Experimental and Numerical Investigations on the Impact of Surface Conditions on Self-Piercing Riveted Joint Quality

Abstract

In this study, experimental and numerical investigations were carried out to achieve a comprehensive understanding of the impact of surface conditions on self-piercing riveting (SPR) joint quality. Oil lubrication and sandpaper grinding were employed in experimental tests to change surface conditions at rivet/top sheet, top/bottom sheets and bottom sheet/die interfaces. A finite element (FE) model for the SPR process was also adopted to numerically assess the impact of surface conditions. Variations in surface conditions were modelled by changing friction coefficients at contact interfaces. The results revealed that the friction coefficient between the rivet and top sheet (μ₁) imposed significant influences on the interlock (I₁) by affecting the deformation of the rivet shank and top sheet. The friction coefficient between the rivet and bottom sheet (μ₂) showed a lower influence on the joint quality because of a smaller contact area and shorter interaction time. The friction coefficient between the top and bottom sheets (μ₃) led to opposite changing trends of remaining bottom sheet thickness at the joint centre (t_c) and under the rivet tip (t_tip). The friction coefficient between the bottom sheet and die (μ₄) demonstrated crucial influences on the remaining bottom sheet at the joint centre. The riveting force was significantly influenced throughout the whole riveting process by the μ₁, but only affected at the end of the joining process by the other three friction coefficients.

1. Introduction

The 5xxx and 6xxx series aluminium alloys have been intensively used in car body-in-white (BIW) structures in recent years. As a mechanical joining approach, self-piercing riveting (SPR) has become the major joining technique for these lightweight alloys and has been widely adopted by automobile companies, such as Audi [1], Jaguar Land Rover (JLR) [2] and BMW [3]. It is suitable for high-ductility materials, and can also be extended to join low-ductility materials such as high-strength steels [4]. Figure 1a shows the four steps of the SPR process, namely clamping, piercing, flaring and tool releasing. Three indicators are usually measured on the SPR joint cross-sectional profile to evaluate the joint quality, as shown in Figure 1b, namely the rivet head height (H₁), interlock (I₁) and minimum remaining bottom sheet thickness (T_min). The quality standard of these indicators varies in different industry sectors or even companies. For instance, according to the criterion of a world-leading car maker, the H₁ should be −0.5 to 0.3 mm and the I₁ must be larger than 0.4 mm for aluminium alloy joints. The T_min should be no less than 0.2 mm [5]. The H₁ can be conveniently controlled by adjusting punch displacement in the riveting system, whilst the I₁ and T_min are directly influenced by plastic deformation of the rivet and sheets [6].

Factors affecting the deformation behaviours of rivets and sheets will inevitably influence the formation processes and magnitudes of I₁ and T_min. The rivet property and die profile are two critical factors determining the I and T_min, and their impacts such as rivet hardness, rivet material, die depth and die diameter have been investigated in the literature [5]. Aside from rivet and die parameters, the formation of the I and T_min are also affected by the surface conditions of the rivet, sheets and die. To successfully punch the rivet into sheets, a high riveting force (20~70 kN) is usually required in the SPR process [7], which leads to strong interaction forces among multiple touching components. Variations in surface conditions will directly alter the friction coefficient at the contact interface and influence the magnitude of friction force [8]. As a result, the deformation behaviours of the rivet and sheets will be unavoidably affected [9], and the final joint quality will also be influenced, as shown in Figure 2 [10].

Some efforts have been made to experimentally investigate the effects of surface conditions on SPR joint quality. Surface modification methods, including coating [11], polishing, grit blasting [10], impression [12] and lubricants [13], were adopted by researchers to change the surface conditions. By altering the bottom surface texture of the top sheet with different impression tools and garnet particles, Li [10] explored the influences of the interface condition between two AA5754 sheets on SPR joint quality. It was found that the local surface modification only slightly changed the magnitudes of joint quality indicators. The same author [12] further modified the contact interface conditions between sheets using hot water washing (around 60 °C), P120 sandpaper grinding and grit blasting. The results revealed that the hot water wash and sandpaper grinding did not show a significant influence on the joint quality. The grit blasting obviously resulted in a greater I₁ but a smaller T_min. Han et al. [11] experimentally studied the effects of different bottom sheet coatings (i.e., E-coating and zinc coating) on the quality of SPR joints with NG5754 top sheet and HSLA350 bottom sheet. The results showed that a larger I₁ but a smaller or even zero T_min were obtained due to the lubricating effect of coatings. Karim et al. [14] compared the influences of mechanically plated Zn-Sn-Al (Almac^®) and electroplated Zn-Ni rivet coatings on SPR joint quality. It was found that the Zn-Ni rivet coating contributed to a greater I₁ compared to the Almac rivet coating. However, SPR joints with the Zn-Ni rivet coating demonstrated lower lap-shear and cross-tensile strengths than those with the Almac rivet coating. These experimental studies extended the understanding of the influences of surface conditions on SPR joint quality. However, because of intrinsic variability of the SPR process (e.g., manufacturing tolerances of sheet thickness, rivet length and hardness), the experimentally measured quality indicators for the same joint configuration usually vary within a certain range. This makes it difficult to properly assess the influences of surface conditions on SPR joint quality.

To overcome the disadvantages of the experimental approach, numerical analyses with a finite element (FE) model have also been conducted in some studies to explore the impact of surface conditions [15,16]. It has been widely proved that a properly calibrated FE model of the SPR process can accurately predict the riveting force [17], material deformation behaviour [18] and final joint quality [19]. More importantly, the FE model always gives a consistent simulation result for the same joint configuration. Variations in surface conditions can be conveniently represented by different magnitudes of friction coefficients at the contact interface. With the help of a three-dimensional (3D) FE model and design of experiment (DOE), Moraes et al. [20] evaluated the importance of friction coefficients at different contact interfaces in the SPR joint with magnesium alloy AM60 top sheet and aluminium alloy AA6082 bottom sheet. It was found that friction coefficients between the die and bottom sheet and between the rivet and top sheet had the most significant influences on the joint quality. Suitable friction coefficients for the studied SPR joints were also identified by proposing four multiple linear equations. Changing trends of joint quality indicators with different friction coefficients were not investigated in their study. With a 3D smoothed particle Galerkin (SPG) model in LS-DYNA/explicit, Huang et al. [21] also discussed the sensitivity of joint quality indicators to friction coefficients at different contact interfaces. Han et al. [9] numerically studied the effects of friction coefficients on joint quality using a two-dimensional (2D) FE model of an SPR joint with a flat plate die. The results revealed that the friction coefficient between the blank-holder and top sheet (0.1~0.3) could affect the movements of sheets along the horizontal direction, while the friction coefficient between the rivet and sheets (0.1~0.3) had significant influences on the formation of I₁ and T_min. The friction coefficient between the top and bottom sheets (0.3~0.5) directly influenced the appearance of gaps in the final joints. The friction coefficient between the bottom sheet and supporting plate (0.2~0.5) significantly affected the deformation of the bottom sheet and rivet shank. With a 2D FE model of the SPR process in MSC Marc, Jacek [22] found that the friction coefficient between the rivet and sheets (0.05~0.25) imposed apparent influences on the deformation behaviours of the rivet shank and top sheet. Similar conclusions were also reached by Hoang et al. [23]: the friction coefficient between the rivet and sheets significantly affected the plastic strain localisation on the rivet shank. Until now, there has not been a comprehensive study about the influences of surface conditions (or friction coefficients) on SPR joint formation and final quality.

In addition, to guide the design of new SPR joints, an in-depth understanding of surface conditions’ impacts will also be helpful to speed up the FE model development for the SPR process. Although different experimental methods can be employed to measure friction coefficients at contact interfaces [10,24,25], the inverse method is still the most straightforward and effective way to determine friction coefficients when developing an FE model of the SPR process.

Table 1. Friction coefficients used in different FE models of the SPR process.

Authors	Model Type	Software	Friction Coefficients
Rusia and Weihe [29]	2D	LS-DYNA	0.12 between deformable parts 0.2 between tools and deformable parts
Wang et al. [26]	2D	DEFORM-2D	0.12 between all parts
Karathanasopoulos et al. [27]	2D	ABAQUS	0.2 between all parts
Hönsch et al. [30]	2D	Simufact.Forming	0.1 for rivet/sheets, 0.3 for sheets/die, 0.2 for others
Deng et al. [28]	2D	Simufact.Forming	0.2 between all parts
Moraes et al. [31]	3D	ABAQUS	0.4 for punch/rivet, 0.15 for others
AMRO et al. [32]	2D	ABAQUS	0.2 between all parts
Huang et al. [33]	3D	ABAQUS	0.2 between all parts
Hirsch et al. [34]	3D	ABAQUS	0.0 for composite sheet/rivet, 0.3 for others
Carandente et al. [19]	2D	Simufact.Forming	0.09 for top/bottom sheets, 0.15 for bottom sheet/die, 0.15 for top sheet/blank-holder
He et al. [35]	2D	LS-DYNA	0.15 for top sheet/blank-holder, 0.15 for top/bottom sheets, 0.25 for others

shows the friction coefficients implemented in FE models of the SPR process in recently published literature. A uniform friction coefficient was used between different contact parts in some FE models [26,27,28]. This can effectively reduce the difficulty of identifying the suitable friction coefficient with the inverse method. However, considering the different surface conditions at multiple contact interfaces, this simplification does not conform with the real conditions. To solve this problem, different friction coefficients were utilised at contact interfaces in other FE models [19,29,30]. This strategy improved the consistency between the FE model and the real SPR process but increased the difficulty of friction coefficient identification. Therefore, to facilitate and speed up friction coefficient identification, it is important to determine how friction coefficients at different contact interfaces affect the simulated joining process and final joint quality.

In this research, experimental SPR tests were carried out to evaluate the influences of different surface conditions on joint quality. Oil lubrication and sandpaper grinding were employed to change the surface conditions at the rivet/top sheet interface, top/bottom sheet interface and bottom sheet/die interface. Meanwhile, a verified simulation model of the SPR process was adopted to systematically assess the impact of surface conditions. Variations in surface conditions were modelled by changing friction coefficients at four critical contact interfaces. Influences of surface conditions on joint quality and deformation of rivets and sheets were also numerically analysed. This study is beneficial for a better understanding of how surface conditions affect the SPR joining results and provides guidelines on how to improve the joint quality by optimising surface conditions in practice. The results of this study are also helpful for the fast identification of friction coefficients when developing an FE model for the SPR process.

2. Experimental Setup

2.1. Rivet and Sheet Materials

The aluminium alloy AA5754 provided by Jaguar Land Rover (JLR) was used for the top and bottom sheets, and its mechanical properties and composition are listed in

Table 2. Mechanical properties and composition of AA5754 (Reprinted with permission from [36]).

Mechanical Properties	Young’s Modulus (GPa)	Tensile Strength(MPa)	Elongation (%)	Hardness (HV)
	70	240	22	63.5
Nominal composition (wt%)	Si	Fe	Cu	Mn	Mg
	0~0.40	0~0.40	0~0.10	0~0.50	2.60~3.60

. Semi-tubular rivets were made of boron steel with hardness 280 ± 30 HV10 and manufactured by Tucker GmbH.

2.2. Experiment Design

As shown in Figure 3a, the SPR system manufactured by Tucker GmbH was employed throughout the experiment. The riveting speed and clamping force were 300 mm/s and 6.0 kN, respectively. The thicknesses of the top sheet and bottom sheet were 1.8 mm and 2.0 mm, respectively. To study the influences of surface conditions on the joint quality, three critical contact interfaces in Figure 3b were modified, namely interfaces between the rivet and top sheet (blue line), between the top and bottom sheets (green line) and between the bottom sheet and die (red line). Two surface modification approaches were utilised, namely oil lubrication to reduce the friction coefficient and P200 sandpaper grinding to increase the friction coefficient. In order to ensure the same surface conditions in repeated tests as much as possible, the same amount of low-viscosity lubricating oil was applied evenly on the sheet surface. A thin layer of oil was formed at the contact interface and thus effectively reduced the friction coefficient. The same P200 sandpaper was used to manually grind the sheet surface for five minutes, which resulted in a higher surface roughness and therefore a greater friction coefficient at the contact interface. The grinding speed and applied force were controlled the same as much as possible to ensure the consistency of the grinding process. As listed in

Table 3. Joint configurations in experimental SPR tests.

Joint No.	Thickness (mm)		Rivet (Boron Steel)	Die	Contact Interface	Surface Modification Method
	Top Sheet/Tt (AA5754)	Bottom Sheet/Tb (AA5754)
1-1	1.8	2.0	C5.3*6.0 (280 ± 30 HV10)	Pip die	Rivet/top sheet	Oil lubrication
1-2						Sandpaper grinding
2-1					Top/bottom sheet	Oil lubrication
2-2						Sandpaper grinding
3-1					Bottom sheet/die	Oil lubrication
3-2						Sandpaper grinding

, six groups of SPR joints with different surface conditions were therefore manufactured. A uniformed specimen shape (i.e., 40 mm × 40 mm in Figure 4a) was used to eliminate possible influences of sheet dimensions on the joint formation and final quality. According to the sheet configuration, 6.0 mm long semi-tubular rivets and a pip die were selected. The nominal dimensions of the rivet and die are illustrated in Figure 4b,c. To facilitate the joining result comparison, the rivet head height (H₁) in all SPR joints was set to 0.0 mm by controlling the rivet displacement. Three repeats for each joint group were performed.

All of the SPR joints were cut along the joint central plane using an abrasive-wheel cutting machine. For the 40 mm × 40 mm specimen, specially designed fixtures were used in the riveting and cutting processes to ensure the cutting plane was as close as possible to the joint central plane [37]. The sectioned joints were polished, and the cross-sectional profile for each joint was inspected using an optical microscope. Although H₁, I₁ and T_min are widely adopted to assess SPR joint quality, they are insufficient to accurately describe the changing trends of joint formation, rivet shank deformation and remaining bottom sheet thickness distribution because the T_min is the minimum remaining bottom sheet and its position changes from joint to joint. The rivet shank deformation behaviour is critical for the final joint quality, but cannot be directly evaluated by any of the three quality indicators. Therefore, to overcome this difficulty, three dimensions were measured on the cross-sectional profile to evaluate the joint formation and final quality, namely the I₁ and the remaining bottom sheet thickness at the joint centre (t_c) and under the rivet tip (t_tip), as shown in Figure 1b. The radius of the outer interlock boundary (R_out) was also extracted to assess the rivet shank deformation.

3. Finite Element (FE) Model

3.1. Model Description

To systematically investigate the influences of surface conditions at different interfaces, a previously developed [38] and validated 2D FE model of the SPR process was adopted as shown in Figure 5a. Commercial software Simufact.Forming 15 was employed due to its strong re-meshing capability. The sheet edges could freely move while all the freedoms of the die were fixed during the riveting process. A 5.3 kN clamping force was applied on the blank-holder to clamp the top and bottom sheets together. The punch had a constant speed (v₁ = 300 mm/s) and moved downward to press the rivet into the sheets. The boron steel rivet and AA5754 sheets were modelled as elastic-plastic bodies, while the punch, blank-holder and die were modelled as rigid bodies. Plastic stress-strain curves for the AA5754 and the boron steel are shown in Figure 5b,c. The temperature effect on the material properties was only considered for the AA5754 sheets but not considered for the boron steel rivet. This is because the maximum temperature within the joining region is usually lower than 250 °C [19] and imposes limited influences on the mechanical properties of the boron steel. Uniaxial tensile tests at four different temperatures were carried out to determine the plastic stress-strain curves for the AA5754 sheets, whilst only the uniaxial tensile test at room temperature was performed to obtain the plastic stress-strain curve for the boron steel rivet. All the deformable parts were meshed using the quad element with four Gauss points, and the global mesh sizes for the rivet, top sheet and bottom sheet were 0.10 mm, 0.10 mm and 0.12 mm, respectively. The automatic re-meshing technique was used to deal with mesh distortion caused by large plastic deformations of the two sheets. A geometrical criterion was implemented to model the blanking of the top sheet [19], and the critical thickness was set to 0.04 mm. The Coulomb friction model was selected, and the inverse method was adopted to identify friction coefficients between different parts. The friction coefficient between the die and bottom sheet was set to 0.22, while that between other solid parts was set to 0.10. To ensure efficiency, the springback of SPR joints during the tool (i.e., punch, blank-holder and die) releasing process was not simulated. More details about the FE model can be found in [38]. Other boundary conditions were kept consistent with those in experimental tests.

3.2. Simulation Design

By changing the magnitude of the friction coefficient, the impacts of surface conditions at four critical contact interfaces on the riveting process and final joint quality were numerically investigated. Considering the difficulty of solely changing surface conditions at the rivet/bottom sheet interface in experimental tests, the impact of surface conditions at the rivet/bottom sheet interface was only numerically investigated in this research. Figure 6 shows the positions of four critical interfaces and corresponding friction coefficients: (1) between the rivet and top sheet (μ₁); (2) between the rivet and bottom sheet (μ₂); (3) between the top and bottom sheets (μ₃); and (4) between the bottom sheet and die (μ₄). Influences of surface conditions at other interfaces are not discussed in this study considering their lower impact on the joining results [20]. The initial FE model setup was regarded as the benchmark. Six levels (i.e., 0.01, 0.1, 0.2, 0.3, 0.4 and 0.5) of each friction coefficient were selected to represent different surface conditions, such as oil lubrication and sandpaper grinding. This variation range of friction coefficients covers the values of friction coefficients used in FE models in the accessible literature [26,27,29,30]. For consistency, all the simulations were terminated when the H₁ was reduced to 0.0 mm. The simulated joint cross-sectional profile, three quality indicators (i.e., I₁, t_c and t_tip) and force-displacement curve were extracted and analysed in detail.

4. Results and Discussion

4.1. Experimental Results

Cross-sectional profiles of SPR joints listed in Table 3 were experimentally captured as shown in Figure 7. It can be noticed that the joint profile is not exactly symmetrical, which might be caused by a slight misalignment between the die and punch axis or by deflection of the C-frame in the SPR system. Through visual observation, it is difficult to identify the differences among these profiles. To quantitatively assess the impact of surface condition on joint quality, mean values of the I₁, t_tip and R_out on the left and right sides were calculated and plotted into histograms. For easier description, the oil-lubricated and sandpaper-ground surfaces are regarded as surfaces with low and high friction coefficients, respectively. Slightly smaller I₁, t_tip and R_out but greater t_c were achieved with a high friction coefficient at the rivet/top sheet interface, as shown in Figure 8a. Obviously smaller I₁, t_c and R_out but greater t_tip were generated with a high friction coefficient at the top/bottom sheet interface, as shown in Figure 8b. Slightly smaller t_tip and R_out but greater I₁ and t_c were achieved with a high friction coefficient at the bottom sheet/die interface, as shown in Figure 8c. These results indicate that lower friction coefficients at the rivet/top sheet interface and top/bottom sheet interface but a higher friction coefficient at the bottom sheet/die interface can contribute to a larger I₁. Higher friction coefficients at rivet/top sheet interface and bottom sheet/die interface but a lower friction coefficient at top/bottom sheet interface can contribute to a larger t_c but a smaller t_tip. Lower friction coefficients at three contact interfaces can always lead to a greater R_out.

4.2. FE Model Validation

Considering the similar cross-sectional profiles and close qualities of six SPR joints (see Figure 7 and Figure 8), the experimental result of joint 1-2 was selected to confirm the effectiveness of the FE model employed in this research. Figure 9 shows the experimentally tested and simulated joint cross-sectional profiles, four indicators (i.e., I₁, R_out, t_c and t_tip) and force-displacement curves. It can be seen from Figure 9a that the simulated cross-sectional profile showed a reasonable agreement with the experimentally tested one: the deformed shapes of rivet shank and sheets were accurately predicted. In Figure 9b, it can be seen that the simulated I₁, t_c and R_out were 89% (0.72 mm vs. 0.64 mm), 99% (0.56 mm vs. 0.55 mm) and 96% (3.99 mm vs. 3.83 mm) of the tested ones, respectively, but the simulated t_tip was only 70% (1.33 mm vs. 0.93 mm) of the tested one. The prediction accuracies for the I₁, t_c and R_out are 19%~29% higher than that for the t_tip in joint 1-2. In previous research [38], this FE model had also been validated by comparing the experimental and simulation results of eleven joints within the same studied range, and the mean absolute error (MAE) for the I₁, t_c and t_tip was 0.066 mm, 0.042 mm and 0.115 mm, respectively, and the corresponding mean absolute percentage error (MAPE) was 10.5%, 12.9% and 19.7%. Overall, the prediction result of the FE model for these joint quality indicators is accurate. The force-displacement curve was also accurately predicted by the FE model: not only the variation trend but also the magnitude of riveting force was accurately predicted, as shown in Figure 9c, except for a small drop presented on the simulated force-displacement curve. This is because a geometrical criterion was implemented to model the blanking of the top sheet [19], and the critical thickness was set to 0.04 mm. When the remaining top sheet thickness is equal to or smaller than the critical thickness value, the sheet elements underneath the rivet tip will be deleted from the FE model to represent the top sheet fracture. Thus, the force decreases suddenly to some extent, and a small drop appears on the force-displacement curve. Overall, the employed FE model can give a reasonable prediction result for the studied SPR joint, and thus it was utilised to numerically investigate the impacts of different surface conditions on the joining results.

4.3. Impact of Friction Coefficients at Different Contact Interfaces

4.3.1. Between Rivet and Top Sheet (μ₁)

The simulated joint cross-sectional profiles with different μ₁ values are shown in Figure 10. It can be found that the deformed shapes of the rivet and sheets were apparently affected by the μ₁. With the μ₁ increasing from 0.01 to 0.5, the inner and outer parts of the top sheet were stretched a greater distance towards the die cavity and underwent larger plastic deformation (see Figure 10e). This is because a higher friction force was generated at the rivet/top sheet interface with a larger μ₁. The top sheet material surrounding the rivet shank was therefore dragged downward rather than rapidly penetrated. Due to the greater friction force, the rivet shank also underwent a larger plastic deformation with a larger μ₁. The rivet shank flared outward but did not experience obvious upsetting when the μ₁ was 0.01, as shown in Figure 10a. Apparent rivet shank bulking occurred when the μ₁ increased to 0.5, as shown in Figure 10f. Owing to the alteration of rivet and top sheet deformation, the distribution of the remaining bottom sheet underneath the inner top sheet was also affected: less bottom sheet material was left underneath the rivet with a larger μ₁ (see Figure 10f). In addition, the filling condition of the rivet cavity was also influenced: it was fully filled with the μ₁ = 0.01 but partially filled with a greater μ₁.

Figure 11a shows the influence of μ₁ on the magnitude of I₁. It can be seen that the I₁ demonstrates a rapid decline when the μ₁ increases from 0.01 to 0.5. A similar result was also obtained by Han et al. [11] through experimental tests, in which a smaller I₁ was achieved after the μ₁ was increased without applying E-coat on the top sheet surface. The E-coat can reduce the sheet surface roughness and thus provide some lubrication at the rivet/top sheet interface. To explain this phenomenon, the radius of inner (R_in) and outer (R_out) interlock boundaries (as shown in Figure 10a) that directly determine the I₁ value were measured, as shown in Figure 11b. The variation in μ₁ altered the rivet and sheet material deformation and thus influenced the two boundary positions. With the increment in μ₁, the R_in kept almost constant and just fluctuated slightly. In contrast, the R_out rapidly declined from about 3.9 to 3.6 mm. This is attributed to greater deformation and even bulking of the rivet shank with a larger μ₁, as shown in Figure 12. Severe plastic deformation of the rivet shank was also reported by Hoang et al. [23] after increasing the friction coefficient between rivet/sheets from 0.0 to 0.8. The different changing trends of R_in and R_out indicate that the μ₁ influences the magnitude of I₁ by affecting the position of the outer interlock boundary. The changing trends of t_c and t_tip with different μ₁ values are shown in Figure 11c. The t_c shows a decreasing tendency with the μ₁ increasing from 0.01 to 0.5. The t_tip demonstrates a complex fluctuation: it first increases and then slowly decreases followed by an increment. This is because the magnitude of t_tip is determined by both the flaring distance along the radial direction and bulking degree of the rivet shank.

The μ₁ also imposed significant influences on the force-displacement curves, as shown in Figure 11d. At the early stage, almost the same riveting force (Zone 1) was observed with different μ₁ values. This is because only a small part of the rivet shank was inserted into the top sheet. The variation in friction force induced by the μ₁ was too small to cause distinct differences in the riveting force. However, with further increment in rivet displacement, a higher riveting force was observed with the increment in μ₁ (Zone 2). At this stage, a larger part of the rivet shank pierced into the top sheet, and the friction force at the rivet/top sheet interface accounted for a large portion of the riveting force. As a result, the riveting force became sensitive to the magnitude of μ₁ and reached a higher level with the increment in μ₁. Changes in the rivet and sheet deformation also caused a faster filling speed of the die cavity space, which led to a larger riveting force. At the end of the joining process, differences in riveting force became smaller and the maximum riveting force values were very close (Zone 3).

From the above results, it can be concluded the friction coefficient at rivet/top sheet interface has significant influences on the I₁, remaining bottom sheet thickness and riveting force. To achieve a high-quality SPR joint, it is recommended to reduce this friction coefficient by applying coatings (e.g., zinc/tin or zinc/tin/aluminium [5]) or lubricants on the rivet shank. In addition, considering the apparent influence of μ₁ on the joining results, it will be better to identify the μ₁ value individually when developing an FE model for the SPR process.

4.3.2. Between Rivet and Bottom Sheet (μ₂)

Figure 13 shows the simulated joint cross-sectional profiles with different μ₂ values. Through visual observation, it is hard to distinguish the differences among these six joint profiles. This is because the μ₂ can only affect the joint formation after the rivet shank comes into contact with the bottom sheet. The limited impact of μ₂ on the joining result might be caused by the short interaction time and the small contact area between the rivet and bottom sheet.

As shown in Figure 14a, the increment in the μ₂ imposes negative but not significant influences on the I₁: it just slightly decreased with the μ₂ increasing from 0.01 to 0.5. Variation curves of the R_in and R_out are shown in Figure 14b. The almost constant values indicate that the μ₂ has limited impacts on the positions of left and right interlock boundaries. Meanwhile, change in the I₁ was not dominated by R_in or R_out alone, but a comprehensive effect of the R_in and R_out. Figure 14c shows the changing trends of t_c and t_tip with different μ₂ values. It can be seen that the t_c kept almost constant and was nearly not affected by the μ₂. This is because the formation of t_c mainly occurs at the stage of rivet shank piercing through the top sheet [38]. In contrast, the t_tip shows an increasing trend with the increment in the μ₂. This might be because the greater friction force at the rivet shank/bottom sheet interface restricted the rivet shank piercing into the bottom sheet. As a result, the rivet tip was slightly upset and led to a greater t_tip. Figure 14d shows the force-displacement curves with different μ₂ values. It can be seen that the change in μ₂ imposed very limited influences on the riveting force. Unsurprisingly, an identical riveting force (Zone 1) was observed before the top sheet was completely penetrated. Minor differences in riveting force were captured when the rivet shank gradually pierced into the bottom sheet (Zone 2). The maximum riveting force was almost the same on the six curves.

Overall, the friction coefficient at the rivet/bottom sheet interface can affect the I₁ and remaining bottom sheet thickness but impose limited influences on the riveting force. Because of surface abrasion when the rivet shank pierces through the top sheet, coating shedding or surface quality degradation of the rivet shank usually happens [14]. For top and bottom sheets with the same material and surface conditions, the μ₂ will be undoubtedly greater than the μ₁. In addition, considering the lower influence of μ₂ on the joining result, an equal or slightly larger μ₂ is recommended compared with the μ₁ when developing an FE model for the SPR process. The μ₂ could be identified at the same time as the μ₁ rather than identified individually.

4.3.3. Between Top and Bottom Sheets (μ₃)

The simulated joint cross-sectional profiles with different μ₃ values are shown in Figure 15. It can be seen that the filling condition of the rivet cavity was apparently affected by the μ₃: the rivet cavity was fully filled with μ₃ = 0.01 as shown in Figure 15a but not filled up with μ₃ = 0.5 as shown in Figure 15f. This is because the inner part of the top sheet applied higher friction force on the bottom sheet, which facilitated the material flow of the bottom sheet from the joint centre to the die cavity. As a result, more bottom sheet material was accumulated in the die cavity (Zone 1 vs. Zone 2) and less sheet material was trapped in the rivet cavity with a greater μ₃. Due to changes in the bottom sheet deformation behaviour and rivet cavity filling condition, the deformed profile of the rivet shank was also affected: the rivet shank flared a larger distance along the radial direction with a greater μ₃ but experienced slight upsetting as shown in Figure 15f.

As shown in Figure 16a, the I₁ first rises with the μ₃ increasing from 0.01 to 0.4 but then decreases with the μ₃ further increasing to 0.5. With the increment in μ₃, both R_in and R_out show increasing tendencies, as shown in Figure 16b, and work together to determine the changing trend of I₁. Figure 16c shows the variation trends of t_c and t_tip with the μ₃ from 0.01 to 0.5. It can be seen that the μ₃ shows opposite influences on the t_c and t_tip: the t_c demonstrates a decreasing trend whilst the t_tip rapidly increases with the increment in μ₃. With a greater μ₃, a larger friction force was generated at the top/bottom sheet interface and caused a stronger stretching effect on the bottom sheet material at the joint centre, which directly caused the reduction in t_c. The increment in t_tip is a comprehensive result of greater rivet shank flaring and upsetting. Force-displacement curves with different μ₃ values are shown in Figure 16d. The μ₃ shows very limited influences on the magnitudes of the riveting force (Zone 1), and apparent differences were only observed at the end of the joining processes (Zone 2). The maximum riveting force shows a declining trend with the increment in μ₃.

In practice, many factors will influence the friction coefficient at the top/bottom sheet interface. For example, lubricants applied on the sheet surface during the rolling process [39] or the stamping process [13] will impose a lubrication effect and result in a smaller μ₃. The application of liquid adhesive at a two-sheet interface may also have a lubrication effect [5]. As a result, the joint quality would be slightly changed. Considering its apparent influences on the t_c and t_tip, it is recommended to tune and identify the μ₃ individually when developing an FE model for the SPR process.

4.3.4. Between Bottom Sheet and Die (μ₄)

The simulated joint cross-sectional profiles with different μ₄ values are shown in Figure 17. It can be found that the deformed shapes of the rivet and sheets, especially the bottom sheet, were apparently affected by the μ₄. This agrees well with the simulation results reported by Moraes et al. [20], in which the significant impact of the μ₄ on joint formation and final quality was highlighted. With the increment in μ₄, the inner part of the top sheet underwent larger deformation (see Figure 17f). Instead, the inner top sheet was deformed and stretched by the rivet shank. The outer part of the top sheet achieved very similar deformation and was less affected by the μ₄. For the bottom sheet, more sheet material was left at the joint central area with a greater μ₄ (see Figure 17e). This is directly caused by the greater friction force at the bottom sheet/die interface, which resisted the flow of bottom sheet material into the die cavity. Slight rivet shank upsetting was observed with the μ₄ = 0.01, as shown in Figure 17a. This is because a large amount of sheet material underneath the rivet cavity was pressed into the die cavity. The fully filled die cavity but unfilled rivet cavity directly led to the upsetting of the rivet shank. With the increment in μ₄, less sheet material was pressed into the die cavity, which alleviated the hostile filling states of rivet and die cavities for rivet shank stability and therefore avoided apparent rivet shank upsetting, as shown in Figure 17f.

As shown in Figure 18a, the I₁ fluctuated within a narrow range when the μ₄ increased from 0.01 to 0.5. Both R_in and R_out demonstrated increasing trends with the increment in μ₄ in Figure 18b. This is because less bottom sheet material was accumulated outside the rivet shank, which led to lower resistance on the outer surface of the rivet shank. The larger amount of sheet material accumulated in the rivet cavity imposed a stronger guidance effect on the rivet shank flaring [6]. Thus, the rivet shank flared a greater distance along the radial direction and resulted in a greater radius of inner and outer interlock boundaries. Variation trends of the t_c and t_tip with different μ₄ values are shown in Figure 18c. It can be seen that the t_c was significantly affected by the μ₄ and rapidly increased from around 0.08 mm to 0.80 mm. As aforementioned, this is also directly caused by the accumulation of bottom sheet material at the joint centre, induced by greater friction forces at the bottom sheet/die interface. In contrast, the t_tip was less influenced and kept almost constant with varying μ₄, which is a result of the comprehensive effects of rivet shank upsetting and flaring. In addition, from the cross-sectional profiles in Figure 17, it is also worth mentioning that the μ₄ is capable of controlling the thickness distribution of the bottom sheet. A proper μ₄ can produce a reasonable bottom sheet thickness distribution and therefore increase the joint strength and reliability to prevent corrosion. Figure 18d shows the force-displacement curves with different μ₄ values. At the early stage of the joining processes, the riveting force was just slightly affected by the μ₄ (Zone 1). An obvious difference in the riveting force was observed at the end of the joining processes (Zone 2): the bigger the μ₄, the larger the riveting force. Moreover, the maximum riveting force demonstrated an increasing trend with the increment in μ₄ from 0.01 to 0.5.

From the above discussion, it can be concluded that the friction coefficient at the bottom sheet/die interface has crucial influences on the joining results, especially the thickness distribution of the bottom sheet. Coatings or lubricants applied on the bottom sheet or die are helpful for rivet shank flaring but will inevitably reduce the remaining bottom sheet material at the joint centre. In contrast, the wear of the die in service will increase the magnitude of μ₄ and impose opposite influences on the joining results. Considering its significant influences, the μ₄ should be identified individually when developing an FE model for the SPR process.

From the above results, it can be found that the four friction coefficients demonstrate different degrees of impact on the joint quality indicators. For easier comparison, the changing trends of I₁, R_in, R_out, t_c and t_tip are summarised in

Table 4. Comparisons of four different coefficients’ influences on joint quality indicators.

Friction Coefficient		I1	Rin	Rout	tc	ttip
Rivet/top sheet (μ1)	↑	↓↓		↓↓	↓	~~
Rivet/bottom sheet (μ2)	↑	↓				↑
Top/bottom sheets (μ3)	↑	~~	↑	↑↑	↓	↑↑
Bottom sheet/die (μ4)	↑	~~	↑	↑	↑↑

Note: (1) increase ↑; (2) rapid increase ↑↑; (3) decrease ↓; (4) rapid decrease ↓↓; (5) fluctuation ~~; (6) almost constant .

. The μ₁ shows the greatest influence on the I₁, whilst the μ₄ demonstrates the greatest impact on the t_c. Both μ₁ and μ₃ impose critical but opposite influences on R_out by affecting the rivet shank flaring behaviour. The μ₃ demonstrates greater effects on t_tip than the other three friction coefficients. Compared with other quality indicators, the variations in friction coefficients impose the lowest influence on the R_in. Overall, altering the friction coefficients at different contact interfaces through coatings, lubricating oil or other strategies is effective and promising for improving SPR joint quality in practice.

5. Conclusions

In this study, the impacts of surface conditions/friction coefficients at different contact interfaces on SPR joint quality were experimentally and numerically investigated. The main conclusions are as follows:

(1)

Reducing the friction coefficient between the rivet and top sheet (μ₁) by applying coatings or lubricating oil on the rivet can effectively increase the magnitudes of interlock (I₁) and remaining bottom sheet thickness at the joint centre (t_c). The joining force can also be reduced with a greater μ₁, providing the benefits of less energy consumption and longer service life of the die.

(2)

The joint quality was less affected by the friction coefficient between the rivet and bottom sheet (μ₂). In practice, reducing the magnitude of μ₂ by rivet coating or other strategies can slightly increase the I₁ without imposing apparent influences on the t_c and riveting force.

(3)

Increasing the friction coefficient between top and bottom sheets (μ₃) can lead to a greater rivet shank flaring distance. The μ₃ imposes opposite influences on the t_tip and t_c and therefore can be adjusted by modifying the contact surface condition to balance the magnitudes of the t_tip and t_c for better joint quality.

(4)

The friction coefficient between the bottom sheet and die (μ₄) imposes a critical impact on the magnitude of the t_c by affecting the bottom sheet deformation behaviour. Reducing the μ₄ by applying lubricating oil at the bottom sheet/die interface or increasing the μ₄ with a rougher die surface can reduce or increase the t_c to optimise the joint quality.

(5)

Among the four friction coefficients at contact interfaces, the μ₁ and μ₄ impose greater influences on the magnitudes of joint quality indicators. The identified changing trends of I₁, R_out, t_tip and t_c with varying friction coefficients are beneficial for a quick selection of friction coefficients with the inverse method in FE model development process.