Optimization of Forming Parameters and Forming Strategy for Stamping of Novel Ultra-Thin Super Ferritic Stainless Steel Bipolar Plates Based on Numerical Simulation

Abstract

This study investigates the forming process (stamping) of bipolar plates which have applied a novel ultra-thin (0.1 mm) super ferritic stainless steel, i.e., SUS470, whose chromium is sufficiently high for corrosion resistance. A three-dimensional finite element model of the stamping process was developed using the commercial software ABAQUS version 2022. The model incorporated optimized die parameters obtained through Central Composite Design (CCD). This model was used to analyze the effects of key forming parameters, including stamping speed and friction coefficient, on the distribution of stress, strain, and thickness reduction during the stamping process. The finite element modeling (FEM) results disclose that the inner corner of the flow channel is a critical defect-prone region, exhibiting stress concentration, uneven strain distribution, and severe thinning. The optimal forming quality can be achieved at a stamping speed of 100 mm/s and a friction coefficient of 0.185 among all varied options. Further, a comparative study of single-stage, conventional two-stage, and optimized two-stage stamping strategies based on previous investigation demonstrates that the optimized two-stage stamping process can effectively alleviate stress and strain concentrations at the corners, significantly reduce thinning problems, and enhance the uniformity and stability during stamping. In summary, this study provides theoretical support for the design of the forming process (stamping) of high-performance super ferritic stainless steel bipolar plates, which is beneficial to subsequent practical engineering application.

1. Introduction

Hydrogen fuel cells (HFCs) are clean energy devices that generate electricity through an electrochemical reaction between hydrogen and oxygen [1]. Due to its high fuel efficiency and zero emissions, it is widely used in transportation, stationary power, and portable devices [2,3,4,5]. Among its components, the bipolar plate (BP) plays a crucial role in influencing the fuel cell’s performance, cost, and weight. The BP is one of the core components of a fuel cell. Its primary functions include separating fuel and oxidant, conducting electricity, providing gas flow channels, and dissipating heat. The BP accounts for 60–80% of the total weight and 30–45% of the cost. Undoubtedly, it determines the ultimate performance of the fuel cell.

The main materials for BPs in fuel cell are graphite materials, composite materials, and metallic materials. Graphite and composites offer excellent electrical conductivity, corrosion resistance, and low density. The high cost, complex manufacturing processes, and high permeability of graphite—which necessitates an increase in thickness to mitigate hydrogen leakage or electrolyte loss—significantly constrain the large-scale commercial application of graphite-based BPs. Nevertheless, increasing the thickness inevitably results in greater BP weight, reduced overall fuel cell efficiency and performance, and elevated material costs, further impeding their widespread commercialization [6]. In contrast, metallic materials have attracted significant attention as alternative materials due to their excellent mechanical properties, processability, and effective cost control. Conventional austenitic stainless steel tends to corrode in the acidic environment of fuel cells, forming a passivation layer that impairs conductivity and necessitates additional surface coating treatments to improve performance [7]. Modified super ferritic stainless steel (SFSS) demonstrates significant advantages in terms of corrosion resistance and long-term stability. SFSS exhibits inherent corrosion resistance, particularly in acidic environments, reducing the need for surface coatings. Additionally, SFSS maintains superior strength stability at high temperatures, making it well-suited for the long-term operation of fuel cells. In this study, a SFSS was selected as a metal candidate which can be applied in this innovative field, i.e., BP in fuel cell. Evidently, as the most important process, forming is the first step for the whole assessment flow of newly-design metallic material, i.e., SFSS.

As a methodology for manufacturing BP for fuel cell, stamping is the mostly applied option due to its high efficiency, low cost, and suitability for mass production [8]. Investigating the forming process for innovative material as a BP is vital to its potential application.

Chen and Ye [9] established an elasto-plastic finite element model for the stamping process of 0.05-mm-thick SUS304 metal BPs, based on an updated Lagrangian formulation. They compared the conventional material model with a model modified using a scale factor. Experimental validation showed that the modified model reflects the BP forming process more accurately, and cracks are most likely to occur at the channel fillets. Hu et al. [10] used forming limit diagrams to determine the safety limits during the stamping process of BPs. They considered variable parameters such as channel dimensions, punch speed, punch and die radii, and draft angle, and conducted experimental validation on 0.15-mm-thick SS304 sheets. By optimizing finite element simulation parameters, they improved the formability of the sheets and reduced the production cost of BPs. The study found that ridging tends to occur at low speeds, while cracking is more likely at higher speeds. A larger punch radius improves stamping safety, whereas a smaller radius leads to greater sheet thinning. In addition, increasing the channel width, depth, and rib width also helps improve sheet formability. Modanloo et al. [11] systematically investigated the stamping behavior of titanium BPs with an initial thickness of 0.1 mm by employing the response surface methodology (RSM) to model and optimize the forming process. Through variance analysis, they identified the effects of input parameters such as die gap, stamping speed, and friction coefficient on the forming process. They also developed a regression model to predict the maximum forming depth of the plate channels under different parameters. The study showed that increasing the die gap and reducing the friction coefficient can enhance the maximum channel depth. Zhao and Peng [12] predicted the fracture points during the stamping 0.1-mm-thick SS304 sheets, based on microscale forming instability criteria. The results showed that considering size effects allowed the model to predict channel forming depth accurately. Moreover, increasing the channel width, die gap, and fillet radius can all contribute to deeper channel formation. Neto et al. [13] employed the Swift hardening model to study the stamping process of 0.15-mm-thick SS304 sheets. They found that reducing the channel/rib width and increasing the fillet radius helps lower the thinning ratio while increasing the channel depth tends to intensify sheet thinning. Bong et al. [8] adopted a multi-stage stamping process to optimize microchannel formation. They optimized the die fillet radius and channel forming depth through finite element simulations and established a mathematical model proposing a multi-pass forming optimization method. This successfully improved channel forming depth and effectively controlled the thinning ratio.

This study focuses on the forming process of ultra-thin SUS470 FSS BPs with a thickness of 0.1 mm. A numerical stamping simulation model was established using ABAQUS version 2022. The effects of stamping process parameters such as punch speed and friction coefficient on forming quality were systematically investigated. In addition, based on previous research, the study compared the forming performance of single-pass stamping, conventional two-pass stamping, and an optimized two-pass stamping strategy. It explored how multi-stage forming paths can improve stress distribution, thickness uniformity, and springback control. Through multidimensional analysis and optimization, this study aims to provide theoretical guidance and process references for the high-precision and cost-effective fabrication of metal BPs, promoting their practical application in hydrogen fuel cell technology.

2. Establishment of the FEM for Stamping Forming

2.1. Materials

In this experiment, ultra-thin ferritic stainless steel SUS470 with a thickness of 0.1 ± 0.01 mm was used as the material for the BPs. The elemental composition is shown in

Table 1. Chemical Composition of the Sheet Material (wt.%).

Element	C	Mn	Si	P	S	Cr	Ni	Fe
wt.%	≤0.10	≤0.10	≤1.00	≤0.04	≤0.03	16~18	≤0.75	Bal.

. Compared with austenitic stainless steel (ASS), SUS470 contains less nickel, making it more cost-effective. Additionally, with a chromium content of 17%, it exhibits superior corrosion resistance in the acidic environment of fuel cells and is less prone to forming passive films that can hinder electrical conductivity. This helps reduce interfacial contact resistance (ICR), eliminating the need for additional conductive coatings. Moreover, SUS470 has a lower coefficient of thermal expansion, offering better dimensional stability during thermal cycling and reducing the risk of material fatigue failure. Overall, SUS470 outperforms ASS in terms of corrosion resistance, electrical and thermal conductivity, cost control, and long-term reliability, making it a more competitive option for fuel cell BPs. To obtain the mechanical properties, uniaxial tensile tests were conducted at room temperature with an engineering strain rate of 10⁻³ s⁻¹. The specimen dimensions and the stress–strain curves of the sheet along the rolling direction are shown in Figure 1. It was found that the material exhibits a Young’s modulus of 200 GPa and a Poisson’s ratio of 0.33.

2.2. Die Design

A simple three-dimensional model was established using ABAQUS/Explicit to simulate the stamping process of SUS470 BPs. Figure 2 shows a schematic diagram of the BP stamping die. To ensure structural consistency and minimize interference from extraneous variables, the channel width and rib width were kept constant throughout the study. These parameters directly affect fluid flow performance and the functional characteristics of the BP and are typically determined based on battery performance requirements and optimized flow field design. According to the Central Composite Design (CCD) principle, three process parameters—channel depth (h), fillet radius (r), and draft angle (α)—were selected as variable factors. The thickness reduction rate and maximum equivalent stress were chosen as response values. A three-factor, five-level response surface experiment was designed accordingly. Each factor was tested at five levels, with the variation ranges shown in

Table 2. The process parameters that change during the stamping forming process.

	Microchannel Depth h (mm)	Corner Radius r (mm)	Pattern Draft α (°)
1	0.30	0.1050	19.50
2	0.32	0.1075	19.75
3	0.35	0.1100	20.00
4	0.38	0.1125	20.25
5	0.40	0.1150	20.50

. All subsequent experimental combinations were based on these parameter ranges. The process parameters held constant during the forming simulations were as follows: Channel width (w): 0.66 mm, Rib width (s): 0.46 mm, stamping speed: 100 mm/s, Friction coefficient: 0.185, Blank holder force: 2000 N, stamping speed and friction coefficient are determined in subsequent experiments.

Using Design-Expert 10 software, a CCD design approach was employed to determine the effects of channel depth, fillet radius, and draft angle on the response values (maximum thinning rate (thinning) and maximum equivalent stress (S). A total of 25 parameter combinations were generated, and the corresponding response values were obtained through simulation. MATLAB, R2024 was then used to fit response surface models via the least squares method, sequentially considering linear, two-factor interaction, and quadratic models. Regression analysis was performed on the selected response variables, and model fitting was evaluated using statistical indicators such as regression coefficients, standard errors, t-values, p-values, and the coefficient of determination (R²). Although the final regression models (Equations (1) and (2)) include nonlinear terms (e.g., squared terms), they are linear in parameters and were therefore fitted using the standard linear regression approach (ordinary least squares). The results indicated that the quadratic model achieved R² values of 0.898 and 0.464 for thinning rate and maximum equivalent stress, respectively, demonstrating superior fitting performance. Thus, the quadratic polynomial regression model, which belongs to the class of linear regression models due to its linearity in parameters, was selected to analyze the relationship between input variables and responses. The statistical data of the quadratic models calculated by the software are shown in

Table 3. The statistical data of the maximum thinning rate quadratic polynomial model.

	Estimate	SE	tstat	P
Constant	5.7503	21.416	0.2685	0.79197
h	11.453	9.0626	1.2638	0.22559
r	−118.17	131.94	−0.89566	0.38458
α	−0.10142	1.9853	−0.051084	0.0002
hr	−29.726	39.704	−0.74869	0.95993
hα	−0.36905	0.39084	−0.94424	0.46562
rα	5.0685	4.1665	1.2165	0.36001
h2	0.86809	5.0194	0.17295	0.24259
r2	114.86	447.64	0.2566	0.865
α2	−0.0085596	0.048097	−0.17797	0.86113
RMSE		0.0233
R2		0.898
F-statistic		14.6	p	6.62 × 106

and

Table 4. The statistical data of the maximum equivalent stress quadratic polynomial model.

	Estimate	SE	tstat	P
Constant	−28,587	42,647	0.67033	0.51284
h	2620.9	18,046	0.14523	0.88646
r	148,090	262,720	0.56368	0.5813
α	1995.5	3953.4	0.50476	0.62106
hr	19,094	79,062	0.24154	0.81243
hα	−875.52	778.28	−1.1249	0.27829
rα	−1137.9	8296.7	−0.13715	0.89273
h2	17,711	9995	1.772	0.096704
r2	−581,540	891,390	−0.6524	0.52402
α2	−38.055	95.775	−0.39773	0.6967
RMSE		46.4
R2		0.464
F-statistic		1.44	p	0.255

, with the response equations presented as Equations (1) and (2).

$$\begin{array}{cc}\hfill thinning\left(\%\right)=& 5.7503+11.453h-118.17r-0.10142\alpha +0.86809h^2\hfill \\ & +114.86r^2-0.0085596{\alpha }^2-29.726hr-0.36905h\alpha \hfill \\ & +5.0685r\hfill \end{array}$$

(1)

$$\begin{array}{cc}\hfill S\left(\mathrm{M}\mathrm{P}\mathrm{a}\right)=& -28587+2620.9h+1.4809\times {10}^{5}r+1995.5\alpha +17711h^2\hfill \\ & -5.8154\times {10}^5{r}^2-38.055{\alpha }^2+19094hr-875.52h\alpha \hfill \\ & -1137.9r\alpha \hfill \end{array}$$

(2)

To validate the accuracy of the regression models, the fitted values were compared with the simulation results. As shown in Figure 3, the model predictions generally follow the same trend as the simulation data for most points. In particular, deviations are smaller in regions with lower channel depth, indicating that the model effectively captures the variation in thinning rate. For larger channel depths, the model tends to slightly overpredict, which may be attributed to model simplification, limited approximation capability of the response surface, or data variability. Figure 3b shows that the fitted values for maximum equivalent stress generally agree with the simulation results, although some deviations exist at individual points, possibly due to complex nonlinear responses or unaccounted variable effects. The residuals are evenly distributed without obvious systematic bias, further supporting the model’s validity. In summary, the regression models can accurately predict the thinning rate and maximum equivalent stress, providing a reliable basis for subsequent optimization.

The weighted combination of thinning rate and maximum equivalent stress was used as the objective function. Optimization of the dimensional parameters was performed using MATLAB’s fmincon and ga functions, with the goal of minimizing thinning rate and maximum equivalent stress to improve the die’s performance in actual manufacturing processes. During the optimization process, constraints on channel depth, fillet radius, and draft angle were set based on the processing technology, design standards, and functional requirements, ensuring that the parameter optimization results remained within a reasonable range and met manufacturing feasibility. The optimized best parameter combination obtained was Channel depth: 0.3513 mm, Fillet radius: 0.1050 mm, Draft angle: 19.5°.

In order to meet the needs of different forming methods, three distinct stamping methods (Case A, Case B, and Case C) were designed based on CCD to create dies with differentiated characteristics. The geometric parameters of the dies are shown in Figure 4. The die design for Case A is a single-stage stamping die that does not include a preforming stage. The die’s geometric shape directly corresponds to the structure of the final formed part. The die for Case B introduces a preforming stage and is divided into two stages: Stage I die is used for preliminary plastic deformation, and Stage II die completes the final forming. This two-stage approach helps to gradually disperse stress concentration and reduce the risk of excessive thinning. Case C builds on Case B by optimizing the die design for Stage I. The preforming die is modified by adding some raised structures (as shown in Figure 4c). These localized adjustments further guide material flow and improve the stress and strain distribution in regions with high stress concentration.

2.3. Establishing the Finite Element Model

The CAD module in ABAQUS was first used to create the model based on the microchannel dimensions determined in the previous section. The initial sheet size before stamping was 30 × 30 mm. Given the high rigidity of the die during the stamping process, its deformation was considered negligible and thus modeled as a rigid body. To accurately analyze the thickness variation of the BP while improving computational efficiency, the S4R shell element was employed for meshing. A total of 22,500 elements and 22,801 nodes were generated. The S4R shell element is computationally efficient, avoids locking issues, supports large deformations, and accurately captures ridging and springback, making it an optimal choice for stamping simulations. Compared to solid elements, it significantly reduces computational cost, and compared to lower-order shell elements, it offers better accuracy and stability. The analysis focuses on the normal pressure and tangential tension during the stamping process, which reflect the compressive action of the die and the tensile behavior of the material, respectively. These parameters are crucial for optimizing process conditions to ensure forming quality and dimensional accuracy.

In the stamping process, to accurately reflect real manufacturing conditions, the lower die was fully fixed to ensure its stability and immobility during forming. The punch is allowed only vertical displacement relative to the sheet material, ensuring that the punch moves along the vertical path, with a displacement of 5 mm. The loading process can be performed at a constant speed or stepwise, ensuring a smooth and controllable forming process. In the stamping simulation, surface-to-surface contact interactions were defined between the workpiece and the forming tools. A total of three contact pairs were established, as illustrated in Figure 5a–c: (a) the lower surface of the punch and the upper surface of the sheet, (b) the upper surface of the die and the lower surface of the sheet, and (c) the lower surface of the blank holder and the upper surface of the sheet. The tangential behavior was modeled using a Coulomb friction formulation, while the normal interaction was defined as “hard” contact. This setup ensures accurate representation of pressure transmission and separation behavior between the interacting surfaces, thereby enhancing the fidelity of the forming process simulation. To prevent edge ridging or irregular deformation, a normal blank holder force of 2000 N is applied along the edges of the workpiece [14]. The pressure is evenly distributed along the vertical direction at the edge of the sheet, ensuring uniform edge loading and maintaining dimensional stability.

In the loading condition setup, the punch was subjected to displacement-controlled loading. Specifically, the punch was driven downward along the Y-axis with a total displacement of 5 mm, as illustrated in Figure 6. The loading was applied at a constant velocity in an incremental (stepwise) manner to ensure a stable forming process. In the finite element simulation, this was implemented by controlling the displacement of the punch in the U2 direction. The punch’s motion path was designed to replicate the actual stamping trajectory used in practical manufacturing.

In the two-stage forming process, the process parameters are the best parameters obtained by the single-stage stamping process. The forming process is shown in Figure 7. The first stage involves pre-deforming the BP. During this process, the predefined field functions in ABAQUS are effectively utilized to handle the physical fields, accurately simulating the stress, strain distribution, and geometry of the material after the first stage of forming. This provides accurate initial conditions for the second stage of forming. In the deformation process of the first stage, the predefined field helps capture and transfer the material’s deformation state, ensuring that the simulation of the second stage can be conducted under realistic initial conditions. Subsequently, based on the BP deformed in the first stage, the second-stage forming simulation is carried out to further optimize its forming quality and performance. By this approach, a more precise multi-stage forming process simulation can be achieved, providing strong support for the final design optimization.

After completing the model setup, the model was fully defined and submitted for computation. The explicit solver in ABAQUS was employed to ensure numerical stability and convergence. During this stage, the time step, increment size, and solver parameters were appropriately adjusted to accurately capture the mechanical behavior throughout the forming process. Upon completion of the simulation, the results were analyzed using the post-processing module. Key output parameters such as thickness distribution, equivalent stress, strain fields, and contact forces were extracted to evaluate forming performance. Visualization of the simulation results was conducted to further assess the forming quality of the BP.

2.4. FEM for Stamping Forming of Bipolar Plate

In the stamping-forming process of BP, stamping speed and friction coefficient are the key parameters that influence the deformation behavior and forming quality. The stamping speed significantly affects the strain rate and the deformation process. A lower speed helps ensure forming stability, while a higher speed can improve efficiency but may lead to tearing. The friction coefficient directly affects material flow and surface quality. A lower friction coefficient facilitates smoother material flow but may cause edge bulging, while a higher friction coefficient restricts material flow and leads to stress concentration. based on the relevant literature [9,15,16,17], the effects of five different stamping speeds (10 mm/s, 50 mm/s, 100 mm/s, 150 mm/s, 200 mm/s) and friction coefficients (0.050, 0.100, 0.185, 0.225, 0.300) on the stress, strain distribution, and thickness distribution of the workpiece.

3. Results and Discussion

3.1. The Influence of Process Parameters on the Forming Quality

Figure 8 and Figure 9, respectively, show the stress, strain, and thickness distribution contour maps, as well as the distribution data of the sheet’s midline at different stamping speeds. The values decrease from red to blue, reflecting the deformation characteristics and quality differences of the material during the forming process. The analysis shows that stamping speed significantly influences the stress distribution and quality during the BP forming process. As the speed increases, the overall stress level rises, while the maximum strain value gradually decreases. However, the strain level in the rib region increases, and the high-strain areas extend toward the corners of the channels. The strain values on the midline of the sheet also increase accordingly. Thickness reduction is primarily concentrated at the corners of the channels, with the minimum thickness showing a trend of first decreasing and then increasing with increasing speed, though the variation range is small. The thickness distribution along the midline gradually decreases as the speed increases.

When the stamping speed is 10 mm/s, stress concentration is mainly distributed at the top and bottom of the channel, showing a localized characteristic. The red area is small, indicating that the load is concentrated at the corner, and the overall stress level is low, with the maximum equivalent stress approximately 632.7 MPa. The high-strain areas are primarily concentrated at the inner and outer corners of the ribs, with a peak value of 7.02%. However, the strain distribution along the midline of the sheet is relatively smooth, with a lower peak value, indicating that the deformation process is stable and the strain is more uniform. Thickness reduction is relatively small, with a maximum thinning rate of 26.6%. At this speed, material flow is slow, and the deformation time is sufficient, which is beneficial for fitting with the die. However, this also leads to significant local plastic deformation accumulation [18].

As the stamping speed increases to 50 mm/s, the high-stress and high-strain regions expand significantly, and the thickness thinning phenomenon becomes more pronounced. When the speed is increased to 100 mm/s, the red high-stress region decreases and symmetry improves, indicating that at moderate speeds, material flowability improves [19]. At this point, the maximum equivalent stress is 647.3 MPa, and the stress distribution along the midline of the sheet becomes more uniform, with the overall stress level being lower, all below 500 MPa. Stress concentration at the channel corners is minimized. Meanwhile, the high-strain region shrinks, and the strain peak decreases to 6.76%. Although the peak of the distribution curve rises slightly, the distribution becomes smoother with no significant abrupt changes. The thickness reduction at the sheet’s corner reaches its maximum value of 26.8%. Overall, as the stamping speed increases, material flowability is significantly enhanced, the strain rate increases accordingly [20], and the material flows more smoothly in the die, avoiding retention in the inner corner areas, which reduces the accumulation of local stress and strain.

However, when the stamping speed exceeds 100 mm/s, the red high-stress region expands extensively to the rib sidewalls and adjacent areas, with significant local stress and strain concentrations, indicating that at high stamping speeds, the material experiences severe local plastic deformation [21]. When the speed increases to 200 mm/s, the deformation rate significantly increases, causing stress concentration to intensify, with the peak stress reaching 649.5 MPa and the stress along the sheet’s midline rising to 642.7 MPa. Due to the reduced material-die contact time, particularly at the corners of the channels, inadequate fit leads to reduced local deformation, and the maximum strain decreases to 6.04%. The material flow is more influenced by inertia, tending to move symmetrically along the center of the die. In the central channel region, due to strong symmetry, the material is “pinched” by the material on both sides, forming a stacking effect, which results in a sharp increase in local strain, causing the strain curve to exhibit sharp fluctuations [22]. At the same time, the shorter flow time worsens the fit [18], and the thickness thinning at the inner corners rebounds, with the maximum value reaching 26.5%. Although the strain value decreases, the overall thickness reduction trend becomes more pronounced, and thinning at the channel corners is particularly severe.

Comprehensive analysis indicates that during the BP forming process, stress, strain concentration, and thickness thinning are mainly concentrated at the inner corners of the flow channels, while the outer corners (as shown in Figure 10, positions 1–5 and 11) have a significantly smaller effect. Among various punching speeds, 100 mm/s provides the best balance of material flow and die conformity, effectively avoiding insufficient flow at low speeds and uneven deformation at high speeds, thereby significantly improving forming quality. At this speed, stress distribution is more uniform, deformation at the corner regions is stable, and both strain and thickness reduction are well controlled, ensuring dimensional accuracy and surface quality of the formed part.

3.2. The Influence of Friction Coefficient on the Forming Quality

As shown in Figure 11, the stress, strain, and thickness distribution contour maps under different friction coefficients indicate that as the friction coefficient increases, the stress concentration in the sheet initially decreases and then increases. Meanwhile, both the maximum strain and maximum thinning rate gradually decrease. However, based on the thickness distribution data along the sheet’s centerline, the overall thickness tends to decrease with the increase in friction coefficient. Changes in the friction coefficient directly affect the relative sliding between the sheet and the die, as well as the material’s flow behavior. Variations in friction significantly influence material flow and thickness distribution [23].

When the friction coefficient is 0.050, the resistance between the material and the die is low, resulting in poor controllability. The material flows too rapidly during the forming process, and due to insufficient contact friction, unstable load transfer occurs. This leads to large areas of red high-stress and strain concentration in the rib fillet and edge regions, with a maximum strain reaching 7.07%, indicating a high risk of instability or cracking [24]. At the channel fillet, thickness thinning is significant, with a maximum thinning rate of 28.3%.

As the friction coefficient increases to 0.100, the areas of high stress and strain slightly decrease. However, noticeable stress peaks still appear in the upper and lower corner regions of the BP and along the midline of the sheet, and the overall strain level remains relatively high (as shown in Figure 12).

When the friction coefficient is 0.185, the stress distribution is significantly improved, with a noticeable reduction in high-stress (red) regions. Most areas exhibit medium to low stress levels. Stress distribution data along the midline of the sheet also indicate that, at a friction coefficient of 0.185, the stress is most evenly distributed, with values below 500 MPa. The strain distribution becomes more uniform as well, with the maximum strain reduced to 6.76%, and only a few isolated points showing high strain. Additionally, the sheet’s thickness distribution is the most consistent, with the maximum thinning reduced to 26.8%, indicating the best forming performance. At this friction level, the material’s flowability and forming stability reach an ideal balance [20]. It avoids excessive thinning in edge areas due to low friction and prevents localized stress and strain concentrations caused by excessive friction.

As the friction coefficient further increases (e.g., to 0.225 and 0.300), the high-stress (red) regions expand again and form continuous zones, particularly at the rib tops and end fillet areas. At this stage, material deformation is hindered, and flowability significantly decreases, resulting in intensified stress concentrations. The stress distribution along the sheet’s midline becomes uneven, with peak stress reaching 647.3 MPa, greatly increasing the risk of defects such as cracks and ridging, which severely affect product quality. High-strain regions also re-expand, with maximum strain rising to 6.90% and 6.81%, especially at the channel fillet areas where strain concentration becomes pronounced. This indicates that excessive friction restricts material flow and causes localized deformation, thereby elevating the risk of forming defects [25]. Due to restricted flowability, the sheet does not deform sufficiently—particularly around fillets—leading to inadequate filling of the die cavity and exacerbating thickness nonuniformity. The overall thickness along the sheet’s midline becomes thinner, with localized thinning becoming more prominent.

Comprehensive analysis shows that during the forming process of the BP, stress, strain concentration, and thickness thinning mainly occur at the inner corner of the channel, where material flow is restricted, resulting in severe deformation. The outer corners experience milder deformation due to lower flow resistance, with smaller changes in thickness (as shown in Figure 13, where 1–5 and 11 represent the outer corners). The comparison of stress, strain, and thickness at the inner and outer corners under different friction coefficients is as follows: When the friction coefficient is 0.185, the material flow and load transfer reach a good balance, with moderate stress, lower strain, and uniform thickness distribution, resulting in the best forming quality [26]. When the friction coefficient is too low (0.05, 0.1), it leads to concentrated stress and strain, and severe thickness thinning. When the friction coefficient is too high (0.225, 0.30), it restricts material flow, causing localized stress and strain concentrations and uneven thickness.

3.3. The Influence of Stamping Method on the Forming Quality

Figure 14 and Figure 15 show the stress, strain, and thickness distribution contour maps under different stamping methods, as well as the distribution along the centerline of the plate after forming.

In single-stage stamping, due to the rapid pressing of the entire sheet into the die cavity in one forming process, the material undergoes intense deformation at the channel corners and complex geometric areas, leading to localized stress and strain concentration. The peak stress reaches 647.3 MPa, and the maximum strain reaches 6.76%. This high stress and strain concentration can easily cause localized material fracture or failure, especially at the complex-shaped microchannel corners. Additionally, the thickness reduction of the sheet after single-stage stamping is relatively severe, mainly concentrated at the inner corner of the channel, with the maximum thinning rate reaching 26.78%. This is because, during the single forming process, the material experiences intense stretching and deformation at the inner corners, causing stress concentration. The material fails to distribute evenly, resulting in significant thinning.

In contrast, the two-stage stamping process, by applying staged loading, makes full use of the material’s flow characteristics in the channel corner region [27]. This allows the material to gradually enter the die cavity, reducing the single deformation amount and overall deformation resistance. At the same time, the use of a die design that closely matches the target geometric profile not only improves the forming depth but also maintains high geometric accuracy.

However, the traditional two-stage stamping process still has certain limitations. Despite optimization of the loading path, the microchannel corner areas still experience significant deformation stress due to the local uneven material flow. In this process, the maximum equivalent stress is 642.7 MPa, which is reduced compared to single-stage stamping, but it still does not reach the ideal level. Step-by-step loading reduces the severe deformation during each forming process to some extent, resulting in a significant reduction in overall strain values, with the maximum strain decreasing to 3.12% [28]. However, due to the lack of precise control over strain distribution, significant strain concentration remains in the microchannel corners and bottom areas. The traditional two-stage stamping process slows down the material deformation rate and improves the overall thickness reduction of the sheet, with the maximum thinning rate reduced to 11.08%. However, stress and strain concentration still exist in the rib areas of the middle channel, and thinning is primarily concentrated in these regions, indicating that material flow and thickness distribution control still need optimization.

To address this issue, the optimized two-stage stamping process introduces a protruding structure in the die design during the pre-forming stage. This structure guides the material through the initial deformation in the microchannel corners and rib areas, promoting uniform distribution of material within the channel and alleviating stress and strain concentration in localized areas [8,29]. As a result, the maximum equivalent stress further decreases to 626.3 MPa, and the maximum strain value is reduced to 3.05%, significantly improving the consistency of material flow. The stress and strain distribution along the sheet midline becomes more uniform, with lower peak values, enhancing the durability of the formed part and reducing the potential risk of failure caused by localized stress and strain concentrations. Although the maximum thinning rate slightly increases to 11.72%, the overall thickness distribution is more uniform, with a smoother thickness distribution in the rib areas. As shown in the thickness distribution along the sheet midline in Figure 14, the optimized two-stage stamping process results in a more uniform thickness distribution, with no significant thinning areas. This indicates that the optimized design effectively guides material flow, improves the overall consistency of the sheet thickness, and significantly mitigates localized thinning.

As shown in Figure 16, the stress, strain, and thickness of the formed sheet at the corner positions were analyzed for different stamping methods (1–5 and 11 represent the outer corners). The results indicate that the traditional two-stage stamping process provides better forming quality compared to the single-stage stamping, and the optimized two-stage stamping process delivers the best results. In single-stage stamping, material flow at the inner corners is obstructed, leading to stress and strain concentration and significant thickness thinning, while deformation at the outer corners is more uniform. The traditional two-stage stamping improves deformation at the inner corners by loading in stages, reducing stress and strain concentration, but significant thinning still occurs. The optimized two-stage stamping process, with refined die design, improves material flow at the inner corner region, reduces stress and strain concentration, and results in more uniform thickness distribution, significantly enhancing the overall forming quality.

In the stamping process of the BP microchannels, elastic recovery during the unloading phase can easily cause deviations in the geometric profile from the target design values, known as springback. This section compares and analyzes the deviation between the actual profile and the design dimensions of the formed part under three different stamping processes (single-stage, two-stage, and optimized two-stage) as shown in Figure 17, and discusses the causes of springback from this perspective. The initial design parameters for the microchannel were a channel depth of 0.3513 mm and a draw angle of 19.50°. In the single-stage forming process, the measured actual channel depth was 0.3210 mm, the draw angle increased to 48.10°, and the overall warpage angle reached 1.41°. This indicates that in the single-stage process, the large deformation occurring in one step led to intense plastic deformation and residual stress release, resulting in significant springback and substantial deviations in forming accuracy [18]. In contrast, the two-stage forming process distributes the deformation over two stages, allowing for more uniform material stress and alleviating local stress concentration. Under this process, the actual depth of the microchannel reached 0.3470 mm, the draw angle was 27.76°, and the warpage angle decreased to 0.84°, improving the forming accuracy. However, because no additional springback compensation strategy was introduced, some level of geometric error still remained. The further optimized two-stage process, based on optimized forming paths and improved die structure, effectively reduced the springback effect [29]. In this approach, the channel depth reached 0.3490 mm, the draw angle decreased to 24.89°, and the warpage angle was only 0.57°, with minimal deviation from the design target, providing the best forming accuracy. These results clearly demonstrate that the optimized two-stage process can more effectively control material springback and improve the dimensional consistency and precision stability of the formed parts.

Due to the lack of experimental conditions and comparable published data, direct experimental validation could not be conducted in this study. Nevertheless, the FEM was developed using established methods, and mesh convergence and sensitivity analyses were carried out to ensure numerical reliability. While the current model has not been experimentally verified, its behavior is consistent with known forming characteristics. Future work will focus on experimental validation, aiming for a model error within 10%.

4. Conclusions

This study systematically investigates the forming behavior and quality of BP microchannels under different stamping speeds, friction coefficients, and stamping methods, and proposes an optimized process scheme. The main conclusions are as follows:

(1)

Process parameters play a critical role in the forming quality of BPs. At a stamping speed of 100 mm/s and a friction coefficient of 0.185, the peak stress and strain are 647.3 MPa and 6.76%, respectively, with a thickness-reduction rate of 26.8%. This enables optimal material flow and die conformity, uniform stress distribution, and effective control of strain and thickness reduction. Proper matching of stamping speed and friction coefficient is key to improving forming quality.

(2)

In terms of stamping methods, the optimized two-stage stamping process outperforms both the single-stage and traditional two-stage processes across multiple indicators. Regarding maximum stress, the optimized process reduces the inner fillet stress from 642.7 MPa (traditional process) to 626.3 MPa; the maximum strain decreases from 3.12% to 3.04%; and the maximum thickness reduction rate significantly drops to 10.2%. Additionally, in terms of forming accuracy, the optimized process achieves a channel depth of 0.349 mm and a channel angle of 24.89°, which are far superior to those obtained with the single-stage and traditional two-stage processes. The warpage angle is minimized to just 0.57°, greatly enhancing dimensional consistency and springback control.