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

: 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 ( µ 1 ) imposed signiﬁcant inﬂuences on the interlock ( I 1 ) by affecting the deformation of the rivet shank and top sheet. The friction coefﬁcient between the rivet and bottom sheet ( µ 2 ) 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 ( µ 3 ) 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 ( µ 4 ) 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 µ 1 , but only affected at the end of the joining process by the other three friction coefﬁcients.


Introduction
The 5xxx and 6xxx series aluminium alloys have been intensively used in car bodyin-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 (H 1 ), interlock (I 1 ) 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 H 1 should be −0.5 to 0.3 mm and the I 1 must be larger than 0.4 mm for aluminium alloy joints. The T min should be no less than 0.2 mm [5]. The H 1 can be conveniently controlled by adjusting punch displacement in the riveting system, whilst the I 1 and T min are directly influenced by plastic deformation of the rivet and sheets [6]. 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 Tmin. 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 Factors affecting the deformation behaviours of rivets and sheets will inevitably influence the formation processes and magnitudes of I 1 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 I 1 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 I 1 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 I 1 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.
Coatings 2023, 13, x FOR PEER REVIEW 3 of 21 zero Tmin 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 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 I 1 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 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.

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

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, 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 (H 1 ) 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 H 1 , I 1 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 I 1 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.
shown in Figure 1b. The radius of the outer interlock boundary (Rout) was also extracted to assess the rivet shank deformation.

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

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 (v 1 = 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.

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 blankholder 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.

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 (µ 1 ); (2) between the rivet and bottom sheet (µ 2 ); (3) between the top and bottom sheets (µ 3 ); and (4) between the bottom sheet and die (µ 4 ). 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 H 1 was reduced to 0.0 mm. The simulated joint cross-sectional profile, three quality indicators (i.e., I 1 , t c and t tip ) and force-displacement curve were extracted and analysed in detail.
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, tc and ttip) and forcedisplacement curve were extracted and analysed in detail.

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, ttip and Rout 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, ttip and Rout but greater tc were achieved with a high friction coefficient at the rivet/top sheet interface, as shown in Figure 8a. Obviously smaller I1, tc and Rout but greater ttip were generated with a high friction coefficient at the top/bottom sheet interface, as shown in Figure 8b. Slightly smaller ttip and Rout but greater I1 and tc 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

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 I 1 , 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 I 1 , 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 I 1 , 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 I 1 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 I 1 . 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 .

FE Model Validation
Considering the similar cross-sectional profiles and close qualities of six SPR joints (see Figures 7 and 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, Rout, tc and ttip) and force-displacement curves. It can be seen from Figure 9a that the simulated crosssectional 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, tc and Rout 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 ttip was only 70% (1.33 mm vs. 0.93 mm) of the tested one. The prediction accuracies for the I1, tc and Rout are 19%~29% higher than that for the ttip 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, tc and ttip 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%.

FE Model Validation
Considering the similar cross-sectional profiles and close qualities of six SPR joints (see Figures 7 and 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, Rout, tc and ttip) and force-displacement curves. It can be seen from Figure 9a that the simulated crosssectional 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, tc and Rout 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 ttip was only 70% (1.33 mm vs. 0.93 mm) of the tested one. The prediction accuracies for the I1, tc and Rout are 19%~29% higher than that for the ttip 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, tc and ttip 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%.

FE Model Validation
Considering the similar cross-sectional profiles and close qualities of six SPR joints (see Figures 7 and 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., I 1 , R out , t c and t tip ) and forcedisplacement 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 I 1 , 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 I 1 , 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 I 1 , 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. 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.

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.  The simulated joint cross-sectional profiles with different µ 1 values are shown in Figure 10. It can be found that the deformed shapes of the rivet and sheets were apparently affected by the µ 1 . With the µ 1 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 µ 1 . 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 µ 1 . The rivet shank flared outward but did not experience obvious upsetting when the µ 1 was 0.01, as shown in Figure 10a. Apparent rivet shank bulking occurred when the µ 1 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 µ 1 (see Figure 10f). In addition, the filling condition of the rivet cavity was also influenced: it was fully filled with the µ 1 = 0.01 but partially filled with a greater µ 1 . Figure 11a shows the influence of µ 1 on the magnitude of I 1 . It can be seen that the I 1 demonstrates a rapid decline when the µ 1 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 I 1 was achieved after the µ 1 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 I 1 value were measured, as shown in Figure 11b. The variation in µ 1 altered the rivet and sheet material deformation and thus influenced the two boundary positions. With the increment in µ 1 , 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 µ 1 , 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 µ 1 influences the magnitude of I 1 by affecting the position of the outer interlock boundary. The changing trends of t c and t tip with different µ 1 values are shown in Figure 11c. The t c shows a decreasing tendency with the µ 1 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 µ 1 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 µ 1 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 µ 1 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 µ 1 (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 µ 1 and reached a higher level with the increment in µ 1 . 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 I 1 , 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 µ 1 on the joining results, it will be better to identify the µ 1 value individually when developing an FE model for the SPR process.   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 (Rin) and outer (Rout) 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 incre- Rivet displacement (mm)  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 Rivet displacement (mm)  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  Figure 13 shows the simulated joint cross-sectional profiles with different µ 2 values. Through visual observation, it is hard to distinguish the differences among these six joint profiles. This is because the µ 2 can only affect the joint formation after the rivet shank comes into contact with the bottom sheet. The limited impact of µ 2 on the joining result might be caused by the short interaction time and the small contact area between the rivet and bottom sheet.

Between Rivet and Bottom Sheet (µ 2 )
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 ttip. 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.  As shown in Figure 14a, the increment in the µ 2 imposes negative but not significant influences on the I 1 : it just slightly decreased with the µ 2 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 µ 2 has limited impacts on the positions of left and right interlock boundaries. Meanwhile, change in the I 1 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 µ 2 values. It can be seen that the t c kept almost constant and was nearly not affected by the µ 2 . 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 µ 2 . 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 µ 2 values. It can be seen that the change in µ 2 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 I 1 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 µ 2 will be undoubtedly greater than the µ 1 . In addition, considering the lower influence of µ 2 on the joining result, an equal or slightly larger µ 2 is recommended compared with the µ 1 when developing an FE model for the SPR process. The µ 2 could be identified at the same time as the µ 1 rather than identified individually. cause 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. Rivet displacement (mm) 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.

Between Top and Bottom Sheets (µ 3 )
The simulated joint cross-sectional profiles with different µ 3 values are shown in Figure 15. It can be seen that the filling condition of the rivet cavity was apparently affected by the µ 3 : the rivet cavity was fully filled with µ 3 = 0.01 as shown in Figure 15a but not filled up with µ 3 = 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 µ 3 . 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 µ 3 but experienced slight upsetting as shown in Figure 15f.
As shown in Figure 16a, the I 1 first rises with the µ 3 increasing from 0.01 to 0.4 but then decreases with the µ 3 further increasing to 0.5. With the increment in µ 3 , both R in and R out show increasing tendencies, as shown in Figure 16b, and work together to determine the changing trend of I 1 . Figure 16c shows the variation trends of t c and t tip with the µ 3 from 0.01 to 0.5. It can be seen that the µ 3 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 µ 3 . With a greater µ 3 , 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 µ 3 values are shown in Figure 16d. The µ 3 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 µ 3 .
Coatings 2023, 13, x FOR PEER REVIEW 15 of 21 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 Rin and Rout 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 tc and ttip with the μ3 from 0.01 to 0.5. It can be seen that the μ3 shows opposite influences on the tc and ttip: the tc demonstrates a decreasing trend whilst the ttip 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 tc. The increment in ttip 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 tc and ttip, it is recommended to tune and identify the μ3 individually when developing an FE model for the SPR process. Rivet displacement (mm)  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 µ 3 . 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 µ 3 individually when developing an FE model for the SPR process.

Between Bottom Sheet and Die (µ 4 )
The simulated joint cross-sectional profiles with different µ 4 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 µ 4 . This agrees well with the simulation results reported by Moraes et al. [20], in which the significant impact of the µ 4 on joint formation and final quality was highlighted. With the increment in µ 4 , 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 µ 4 . For the bottom sheet, more sheet material was left at the joint central area with a greater µ 4 (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 µ 4 = 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 µ 4 , 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 Rin and Rout 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 tc and ttip with different μ4 values are shown in Figure 18c. It can be seen that the tc 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 ttip was less influenced and As shown in Figure 18a, the I 1 fluctuated within a narrow range when the µ 4 increased from 0.01 to 0.5. Both R in and R out demonstrated increasing trends with the increment in µ 4 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 µ 4 values are shown in Figure 18c. It can be seen that the t c was significantly affected by the µ 4 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 µ 4 , 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 µ 4 is capable of controlling the thickness distribution of the bottom sheet. A proper µ 4 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 µ 4 values. At the early stage of the joining processes, the riveting force was just slightly affected by the µ 4 (Zone 1). An obvious difference in the riveting force was observed at the end of the joining processes (Zone 2): the bigger the µ 4 , the larger the riveting force. Moreover, the maximum riveting force demonstrated an increasing trend with the increment in µ 4 from 0.01 to 0.5. 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, Rin, Rout, tc and ttip are summarised in Table 4. The 1 shows the greatest influence on the I1, whilst the 4 demonstrates the greatest impact on the tc. Both 1 and 3 impose critical but opposite influences on Rout by affecting the rivet shank flaring behaviour. The 3 demonstrates greater effects on ttip than the other three friction coefficients. Compared with other quality indicators, the variations in friction coefficients impose the lowest influence on the Rin. Overall, altering the friction coefficients at different contact interfaces through coatings, lubricating oil or other strategies is effective and promising 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 µ 4 and impose opposite influences on the joining results. Considering its significant influences, the µ 4 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 I 1 , R in , R out , t c and t tip are summarised in Table 4. The µ 1 shows the greatest influence on the I 1 , whilst the µ 4 demonstrates the greatest impact on the t c . Both µ 1 and µ 3 impose critical but opposite influences on R out by affecting the rivet shank flaring behaviour. The µ 3 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.

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 (tc). 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 tc and riveting force.

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 (tc). 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 tc 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 ttip and tc and therefore can be adjusted by modifying the contact surface condition to balance the magnitudes of the ttip and tc for better joint quality. (4) The friction coefficient between the bottom sheet and die (μ4) imposes a critical impact on the magnitude of the tc 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 tc to optimise the joint quality.

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 (tc). 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 tc 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 ttip and tc and therefore can be adjusted by modifying the contact surface condition to balance the magnitudes of the ttip and tc for better joint quality. (4) The friction coefficient between the bottom sheet and die (μ4) imposes a critical impact on the magnitude of the tc 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 tc 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, Rout, ttip and tc with varying friction coefficients are beneficial for a quick selection of friction coefficients with the inverse method in FE model development process.

Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.

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 (tc). 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 tc 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 ttip and tc and therefore can be adjusted by modifying the contact surface condition to balance the magnitudes of the ttip and tc for better joint quality. (4) The friction coefficient between the bottom sheet and die (μ4) imposes a critical impact on the magnitude of the tc 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 tc to optimise the joint quality.

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 (µ 1 ) by applying coatings or lubricating oil on the rivet can effectively increase the magnitudes of interlock (I 1 ) and remaining bottom sheet thickness at the joint centre (t c ). The joining force can also be reduced with a greater µ 1 , 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 (µ 2 ). In practice, reducing the magnitude of µ 2 by rivet coating or other strategies can slightly increase the I 1 without imposing apparent influences on the t c and riveting force. (3) Increasing the friction coefficient between top and bottom sheets (µ 3 ) can lead to a greater rivet shank flaring distance. The µ 3 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 (µ 4 ) imposes a critical impact on the magnitude of the t c by affecting the bottom sheet deformation behaviour. Reducing the µ 4 by applying lubricating oil at the bottom sheet/die interface or increasing the µ 4 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 µ 1 and µ 4 impose greater influences on the magnitudes of joint quality indicators. The identified changing trends of I 1 , 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. Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.