# Spring-Back Characteristics on Bent Holed Parts in V-Die Bending Process

Authors: Sutasn Thipprakmas; Arkarapon Sontamino
Journal: Advances in Materials Science and Engineering
 (2022)

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## Abstract

In recent years, the bending of holed blank to fabricate the bent holed parts has been increasingly applied in almost all industrial fields and they also need much more complexity in shaped part and precision in dimensions. However, most of past research studies were carried out on bent nonholed parts. This causes an insufficient database and information for die design to fabricate bent holed parts. In the present research, to achieve a good design of V-bending die for fabrication of these bent holed parts, the bending mechanism and spring-back characteristic were clearly clarified based on experimental works. By making hole, it usually caused the decreases in generated bending characteristic on bending allowance zone as the hole located at center as well as the decreases in the generated reversed bending characteristics on next to bending allowance zone as the hole located next to bending allowance zone. The hole also caused the increases in additional elastic zone on hole especially for hole located at center due to the hole distortion during bending process. The effects of hole diameter were also investigated. The results elucidated that the larger hole diameter applied, the larger amount of spring-back obtained. Therefore, to achieve a good design of V-bending die for fabrication of V-bent parts of holed blank, the hole position and diameter should be carefully considered.


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## Body

## 1. Introduction

In recent years, bent sheet-metal parts have been increasingly applied in almost all industrial fields, such as the automotive, aerospace, electronics, and housewares industries. These parts also need much more complexity in shaped part and precision in dimensions. This results in growing much more severe competition in sheet-metal bent part industries. The manufacturers take actions for surviving by designing a good bending die for achieving precise bent shaped parts with getting rid of secondary operations to reduce the production cost- and time-consuming and to increase the productivity. In addition, the researchers take actions by doing much more researches for deep understanding of bending mechanism and controlling the precision on bent parts with various bending process, including L-, V-, U-, and Z-bending processes, by using finite element method (FEM), artificial neural networks (ANNs), and experimental works [1–21]. Many researches were carried out to achieve the accuracy of spring-back prediction. Gautam et al. [1] proposed the analytical prediction of spring-back in bending of tailor-welded blanks incorporating effect of anisotropy and weld zone properties. Ao et al. [2] studied the effects of electropulsing on spring-back during V-bending of Ti-6Al-4V titanium alloy sheet. Lawanwong et al. [3] proposed the double-action bending technique for eliminating spring-back in hat-shaped bending of advanced high-strength steel sheet. Etemadi et al. [4], using experimental works, investigated the spring-back phenomenon through an L-die bending process for multilayered sheets produced by the accumulative press bonding technique. Many researches were also carried out by using the FEM technique or experimental works to investigate the effects of material properties and bending process parameters including tool shape and bending temperature on the spring-back characteristics with high-strength low-alloy (HSLA) sheets [3, 5], aluminum alloy sheets [9–11], and copper alloy sheets [13]. However, most of these past researches were carried out for bent nonholed parts. It was vice versa due to the fact that bent holed parts have become increasingly critical in many industrial fields. Basically, as per the basic bending theory and literature [22, 23], the hole located on the bend radius effects on spring-back characteristics as well as the hole distortion is formed. There are few researches, in recent years, to study the bending process on bent holed parts. Nasrollahi and Arezoo [23] used the FEM code and neural network technique to predict the spring-back characteristics in sheet-metal components with various hole types. Circular holes have the most spring-back, followed by oblong and square holes. Its results showed the manner of spring-back characteristics for bent holed parts on the L-bending process, which agreed with the theory behind the basic bending process [23]. However, in the past researches, only the hole located on bend radius was investigated and its effects on spring-back characteristics were reported as well as it was performed only in the wiping-die bending process. In terms of hole positions and dimensions, there are not any researches performed to clearly clarify the spring-back characteristics with respect to various hole positions and dimensions on spring-back characteristics. In addition, the research on bending of holed sheet using other bending processes is still lacked (i.e., V-bending process). Therefore, based on the past researches, there is insufficient database and information for die design to fabricate bent holed parts. On the basis of V-bending process advantages in which the complex curvature shape with the low production cost could be achieved, in this present research, the V-bending process is focused on. Therefore, in the present research, the effects of hole positions and dimensions on spring-back characteristics in V-die bending process were investigated. In addition, the bending mechanism and spring-back characteristics were also clearly investigated. They were investigated by experimental works. In the present research, the results clearly characterized the bending mechanism of holed blank. The results showed the effects of hole located on bend radius zone on the spring-back characteristics, which agreed well with the bending theory. However, the results have stood out against the theory behind the basic bending process [22]. Specifically, interesting results were revealed such that the hole located next to bend radius zone affected on the spring-back characteristics. In addition, it was again revealed that, comparing with the bent nonholed parts, the hole located on bend radius zone and the hole located next to bend radius zone increased in the spring-back characteristics. However, the increases in spring-back characteristic in the case of the hole located on bend radius zone were larger than those located next to bend radius zone. In contrast, the hole located on leg zone had no any effects on the spring-back characteristic. The effects of hole diameters on the spring-back characteristics were also investigated in the present research. Therefore, to achieve the precise bend angle, the hole positions and diameters should be strictly considered for the fabrication of the bent holed parts.


## 2. The Experimental Procedures

In the present research, the investigated V-die bending model in this present research was illustrated in Figure1. The investigated bend angles were 60° and 120°. The punch radius of 14.5 mm and die radius of 5 mm were applied. The workpiece material used was aluminum 1100 alloy (AA1100-O, JIS) with the material thickness of 3 mm. The initial workpiece with dimensions of 30 mm in width and 200 mm in length was used as illustrated in Figure 2. In addition, the workpiece with and without hole were investigated as shown in Figure 2. To prepare the hole, in the present research, the drilling process was applied for making circular hole shape. The drilling process might induce high residual stress, which possibly caused sheet bending. Therefore, after drilling process, all drilled blanks were again examined for blank flatness. The holed blank showed the somewhat same level of holed blank flatness as that of nonholed blank flatness. Therefore, the effects of drilling process of the amount of spring-back in bent holed parts in V-die bending process in the present research could be ignored. The three positions of holes were located on workpiece including at bend radius zone (bending allowance zone), next to bend radius zone, and at leg zone as shown in Figure 2. The details of these hole positions were listed in Table 1. The three levels of 5 mm, 8 mm, and 11 mm in diameter of circular hole were investigated as also listed in Table 1. The experimental works were performed by using the 5-ton universal testing machine (Lloyd Instruments Ltd.) as the press machine, as shown in Figure 3(a). The set of V-bending dies and workpieces were shown in Figures 3(b) and 3(c), respectively. In the present research, as per the past researches [14–16], five samples from each bending condition were used to inspect the obtained bend angles. The bend angle after unloading was measured using a profile projector (Mitutoyo Model PJ-A3000). The amount of spring-back was calculated based on these obtained bend angles and the average spring-back values with the standard deviation (SD) were reported.Figure 1
V-die bending model.Figure 2
Illustration of hole positions on blank sheet. (a) Without hole. (b) Hole at bend radius zone. (c) Hole at next to bend radius zone. (d) Hole at leg zone.
(a)(b)(c)(d)Table 1
Experimental conditions.
Workpiece material (AA1100-O)Tensile strength (ϭu): 92.50 MPaElongation (δ): 43.5%Young’s modulus (E): 68900 MPaPoisson’s ratio (ν): 0.33Flow curve equationσ¯=153.5ε¯0.20+88Workpiece geometryWorkpiece thickness: 3 mmWorkpiece length: 200 mmWorkpiece width: 30 mmBending dieBend angle60°, 120°Punch radius14.5 mmDie radius5 mmHole diameter5, 8, 11 mmDrilling distance ABend angle 60°35 mmBend angle 120°25 mmDrilling distance BBend angle 60°85 mmBend angle 120°85 mmFigure 3
Machine, die set, and workpiece for experiments. (a) Press machine. (b) Die set. (c) Workpiece.
(a)(b)(c)


## 3. Results and Discussion

### 3.1. Comparison of Spring-Back Characteristics on Bent Nonholed Parts and Bent Holed Parts

The spring-back characteristics on bent nonholed parts and bent holed parts were illustrated in Figure4. In the case of bent nonholed parts, the results illustrated that the spring-back characteristics were generated in the bending condition of 60° and 120° bend angles as shown in Figure 4(a). In this case, the amounts of spring-back approximately of −0.67° and −2.25° were generated in the cases of 60° and 120° bend angles. This manner of spring-back characteristic corresponded well with the bending theory and the literature [14–16, 22]. Next, in terms of bent holed parts, the results showed the changes in spring-back characteristics compared with that in the case of bent nonholed parts, as shown in Figure 4(b)–4(d). By comparing with the spring-back characteristics in the case of bent nonholed parts, the spring-back characteristic increased when the hole was located at bend radius zone as shown in Figure 4(b). In this case, the amounts of spring-back approximately of 0.33° and −0.17° were generated in the cases of 60° and 120° bend angles. Next, in the case of hole located next to bend radius zone as shown in Figure 4(c), the results showed the increases in spring-back characteristic. In this case, the amounts of spring-back approximately of −0.42° and −1.75° were generated in the cases of 60° and 120° bend angles. It was also observed that the increase in spring-back characteristic generated in the case of hole located at bend radius zone was higher than that in the case of hole located next to bend radius zone. In contrast, in the case of hole located at leg zone as shown in Figure 4(d), the results showed the same level of spring-back characteristics as that in the case of bent nonholed parts. In this case, the amounts of spring-back approximately of −0.75° and −2.17° were generated in the cases of 60° and 120° bend angles. These results revealed that not only the hole located at bend radius zone where the bending allowance zone was generated affected the spring-back characteristics, but the hole located next to bend radius zone where the workpiece was not bent also affected the spring-back characteristics. These interesting results revealed that they stood out against the past bending theory that only the bending allowance zone affected on the spring-back characteristics [22].Figure 4
Comparison of bent parts and spring-back characteristic between bent parts with and without hole (hole diameter: 5 mm). (a) Without hole. (b) Hole at bend radius zone. (c) Hole at next to bend radius zone. (d) Hole at leg zone.
(a)(b)(c)(d)


### 3.2. Effects of Hole Positions of Bent Parts on the Spring-Back Characteristics and the Bending Mechanisms

#### 3.2.1. Hole Located at Bend Radius Zone

Figure5 shows the deformation of hole after bending process in the case of hole located at bend radius zone. The experimental results clearly showed that the plastic deformation of hole was generated as shown in Figure 5(a). Specifically, the circular hole was formed to be the elliptical or oval shape. The experimental results also showed that this deformation in bend radius zone was different in each side of workpiece. On the inner radius side, as per the bending theory [22], the compressive stress was generated on this side. Therefore, as shown in Figure 5(a)-2, the circular hole was compressed on the x-axis and then the elliptical shape was deformed by the major axis along with the width of workpiece (y-axis direction) and the minor axis along with the length of workpiece (x-axis direction). Vice versa, on the outer radius side, again as per the bending theory [22], the tensile stress was generated on this side. Therefore, as shown in Figure 5(a)-3, the circular hole was tensioned on the x-axis and then the elliptical shape was deformed by the major axis along with the length of workpiece (x-axis direction) and the minor axis along with the width of workpiece (y-axis direction). Based on these deformed elliptical shape characteristics, the plastic deformation of stress distribution especially on the deformed hole could be analyzed as depicted in Figure 5(b). On the inner radius side as depicted in Figure 5(b)-2, owing to the compressive stress generated during bending process, the compressive stress was generated on circular hole on the x-axis direction as well. This caused the deformed hole of circular shape to be elliptical shape and the compressive stress was generated on each endpoint of the minor axis or a co-vertex of the ellipse. Vice versa, based on the deformed elliptical shape, the tensile stress was generated on each endpoint of the major axis or a vertex of the ellipse. On the basis of this stress distribution analysis, along the perimeter of elliptical shape, the compressive stress generated on each endpoint of minor axis was decreased and changed to the tensile stress. This tensile stress increased and reached the maximum on each endpoint of the major axis. Therefore, the four elastic zones were formed on the elliptical shape as depicted in Figure 5(b)-2. Next, as the same manner of inner radius side, these plastic deformation and stress distribution analyses were also generated on outer radius side as depicted in Figure 5(b)-3. Specifically, owing to the tensile stress generated during bending process, the tensile stress was generated on circular hole on the x-axis direction as well. This caused the deformed hole of circular shape to be elliptical shape and the tensile stress was generated on each endpoint of the major axis or a vertex of the ellipse. Vice versa, based on the deformed elliptical shape, the compressive stress was generated on each endpoint of the minor axis or a co-vertex of the ellipse. On the basis of this stress distribution analysis, again the tensile stress generated on each endpoint of major axis was decreased along the perimeter of elliptical shape and changed to the compressive stress. This compressive stress increased and reached the maximum on each endpoint of the minor axis. Therefore, the four elastic zones were formed on the elliptical shape as depicted in Figure 5(b)-3. As these stress distribution analyses on deformed hole during bending process, it was found that the four elastic zones were generated on each bend radius side (i.e., inner and outer radius sides). By making hole, the bending allowance was decreased and resulted in the decreases in spring-back characteristics. However, the new eight elastic zones were generated on hole during bending process and resulted in the increases in spring-back characteristics. Therefore, after unloading, the amount of spring-back generated in the case of bent holed parts was larger than that in the case of bent nonholed parts.Figure 5
Illustration of plastic deformation and stress analysis on hole in the case of hole located at bend radius zone (hole diameter: 5 mm, bend angle: 60°). (a) Experiment. (b) Analysis.


#### 3.2.2. Hole Located next to Bend Radius Zone

Figure6 shows the deformation of hole after bending process in the case of hole located next to bend radius zone. The experimental results showed the deformation of hole as shown in Figure 6(a). The results showed that the circular hole rarely deformed on each side of inner radius and outer radius. These deformations could be explained as per the past researches [14–16, 22], [24]. Although the reversed bending characteristics were generated next to bend radius zone and caused the spring-forward or spring-go characteristics, these reversed bending characteristics rarely affected the deformation of circular hole and rarely caused the distortion of it. Therefore, there rarely were any stress distributions generated on circular hole due to the hole deformation on each side of inner radius and outer radius as depicted in Figures 6(b)-2 and 6(b)-3. After unloading, the effects of hole only resulting in the decreases in the reversed bending characteristics as well as in the spring-go characteristics were clearly illustrated. After compensating these spring-back characteristics generated on the bend radius zone and spring-go characteristics generated next to bend radius zone, by comparing with the case of nonholed blank, the amount of spring-back of the bent holed parts was increased.Figure 6
Illustration of plastic deformation and stress analysis on hole in the case of hole located next to bend radius zone (hole diameter: 5 mm, bend angle: 60°). (a) Experiment. (b) Analysis.


#### 3.2.3. Hole Located at Leg Zone

Figure7 shows the deformation of hole after bending process in the case of hole located at leg zone. The experimental results showed the deformation of hole as shown in Figure 7(a). The results showed that the circular hole did not deform on each side of inner radius and outer radius. These deformations could be explained that, as per the bending theory and past researches [14–16, 22, 24], there were not any bending characteristics generated on leg zone. Absolutely, there were not any stress distributions generated on circular hole on each side of inner radius and outer radius as well as there was not any hole formation as depicted in Figure 6(b)-2 and 6(b)-3. After unloading, there were not any effects of hole on the bending characteristics generated at bend radius zone and the reversed bending characteristics generated at next to bend radius zone. Therefore, there were not any effects on in the spring-back and spring-go characteristics on the bent holed parts. Therefore, after unloading by comparing with the case of bent nonholed parts, the amount of spring-back of the bent holed parts was the same level.Figure 7
Illustration of plastic deformation and stress analysis on hole in the case of hole located at leg zone (hole diameter: 5 mm, bend angle: 60°). (a) Experiment. (b) Analysis.As these results shown, although only three cases of hole position including at center, at next to bend radius, and at leg zones were examined, the effects of hole position on the amount of spring-back were clearly shown. Specifically, in the case of hole positioned at center zone, the amount of spring-back generated in the case of bent holed parts was larger than that in the case of bent nonholed parts. In the case of hole positioned at leg zone, there completely were not any effects of hole on the amount of spring-back. The amount of spring-back of the bent holed parts was the same level by comparing with the case of bent nonholed parts. In the case of at next to bend radius zone, by comparing with the case of nonholed blank, the amount of spring-back of the bent holed parts was increased. However, the bend radius zone directly depended on the bending conditions including bend angle and bend radius. The distance from center of blank (A) in this case was sensitively depended on these bending conditions. Therefore, this distance should be carefully aware based on the bending condition applied. Based on these results, they were useful for the industrial applications to design suitable V-bending die related to the spring-back characteristics for bent holed parts in V-die bending process.


### 3.3. Effects of Hole Diameters on the Spring-Back Characteristics

Figure8 shows the effects of hole diameters on the spring-back characteristics with respect to hole positions. First, as the horizontal lines shown, the bend angles were approximately of 60° and 120° in the case of bending angles of 60° and 120°, respectively. In the case of hole located at bend radius zone, as shown in Figure 8(a), the results showed that the amount of spring-back increased as the hole diameter increased in the cases of bending angle of 60° and 120°. As aforementioned stress distribution analysis on hole during bending process, the four elastic zones were generated on each side of inner radius and outer radius. Furthermore, these elastic zones were enlarged as the hole diameter increased due to the increases in the major axis and minor axis of ellipse. Therefore, although the bending allowance was decreased by making hole, the increases in elastic zone resulted in the increases in spring-back characteristics. Therefore, after compensating these characteristics, the amount of spring-back increased comparing with that in the case of bent nonholed parts. In addition, the lager hole diameters were applied the higher amount of spring-back were obtained. Namely, the larger bend angle could be observed as the larger hole diameter was as shown in Figure 8(a). Next, Figure 8(b) shows the obtained bend angle the case of hole located at next to the bend radius zone. As aforementioned, in this case, the hole only decreased the reversed bending characteristics generated next to bend radius zone. However, the hole was rarely deformed. Therefore, the hole only decreased the spring-go characteristics generated next to the bend radius zone but did not increase the additional elastic zone on hole. After compensating these characteristics, the amount of spring-back increased comparing with that in the case on bent nonholed parts. In addition, the lager hole diameters were applied the higher amount of spring-back were obtained. Namely, the larger bend angle could be observed as the larger hole diameter was as shown in Figure 8(b). However, the increase in the amount of spring-back in this case was smaller than that in the case of hole located at bend radius zone. Finally, Figure 8(c) shows the obtained bend angle the case of hole located at leg zone. Again, as aforementioned, there were not any deformations in this zone during bending process. The stress distribution was not generated as well as the hole was not deformed. Therefore, the obtained bend angles were somewhat the same level of those obtained in the case of bent nonholed parts. As per these results, it is clearly revealed that the hole position on bent parts and the hole diameter had a great effect on the amount of spring-back on bent holed parts. Based on these results, they were again useful for the industrial applications to design suitable V-bending die related to the spring-back characteristics for bent holed parts in V-die bending process. Namely, the amount of spring-back increased as the hole diameter increased when it was positioned at the center and next to the bend radius zone. Vice versa, in the case of hole positioned at leg zone, the hole diameter absolutely did not have any effects on the amount of spring-back.Figure 8
Effect of hole diameter on spring-back characteristic at center. (a) Hole at center. (b) Hole next to center. (c) Hole at legs.
(a)(b)(c)


## 3.1. Comparison of Spring-Back Characteristics on Bent Nonholed Parts and Bent Holed Parts

The spring-back characteristics on bent nonholed parts and bent holed parts were illustrated in Figure4. In the case of bent nonholed parts, the results illustrated that the spring-back characteristics were generated in the bending condition of 60° and 120° bend angles as shown in Figure 4(a). In this case, the amounts of spring-back approximately of −0.67° and −2.25° were generated in the cases of 60° and 120° bend angles. This manner of spring-back characteristic corresponded well with the bending theory and the literature [14–16, 22]. Next, in terms of bent holed parts, the results showed the changes in spring-back characteristics compared with that in the case of bent nonholed parts, as shown in Figure 4(b)–4(d). By comparing with the spring-back characteristics in the case of bent nonholed parts, the spring-back characteristic increased when the hole was located at bend radius zone as shown in Figure 4(b). In this case, the amounts of spring-back approximately of 0.33° and −0.17° were generated in the cases of 60° and 120° bend angles. Next, in the case of hole located next to bend radius zone as shown in Figure 4(c), the results showed the increases in spring-back characteristic. In this case, the amounts of spring-back approximately of −0.42° and −1.75° were generated in the cases of 60° and 120° bend angles. It was also observed that the increase in spring-back characteristic generated in the case of hole located at bend radius zone was higher than that in the case of hole located next to bend radius zone. In contrast, in the case of hole located at leg zone as shown in Figure 4(d), the results showed the same level of spring-back characteristics as that in the case of bent nonholed parts. In this case, the amounts of spring-back approximately of −0.75° and −2.17° were generated in the cases of 60° and 120° bend angles. These results revealed that not only the hole located at bend radius zone where the bending allowance zone was generated affected the spring-back characteristics, but the hole located next to bend radius zone where the workpiece was not bent also affected the spring-back characteristics. These interesting results revealed that they stood out against the past bending theory that only the bending allowance zone affected on the spring-back characteristics [22].Figure 4
Comparison of bent parts and spring-back characteristic between bent parts with and without hole (hole diameter: 5 mm). (a) Without hole. (b) Hole at bend radius zone. (c) Hole at next to bend radius zone. (d) Hole at leg zone.
(a)(b)(c)(d)


## 3.2. Effects of Hole Positions of Bent Parts on the Spring-Back Characteristics and the Bending Mechanisms

### 3.2.1. Hole Located at Bend Radius Zone

Figure5 shows the deformation of hole after bending process in the case of hole located at bend radius zone. The experimental results clearly showed that the plastic deformation of hole was generated as shown in Figure 5(a). Specifically, the circular hole was formed to be the elliptical or oval shape. The experimental results also showed that this deformation in bend radius zone was different in each side of workpiece. On the inner radius side, as per the bending theory [22], the compressive stress was generated on this side. Therefore, as shown in Figure 5(a)-2, the circular hole was compressed on the x-axis and then the elliptical shape was deformed by the major axis along with the width of workpiece (y-axis direction) and the minor axis along with the length of workpiece (x-axis direction). Vice versa, on the outer radius side, again as per the bending theory [22], the tensile stress was generated on this side. Therefore, as shown in Figure 5(a)-3, the circular hole was tensioned on the x-axis and then the elliptical shape was deformed by the major axis along with the length of workpiece (x-axis direction) and the minor axis along with the width of workpiece (y-axis direction). Based on these deformed elliptical shape characteristics, the plastic deformation of stress distribution especially on the deformed hole could be analyzed as depicted in Figure 5(b). On the inner radius side as depicted in Figure 5(b)-2, owing to the compressive stress generated during bending process, the compressive stress was generated on circular hole on the x-axis direction as well. This caused the deformed hole of circular shape to be elliptical shape and the compressive stress was generated on each endpoint of the minor axis or a co-vertex of the ellipse. Vice versa, based on the deformed elliptical shape, the tensile stress was generated on each endpoint of the major axis or a vertex of the ellipse. On the basis of this stress distribution analysis, along the perimeter of elliptical shape, the compressive stress generated on each endpoint of minor axis was decreased and changed to the tensile stress. This tensile stress increased and reached the maximum on each endpoint of the major axis. Therefore, the four elastic zones were formed on the elliptical shape as depicted in Figure 5(b)-2. Next, as the same manner of inner radius side, these plastic deformation and stress distribution analyses were also generated on outer radius side as depicted in Figure 5(b)-3. Specifically, owing to the tensile stress generated during bending process, the tensile stress was generated on circular hole on the x-axis direction as well. This caused the deformed hole of circular shape to be elliptical shape and the tensile stress was generated on each endpoint of the major axis or a vertex of the ellipse. Vice versa, based on the deformed elliptical shape, the compressive stress was generated on each endpoint of the minor axis or a co-vertex of the ellipse. On the basis of this stress distribution analysis, again the tensile stress generated on each endpoint of major axis was decreased along the perimeter of elliptical shape and changed to the compressive stress. This compressive stress increased and reached the maximum on each endpoint of the minor axis. Therefore, the four elastic zones were formed on the elliptical shape as depicted in Figure 5(b)-3. As these stress distribution analyses on deformed hole during bending process, it was found that the four elastic zones were generated on each bend radius side (i.e., inner and outer radius sides). By making hole, the bending allowance was decreased and resulted in the decreases in spring-back characteristics. However, the new eight elastic zones were generated on hole during bending process and resulted in the increases in spring-back characteristics. Therefore, after unloading, the amount of spring-back generated in the case of bent holed parts was larger than that in the case of bent nonholed parts.Figure 5
Illustration of plastic deformation and stress analysis on hole in the case of hole located at bend radius zone (hole diameter: 5 mm, bend angle: 60°). (a) Experiment. (b) Analysis.


### 3.2.2. Hole Located next to Bend Radius Zone

Figure6 shows the deformation of hole after bending process in the case of hole located next to bend radius zone. The experimental results showed the deformation of hole as shown in Figure 6(a). The results showed that the circular hole rarely deformed on each side of inner radius and outer radius. These deformations could be explained as per the past researches [14–16, 22], [24]. Although the reversed bending characteristics were generated next to bend radius zone and caused the spring-forward or spring-go characteristics, these reversed bending characteristics rarely affected the deformation of circular hole and rarely caused the distortion of it. Therefore, there rarely were any stress distributions generated on circular hole due to the hole deformation on each side of inner radius and outer radius as depicted in Figures 6(b)-2 and 6(b)-3. After unloading, the effects of hole only resulting in the decreases in the reversed bending characteristics as well as in the spring-go characteristics were clearly illustrated. After compensating these spring-back characteristics generated on the bend radius zone and spring-go characteristics generated next to bend radius zone, by comparing with the case of nonholed blank, the amount of spring-back of the bent holed parts was increased.Figure 6
Illustration of plastic deformation and stress analysis on hole in the case of hole located next to bend radius zone (hole diameter: 5 mm, bend angle: 60°). (a) Experiment. (b) Analysis.


### 3.2.3. Hole Located at Leg Zone

Figure7 shows the deformation of hole after bending process in the case of hole located at leg zone. The experimental results showed the deformation of hole as shown in Figure 7(a). The results showed that the circular hole did not deform on each side of inner radius and outer radius. These deformations could be explained that, as per the bending theory and past researches [14–16, 22, 24], there were not any bending characteristics generated on leg zone. Absolutely, there were not any stress distributions generated on circular hole on each side of inner radius and outer radius as well as there was not any hole formation as depicted in Figure 6(b)-2 and 6(b)-3. After unloading, there were not any effects of hole on the bending characteristics generated at bend radius zone and the reversed bending characteristics generated at next to bend radius zone. Therefore, there were not any effects on in the spring-back and spring-go characteristics on the bent holed parts. Therefore, after unloading by comparing with the case of bent nonholed parts, the amount of spring-back of the bent holed parts was the same level.Figure 7
Illustration of plastic deformation and stress analysis on hole in the case of hole located at leg zone (hole diameter: 5 mm, bend angle: 60°). (a) Experiment. (b) Analysis.As these results shown, although only three cases of hole position including at center, at next to bend radius, and at leg zones were examined, the effects of hole position on the amount of spring-back were clearly shown. Specifically, in the case of hole positioned at center zone, the amount of spring-back generated in the case of bent holed parts was larger than that in the case of bent nonholed parts. In the case of hole positioned at leg zone, there completely were not any effects of hole on the amount of spring-back. The amount of spring-back of the bent holed parts was the same level by comparing with the case of bent nonholed parts. In the case of at next to bend radius zone, by comparing with the case of nonholed blank, the amount of spring-back of the bent holed parts was increased. However, the bend radius zone directly depended on the bending conditions including bend angle and bend radius. The distance from center of blank (A) in this case was sensitively depended on these bending conditions. Therefore, this distance should be carefully aware based on the bending condition applied. Based on these results, they were useful for the industrial applications to design suitable V-bending die related to the spring-back characteristics for bent holed parts in V-die bending process.


## 3.2.1. Hole Located at Bend Radius Zone

Figure5 shows the deformation of hole after bending process in the case of hole located at bend radius zone. The experimental results clearly showed that the plastic deformation of hole was generated as shown in Figure 5(a). Specifically, the circular hole was formed to be the elliptical or oval shape. The experimental results also showed that this deformation in bend radius zone was different in each side of workpiece. On the inner radius side, as per the bending theory [22], the compressive stress was generated on this side. Therefore, as shown in Figure 5(a)-2, the circular hole was compressed on the x-axis and then the elliptical shape was deformed by the major axis along with the width of workpiece (y-axis direction) and the minor axis along with the length of workpiece (x-axis direction). Vice versa, on the outer radius side, again as per the bending theory [22], the tensile stress was generated on this side. Therefore, as shown in Figure 5(a)-3, the circular hole was tensioned on the x-axis and then the elliptical shape was deformed by the major axis along with the length of workpiece (x-axis direction) and the minor axis along with the width of workpiece (y-axis direction). Based on these deformed elliptical shape characteristics, the plastic deformation of stress distribution especially on the deformed hole could be analyzed as depicted in Figure 5(b). On the inner radius side as depicted in Figure 5(b)-2, owing to the compressive stress generated during bending process, the compressive stress was generated on circular hole on the x-axis direction as well. This caused the deformed hole of circular shape to be elliptical shape and the compressive stress was generated on each endpoint of the minor axis or a co-vertex of the ellipse. Vice versa, based on the deformed elliptical shape, the tensile stress was generated on each endpoint of the major axis or a vertex of the ellipse. On the basis of this stress distribution analysis, along the perimeter of elliptical shape, the compressive stress generated on each endpoint of minor axis was decreased and changed to the tensile stress. This tensile stress increased and reached the maximum on each endpoint of the major axis. Therefore, the four elastic zones were formed on the elliptical shape as depicted in Figure 5(b)-2. Next, as the same manner of inner radius side, these plastic deformation and stress distribution analyses were also generated on outer radius side as depicted in Figure 5(b)-3. Specifically, owing to the tensile stress generated during bending process, the tensile stress was generated on circular hole on the x-axis direction as well. This caused the deformed hole of circular shape to be elliptical shape and the tensile stress was generated on each endpoint of the major axis or a vertex of the ellipse. Vice versa, based on the deformed elliptical shape, the compressive stress was generated on each endpoint of the minor axis or a co-vertex of the ellipse. On the basis of this stress distribution analysis, again the tensile stress generated on each endpoint of major axis was decreased along the perimeter of elliptical shape and changed to the compressive stress. This compressive stress increased and reached the maximum on each endpoint of the minor axis. Therefore, the four elastic zones were formed on the elliptical shape as depicted in Figure 5(b)-3. As these stress distribution analyses on deformed hole during bending process, it was found that the four elastic zones were generated on each bend radius side (i.e., inner and outer radius sides). By making hole, the bending allowance was decreased and resulted in the decreases in spring-back characteristics. However, the new eight elastic zones were generated on hole during bending process and resulted in the increases in spring-back characteristics. Therefore, after unloading, the amount of spring-back generated in the case of bent holed parts was larger than that in the case of bent nonholed parts.Figure 5
Illustration of plastic deformation and stress analysis on hole in the case of hole located at bend radius zone (hole diameter: 5 mm, bend angle: 60°). (a) Experiment. (b) Analysis.


## 3.2.2. Hole Located next to Bend Radius Zone

Figure6 shows the deformation of hole after bending process in the case of hole located next to bend radius zone. The experimental results showed the deformation of hole as shown in Figure 6(a). The results showed that the circular hole rarely deformed on each side of inner radius and outer radius. These deformations could be explained as per the past researches [14–16, 22], [24]. Although the reversed bending characteristics were generated next to bend radius zone and caused the spring-forward or spring-go characteristics, these reversed bending characteristics rarely affected the deformation of circular hole and rarely caused the distortion of it. Therefore, there rarely were any stress distributions generated on circular hole due to the hole deformation on each side of inner radius and outer radius as depicted in Figures 6(b)-2 and 6(b)-3. After unloading, the effects of hole only resulting in the decreases in the reversed bending characteristics as well as in the spring-go characteristics were clearly illustrated. After compensating these spring-back characteristics generated on the bend radius zone and spring-go characteristics generated next to bend radius zone, by comparing with the case of nonholed blank, the amount of spring-back of the bent holed parts was increased.Figure 6
Illustration of plastic deformation and stress analysis on hole in the case of hole located next to bend radius zone (hole diameter: 5 mm, bend angle: 60°). (a) Experiment. (b) Analysis.


## 3.2.3. Hole Located at Leg Zone

Figure7 shows the deformation of hole after bending process in the case of hole located at leg zone. The experimental results showed the deformation of hole as shown in Figure 7(a). The results showed that the circular hole did not deform on each side of inner radius and outer radius. These deformations could be explained that, as per the bending theory and past researches [14–16, 22, 24], there were not any bending characteristics generated on leg zone. Absolutely, there were not any stress distributions generated on circular hole on each side of inner radius and outer radius as well as there was not any hole formation as depicted in Figure 6(b)-2 and 6(b)-3. After unloading, there were not any effects of hole on the bending characteristics generated at bend radius zone and the reversed bending characteristics generated at next to bend radius zone. Therefore, there were not any effects on in the spring-back and spring-go characteristics on the bent holed parts. Therefore, after unloading by comparing with the case of bent nonholed parts, the amount of spring-back of the bent holed parts was the same level.Figure 7
Illustration of plastic deformation and stress analysis on hole in the case of hole located at leg zone (hole diameter: 5 mm, bend angle: 60°). (a) Experiment. (b) Analysis.As these results shown, although only three cases of hole position including at center, at next to bend radius, and at leg zones were examined, the effects of hole position on the amount of spring-back were clearly shown. Specifically, in the case of hole positioned at center zone, the amount of spring-back generated in the case of bent holed parts was larger than that in the case of bent nonholed parts. In the case of hole positioned at leg zone, there completely were not any effects of hole on the amount of spring-back. The amount of spring-back of the bent holed parts was the same level by comparing with the case of bent nonholed parts. In the case of at next to bend radius zone, by comparing with the case of nonholed blank, the amount of spring-back of the bent holed parts was increased. However, the bend radius zone directly depended on the bending conditions including bend angle and bend radius. The distance from center of blank (A) in this case was sensitively depended on these bending conditions. Therefore, this distance should be carefully aware based on the bending condition applied. Based on these results, they were useful for the industrial applications to design suitable V-bending die related to the spring-back characteristics for bent holed parts in V-die bending process.


## 3.3. Effects of Hole Diameters on the Spring-Back Characteristics

Figure8 shows the effects of hole diameters on the spring-back characteristics with respect to hole positions. First, as the horizontal lines shown, the bend angles were approximately of 60° and 120° in the case of bending angles of 60° and 120°, respectively. In the case of hole located at bend radius zone, as shown in Figure 8(a), the results showed that the amount of spring-back increased as the hole diameter increased in the cases of bending angle of 60° and 120°. As aforementioned stress distribution analysis on hole during bending process, the four elastic zones were generated on each side of inner radius and outer radius. Furthermore, these elastic zones were enlarged as the hole diameter increased due to the increases in the major axis and minor axis of ellipse. Therefore, although the bending allowance was decreased by making hole, the increases in elastic zone resulted in the increases in spring-back characteristics. Therefore, after compensating these characteristics, the amount of spring-back increased comparing with that in the case of bent nonholed parts. In addition, the lager hole diameters were applied the higher amount of spring-back were obtained. Namely, the larger bend angle could be observed as the larger hole diameter was as shown in Figure 8(a). Next, Figure 8(b) shows the obtained bend angle the case of hole located at next to the bend radius zone. As aforementioned, in this case, the hole only decreased the reversed bending characteristics generated next to bend radius zone. However, the hole was rarely deformed. Therefore, the hole only decreased the spring-go characteristics generated next to the bend radius zone but did not increase the additional elastic zone on hole. After compensating these characteristics, the amount of spring-back increased comparing with that in the case on bent nonholed parts. In addition, the lager hole diameters were applied the higher amount of spring-back were obtained. Namely, the larger bend angle could be observed as the larger hole diameter was as shown in Figure 8(b). However, the increase in the amount of spring-back in this case was smaller than that in the case of hole located at bend radius zone. Finally, Figure 8(c) shows the obtained bend angle the case of hole located at leg zone. Again, as aforementioned, there were not any deformations in this zone during bending process. The stress distribution was not generated as well as the hole was not deformed. Therefore, the obtained bend angles were somewhat the same level of those obtained in the case of bent nonholed parts. As per these results, it is clearly revealed that the hole position on bent parts and the hole diameter had a great effect on the amount of spring-back on bent holed parts. Based on these results, they were again useful for the industrial applications to design suitable V-bending die related to the spring-back characteristics for bent holed parts in V-die bending process. Namely, the amount of spring-back increased as the hole diameter increased when it was positioned at the center and next to the bend radius zone. Vice versa, in the case of hole positioned at leg zone, the hole diameter absolutely did not have any effects on the amount of spring-back.Figure 8
Effect of hole diameter on spring-back characteristic at center. (a) Hole at center. (b) Hole next to center. (c) Hole at legs.
(a)(b)(c)


## 4. Conclusions

To achieve the proper V-die designs for controlling bend angle precision in bent holed parts, the bending mechanisms and spring-back characteristics on bent holed pats in V-die bending process were investigated in the present research. First, the bending mechanisms and the spring-back characteristics were investigated by comparing with those in the case of bent nonholed parts. The results revealed that, in the case of hole located at bend radius zone and next to bend radius zone, the bending mechanisms and spring-back characteristics in the case of bent holed parts were different from those in the case of bent nonholed parts. Vice versa, they were the same in the case of hole located at leg zone. These results were clearly clarified based on the stress distribution analysis. Although the bending characteristics decreased by making hole when the hole was located at bend radius zone, the additional elastic zone was formed on the hole during hole deformation. Therefore, the amount of spring-back was increased. In addition, it increased as the hole diameter increased. With the hole located next to bend radius zone, in this zone the reversed bending characteristic was formed but there rarely was any distortion of hole. Therefore, by making hole, this reversed bending characteristics decreased and the amount of spring-back increased. In addition, the amount of spring-back increased as the hole diameter increased. However, with the hole located at leg zone, in this zone there was not any plastic deformation and then the hole had not any effect on spring-back characteristics. As per these results, to achieve a good design of V-bending die for fabrication of V-bent parts of holed parts, the hole positions and diameters should be carefully considered.



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*Source: 6488261-2022-06-02.xml*