Numerical simulation on the dynamic cold extrusion of bolted single-lap Al/Al joint under interference-fit

The installation process for the dynamic cold extrusion of Al/Al interference-fit bolted joint applied by electromagnetic force was investigated by numerical simulation. The simulation results show that the deformation distribution of the bore wall at joint installed by the electromagnetic force is more uniform than that of the traditional installation technologies. And in the axial direction of bore wall without pin, the maximum stress region occurs at its outlet regardless of the values of interference-fit. Additionally found that the critical interference-fit value for a joint to reach yield strength is about 1 %, and when the amount of interference-fit is less than 1%, the joint mainly exhibits elastic deformation, and when the interference is more than 1 %, the plastic deformation is its main manifestation.


Introduction
Aviation aluminum alloys are widely used as important components such as frames, beams, and chords of aircraft due to their high specific strength, high specific stiffness and high toughness [1].The electromagnetic force, a new loading technology, has been widely attention from scholars at home and abroad in the field of mechanical connection due to its characteristics such as fast loading rate, high reliability, non-destructive installation of large-diameter bolt fasteners accompanied with the large interference-fit amount [2].In fact, electromagnetic force loading is a single high-speed impact forming behavior under a single action [3], which can achieve uniform interference-fit of bolted joints.
At present, the bolted joint tests on metal laminated structures have been studied by many scholars.Zhang et al. [4] conducted an experiment on titanium alloy riveted joint loaded with electromagnetic force, and found that the joint had a high interference-fit quality.Zuo [5] investigated that the greater the amount of interference, the greater the installation resistance of CFRP/Ti interference-fit bolted structures, but the dynamic extrusion installation loaded by electromagnetic force can effectively reduce the installation resistance.Meanwhile, under the impact load, Liu et al. [6] found that the bolted joints had a certain energy absorption capacity derived from cushioning, and the energy absorption effect could be enhanced by appropriately increasing the bolt clearance.In addition, in view of the bearing capacity problem of CFRP/Ti laminated plates treated by hybrid bonding/bolt connection with the different bolt numbers, Zheng et al. [7] found that the failure load was affected by the lap distance, and showed a trend of increasing accordingly.However, there are few reports on the non-destructive interference installation of large-diameter bolt fasteners on the medium-thick plates under electromagnetic force.
Based on this, the bolted single-lap Al/Al joint is investigated, the installation process for the dynamic cold extrusion of interference-fit joint under electromagnetic force in ABAQUS platform is simulated and analyzed.From the three aspects of displacement deformation, stress distribution and installation force of bore wall, its installation process and mechanical behavior under cold extrusion state accompanied are analyzed, and the extrusion installation mechanism of the interference-fit bolted joint is revealed, which provide reference for future relevant on-site experimental research.

Numerical simulation
The combined interference-fit joint under 7050-T7651 Al plate and TC4 hi-lock bolt self-made are taken as the research object, the dynamic cold extrusion process of the bolted joint treated by electromagnetic loading was analyzed by finite element method using ABAQUS under interference-fit quantities of 0.6 %, 1 % and 1.4 %.The diameter of self-made hi-lock bolt is Φ11.73 mm, with an Al plate thickness of 14 mm and apertures of Φ11.66 mm, Φ11.61 mm and Φ 11.57mm, and the bolted structure is shown in Figure 1.It should be noted that in order to ensure the efficiency and accuracy of FE, the assembly of Al plate in simulation model is simplified, and the screw structure of bolt fastener is also ignored.The force-displacement changes of bore wall in joint are only analyzed in whole simulation.In this paper, the Johnson-Cook model [8] is used to characterize the damage failure process of bolted joint under electromagnetic impact loading.Table 1 shows the Johnson-Cook constitutive model and performance parameters assigned for the bolted joint.where the Young 's modulus of 7050-T7651 Al plate is 70.3 GPa, and the Poisson 's ratio is 0.33, Tmelt and Troom are melting temperature and room temperature, ℃.A, B, n, m and C are the experimental fitting parameters, respectively.Among them, A stands for the yield strength, Pa, B is the strain hardening modulus, MPa, the parameters n and m are in turn the strain hardening index and the thermal softening index, C is the strain rate sensitivity.

Deformation and stress analysis
The deformation and stress distribution in the aperture region of bolted joint are closely related to the damage degree of the inlet and outlet at the bore wall of Al plate [9].Considering the fact that the deformation and stress concentration are more serious because the bolt fasteners first contact with the entrance of bore wall during the process of interference-fit installation acted by electromagnetic force.Therefore, the inlet end of the above-mentioned joint is selected to analyze the deformation distribution of radial displacement, which presents the corresponding deformation degree of radial displacement under different interference values in Figure 2. As can be seen from Figure 2, with the increase of interference, the radial displacement of the hole wall and the fluctuation of the displacement curve also increase.But, the displacement deformation distribution at the inlet aperture of joint is uniform under different interference quantities.
Under the loading of electromagnetic force, due to the interference-fit bolted joint subjected by the dual influence of high-velocity impact and boundary effect, the phenomena on both the stress concentration and uneven stress in the bore wall area at the inlet ends is easily produced.Figure 3 shows the stress contour for the boltless bore wall of joint with the interference ranges from 0.6 % to 1.4 %.It can be observed from Figures 3a and 3c, the range of stress ring at the inlet of aperture gradually expands, and the variation degree of stress (red range) intensifies (becoming redder and wider) with the increase of interference amount.At the same time, it is easy to see from Figures 3d and 3f, with the increase of the insertion depth of fastener, the stress at the plate of bore wall spreads around along the radius direction.In addition, it can also be found that the maximum stress region appears at the outlet end of the bore wall regardless of the interference values.

Installation force analysis
According to the relationship between the interference amount and the stress at bore wall [10], the interference-fit amount can be divided into three regions: elastic influence zone, elastic-plastic influence zone and plastic influence zone.When the material stress, being in the elastic influence zone, is lower than the yield strength of alloy plate, the interference at bore wall is small, and only elastic deformation or minor plastic deformation occurs in the bore wall of joint.When the stress is in the plastic influence zone, and the interference-fit at bore wall is relatively large, the material at bore wall occurs the large plastic deformation.The elastoplasticity influence zone is the transition zone between the above two intervals, when the material stress reaches the yield strength, and the bore wall material is gradually transformed to plastic deformation from elastic deformation.
During the installation process for the dynamic cold-extrusion of bolted joint, the installation force implemented by electromagnetic load is mainly converted into two parts: axial friction and tangential extrusion forces borne by the bore wall [11].As can be seen in Figure 4, the force-displacement curve during installation is divided into four stages.The first stage of 0 mm to 7 mm, is the process of inserting the bolt fastener into the inlet end of joint, it is obvious that the installation force increases in an instantaneous linear manner.When the fastener is located in the second stage changing from 7 mm to 14 mm, the installation force curve increased instantaneously gradually transforms into a horizontal line.When the fastener is inserted into the lower Al plate, that is the stages 3 and 4, the installation force is consistent with the changing trend of the upper Al plate, so there is no more analysis.In addition, it is also found that the corresponding curves appeared significantly different when the interference exceeds 1%.It can be seen when the interference exceeds 1 %, the installation force has approximately the same curve trend as the insertion depth increases.When the fastener is inserted to a displacement of 14 mm, there is a transient large drop in the installation force due to the sudden absence of installation resistance in the overlap layer between the upper and lower Al plates at the time of the large interference extrusion.Further, near 7 mm and 22 mm from the upper Al plate, the installation force curve falls back, which may be caused by the fact that the elastic and plastic influence zones of bore wall cooperatively regulate each other during the large interference extrusion, prompting the material to fluctuate up and down in the yield strength.Therefore, it can be inferred that in installation process for the dynamic cold extrusion of the above-mentioned interference-fit bolted joint, the critical interference amount for the stress at the bore wall to reach the yield strength is about 1 %, when the interference value is less than 1 %, the elastic deformation occurs at the joint, when the interference amount exceeds 1 %, the joint mainly undergoes plastic deformation.

Conclusion
This paper numerically simulates the dynamic cold extrusion of bolted single-lap joint installed by interference-fit, and the force and displacement data under different interference-fit are compared and analyzed, and draws the following conclusions: (1) The deformation generated by the dynamic cold-extruded installation at the aperture wall of joint is more uniform under electromagnetic force loading.It is also found that in the axial direction of the bore wall without pin, the maximum stress region occurs at its outlet regardless of the values of interference-fit.
(2) Interference bolted joint installed by conducting the dynamic cold extrusion, the critical interference amount for the stress at the bore wall reaching the yield strength is about 1 %, when the interference value is less than 1 %, the elastic deformation occurs at the joint, When the interference amount exceeds 1 %, the joint mainly undergoes the plastic deformation.

Figure 1 .
Figure 1.Simplified schematic diagram of FE simulation model of Al/Al interference-fit bolted component

Figure 2 .
Figure 2. The deformation distribution of the aperture at the inlet of joint under different interference-fit

Figure 3 .
Figure 3.The stress contour diagrams of (a) ~ (c) radial direction, and (d) ~ (f) axial direction for boltless bore wall of joint under different interference-fit

Table . 1
Johnson-Cook model parameters and performance parameters assigned of bolted joint