3.1. Tool design: shell thickness optimization
Simulation conditions
To minimize computational cost, the optimum thickness of the outer shell die was determined by performing FE simulations for cup drawing with a simple geometry shown in Fig. 3. The conditions for cup drawing were designed to closely mirror those of UFT forming. The punch and die radii for cup drawing were selected to be similar to the tightest tool radius in the UFT die. Additionally, the 3.4 mm gap between punch and die was maintained. For the initial circular blank, the same 1.539 mm thick HSS 590 sheet was employed. As for the shell and backfill materials, FDM-produced CF-Nylon and concrete were used, respectively. To further save computational cost, a quarter model was utilized for the FE simulations. Three different shell thicknesses were considered for the optimization simulations: 2.5 mm, 5 mm, and 10 mm. Figure 4 shows the simulation model for different shell thicknesses.
The contact condition at the interface between the shell and backfill has uncertainties in terms of friction and bonding. The surface of the CF-Nylon shell, produced by the FDM process, may exhibit irregularities, and the interfacial bonding can become extremely weak due to dry shrinkage and capillary water evaporation during the concrete curing process. Therefore, the simulations need to account for any possible interface condition and select the most suitable shell thickness. Two extreme scenarios were considered for the FE simulations to include all possible friction conditions: 1) smooth contact to simulate no friction or bonding/adhesion between the shell and backfill, and 2) bonded interface to simulate infinite friction or perfect bonding between the shell and backfill. The bonded interface condition was simulated using tie constraints between nodes on the surfaces of shell and backfill that are in contact with each other. With 3 different shell thicknesses and 2 different interface conditions, a total of 6 unique simulation conditions were examined.
Simulation results
FE simulations of cup drawing using the shell and backfill tools showed that the bonding between the shell and backfill at the interface has a significant effect on the tool performance in terms of resultant stress, strain, and plastic deformation. Critical areas in the tools such as the punch and die corner radii as well as the corner radii at the shell and backfill interface were examined for different shell thicknesses and two extreme interface conditions as described previously. Figure 5 shows a comparison of the effective plastic strain (PEEQ) on the CF-Nylon punch shell for all 6 simulation cases. The two interface conditions, namely perfect bonding and no bonding, generated reverse trends in the amount of plastic strain as a function of the shell thickness. Increasing shell thickness led to higher accumulated plastic strain near the punch corner of the CF-Nylon shell in the perfect bonding interface condition. Conversely, in the no bonding case, as the shell thickness increased, the amount of accumulated plastic strain in the CF-Nylon shell decreased. As the interface condition is uncertain, the optimal shell thickness should be chosen based on the lowest accumulated plastic strain in both extreme interface conditions. In this case, 5 mm thickness was found to be optimal. For the 5 mm shell thickness case, the no bonding interface condition was found to have maximum plastic strains of 2–3% in the shell. As forming tools mostly experience compressive loads, the higher value of 2–3% plastic strain is still below failure strain [18].
However, the effect of shell thickness and interface condition on the backfill material should be confirmed before finalizing the optimal shell thickness. Figure 6 shows the effective plastic strain in the concrete punch backfill for the 6 simulation cases. The backfill concrete demonstrated an increase in the accumulated plastic strain as the shell thickness increased in both interface conditions. Unlike the CF-Nylon shell shown in Fig. 5, the concrete backfill exhibited higher plastic strain in the perfect bonding interface case. This is the result of a more effective transfer of load from the shell to the backfill when there is bonding between the two. In the no bonding interface condition, shear load and plastic deformation remains isolated within the shell. In general, some bonding between the two materials is desired so that the shell does not experience very high deformations which may lead to part deviations or tool failure. Considering the resultant plastic strain on both shell and backfill materials under the two interface conditions, 5 mm shell thickness was found to be optimal. However, if there is good bonding between AM material and concrete, the concrete material is likely to develop internal cracks. As the backfill is completely surrounded by the polymer shell, risk of catastrophic failure due to concrete was considered to be low. A similar analysis was performed for the cup drawing die, considering FDM Nylon shell and concrete backfill to obtain the optimized die shell thickness. Shell thickness of 5 mm was again found to be the most suitable.
3.2. Experimental stamping trial
Based on the shell thickness optimization presented in the previous section, tool shells with 5 mm wall thickness were fabricated with CF-Nylon using FDM technique for the UFT forming. A track width of 0.5 mm in the build plane (X-Y) and a layer height of 0.254 mm along the build direction (Z) were used to make all tools. In this case, the punch travel is in Z direction as well. Each layer was printed using a single perimeter pass and filled with an alternating raster orientation of ± 45 degrees from the X axis. Printed tools were then backfilled with concrete and allowed to cure for the specified amount of time. Figure 7 shows the tools before and after the backfilling operation. The original steel toolset for the UFT geometry cost $20,500. The FDM CF-Nylon shell for the punch and die combined cost $7,100 and the concrete backfill cost $10. The CF-Nylon shell and concrete backfill toolset achieved 65% cost reduction compared to the conventional toolset. As the same steel blank holder was used for both toolsets, it was left out of the cost comparison.
Stamping of HSS 590 blanks was performed with a steel blank holder using process parameters described in Section 2.4. A total of 39 parts were stamped with the shell and backfill toolset.
3.3. Numerical analysis of stamping
FE simulations of the stamping of HSS 590 blanks with shell and backfill tooling were performed using the Abaqus/Explicit commercial solver. Relevant simulation conditions and material model details are given in Section 2.3. Figure 8 shows a sectional view of the Abaqus simulation model used for the FE analysis. Boundary conditions for controlling the displacement of punch and die were determined considering the physical attachment points where tools were attached to the press plates during the stamping trials indicated by red circles in Fig. 9 (a). Specifically, displacement boundary conditions, including punch displacement in Z direction and fixed displacements in X and Y directions (\({U}_{X}={U}_{Y}=0\)), were applied to the corresponding elements highlighted in red in Fig. 9 (b). Additionally, similar to the shell thickness optimization simulations in Section 3.1, two interface conditions corresponding to perfect bonding and no bonding were considered to evaluate the effect of the interface between shell and backfill.
3.4. Results
During the experimental stamping trial with shell and backfill tools, 39 parts were formed before stopping due to failure of the tool shell that accumulated over the course of the trial as shown in Fig. 10. Progressively increasing wrinkling was observed in the flange region of the stamped parts, which finally caused die failure at the location of the largest wrinkle due to the penetration of the wrinkle into the polymer die shell as shown in Fig. 11.
Both the punch and die were observed to be bulging outwardly on the outer vertical walls. This indicates insufficient adhesion or bonding between the shell and backfill. Due to the outward bulging, the punch sustained visible damage on the outer walls rubbing against the blank holder during each stamping pass. ATOS 3D scans were conducted to measure the deformation of the tools after the stamping trials. Figure 12 shows a maximum bulging of 1.18 mm on the die wall, while Fig. 13 shows bulging of 1.11 mm to 4.38 mm at different locations on the punch wall. ATOS 3D scans in both figures show the comparison of the deformed tool surfaces (after stamping 39 parts) with respect to the original tool surfaces (before the stamping trial). Here the outward direction from the tool surface is assigned positive sign. In other words, positive values indicate the tool surface has expanded outward compared to the original tool surface.
One of the motivations behind using the shell and backfill die design was to mitigate the issue of the shallow draw as seen with the solid AM polymer tooling [22]. By using a backfill material with a higher elastic modulus, the elastic deformation of the tools is reduced, resulting in stamping deeper parts as intended. Figure 14 shows a cross-section of the formed part after #1 trial using this tooling and a comparison with that of a steel-stamped part as obtained from ATOS 3D scanning. No draw deficit was observed with the new CF-Nylon shell and concrete backfill tooling. However, a small amount of flattening of the stamped part at the die insert nose region is observed as compared to the steel-stamped part due to the deformation of the polymer die at that location.
Final part strains compared between experimental values obtained through ARGUS strain analysis and those from simulation results show good agreement, providing a basic validation of simulation results as shown in Fig. 15. The ARGUS grid pattern was washed out from some regions on the part during stamping where strain measurements could not be obtained. Differences between simulations and experiments are attributed to different averaging methods and averaging areas used between ARGUS and simulations.
Figure 16 shows the deformation of the CF-Nylon die shell walls at the end of the stamping stroke with no bonding interface condition between the shell and backfill. Like the experimental observations, the die shell walls showed outward deformation or bulging. The excessive wrinkling of stamped parts seen in the experimental trials (refer to Fig. 11) is thought to result from the uneven bulging of the shell and the consequent uneven distribution of blank holding force. This claim is supported by simulation results showing non-uniform deformation of the top surface of the die shell in the stamping direction. Figure 17 shows a comparison of die top surface deformation in the Z direction (stamping direction) between the two simulation cases of perfect bonding and no bonding. The perfect bonding case shows negligible deformation of the die surface near the flange area. However, the no bonding case shows highly non-uniform deformation, which could create uneven gaps in between the die and blank holder, resulting in non-uniform blank holder force in different areas of the flange, promoting wrinkling. Actual location and height of wrinkles on the formed part could not be accurately predicted with the simple material model used for the blank, as wrinkling and formability of the formed part were not the focus of this study.
Additionally, the simulation was able to qualitatively predict the deformation of the die insert area, which is the highest-stress area in the tool. Figure 18 shows a comparison of experimental die scan results after 39 stamping and simulation results of the same at the end of the first stamping pass. Accurate quantitative prediction of plastic deformation depends on the material model for AM polymers which should account for various effects such as anisotropy, tension-compression asymmetry, and strain rate sensitivity. Successful qualitative and quantitative prediction of FDM CF-Nylon tool deformation was demonstrated through the use of appropriate material models previously [18]. In the case of shell and backfill die design, the plastic deformation is also dependent on the material model used for the backfill and the unloading behavior of the backfill.
To assess the damage to the concrete backfill, Fig. 19 shows the hydrostatic pressure and effective plastic strain (PEEQ) in the insert region of the die at the end of the stamping simulation. The maximum hydrostatic pressure is 196 MPa, which is more than 7 times the nominal compressive strength of concrete. As mentioned in Section 2.3, when hydrostatic pressure is twice the nominal compression strength, the compressive strength can increase up to four times compared to scenarios without hydrostatic pressure. Additionally, the maximum PEEQ in the concrete backfill of the die was 2.1%, which is well within the safe zone for such high confining pressure.