2024 年 65 巻 2 号 p. 144-151
A hot-stamping method was established for manufacturing high-strength automotive parts with good shape fixability. The hot-stamping method has recently been applied to high-performance parts with tailored properties. CAE is indispensable for the design of such parts. To design hot-stamped parts, the forming simulation must be coupled with thermal analysis to consider the effect of temperature on formability. The final shape does not need to be predicted because of its good fixability. However, for high-performance parts with tailored properties, predicting the effect of phase transformations on the final shape is important. A CAE method that considers the phase transformation effects was developed to predict the final shape of the hot-stamped parts. The accuracy of the final shape calculation utilizing the CAE method is also investigated. Hot-stamping experiments were conducted to obtain parts of different shapes via cooling control, and a CAE analysis of the final shape for each experimental condition was conducted. It was clarified that the final shape varied by changing the cooling process and that the results of CAE, including phase transformation, agreed with the tendency for shape change in the cross-section.
This Paper was Originally Published in Japanese in J. JSTP 63 (2021) 52–57. Figure 8 was slightly modified.
Comparison of prediction results of wall and flange shape changes of real-scale hot-stamped parts under different quenching conditions by phase transformation CAE and conventional CAE results that do not consider phase transformation.
The application of high-strength steel in automotive parts is progressing to achieve weight reduction in car bodies and improve automobile crash safety performance. Most parts are manufactured by press forming, but the difficulty increases with steel sheet strength. As a countermeasure, hot stamping, in which a steel sheet is hot-press-formed, hardened by quenching, and sandwiched between dies for forming, has become widespread. Moreover, for applications of tailored properties in parts, the hot-stamping method is currently utilised to increase strength by quenching and reducing the weight of parts with enhanced functionality.1) This technique is expected to be applied to crash structural parts to cope with the battery protection of battery-powered electric vehicles, which has rapidly become common in recent years, as well as the increase in vehicle weight owing to battery mounting.
To evaluate the application of hot stamping, variations in material properties owing to temperature must be considered, and it is essential to apply CAE coupling between the forming and thermal phenomena.2) However, the final shape accuracy, such as springback prediction after forming, generally performed in the CAE applications of cold stamping, was not calculated for hot stamping. This is because the shape fixability is excellent owing to the absorption effect of the shape difference during high-temperature forming due to transformation plasticity.3) However, when different thermal histories are provided within a part, such as a tailored property part, a shift in the start timing of the transformation and thermal contraction occurs within the part. In this case, because the absorption site of the shape difference due to transformation plasticity and the timing of occurrence differ within the part, stress and strain differences occur within that part, affecting the final shape. For such parts, it is necessary to consider the effects of the phase transformation on the shape evaluation. An analysis method was developed to reflect the phase transformation in hot-stamping analysis. However, this method has been limited to predicting the properties after forming, such as the hardness distribution based on the temperature history, considering the change in the heat transfer state caused by the latent heat of the phase transformation and the volume change attributed to the transformation.4)
Verification was performed with a small-scale model for R50 U-bending tests with specimens of 190 mm in length and 40 mm in width to simulate the reproduction of shape change utilising a CAE method that introduced physical properties reflecting phase transformation.5,6) We developed and applied a method to an actual automotive part scale model with a length of approximately 500 mm to make it easy to evaluate the shape changes that include cross-sectional deformation, longitudinal warping, and twisting deformation. We attempted to confirm the effect of the phase-transformation CAE technique on the final shape prediction of actual parts. We demonstrated its usability by comparing and analysing the results with the part shapes obtained from hot stamping tests.
Figure 1 illustrates the design shape of the part for the forming and cooling tests performed to evaluate the shape change in the hot-stamped part. This part was simulated to reproduce various shape changes caused by the influence of the part shape and temperature distribution by providing an asymmetrical ridgeline in the cross-section and a change in the cross-sectional height in the longitudinal direction. Figure 1 presents the names of the shape evaluation sites obtained in Chapters 3, 4, and 5. A die structure for hot stamping with direct water quenching was adopted as the test die, as illustrated in Fig. 2. On the surface of the die, an uneven shape called a micro-patterned texture (indicated in the upper left of Fig. 2), a cooling water spout nozzle, and a vacuum nozzle (indicated in the upper right of Fig. 2) were processed. This structure maintains water paths between the blank and the tool. The direct water-quenching method achieves a high cooling rate with cooling water paths.7) The micro-patterned texture of the test die had circular contact surfaces of 3-mm diameter arranged at a 4.5-mm pitch, and the depth of the surrounding dent was 0.5 mm. The hole size of the spout and vacuum nozzles was 5 mm, owing to the durability restrictions of the drilling tools. However, as depicted in the cross-sectional view on the upper-right side of Fig. 2, the spout nozzle had a structure that decreased the diameter to 1 mm on the die surface and increased the flow velocity at a low flow rate. However, a vacuum nozzle was utilised to improve drainage without reducing the hole diameter. An overall view of the test die (lower die) is presented in the lower part of Fig. 2. The cooling water system was centralised at the die base and branched into holes on the surface. The upper die can also be cooled with similar structures on the upper and lower sides. The flow velocity of the spout (calculated based on the flow rate and cross-sectional area) was set as 5–6 m/s.
Shape design of trial part.
Schematic of tools for direct water quenching.
Hot stamping with direct water quenching attempts to quench the entire surface of the part. However, in this die structure, the ridgeline R part was not processed to prevent damage from scratching and wear caused by contact and sliding between the edge of the circular part of the micro-patterned texture and the blank during mass production. In addition, structural constraints exist in hole drilling, and there are differences in the path length of the cooling water system; hence, differences in the cooling conditions occur for each site. The difference in the temperature history of each part, caused by the difference in the cooling conditions, affects the shape accuracy.8) By utilising the analysis results, the spout design and vacuum arrangement can be optimised while considering the structural constraints and controlling the part’s final shape through fine adjustments to the cooling conditions in mass production. However, this study applied a cooling condition adjustment to induce shape changes, and parts with different shapes were manufactured.
The material utilised for the test was a 1500-MPa-grade GA-coated steel sheet for hot stamping (22MnB5) with a thickness of 2.6 mm. The blank was a rectangle with a length of 495 mm and a width of 245 mm. The blank was heated to 950°C for 5 min. After forming with a servo-hydraulic press machine, hot stamping was performed by applying a holding force of approximately 3000 kN.
Table 1 summarises the cooling conditions utilised during the holding process. The holding time for die cooling without water quenching was set to two levels: temperature comparison utilising hot stamping with direct water quenching (2 s) and shape evaluation (10 s). Hot stamping with direct water quenching was performed with three systems: upper and lower direct water quenching (in which both the upper and lower dies were spouted), upper direct water quenching (in which only the upper die was spouted), and lower direct water quenching (in which only the lower die was spouted). The spouting was set to start simultaneously with the bottom dead centre. The holding and spouting times were both set to 2 s.
Figure 3 illustrates the application of the phase-transformation CAE. Conventional hot-stamping CAE analyses the deformation of super-cooled austenite by coupling the temperature-dependent stress–strain relationship with the temperature variation based on heat transfer calculations. Although conventional hot-stamping CAE can perform formability evaluations, they cannot address the influence of subsequent transformations. Although there are reports on hardness predictions that reflect phase transformations,4) basic studies on final shape prediction are scarce.
Outline of phase transformation CAE.
Therefore, based on the original data, such as the phase transformation properties of hot-stamped materials, we developed a material model as a subroutine in LS-DYNA, a general-purpose solver. This model comprises the structural material property, “umat”, which simulates deformation behaviour induced by transformation strain and transformation plasticity, and a thermal material property, “thumat”, which simulates heat generation and physical property changes caused by transformation.
Detailed calculations of the deformation behaviour accompanied by phase transformation during the cooling process (transport, forming, and cooling) of hot stamping after blank heating were made possible. Transformation behaviour calculations in a single element utilising this method and shape changes attributed to the presence or absence of the phase transformation of simple-shaped parts have already been evaluated and verified.5,6) We attempted to apply it to shape change during phase transformation, such as general hot stamped materials, which have not yet been verified.
Figure 4 presents an overview of the analysis model and calculation procedure. The analysis model was a half-part model in the longitudinal direction, with the centre of the plane view presented in Fig. 1 as the plane of symmetry. The employed element was a four-node-thick shell element considering the temperature differences in the sheet-thickness direction. The element size of the tool varied according to the shape of the designed surface. The heat capacity of the tool was set to ten times the blank sheet thickness (empirical value) to reproduce the heat transfer state. The stress–strain characteristics of each phase of the test material (22MnB5) at each temperature were utilised to determine the material deformation characteristics. The transformation characteristics were calculated with the structural material property, “umat”, and the thermal material property, “thumat”. The MS point of the test material was approximately 400°C. For the cooling properties and expansion/contraction behaviour, the data verified in the aforementioned single-element evaluation were utilised. This confirms the consistency between the experiment and the analysis in the above evaluation and verification. Data that considered temperature dependence were applied regarding Young’s modulus, specific heat, and thermal conductivity.
FEM model and calculation step for hot stamping.
The calculation process was divided into four steps: Step 1/forming, Step 2/cooling inside the die, Step 3/air cooling after removal from the tools and Step 4/springback. A general-purpose solver, LS-DYNA, was utilised for the calculations, and the phase-transformation material model was applied to determine Steps 1–3.
In Step 1/forming, based on the experiment, after going through 15.5 blank air-cooling calculations from 900°C after heating to 700°C on the commencement of forming, forming calculations were performed at a simulated speed of 22 times the forming speed of 40 mm/s. After forming, information regarding temperature distribution, sheet thickness distribution, and phase transformation fractions was transmitted to the stress and strain states. Step 2/cooling analysis was performed. In Step 2, the boundary conditions for the heat transfer were set based on the cooling conditions, and cooling calculations were performed to simulate each pattern of die cooling and direct water quenching. The holding time was set to 10 s for die cooling and 2 s for direct water quenching, according to the test. (However, for the direct water-quenching test, a holding equivalent time of approximately 3 s after stopping the spouting was included because of the operational delay of the press machine. Thus, with this added time, the calculations were performed at 5 s.) Utilising the results of the formed part, except for the tools in Step 2, Step 3/air cooling after removal from tool analysis was performed. Step 3 was aimed only at the formed product, and coupled calculations of the deformation and thermal phenomena were performed for 600 s from the time of removal from the tools until 30°C was reached. During Step 3 calculations, no displacement restraint by the die was observed; hence, elastic vibration occurred owing to springback and thermal contraction. Therefore, Step 4/springback analysis (implicit method) was performed to eliminate the effects of elastic vibration and obtain the final shape.
In addition, because the temperature history directly influences the phase transformation behaviour, the temperature distribution must be simulated more precisely than in the conventional CAE. In conventional forming CAE, the heat transfer coefficient between the die and blank is set by considering, for example, the effect of contact pressure. This setting, common in simulating the material strength distribution and predicting the formability by reproducing the heat transfer intensity, was utilised to calculate the contact heat transfer in Steps 1 and 2. For the shape change evaluated here, reproducing the transformation timing of each part in Step 2/cooling was critical. Therefore, as illustrated in Fig. 5, the temperature history was tuned by superimposing the boundary conditions for heat transfer (Hc3, 4, 5, and 6) for each die site, considering the effect of the cooling water in direct water quenching on the boundary condition region for heat transfer (Hc1 and 2) between the die and blank in Step 1/forming. Based on the test results, the heat transfer coefficient was set to 500–2500 W/m2 K for the die cooling part and 2000–10000 W/m2 K for the direct water quenching part. In Fig. 5, W indicates the site affected by water cooling, and C indicates the site affected by contact heat transfer. Most sites were affected by both, and the ridgelines without a micro-patterned texture (Hc4, 5) were only affected by contact. An increased number of boundary condition sections effectively reproduced the complex temperature distributions. However, to avoid an increase in the number of cases for condition tunings, it was empirically limited to six sections to reproduce the temperature history difference between the ridge line and flat parts, which are considered to have a strong relationship with the longitudinal warp and wall slope. Precise heat transfer settings are crucial for reproducing temperature histories with material models. However, the problem is that the number of settings for the heat transfer conditions becomes massive, complicating model creation and increasing computational time.
Definition of heat transfer condition (Hc) for Step 2.
Figure 6 presents the temperature distribution of the part surface immediately after the hot-stamping tools were removed. The thermal images were captured from the front in the longitudinal direction. During die cooling, under the same holding time of 2 s as the direct water quenching condition, a high-temperature part remained at approximately 500°C. Even at a holding time of 10 s, a high-temperature part of approximately 300°C remained when the entire part was quenched. However, all the conditions for the direct water-quenching application had a holding time of 2 s and a lower temperature than the condition of a holding time of 10 s for die cooling, and the effect of shortening the cooling time was observed. A thorough examination revealed that the upper and lower direct water-quenching regions exhibited the broadest low-temperature regions. Many regions had flanges at approximately 50°C and the wall and top surface at approximately 100°C. A high-temperature part at approximately 300°C remained in parts where micro-patterned texture and spout nozzle could not be processed, such as around the blank support. For upper direct water quenching, the flange portion temperature was lower than 100°C, and the region of approximately 200°C around the top surface expanded. For the lower direct water quenching, the flange portion temperature became lower than 100°C, and the temperature of the top surface ridgeline portion became at least 250°C. A difference in the temperature distribution between the upper and lower direct water quenching and a decrease in the temperature change width due to the upper and lower direct water quenching (homogenisation) were observed. The results satisfy the purpose of determining the temperature history difference obtained with cooling methods.
Temperature distribution of parts after hot stamping.
Figure 7 presents the shape-measurement results for the parts, each with a different temperature history obtained from the test. A noncontact three-dimensional laser scanner was utilised to measure the shape of the front surface. The deviation from the design surface in the normal direction was presented as a contour. The measured shape data best fit the flat part at the centre of the top surface of the design surface. Figure 7 presents the top view of this section. The positive side indicates displacement in the opening direction toward the outside of the surface design. In contrast, the negative side indicates displacement in the direction close to the inside of the surface design.
Final shape of trial parts.
During die cooling and upper and lower direct water quenching near the longitudinal centre of the part, the top surface and flange were close to the flat design surface. Displacement occurred in the positive direction toward both longitudinal ends of the top surface, and irregular positive and negative direction displacements were observed at the four corners of the flange. However, under these two conditions, the deviation from the design surface was within ±0.5 mm, which is generally regarded as a level for a good shape. In contrast, a significant change in shape was observed under single-sided direct water-quenching conditions. For the upper direct water quenching, the displacements toward both longitudinal ends of the top surface were smaller than those for die cooling and upper and lower direct water quenching. However, a positive slope toward the outside in the part-width direction was observed along the entire flange length. Positive warping toward both longitudinal ends of the top surface and a negative slope toward the outside in the part-width direction across the entire flange length were observed for lower direct water quenching.
The boundary conditions for heat transfer were defined via several trial calculations to simulate the difference in temperature distribution utilising the cooling methods. The temperature distributions corresponding to tool removal times under 10 s die cooling and 2 s direct water quenching were determined. Figure 8 illustrates the obtained temperature distributions. The images were displayed symmetrically around the centre in the longitudinal direction, and the display directions were aligned such that the angle of view was the same as that of the test images. In addition, the average temperature in the longitudinal direction at each site was plotted together with the test results. The CAE results revealed that the width of the temperature fluctuation between the sites was significantly smaller than that of the test results. However, the characteristics of the temperature distribution of the high-temperature site of the top surface during die cooling, cooling speed in upper and lower direct water quenching, high-temperature site from the top surface to the die shoulder ridgeline in upper direct water quenching, and high-temperature site on the top surface ridgeline in lower direct water quenching confirmed in the experiments were also confirmed in the CAE results. Hence, the shape computations were evaluated with the computational results.
Calculated results of temperature distribution.
Figure 9 presents the shape calculation results when air cooling was completed from the temperature distribution after removing the tools to 30°C. Figure 9 illustrates a contour representation of the deviation in the part-height direction of the shape after air cooling with respect to the shape at the bottom dead centre (which matches the design surface). The displacement direction was defined in the same manner as that utilised in the test, and the colour gradation was fit to the test results. The heat transfer conditions for die cooling were consistent with those of the design surface. The flange was slightly displaced upward under the heat transfer conditions of upper and lower direct water quenching. Under the heat transfer condition of upper direct water quenching, the flange slanted to the positive side in the outside width direction. Under the heat-transfer condition of lower direct water quenching, the flange slanted toward the negative side.
Calculated results of shape of parts.
In contrast, no significant warping occurred at either longitudinal end of the top surface under any condition. Regarding the computational time, Steps 1 and 2 were similar to the conventional analysis that did not consider phase transformation; however, Step 3 was approximately ten times longer. This was due to the accumulation of phase-transformation computational time during air cooling. The increments in the phase transformation computations need to be improved depending on the temperature range when performing computations with larger parts.
A longitudinal warp was not observed in the CAE because, from the CAE case example of simulating the warp caused by the temperature difference between the top surface and wall, which is the distance from the neutral plane of the cross-section of the essential hat-shaped parts,8) it is presumed that the temperature difference at each cross-sectional part is insufficiently reproduced. Moreover, a more precise setting of the heat transfer setting is necessary. Regarding the flange behaviour, for which the same trend as the deformation was obtained experimentally, no apparent cause of occurrence could be revealed until now, and this was an issue when applying hot stamping with direct water quenching. A detailed calculation result analysis, in which the shape tendencies are consistent, will help identify the effect of the cooling design on the shape characteristics and deformation starting points and apply efficient shape countermeasures. Therefore, to confirm the flange surface slope and associated deformation of the wall, we extracted the cross-sectional shape of the longitudinal centre of the part and compared the shapes of the flange and wall for each cooling method.
Figure 10 presents a comparison of the test shapes. The position of the cross-section was aligned with the cross-sectional design at the centre of the flat part of the top surface (X = 0 mm), and the shapes of the flange and wall on the left side were compared. The flange was consistent with the cross-sectional design in die cooling and became almost parallel to the cross-sectional design in upper and lower direct water quenching. A clear upward warp slope was observed for the upper direct water quenching, and a downward warp was observed for the lower direct water quenching. The wall was consistent with springback in the upper direct water quenching and the cross-sectional design in the upper and lower direct water quenching. A spring-go tendency was observed during die cooling and lower direct-water quenching. No wall warp was observed, which was assumed to be a deformation at the origin of the punch shoulder ridge line.
Change in shape by methods of quench in tools.
Similarly, Fig. 11 presents the cross-sectional shapes obtained with CAE. Although the deformation direction of the flange portion is consistent with that of the test, the slope is smaller than that of the test, and the height of the flange origin is different from that of the test. In contrast, wall deformation demonstrated a slight spring-go tendency under the upper and lower direct water-quenching conditions. However, almost the same state as that in the test results was reproduced.
Change in shape with thermal conditions by FEM.
Variations in the slope angles of the wall and flange on both sides of the cross-section with respect to the design cross-section were obtained to quantify the shape (Fig. 12). Figure 12(a) and (b) present the results for the walls and flanges, respectively. This angle is considered positive in the cross-sectional opening direction. In addition to the above test and CAE results, conventional CAE results obtained under upper and lower direct water-quenching conditions are presented for comparison of the computational methods.
Shape accuracy under each condition, evaluated by CAE.
For the test results (○ in Fig. 12), variations in the angle of a slightly negative side with the die cooling, slightly positive side with the upper and lower direct water quenching, clear positive side of approximately 0.7° with the upper direct water quenching and clear negative side of approximately 0.7° with the lower direct water quenching were observed for the wall. For the flange, the angle variations for die cooling and the upper and lower direct water quenching were the same as those for the wall. However, it was 1.2° on the positive side with upper direct water quenching and 1–1.2° on the negative side with lower direct water quenching, which was larger than the angle of the wall. Thus, the angle of the die shoulder ridge line changes depending on the cooling conditions, thereby influencing the flange slope angle. In addition, the difference between Parts A and B was slight, and no significant effect of the asymmetrical shape was observed.
Next, for the CAE results (△ in Fig. 12), the direction and magnitude relationship of the angle variation owing to the cooling method was reproduced. However, the angle values in the CAE results differ from those in the test results. For the wall, they were in good agreement with the die-cooling case. However, for the other conditions, they were approximately 0.2° smaller than the absolute value. For the flange, they were approximately 0.2° smaller in absolute value for die cooling and upper and lower direct water quenching and became almost zero. The upper and lower direct water quenching was approximately 0.7° smaller than the absolute value and almost the same as that of the wall. In addition, the effect of asymmetry, which was only slightly observed in the test, was barely observed in the CAE model.
As the conventional CAE neglects phase transformation (◇ in Fig. 12), it was impossible to replicate the state with slight angle variations in the upper and lower direct water quenching. The results indicate that applying CAE with phase transformation effectively calculates the shape change, which has been challenging to reproduce.
Although an angle mismatch was observed because of the heat transfer condition, part of the deformation trend could be reproduced by applying phase-transformation CAE, and additional influencing factors were evaluated. The stress distribution in the sheet-thickness direction, such as in the ridge line R, is presumed to influence the slopes of the wall and flange. Therefore, we extracted the data of the shell elements of the punch shoulder R, die shoulder R, and intermediate wall parts of the shape comparison cross-section of the CAE results. We also examined how the maximum principal stress of the sheet thickness direction integration points (seven points) changed during hot stamping. For example, Fig. 13 illustrates the variation in the stress of the die shoulder R during the upper direct water quenching. Based on the low-stress state after forming, the stress increased with cooling inside the die; however, it was released with the martensitic transformation. Subsequently, the stress increased again inside the die after its removal from the tools and was released during air cooling. However, because the stress in the sheet thickness direction upon removal from the tools was unevenly distributed, an out-of-plane bending moment was generated during the release, and the shape changed from the die to the final shape.
Stress history through hot stamping by CAE [Sample at die shoulder in upper direct water quenching].
The difference in the shape trend caused by the cooling conditions was attributed to the difference in the bending moment before and after the removal from the tools. Figure 14 illustrates the variations in the bending moment before and after removal from the tools, in which the stress at the integration points in the sheet thickness direction was converted based on the thickness centre. The positive and negative moments were aligned with the change in the angle direction described above. They were expressed as numerical values per meter in the longitudinal direction of the part. Under the die cooling condition, the values in each part were low and slightly negative in the punch shoulder R part, indicating the influence of the shape on the test and calculation. In the calculations of the hot stamping under direct water quenching conditions, both moments were approximately −30 N·m in the die shoulder R part. However, the correlation between the shape tendency of the test and the calculation could not be explained, except for lower direct water quenching. For the punch shoulder R and wall parts, the positive moment of the punch shoulder R part was slightly larger than the negative moment of the wall for the upper and lower direct water quenching. The positive moments at both sites were significant for the upper direct water quenching. For lower direct water quenching, the negative moment of the wall was larger than the positive moment of the punch shoulder. This result may explain the shapes of the tests and calculations.
Estimated bending moment of elements at shoulder portion and wall under each condition.
This study demonstrated that each site’s transformation, release, and subsequent thermal contraction history affect the final shape. The reason for the significant value of the moment of the die shoulder R, in the calculation of direct water quenching is that the flange temperature was higher than that in the test, and the thermal history simulation was insufficient. In addition, we evaluated only a few elements in the calculation model. However, further extensive analysis of the results is required to reproduce the shape in more detail.
The shape change of the hot-stamped part was studied by varying the cooling method, and an attempt was made to reproduce these shape changes after hot stamping utilising a forming-phase transformation-coupled CAE. The following conclusions were obtained based on the experimental and numerical studies.
As described above, the effectiveness of phase-transformation CAE has been demonstrated, although problems exist with temperature simulations for accurate shape prediction.
