Effect of die designed geometrical parameters on riveting quality of self-piercing riveting joints in 5052 aluminium alloy | Scientific Reports

Scientific Reports volume 15, Article number: 7239 (2025) Cite this article

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This paper investigates the effects of die design geometrical parameters on self-piercing riveting (SPR) operations and the joint quality of 5052 aluminum alloy. Piped-die types with various designed diameters and depths were prepared. Subsequently, a 2D axisymmetric simulation model was developed to analyze the riveting efficiency and forming mechanism of SPR joints. The forming quality of specimens was studied by evaluating the cross-sections of joints obtained from the 2D simulation model and experiments. The mechanical properties of the specimens were analyzed by comparing the maximum shear load and energy absorption. The results indicate that a larger die diameter results in better rivet flaring, forming quality and mechanical properties of the specimens. Additionally, the forming quality improves with an increase in die depth, while the mechanical properties initially decrease and then increase. A smaller die depth benefits rivet flaring but affects the rivet penetration process. The maximum interlock value of 0.28 mm was recorded for the specimen obtained using a die with a depth of 1.25 mm; however, the forming quality deteriorated due to a large head height of 0.37 mm.

Aviation and automobiles have emerged as a global concern due to their significant contributors to carbon emissions. Implementing lightweight designs is one of the most efficient strategies for reducing carbon emissions. Lightweight construction has become an essential aspect of optimizing core performance in design1. Various alloy in aluminum series has become the most used lightweight metal to replace traditional steel in weight reduction strategies due to many related merits. For instance, 5xxx series (Al-Mg) offer excellent corrosion resistance particularly in marine environments, while also being highly weldable and exhibiting moderate to high strength. The traditional connecting methods such as resistance spot welding (RSW) have shown some limitations in connecting the lightweight materials2. The physical and chemical properties of lightweight metals differ from those of traditional metals like steel, primarily due to the formation of numerous intermetallic compounds (IMCs) during the joining process. These components adversely affect the joint performance3,4. Self-piercing rivet (SPR) is a fast and efficient mechanical cold-forming process. Based on forming principles, the plastic deformation and rebound of rivets form a mechanical internal locking with the joint plates, enabling the connection of several similar and dissimilar light alloy sheets5. Moreover, SPR is green low-cost method that makes it widely used in automotive, aerospace and other industries6,7.

Several researchers have recently studied the SPR technology due to its excellent performance. He et al.8 analyzed the mechanism of joint formation and the possible types of defects, discussing the main properties of SPR joints. Zhao et al.9 studied the effects of plate thickness and rivet length on the mechanical properties of 5052 aluminum alloy SPR joints. The results showed that increasing the plate thickness and rivet length improve the joint forming quality and mechanical properties. Liu et al.10 applied experimental and simulation method to investigate the fatigue reliability of 5052 aluminum alloy with SPR joints. Casalino et al.11 utilized LS-DYNA software to develop a simulation model for the self-pierce riveting (SPR) process of 6060-T4 aluminum alloy. The work provided a comprehensive analysis of riveting process including riveting force and forming outcomes along with the fundamental algorithm for creating and running the finite element model for SPR. Wang et al.12 employed the Smooth Particle Galerkin (SPG) algorithm to construct three-dimensional finite element models of SPR for steel and aluminum plates. The study simulated the forming and transverse tensile processes of the joints, exploring the effects of rivet length, edge angle, sheet thickness, die diameter, and die depth on joint quality and transverse tensile strength. Du et al.13 developed a two-dimensional axisymmetric numerical model of the SPR process using the r-adaptivity method, examining the influence of material strength and plate thickness on the connectability and quality of SPR joints. Moreover, other processing techniques were combined with the SPR technology to achieve better riveting results such as friction self-piercing riveting (F-SPR)14, electromagnetic self-piercing riveting (E-SPR)15, pre-hole self-piercing riveting (PH-SPR)16 and post-curing self-piercing riveting (PC-SPR)17.

Numerous researchers have extensively studied the impact of rivet and die geometries as a major parameter that affects the efficiency of the SPR process to evaluate the performance and quality of SPR joints. Ma et al.18 investigated the effect of die geometrical parameters on the SPR joint quality in AA6061-T6 with CR4 mild steel. It was shown that a large die diameter can enhance the rivet flaring but reduce the strength of the joint. A smaller die diameter reduces the rivet flaring efficiency but increases the joint strength. Deng et al.19 investigated the die-designed geometrical parameters effects on the riveting quality for AA6061-T6 and mild steel dissimilar joints. While the die pipe height was the most important parameter affecting the surface quality of the joint, a vertical-wall die type achieved the joints with maximum shear load and energy absorption. Liu et al.20 investigated the effect of die-designed geometrical parameters on the deformation of the rivet and sheets. The flared rivet shank radius showed an increasing trend with the increment of the die diameter and the die pip height while it decreased with the increment of the die depth. Karathanasopoulos et al.21 investigated the feasibility of joints and the correlation between riveting quality and the dimensions of rivets and molds. Their findings revealed that an increase in the inner radius of the rivet leg reduces joint feasibility but enhances joint quality while the depth of the mold’s center tip has no significant effect on either joint feasibility or riveting quality. Pickin et al.22 analyzed how the geometric parameters of the die influence rivet flare. It concluded a larger die diameter combined with a smaller die depth enhances rivet flare. Abe et al.23 examined the relationship between die dimensions and punch load, demonstrating that increasing both die diameter and depth effectively reduces the punch load. The existing literature highlights the critical role of die geometry in optimizing the efficiency and quality of SPR joints. However, further investigation is needed to understand how variations in die design specifically impact joint quality. While most studies have concentrated on flat dies and research on the effects of pip dies remains underexplored particularly regarding changes in rivet flare and riveting force during the process. Integrating simulation methods with experimentation is essential for a comprehensive understanding and precise control of the SPR process. Therefore, a more systematic and robust approach is required to explore the relationship between die design and SPR joint performance.

In this study, a piped-type die with various geometrical parameter values was specifically designed to examine the impact of die geometry on the SPR joint quality of 5052 aluminum alloy (AA5052). Metallographic scanning was utilized to measure and verify the accuracy of the die dimensions. A two-dimensional axisymmetric simulation model using LS-Dyna was developed to evaluate process efficiency and elucidate the forming mechanism of SPR joints. Following this, riveting experiments were conducted. The combined simulation and experimental results were analyzed to assess the influence of die diameter (D) and die depth (H) on the forming quality and mechanical properties of AA5052 SPR joints.

In this study, a single-lap riveting experiment was conducted using two identical sheets and a semi-tubular rivet. AA5052, from the 5xxx aluminum series, was selected as the sheet material for the joint specimens, while the rivets were made from 36MnB4 steel alloy with a countersunk head design, manufactured by Shenzhen Epress Company. The die design with the studied geometric parameters including the die diameter (D), die depth (H) and pip angle (θ) is shown in Fig. 1a. The dimensions of the selected rivet are shown in Fig. 1b while the sheet dimensions are 110 × 20 × 1.5 mm as shown in Fig. 1c. To minimize anisotropic effects in the experimental procedure, the length of the sheets was aligned with the rolling direction. The mechanical properties of both the plate material and the rivet were tested using the MTS-CMT4304 microcomputer-controlled electronic universal testing machine. Meanwhile, uniaxial tension tests under strain rate 0.01s-1 at 20 °C are used for the sheet material, while the compression tests of rivets have been conducted to characterize the mechanical behavior of the rivet. The stress–strain curves of the sheet specimens and rivets are shown in Fig. 2a and b, respectively. The results are presented in Table 1.

(a) Die design with the studied geometric parameters, (b) Rivet dimensions and (c) Configuration of the SPR joint.

Stress-strain curves for the sheet and rivet: (a) AA5052 Sheet and (b) 36MnB4 Rivet with a real view of the test specimens.

The specimens were prepared using the EPRN-TF type SPR equipment produced by Shenzhen Epress Company as shown in Fig. 3a. The riveting parameters were selected according to a series of preliminary tests. The punch moved under the applied pressure at a constant rate of 10 mm/min. The rivets were pressed into the overlapping AA5052 stacking-up plates to complete the riveting process and joint formation. To study the influence of the pip die-designed geometric parameters on the forming quality and mechanical properties of the prepared joints, a total of five dies with three diameters (D) and three depths (H) were designed. Table 2 shows the experimental design for this study while Fig. 3b shows the macroscopic configuration of all specimens.

(a) SPR equipment for the experiments and (b) Groups of prepared SPR joint specimens.

In this work, the pipe-die type was used to carry out the designed experiments and preparing the SPR joint specimens. The die geometries, with the determined values are shown in Fig. 4a–e. A cone is formed in the die cavity with its height flush not exceeding the die surface. The cone consists of three segments: arcs with radius 1.5 mm and two tangents: the pip angle (\(\:\theta\:\)) is formed by the two tangents and varies according to the varying die diameter (D) and/or depth (H). The inner wall on both sides of the cavity consists of two circular arcs of radius 0.5 mm and tangent lines; the angle of the left and right tangent lines is 21°. The end-point at the bottom of the inner walls on both sides is also the cone’s starting point and the die cavities deepest point. The axial distance from this point to the die surface represents the depth (H).

The changing angle (\(\:\theta\:\)) is achieved as follows: as the die diameter changes, the depth (H) remains a 1.7 mm value and the outer sides of the die cavity do not change. Meanwhile, the starting points of the cone sides move toward the die inner sides of the die, resulting in a change of the angle (\(\:\theta\:\)). When the die depth (H) changes, the diameter (D) remains a 9.3 mm value. The tangents on the inner wall of the die cavity become shorter or longer as the cone starting points move inward or outward, resulting in the change of the angle (\(\:\theta\:\)). However, the two angles formed by the inner and cone sides remain constant at 21\(\:^\circ\:\). A total of five different die designs used in the experiments is shown in Fig. 4.

The SPR designed die geometrical parameters: (a) DH, (b) H125, (c) H215, (d) D108 and (e) D123.

After preparing the SPR specimens, the joints were cut along their central axis using a diamond wire-cutting machine at a constant displacement rate of 0.2 mm/min. The cut specimens were then polished using 320, 800, and 2000 SiC sandpaper. Subsequently, the joints were cleaned with an ultrasonic cleaner to remove residual wire-cutting debris and sandpaper particles from the surface polishing process. Finally, the cross-section of each joint was examined using an optical microscope. The interlock (I), head height (h) and remaining thickness (T) were the main parameters used to assess the joint cross-section. A typical cross-section of an SPR specimen joint is shown in Fig. 5.

The head height (h) refers to the axial distance between the rivet head surface and the upper sheet surface. Excessive head height can negatively impact the corrosion resistance of the joint, while insufficient head height can lead to significant stress concentration in the sheet metal near the rivet head24. The interlock (I) refers to the radial distance between the deformed rivet tip and the point where the rivet passes through the upper sheet, which greatly influences the mechanical properties of the joint25. The remaining thickness (T) is the axial distance between the bottom of the rivet and the bottom surface of the lower sheet. A value of T < 0.2 mm indicates a risk of cracking or detachment of the bottom material during use which could affect the anticorrosion properties of the26.

Typical cross-section of SPR specimen joint.

The tension test was performed using an MTS-CMT4304 microcomputer-controlled electronic universal testing machine to evaluate the mechanical properties of the SPR joints. During the experiment, the lower fixture was fixed and the upper fixture was moved upward at a constant displacement rate of 5 mm/min until the specimen failed27. To eliminate additional torque due to force misalignment during the stretching process, a spacer was added to the clamping area at both ends of the specimen. The spacer dimensions were 20 mm × 20 mm × 1.5 mm28. To ensure the accuracy and stability of the test, the average values of the test data were recorded as the final tensile test results. The clamping of specimens during tensile tests is shown in Fig. 6.

Clamping of the SPR joint specimens for tensile tests.

In this paper, a 2D axisymmetric finite element model (using LS-DYNA software) was developed to simulate the riveting process of SPR. As shown in Fig. 7, the model consists of six parts: (1) punch, (2) clamping ring, (3) rivet, (4) upper plate, (5) lower plate and (6) bottom mold. In this model, the punch, holder and die are slightly deformed and treated as rigid bodies (type 20) to reduce simulation time. The rivet, upper plate and lower plate were modeled as elastic-plastic deformers (type 24). All components were represented using shell elements. However, the rigid components had one Gaussian integration point while the deformable components had four Gaussian integration points29.

Axisymmetric two-dimensional description of self-piercing riveting system.

It is well known that finer mesh sizes can effectively minimize the impact of mesh size on the results, producing simulation outcomes that more closely align with experimental data. However, the simulation time increases exponentially as the mesh size decreases. To balance accuracy and simulation time, this study tested the effect of different mesh sizes on the results and simulation duration. Figure 8a–d shows the simulation results for specimen no. 3 with different mesh sizes. As seen in zone 1 and zone 2, the simulation results for both the maximum mesh size (0.2 mm) and the minimum mesh size (0.05 mm) exhibit abnormal mesh deformation. Additionally, compared to the mesh size of 0.15 mm by using a mesh size of 0.1 mm results in significantly more refined simulations with smaller voids in key areas such as the contact between the rivets and the two plies. After careful consideration, the mesh size for each component was set to 0.1 × 0.1 mm.

Simulation results for different mesh sizes of specimen No. 3: (a) mesh size 0.2 mm, (b) mesh size 0.15 mm, (c) mesh size 0.10 mm and (d) mesh size 0.05 mm.

The contact algorithm plays a crucial role in determining the accuracy and reliability of the model. In this study, the contact algorithm was set to an automatic 2D single-surface method to prevent interpenetration between different materials. Friction has a significant influence on the simulation results. Due to the limitations of experimental conditions and to determine the appropriate and accurate value, we referred to existing literature and summarized the friction coefficients used by other researchers4. The friction coefficient was then set to 0.2 using the inverse method (by comparing the experimental results with the simulation outcomes). Meanwhile, ALE grid adaptive control was employed to prevent grid distortion and ensure the stability and accuracy of the simulation analysis. Better simulation results and longer simulation times are achieved with shorter intervals between mesh adaptations. The effects of different grid adaptation intervals on simulation results and time were tested, and the grid adaptation interval was set to 0.9 ms.

During the riveting process, the rivet penetrates the upper sheet. To model this phenomenon, a geometrical criterion was applied. Once the thickness of the upper sheet reduces to a predefined critical minimum value, material separation is triggered with the assistance of the advancing front quadrilateral mesh. This critical thickness value significantly affects the simulation results. The upper plate fractures prematurely with a large critical value but undergoes unrealistic deformation with a very small critical value. In this model, these factors were determined using the inverse method. The critical thickness for the upper sheet was set to 0.1 mm30.

The material constitutive models play a crucial role in the development of the simulation model. In this paper, both the rivet and sheet materials were characterized using plastic stress-strain curves. Since the actual temperature change of the sheet during the riveting process is small. The plastic stress-strain data for the sheet was applied to the rivet (Fig. 2a) as described earlier in Sect. 2.131. The material properties of the rivet were tested in compression test following the method of R. Porcaro to obtain the plastic stress-strain curve for the rivets (Fig. 2a)32. Refer to Table 1.

To verify the accuracy of the simulation results, the results from the five groups in both the simulation and experiments were compared to monitor joint deformation. The joint cross-sections from the experimental and simulation results are shown in Fig. 9. It can be observed that the deformation of the rivets and plates was accurately predicted. The material folds in zone 1 were well captured in zone 2, and the gap between the two sheet layers in zone 4 was similarly predicted in zone 3. The cross-section quality indicators for the five groups of specimens are shown in Table 3. The rivet head height (h) from the experiment was used as the termination criterion for the SPR simulation. In other words, the simulation was stopped when the simulated rivet head height matched the experimental value.

Therefore, the errors in head height (h) obtained from both the simulation and experiments for the five groups of specimens are approximately not exist, leading to the use of the interlock (I) and remaining thickness (T) to assess the accuracy of the simulation model. The errors between the simulation and experiment for the interlock (I) values of the five groups of specimens are less than 5%, with the errors for specimens No. 1 and No. 4 being zero. For the remaining thickness (T) values, the errors between simulation and experiment were less than 5% for all three groups of specimens, except for specimens No. 1 and No. 2. However, it is worth noting that the absolute errors between simulation and experiment for specimens No. 1 and No. 2 are very small, specifically 0.04 and 0.03, respectively. Therefore, the error analysis indicates that the simulation results are in satisfactory agreement with the experimental results.

Quality indicators for SPR joint specimen cross-sections obtained from the experiment and simulation.

This section provides an analysis of the performance of the designed dies, along with an evaluation of how the die geometry parameters influence the joining process. The efficiency of the SPR joint is assessed by analyzing the riveting mechanism, riveting force, and forming quality indicators. As previously mentioned, the forming quality indicators include remaining thickness (T), interlock (I), and head height (h).

To more intuitively analyze the effect of die diameter (D) on the riveting mechanism, joint cross-sections for different diameters (D) under various axial displacements of the rivet in the simulation results were extracted, as shown in Fig. 10 (where A indicates the axial displacement of the rivet)33. The maximum distance from the rivet leg to the center axis at different stages was measured (R), and the difference between these measurements represents the flare of the rivet (∆R).

It can be observed that when A ≤ 3 mm, the rivet directly penetrated the upper sheet under the punch pressure, and the sheet inside the rivet cavity gradually expanded with the axial displacement of the rivet. Since the elastic modulus of the rivet was higher than that of the sheet, no significant rivet deformation was observed during this process. However, a small axial flare of the rivet occurred due to the friction between the rivet leg and the sheet, as well as the reaction force from the die. When A reached 4 mm, the rivet successfully pierced the upper sheet and embedded into the lower sheet under the punch pressure. The rivet cavity was almost filled by the sheet, and a noticeable flare of the rivet was observed. Once the rivet cavity was filled, the internal sheet underwent plastic deformation due to axial pressure.

The applied force caused the rivet to flare rapidly. Therefore, the sooner the rivet cavity was filled, the quicker the rivet flared. As observed in zones 1, 2, and 3, a larger die diameter (D) resulted in a smaller unfilled area in the cavity, particularly in zone 3, where the rivet cavity was filled. This indicates that a larger die diameter facilitates earlier rivet flare. As the sheet filled the rivet cavity with the flaring rivet, the reaction force from the die’s inner wall prevented further rivet flare once the sheet contacted the inner wall. As seen in zones 4, 5, and 6, the unfilled area in the die cavity increased with a larger die diameter (D), suggesting that a larger die diameter reduces obstruction to the rivet flare by the die’s inner wall. When riveting was completed, the value of R increased from 3.18 mm to 3.52 mm and 3.72 mm as the die diameter increased from 9.3 mm to 10.8 mm and 12.3 mm, respectively, indicating that a larger die diameter facilitates rivet flare.

Riveting process mechanism of SPR joint specimens with different die diameters at several axial steps.

Figure 11 illustrates the relationship between the riveting force (F) and die diameter (D) as the rivet penetrates the stacking sheets. The riveting force drives the rivet through the joint, piercing the upper sheet and creating the mechanical interlock with the lower sheet. As the axial displacement of the rivet increases, the riveting force initially follows a logarithmic pattern until it reaches a certain point. Beyond this point, the force increases linearly up to the peak value. This trend shows that a larger die diameter reduces the riveting force required to form the SPR joint. Specifically, the maximum riveting force decreases from 7.95 kN to 5.50 kN and 4.96 kN as the die diameter (D) increases from 9.3 mm to 10.8 mm and 12.3 mm, respectively.

This can be explained as follows: The sheets positioned over the die cavity can be treated as a cantilever beam. The larger the die diameter, the greater the bending rate for a constant die depth (H). Two primary constraints influence the riveting process: the upper sheet and the die. The upper sheet provides upward resistance to the rivet as it is pierced, according to its elastic deformation capacity. The higher the deformation rate of the upper sheet, the greater the damage and the lower the resistance. As seen in zones 1, 2, and 3, a larger die diameter (D) results in a greater degree of deformation of the upper sheet and a smaller contact area between the die and the lower sheet. Consequently, the riveting process encounters less resistance and requires a smaller riveting force. This allows the rivet to experience less restriction and resistance during insertion and flaring. In contrast, the smaller die diameter (D) creates more limited space for the rivet, increasing riveting resistance and requiring more force to drive the rivet through the sheets and achieve the necessary flare.

Riveting force of SPR joint specimens with different die diameters.

The effect of die diameter (D) on the remaining sheet thickness (T) is shown in Fig. 12. The remaining thickness (T) significantly influences the SPR joint’s strength and durability, serving as a key indicator of joint quality. In this study, as the die diameter increases, the value of T increases for both simulation and experimental results. Specifically, the remaining thickness (T) increased from 0.46 mm to 0.53 mm and then to 0.67 mm as the die diameter (D) increased from 9.3 mm to 10.8 mm and 12.3 mm, respectively, in the simulation results. For smaller die diameters, the rivet’s downward movement is constrained as the die cavity fills with material at a faster rate. The normal pressure applied to the joint increases as the riveting force rises for smaller die diameters, leading to a reduction in the remaining thickness (T).

Remaining thickness (T) of SPR joint specimens at varying die diameter (D).

Figure 13 illustrates the impact of die diameter (D) on the joint interlock (I). It shows that the joint interlock (I) increases with an increase in die diameter. Specifically, the joint interlock value rose from 0.23 mm to 0.25 mm and then to 0.28 mm as the die diameter (D) increased from 9.3 mm to 10.8 mm and 12.3 mm, respectively, in the simulation results. A smaller die diameter restricts the rivet’s ability to expand radially, limiting its flare. As the die diameter increases, more space is provided for the rivet to expand radially, thereby enhancing the interlocking of the joint.

Interlock (I) of SPR joint specimens at varying die diameters (D).

Figure 14 illustrates the effect of die diameter (D) on joint head height (h). Increasing the die diameter significantly reduces the head height (h). Specifically, the joint head height decreased from 0.32 mm to 0.09 mm and 0.04 mm as the die diameter (D) increased from 9.3 mm to 10.8 mm and 12.3 mm, respectively. With a smaller die diameter, the available space for the rivet to move downward is more constrained as the die cavity fills, resulting in less displacement of the rivet. Consequently, the unpierced portion of the rivet creates a larger head height (h).

The head height (h) of SPR joint specimens at varying die diameters (D).

The cross-section of joint with different die depth (H) under different axial displacement of rivet in the simulation results was intercepted as shown in Fig. 15. It can be observed that when A ≤ 3 mm, the riveting process follows the same pattern as described previously. In zones 1, 2, and 3, as the die depth (H) increases, the unfilled area in the rivet cavity also increases, with the rivet cavity already filled in zone 1 when A reaches 4 mm. This suggests that a larger die depth (H) facilitates earlier rivet flare. Additionally, the unfilled area in the die cavity also increases and the cavity is nearly filled at zone 4 in zones 4, 5 and 6 as die depth (H) increases. The greater the die depth (H), the smaller the obstruction to the rivet flare. The value of R decreased from 3.40 mm to 3.18 mm and 3.06 mm as the die depth increased from 1.25 mm to 1.7 mm and 2.15 mm, respectively, upon completion of the riveting. This indicates that a smaller die depth facilitates rivet flare.

Riveting process mechanism of SPR joint specimens with different die depths at several axial steps.

Figure 16 illustrates the relationship between the riveting force (F) and die depth (H) as the rivet moves into the stacked sheets. It is evident that an increase in die depth reduces the required riveting force to complete the SPR joint formation. The maximum riveting force decreased from 9.88 kN to 7.95 kN and 5.50 kN as the die depth (H) increased from 1.25 mm to 1.7 mm and 2.15 mm, respectively. This can be explained as the following: with a smaller die depth, the die cavity at a constant diameter (D) becomes smaller, reducing the free space available for the rivet to move downward. As a result, the die cavity fills earlier. To achieve the same punch displacement, the machine needs to apply more force, which in turn increases the riveting force.

Riveting force of SPR joint specimens with different die depths.

The effect of the die depth (H) on the remaining thickness (T) is illustrated in Fig. 17. As the die diameter increases, the T value increases for both simulation and experimental results. The remaining thickness (T) increased respectively from 0.44 mm to 0.46 mm and then to 0.57 mm for the die depth (H) of 1.25 mm, 1.7 mm, and 2.15 mm in case of experimental results. The free space for rivet to move downward is smaller with the smaller die depth. As the riveting force increases for the smaller die depth (H), the normal pressure applied to the joint and the displacement for rivet to move downward increases, resulting in a smaller remaining thickness (T).

Remaining thickness (T) of specimens at varying die depth (H).

Figure 18 illustrates the effect of die depth (H) on the interlock (I). The results show that the interlock (I) initially decreases and then increases as the die depth increases. The interlock value decreased from 0.28 mm to 0.23 mm and then increased to 0.26 mm as the die depth (H) increased from 1.25 mm to 1.7 mm, and 2.15 mm, respectively in the experimental results. A larger die depth restricts the flare of the rivet. However, it compresses more sheets within the die cavity, resulting in a greater portion of the rivet piercing into the lower sheet and thus improving the interlock (I) of the joint.

The interlock (I) of specimens at varying die depth (H).

The effect of the die depth (H) on the joint head height (h) is illustrated in Fig. 19. Increasing the die depth significantly reduces the head height (h). The joint head height (h) decreased from 0.37 mm to 0.32 mm and then to 0.08 mm as the die depth (H) increased from 1.25 mm to 1.7 mm and 2.15 mm, respectively, in the experimental results. The reduced free space for the rivet to move downward, due to the smaller die depth, results in less displacement of the rivet. As a result, the unpierced portion of the rivet creates a larger head height (h).

The head height (h) of specimens at varying die depth (H).

The load-displacements curves of the five groups of specimens obtained from the tensile tests are shown in Fig. 20. As displacement increased, the load-displacement curves of all specimens initially followed a logarithmic pattern, rising until reaching a peak value. Afterward, the curves began to decline gradually as the displacement continued, ultimately leading to specimen failure. The entire tensile process can be divided into three distinct phases34:

Load-displacement curves for the five SPR group specimens.

(I) Elastic Stage: During this phase, the load-displacement curves of the specimens exhibited a linear and rapid increase. The force applied by the testing machine acted on the sheets and rivet, causing them to deform elastically. The load-displacement curves for all specimens in this stage were closely aligned as the materials of the plates and rivets were identical.

(II) Plastic Stage: In this stage, the load-displacement curves of the specimens increased slowly and non-linearly until they reached the peak. This behavior occurred as the force exerted by the machine reached the yield strength of the sheet. The bottom of the upper sheet began to buckle, with the buckling amplitude increasing as the load continued to rise. As a result, the force applied by the machine to the sheet was transferred to the rivet due to the obstruction from the self-locking structure. The primary load was then absorbed by the self-locking structure of the joint. Once the force limit of the self-locking structure was reached, an audible fracture sound could be heard. Concurrently, the load-displacement curves of the specimens reached their peak.

(III) Failure Stage: In this stage, the load-displacement curves of the specimens exhibited a rapid and nonlinear decrease after a brief period of slow and nonlinear decline. This occurred as the force exerted by the machine reached the strength limit of the specimens. At this point, the self-locking structure between the rivet and the sheets failed. However, the rivet was not fully detached from the lower sheet due to friction between the rivet leg and the sheets. The machine had to continue applying force to overcome this friction, allowing the rivet to be completely detached from the lower sheet.

The mechanical property indicators for specimens with different die diameters (D) are shown in Fig. 21. The maximum shear load and energy absorption were selected as key indicators to evaluate the mechanical properties of the specimens. It can be observed that both the maximum shear load and energy absorption increase as the die diameter (D) increases, suggesting that a larger die diameter results in better mechanical properties. The mechanical properties of SPR specimens are primarily influenced by the material strength and the forming quality of the specimens35. Since all specimens used the same sheet and rivet materials, the trend of the mechanical properties’ change with varying die diameter (D) mirrors the trend observed in the forming quality of the specimens. Additionally, it is worth noting that with a larger die diameter, the error in the peak load data decreases, indicating that specimens formed with larger die diameters exhibit more stable mechanical properties.

The indicators of mechanical property for specimens at varying die diameter (D).

The mechanical property indicators for specimens with different die depths (H) are shown in Fig. 22. It can be observed that as the die depth (H) increases, the maximum shear load and energy absorption initially decrease and then increase. The optimal mechanical properties were achieved when the die depth (H) was 1.25 mm. This suggests that an appropriate die depth is essential for optimizing the mechanical properties of the specimens.

The indicators of mechanical property for specimens at varying die depth (H).

This study investigates the effects of die diameter and die depth on the forming quality and mechanical properties of AA5052 SPR specimens. A total of five dies, featuring three different diameters and three different depths, were designed for this research. Both experimental and simulation methods were used to determine the head height, interlock, and remaining thickness of the specimens to analyze the influence of die diameter and die depth on forming quality. The forming mechanism was examined through numerical simulations of the riveting process. Additionally, load-displacement curves were obtained through tensile tests. The trends in maximum shear load and energy absorption as a function of die diameter and die depth were analyzed. The following conclusions were drawn:

The developed simulation model demonstrates a reliable capability to predict the events occurring during the riveting process and to assess the quality of joint formation. The errors between the simulation and experimental results for interlock (I) and remaining thickness (T) which were used to evaluate model accuracy were all less than 10% with absolute errors even smaller than 0.05.

A larger die diameter leads to quicker filling of the rivet cavity, resulting in enhanced rivet flare, interlock as well as a more compact head height, improving the overall forming quality of the specimens. Conversely, a smaller die depth also accelerates the filling of the rivet cavity but negatively affects the rivet flare.

A smaller die depth may lead to an excessively high head height in the specimens, while a deeper die depth enhances the interlock between the specimens. Therefore, a larger die depth generally results in better forming quality of the specimens.

The mechanical properties including shear load and energy absorption are significantly improved with larger die diameters, though an optimal die depth is required to fully enhance joint strength. The mechanical property of specimens showed decreasing and then increasing trend with the increase of die depth.

The datasets used and/or analyzed during the current study are available from the corresponding author upon reasonable request.

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This research is supported by Africa New Energies Limited, United Kingdom (Grant No. ANE096) and Post-doctoral Later-stage Foundation Project of Shenzhen Polytechnic University (No. 6023271014 K).

Faculty of Intelligent Manufacturing Engineering, Guizhou Industry Polytechnic College, Guiyang, 551400, China

Ao Zhang, Lun Zhao, Liya Li & Zeshan Abbas

Materials and Chemical Engineering, University of Science and Technology Liaoning, Anshan, 114051, China

Ao Zhang & Jiguang Li

Institute of Ultrasonic Technology, Shenzhen Polytechnic University, Shenzhen, 518055, China

Lun Zhao, Zeshan Abbas, Yizhi Shao, Jiyuan Liu & Amr Monier

Department of Electrical Engineering, College of Engineering, United Arab Emirates University, Al-Ain, 15551, United Arab Emirates

Saad Saleem Khan

Africa New Energies Limited, Villa Florita, East Road, St Georges Hill, Weybridge, UK

Stephen Larkin

Mechanical Engineering Department, Shoubra Faculty of Engineering, Benha University, Cairo, 11629, Egypt

Amr Monier

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Writing-original draft, Ao Zhang; methodology, Ao Zhang; software, Ao Zhang; data curation, Zeshan Abbas; validation, Ao Zhang; Data curation, Ao Zhang; conceptualization, formal analysis, Lun Zhao; resources, Lun Zhao; supervision, Zeshan Abbas and Amr Moiner; project administration, Lun Zhao; funding acquisition, Lun Zhao; formal analysis, Amr Moiner; investigation, Amr Moiner; data curation, Amr Moiner; investigation, Yizhi Shao; data curation, Liya Li; writing—review and editing , Yizhi Shao; investigation, Jiyuan Liu; validation, Jiyuan Liu; data curation, Jiyuan Liu; writing—review and editing, Amr Moiner; writing—review and editing, Zeshan Abbas; writing—review and editing, Jiguang Li, Saad Saleem Khan; writing—review and editing, Stephen Larkin; writing—review and editing. All authors have read and agreed to the published version of the manuscript.

Correspondence to Lun Zhao.

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Zhang, A., Zhao, L., Li, L. et al. Effect of die designed geometrical parameters on riveting quality of self-piercing riveting joints in 5052 aluminium alloy. Sci Rep 15, 7239 (2025). https://doi.org/10.1038/s41598-025-92142-1

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Received: 21 October 2024

Accepted: 25 February 2025

Published: 28 February 2025

DOI: https://doi.org/10.1038/s41598-025-92142-1

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