of the failed joints are shown in Fig. 14. There are two failure modes when the mechanical clinched joints are failed: pulling out and neck fracture. Under the shear condition, the load is mainly caused by the neck of the upper sheet in the joint. It can be seen from Fig. 15 (a) that the stress concentration is mainly located at the neck of the upper sheet. It can be speculated that under the external load, the upper sheet will gradually separate from the lower sheet, which will eventually lead to fracture failure of the joint. Under the peel condition, the stress concentration is located at the contact area on the right side of two sheets, as shown in Fig. 15 (b). Therefore, it is a dangerous area during the peeling process due to the pressing force. Similarly, under the cross tensile condition, the load is mainly caused by the friction and interlock structure between two the sheets, so the dangerous area is located at the interlock area of the upper sheet, as shown in Fig. 15 (c). The failure of the interlock structure causes the pulling out of the joint.
Fig. 16 shows the load-displacement curves of experiments and simulations. The detailed quantitative comparison between the results in the three conditions is shown in Table 3. The peak load, the peak load displacement and the failure displacement were chosen to evaluate the mechanical properties of the clinched joints under different conditions. According to the data shown in Table 3, the clinched joints under shear condition have a peak force of 4354N, which is much higher than that of the peel (624N) and cross tensile (1046N) conditions. The error of the peak load between the simulation and experimental results is within 6.31%; the error of the peak force displacement is less than 16.32%; and the error of the failure displacement is within 8.37%. And from the results of section 5.1, the failure modes of FE simulations and tests are consistent. These results indicate that the FE simulation results are in good agreement with the experimental ones, especially for the prediction of the failure mode, the peak force and the displacement at failure. These results also indicate that the numerical method based on GTN damage model can accurately
Fig. 10. Test samples of mechanical properties for clinched joints.
Fig. 8. Mechanical clinching tools and clinched samples.
Please cite this article as: Y. Song et al., Numerical and experimental study on failure behavior of steel-aluminium mechanical clinched joints under multiple test conditions, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2018.12.005
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Fig. 11. Simulation and experimental test results under shear condition.
Fig. 12. Simulation and experimental test results under peel condition.
Fig. 13. Simulation and experimental test results under cross tensile condition.
Fig. 14. Failure modes of the clinched joints.
predict the mechanical properties and failure modes of the clinched joints. It's also found that the clinched joints have the maximum peak load and the minimum failure displacement under shear condition. In the shear condition, as mentioned in section 5.1, the shear force is mainly caused by the neck of the upper sheet in the clinched joint. It can make full use of the material properties of the joint because of
its special shape, resulting in stronger shear resistance of the joint and the failure mode of neck fracture. In the cross tensile and peel conditions, the force mainly depends on the friction between the two sheets in the joints to resist failure. Thus, it is unable to make full use of the material properties at the joints, resulting in a lower peak force and a weaker anti-pull out capacity in the two cases, so the failure mode is pulling out in the two conditions.
Please cite this article as: Y. Song et al., Numerical and experimental study on failure behavior of steel-aluminium mechanical clinched joints under multiple test conditions, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2018.12.005
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Fig. 15. Stress distribution under three conditions.
Fig. 16. Experimental and simulated results of clinched joints under three conditions.
Table 3 Comparison of mechanical properties under three conditions. Test conditions
Items
Peak load (N)
Peak load Displacement (mm)
Failure Displacement (mm)
Failure mode
Shear
Test ðTav Þ Simulation (S) Errora (%) Test ðTav Þ Simulation (S) Error (%) Test ðTav Þ Simulation (S) Error (%)
4354 4242 2.57 624 654 4.80 1046 1112 6.31
2.45 2.05 16.32 8.75 9.49 8.46 7.76 7.60 2.06
3.40 3.52 3.50 9.56 10.36 8.37 7.89 7.78 1.39
Neck fracture Neck fracture
Peel
Cross tensile
a
Pulling out Pulling out Pulling out Pulling out
The error was computed as Tav-S /Tav 100%. Tav and S stand for the average value of the test results and the simulation result respectively.
Please cite this article as: Y. Song et al., Numerical and experimental study on failure behavior of steel-aluminium mechanical clinched joints under multiple test conditions, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2018.12.005
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6. Conclusions In this work, the FE simulation and experimental tests were conducted to measure the mechanical properties and failure behavior of steel-aluminium mechanical clinched joints. The Gurson-Tvergaard-Needleman (GTN) damage model implemented in ABAQUS was used in the FE simulation. The parameters of the damage model were obtained by comparing the results of simulation and experiments through orthogonal design. The major findings can be summarized as follows: 1. For the load-displacement curves and the failure modes of the clinched joints, the FE simulation results are close to the experimental ones. It indicates that the numerical method based on GTN damage model can accurately predict the mechanical properties and failure modes of the clinched joints. 2. The shear strength of the mechanical clinched joints is much higher than that of the tensile and peel strengths, while the peak load displacement and failure displacement have the opposite law. 3. Under the shear condition, the failure mode is neck fracture because of the shear force in the neck of the upper sheet in clinched joints. Under the peel and cross tensile conditions, the failure mode is pulling out because of the friction between the two sheets in the clinched joints. 4. Under shear and cross tensile conditions, the stress concentration is mainly located at the neck of the upper sheet. Under the peel condition, the stress concentration is located at the contact area on the right side of two sheets because of the pressing force during the peeling process. These are dangerous areas that may lead to cracking or fracture when tested.
Declarations of interest The authors declare that there is no conflicts of interest. Acknowledgment This work was supported by the National Natural Science Foundation of China [Grant number 51675392]; China Automobile Industry Innovation and Development Joint Fund [Grant number U1564202]; and the 111 project [Grant number B17034]. References
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Please cite this article as: Y. Song et al., Numerical and experimental study on failure behavior of steel-aluminium mechanical clinched joints under multiple test conditions, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2018.12.005
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Original Article
Numerical and experimental study on failure behavior of steelaluminium mechanical clinched joints under multiple test conditions Yanli Song a, b, c, *, Lulu Yang a, b, Genpeng Zhu c, Lin Hua a, b, c, Runze Liu a, b a
Hubei Key Laboratory of Advanced Technology for Automotive Components, Wuhan University of Technology, Wuhan, 430070, China Hubei Collaborative Innovation Center for Automotive Components Technology, Wuhan University of Technology, Wuhan, 430070, China c School of Automotive Engineering, Wuhan University of Technology, Wuhan, 430070, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 13 October 2018 Received in revised form 20 November 2018 Accepted 20 December 2018 Available online xxx
In this work, the numerical and experimental study was performed to explore the mechanical properties and failure behavior of steel-aluminium mechanical clinched joints under multiple test conditions. The stress distribution of the clinched joints and the failure mode were analyzed using finite element analysis software ABAQUS. The Gurson-Tvergaard-Needleman (GTN) model was used to simulate damage and failure of the joints. The experimental tests were conducted for the verification. It was found that the clinched joints under shear condition had a peak force of 4354N, which was much higher than that of the peel (624N) and cross tensile (1046N) conditions, while the peak load displacement and failure displacement have the opposite law. The failure mode of shear condition was neck fracture, while that of tensile and peel conditions were both pulling out failure. The finite element simulation results were in good agreement with the experimental ones and the failure mode was consistent. The Gurson-tvergaardNeedleman (GTN) model can accurately predict the mechanical properties and failure mode of clinched joints. © 2018 The Authors. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/).
Keywords: Steel-aluminium mechanical clinching Mechanical properties Damage model Finite element simulation
1. Introduction In recent years, lightweight of automobiles has become a high demand worldwide due to the environmental pollution and energy shortage [1]. And the demand for coupling performances with reductions of cost, weight, fuel consumption, air pollution and the improvement of safety is stronger and stronger [2]. Since aluminium alloy has the advantages of low density, excellent lightweight performance, good collision energy absorption and so on, the proportion of aluminium alloy in the body in white (BIW) has been increased year by year. Therefore, the traditional steel body has been gradually developed into a steel-aluminium composite body. For example, the dosage of steel and aluminium alloy in Audi TT/TTS Coupe body is 35.8% and 62.6% respectively. Accordingly, the connection between the steel and aluminium alloy sheets becomes an issue.
* Corresponding author. Hubei Key Laboratory of Advanced Technology for Automotive Components, Wuhan University of Technology, Wuhan, 430070, China. Fax: þ86 27 8716 8391. E-mail address: [email protected] (Y. Song).
Mechanical clinching is a mechanical joining process where the sheet metal parts are joined together by an interlock formed through local plastic deformation without cutting or the use of any external elements such as a fastener or rivet [3]. It is an efficient, reliable and low-cost connection method, especially suitable for the connection of steel and aluminium [4]. The quality of the clinched joint is influenced by the sheet type, sheet thickness and die parameters [5]. A desired joint can be obtained by designing clinching tools based on the analytical model used to predict the strength of the joint [6]. Recent years, mechanical clinching has attracted wide attention of scholars. Most concerned the effect of die parameters on the strength of clinched joint. Lambiase and Di Ilio [7] optimized the geometric parameters of clinching dies for the steel sheet joints by artificial neural network and genetic algorithm. Abe et al. [8] developed a mechanical clinching method using counter pressure of a rubber ring to join the galvanized ultra-high strength steel sheets with low ductility. Chen et al. [9] reduced the height and improved the strength of clinched joints under shear and cross-tensile conditions by compressing the joints for Al6061 sheets. Kam et al. [10] studied the effect of the eccentricity
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Please cite this article as: Y. Song et al., Numerical and experimental study on failure behavior of steel-aluminium mechanical clinched joints under multiple test conditions, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2018.12.005
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of the dies on the clinched joint strength for coated mild steel sheets. Eshtayeh and Hrairi [11] introduced the implementation of the Taguchi-based Grey optimization of the mechanical clinching with fixed dies for AA7075 and mild steel and derived the optimal process parameters combination that leads to a high strength connection. Lambiase [12] investigated the influence of clinching tool design on the cross section of a clinched joint in joining low carbon steel sheets by the clinching process with extensible dies. Liu [13] studied the forming law of mechanical clinching and obtained the influence of die parameters on the joining quality. Other studies focused on the properties and failure of the mechanical clinching. Abe et al. [14] experimentally studied the effects of the shape and size of dies on the metal flow and forming defects of the clinched joints for high strength steel and aluminium alloy sheets. Pirondi and Moroni [15] studied the failure behavior of clinch-bonded and rivet-bonded joints using the finite element method (FEM). Zhou et al. [16] established a finite element simplified model of body collision, and studied the failure model of mechanical clinching. Calabrese et al. [17] studied the effect of corrosion phenomena in critical environmental conditions on the mechanical performance of steel-aluminium clinched joints by ageing in salt spray environment. Mori et al. [18] compared the static and fatigue strength of mechanical clinched and self-pierced joints with a resistance spot welded joint and found that the former two joints have superior fatigue resistance. Abe et al. [4] compared the static and fatigue strengths of the clinched joints with those of the resistance spot welded joints. It was found that the shear and cross tensile strength of the clinched joints were lower than those of the resistance spot welded joints, while the fatigue strength the opposite results. In this paper, the finite element (FE) simulation of the clinched steel-aluminium joints was built with the Gurson-TvergaardNeedleman (GTN) damage model to simulate the mechanical properties and failure behavior under shear, peel and cross tensile conditions. The experimental tests were conducted for the verification.
3. Finite element simulation 3.1. Damage model As is known, when a joint is subjected to a tensile or shear force, it may fail and lead to fracture of the material. Therefore, a reasonable material damage or failure model should be chosen in the FE simulation of the clinched joints. The ductile damage model is a phenomenological model for predicting the onset of damage from the perspective of mechanics [19]. The modified Rousselier model can describe the failure process and evolution mechanism. It is used to predict the shear-dominated fracture and stress distribution on the clinched joint [20]. The modified Gurson model can explain the macroscopic phenomena by describing the mesoscopic behavior of the clinched joint during the clinching process. It allows for the numerical simulation of the elasticeplastic behavior until fracture and describes the localization and fracture in sheardominated stress states with low triaxiality. A distinct advantage of this model is the exact implementation of void growth behavior [21]. The Gurson-Tvergaard-Needleman (GTN) model has a clear process mechanism and is close to the actual damage of materials. It has been proven to predict the damage caused by the aggregation and growth of cavity of the internal voids of the metal and thus accurately simulate the failure of the mechanical clinching [15]. It has good performance in prediction of fracture location and parameters in fracture as equivalent plastic strain and displacement [22]. As it has a quantitative damage value of volume fraction, it is a mature and widely used theory of damage mechanics. In this work, we chose the GTN model as an alternative to simulate the damage and failure behavior of the clinched joints. From the perspective of microscopic void failure mechanism, the failure process of ductile materials involves void nucleation, void growth and void coalescence. The yield condition for porous materials proposed by Gurson is given by the following equation [15,22]:
2. Material properties In this work, the materials were dual-phase high strength steel DP590 sheet and aluminium alloy AA6061-T6 sheet which were commonly used in car bodies, and their thicknesses were 1.6 mm and 1.5 mm respectively. The uniaxial tensile mechanical properties of the two materials were tested according to the national standard GB/T 228-2002 metal tensile test method. The samples of the uniaxial tensile tests are shown in Fig. 1. To reduce the measurement error, the uniaxial tensile test was conducted three times for each material. The engineering stress-strain curves were transformed into the true stress-strain curves (Fig. 2) using for the finite element simulation through the following equations:
ðl εtrue ¼
dl l ¼ ln ¼ lnð1 þ εnom Þ l l0
strue ¼
F F ¼ ¼ snom ð1 þ εnom Þ A A0 l0
l
Where εnom and εtrue stand for the engineering strain and true strain respectively; snom and strue for engineering stress and true stress. The mechanical properties of the materials are shown in Table 1.
2 seq 2 3 sm 1 q3 f * ¼ 0 þ 2q1 f * cosh q2 2 s0 s0 2
F¼ f* ¼
d¼ (2)
(3)
Where F stands for the plastic potential; s0 is the yield stress; seq is the Von Mises equivalent stress and sm is the hydrostatic component of the stress state. When f ¼ 0, the material is homogeneous without damage, and formula (3) degenerates into the traditional Mises yield surface. The proposed model makes it possible for the void damage to describe the deformation behavior of the material. Needleman and Tvergaard [23] improved the model on the basis of the Gurson model and proposed the modified yield condition:
(1)
l0
seq 2 3 sm 1 f2 ¼ 0 þ 2fcosh 2 s0 s0 2
F¼
1 q1
f fC þ dðf fC Þ f
fF fC
if f < fC otherwise
(4)
(5)
(6)
Where q1 , q2 , q3 are the parameters considering the interaction of the voids; f * is an effective porosity; fC is the critical value of porosity ratio at the onset of void coalescence; fF is the failure value of void volume fraction. The evolution equation of the void volume fracture consists of two terms resulting from the growth rate of existing voids f_g and the nucleation rate of new voids f_n :
Please cite this article as: Y. Song et al., Numerical and experimental study on failure behavior of steel-aluminium mechanical clinched joints under multiple test conditions, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2018.12.005
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Fig. 1. Uniaxial tensile test samples.
SN ; fN ; fF ; fC ) need to be input into the definition of material in finite element analyze software. In general, q1 ¼ 1.5; q2 ¼ 1; q3 ¼ q12 ¼ 2.25; 3N ¼ 0.3; SN ¼ 0.1, so there are only three crucial parameters (fN ; fF ; fC ) need to be determined. In this work, the orthogonal simulations were conducted with GTN model to compare with the uniaxial tensile test results, thus the best parameters were determined. A 3-factor-3-level orthogonal design was carried out, the levels of the parameters are shown in Table 2. The uniaxial tensile simulation model were established in ABAQUS according to the samples described in part 2 and the element type was set to C3D8R. The uniaxial tensile simulation and test results of AA6061-T6 and DP590 are shown in Figs. 3 and 4. By comparing the load-displacement results of simulation and uniaxial tensile test, the simulation results have good agreement with the test results, and the fracture form was consistent. The best parameters were determined as: fN1 ¼ 0.0012; fF1 ¼ 0.04; fC1 ¼ 0.005 (AA6061T6); fN2 ¼ 0.008; fF2 ¼ 0.25; fC2 ¼ 0.05 (DP590). It can be seen from Figs. 3 (b) and Fig.4 (b) that the simulations without GTN damage model were inaccurate because of no fractures.
Fig. 2. True stress-true strain curves of steel and aluminium alloy.
f_ ¼ f_g þ f_n 8 > > > < > > > :
(7)
3.2. Simulation of mechanical properties and failure behavior
(8)
In order to test the mechanical properties of the joints. Threedimensional models of the steel-aluminium mechanical clinched joints under three conditions, i.e., shear, peel and cross tensile, were established respectively in the software ABAQUS. The dimensions
"
f_g ¼ ð1 f Þ_εpkk
# fN 1 εp εN 2 P _ ε_ fn ¼ pffiffiffiffiffiffi exp 2 SN SN 2 p
p
Where ε_ kk is the plastic strain rate; fN is the volume fraction of void nucleating particles; εN is the mean strain for nucleation; SN is the standard deviation of εN ; εp is the von Mises plastic strain; and ε_ P is the von Mises plastic strain rate. In order to accurately predict the damage and failure behavior of the clinched joint, the parameters in GTN model (q1 ; q2 ; q3 ; εN ;
Table 2 Levels of orthogonal experiment. level
fN (AA6061-T6/DP590)
fF (AA6061-T6/DP590)
fC (AA6061-T6/DP590)
1 2 3
0.0012/0.0008 0.006/0.008 0.03/0.08
0.04/0.25 0.12/0.40 0.36/0.60
0.005/0.015 0.015/0.05 0.045/0.1
Table 1 Mechanical properties of materials used in finite element simulation. Materials
Elastic modulus E (GPa)
Poisson's ratio v
Yield strength ds (MPa)
Tensile strength db (MPa)
Elongation
Densityr (g.cm3)
d P590 AA6061-T6
210 69
0.3 0.33
385 278
786 375
0.31 0.15
7.8 2.7
Please cite this article as: Y. Song et al., Numerical and experimental study on failure behavior of steel-aluminium mechanical clinched joints under multiple test conditions, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2018.12.005
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Fig. 3. Comparison of simulation and test results of AA6061-T6.
Fig. 4. Comparison of simulation and test results of DP590.
and geometric parameters of the three kinds of joints are shown in Fig. 5aec, respectively. In each joint, the upper sheet was dual-phase steel DP590 with thickness of 1.6 mm, while the lower one was AA6061-T6 with thickness of 1.5 mm. In order to take into account the simulation
accuracy and efficiency, the mesh size in the joints was 0.3 mm, while those in the other areas were 3 mm. The friction coefficient between the two sheets was set to 0.35 [13]. The three-dimensional finite element models and boundary conditions are shown in Fig. 6. 4. Experimental tests The experiments of mechanical properties of the joints were carried out. The test samples were made by press riveter LX8-500C (Fig. 7a) according to Fig. 5. The punch and die of the clinching equipment were shown in Fig. 8 (a). Through several times’ clinching, it was found that the clinching samples had a good repeatability, see Fig. 8 (b). The cross-sectional shape of the joint sample was obtained to compare with the simulation one, as shown in Fig. 9. It was found that the simulation result was in good agreement with the experimental one. To reduce the experimental error, three samples were prepared in each test and numbered as follows: the shear samples were
Fig. 5. Sample size of mechanical clinching.
Fig. 6. Three-dimensional finite element models.
Please cite this article as: Y. Song et al., Numerical and experimental study on failure behavior of steel-aluminium mechanical clinched joints under multiple test conditions, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2018.12.005
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Fig. 9. Comparison of the cross section shapes of joined sample and simulation one.
5.2. Mechanical properties of the joints
Fig. 7. Experimental equipment.
numbered as L01, L02 and L03, the peel samples were numbered as S01, S02 and S03, and the cross tensile samples were numbered as C01, C02 and C03 (Fig. 10). Then, the samples were tested on the microcomputer controlled electronic universal testing machine CMT6104 (Fig. 7b). In the tests, the ends of the aluminium alloy sheets were fixed, while the steel sheets were stretched by the testing machine. The tensile speed was 2 mm/min. 5. Results and discussion 5.1. Failure modes Figss. 11e13 show the FE simulation and experimental test results of the failed samples under three conditions. It can be found that failure mode is neck fracture in shear condition, while that is pulling out in peel and cross tensile conditions, and the FE simulation results of the failure modes are in good agreement with the experimental ones. The cross section shapes of the failed joints are shown in Fig. 14. There are two failure modes when the mechanical clinched joints are failed: pulling out and neck fracture. Under the shear condition, the load is mainly caused by the neck of the upper sheet in the joint. It can be seen from Fig. 15 (a) that the stress concentration is mainly located at the neck of the upper sheet. It can be speculated that under the external load, the upper sheet will gradually separate from the lower sheet, which will eventually lead to fracture failure of the joint. Under the peel condition, the stress concentration is located at the contact area on the right side of two sheets, as shown in Fig. 15 (b). Therefore, it is a dangerous area during the peeling process due to the pressing force. Similarly, under the cross tensile condition, the load is mainly caused by the friction and interlock structure between two the sheets, so the dangerous area is located at the interlock area of the upper sheet, as shown in Fig. 15 (c). The failure of the interlock structure causes the pulling out of the joint.
Fig. 16 shows the load-displacement curves of experiments and simulations. The detailed quantitative comparison between the results in the three conditions is shown in Table 3. The peak load, the peak load displacement and the failure displacement were chosen to evaluate the mechanical properties of the clinched joints under different conditions. According to the data shown in Table 3, the clinched joints under shear condition have a peak force of 4354N, which is much higher than that of the peel (624N) and cross tensile (1046N) conditions. The error of the peak load between the simulation and experimental results is within 6.31%; the error of the peak force displacement is less than 16.32%; and the error of the failure displacement is within 8.37%. And from the results of section 5.1, the failure modes of FE simulations and tests are consistent. These results indicate that the FE simulation results are in good agreement with the experimental ones, especially for the prediction of the failure mode, the peak force and the displacement at failure. These results also indicate that the numerical method based on GTN damage model can accurately
Fig. 10. Test samples of mechanical properties for clinched joints.
Fig. 8. Mechanical clinching tools and clinched samples.
Please cite this article as: Y. Song et al., Numerical and experimental study on failure behavior of steel-aluminium mechanical clinched joints under multiple test conditions, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2018.12.005
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Fig. 11. Simulation and experimental test results under shear condition.
Fig. 12. Simulation and experimental test results under peel condition.
Fig. 13. Simulation and experimental test results under cross tensile condition.
Fig. 14. Failure modes of the clinched joints.
predict the mechanical properties and failure modes of the clinched joints. It's also found that the clinched joints have the maximum peak load and the minimum failure displacement under shear condition. In the shear condition, as mentioned in section 5.1, the shear force is mainly caused by the neck of the upper sheet in the clinched joint. It can make full use of the material properties of the joint because of
its special shape, resulting in stronger shear resistance of the joint and the failure mode of neck fracture. In the cross tensile and peel conditions, the force mainly depends on the friction between the two sheets in the joints to resist failure. Thus, it is unable to make full use of the material properties at the joints, resulting in a lower peak force and a weaker anti-pull out capacity in the two cases, so the failure mode is pulling out in the two conditions.
Please cite this article as: Y. Song et al., Numerical and experimental study on failure behavior of steel-aluminium mechanical clinched joints under multiple test conditions, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2018.12.005
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Fig. 15. Stress distribution under three conditions.
Fig. 16. Experimental and simulated results of clinched joints under three conditions.
Table 3 Comparison of mechanical properties under three conditions. Test conditions
Items
Peak load (N)
Peak load Displacement (mm)
Failure Displacement (mm)
Failure mode
Shear
Test ðTav Þ Simulation (S) Errora (%) Test ðTav Þ Simulation (S) Error (%) Test ðTav Þ Simulation (S) Error (%)
4354 4242 2.57 624 654 4.80 1046 1112 6.31
2.45 2.05 16.32 8.75 9.49 8.46 7.76 7.60 2.06
3.40 3.52 3.50 9.56 10.36 8.37 7.89 7.78 1.39
Neck fracture Neck fracture
Peel
Cross tensile
a
Pulling out Pulling out Pulling out Pulling out
The error was computed as Tav-S /Tav 100%. Tav and S stand for the average value of the test results and the simulation result respectively.
Please cite this article as: Y. Song et al., Numerical and experimental study on failure behavior of steel-aluminium mechanical clinched joints under multiple test conditions, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2018.12.005
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6. Conclusions In this work, the FE simulation and experimental tests were conducted to measure the mechanical properties and failure behavior of steel-aluminium mechanical clinched joints. The Gurson-Tvergaard-Needleman (GTN) damage model implemented in ABAQUS was used in the FE simulation. The parameters of the damage model were obtained by comparing the results of simulation and experiments through orthogonal design. The major findings can be summarized as follows: 1. For the load-displacement curves and the failure modes of the clinched joints, the FE simulation results are close to the experimental ones. It indicates that the numerical method based on GTN damage model can accurately predict the mechanical properties and failure modes of the clinched joints. 2. The shear strength of the mechanical clinched joints is much higher than that of the tensile and peel strengths, while the peak load displacement and failure displacement have the opposite law. 3. Under the shear condition, the failure mode is neck fracture because of the shear force in the neck of the upper sheet in clinched joints. Under the peel and cross tensile conditions, the failure mode is pulling out because of the friction between the two sheets in the clinched joints. 4. Under shear and cross tensile conditions, the stress concentration is mainly located at the neck of the upper sheet. Under the peel condition, the stress concentration is located at the contact area on the right side of two sheets because of the pressing force during the peeling process. These are dangerous areas that may lead to cracking or fracture when tested.
Declarations of interest The authors declare that there is no conflicts of interest. Acknowledgment This work was supported by the National Natural Science Foundation of China [Grant number 51675392]; China Automobile Industry Innovation and Development Joint Fund [Grant number U1564202]; and the 111 project [Grant number B17034]. References
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Please cite this article as: Y. Song et al., Numerical and experimental study on failure behavior of steel-aluminium mechanical clinched joints under multiple test conditions, International Journal of Lightweight Materials and Manufacture, https://doi.org/10.1016/j.ijlmm.2018.12.005