Investigation on Springback Behavior of Cu/Ni Clad Foils during Flexible Die Micro V-Bending Process

With the increasing demand for micro parts using metal laminates in modern production, the manufacturing processes of thin sheet parts have been elevated. However, it is difficult to predict the deformation behavior with miniaturization because of size effects in micro-scale. In this study, the flexible die micro V-bending behavior of Cu/Ni clad foils was investigated. The bending experiments with three different punch angles and Cu/Ni clad foils under different annealed temperatures were performed. The results show that the springback angle increases with the increase of bending angle and annealing temperature. The placement of Cu/Ni clad foils induced compressive stress results in the more obvious thinning of thickness and decreasing of springback angle. The interactive effects of the distribution of deformation zones and compressive stress induced by the interface layer result in the springback behavior of Cu/Ni clad foils during the flexible die micro V-bending process.


Introduction
With the development of products toward miniaturization and complex function, monolayer metal or alloy gradually fails to meet the demand for comprehensive properties of materials in modern production [1,2]. Clad metals are widely used in various fields because of their good comprehensive performance and superior cost performance [3]. In comparison with the micro-machining and other micro-manufacturing technologies, micro-forming is one of the most suitable and economical manufacturing processes for mass production of micro-metal components [4]. However, the conventional understanding and the established knowledge of material deformation behaviors in macro-forming are no longer valid or accurate in micro-forming due to the occurrence of size effects [5].
Leu [6] developed a material constitutive model to distinguish the tensile flow stress of metal sheets from the micro-scale to the macro-scale. Zhao et al. [7] carried out micro-tensile experiments on magnesium alloy foils with different thickness and grain size, and the results showed an obvious size effect on flow stress. Subsequently, they introduced the size factor (t/d) parameter into the Swift constitutive model and constructed the constitutive model of magnesium alloy foils considering size effects. Tensile properties and fracture characteristics of high purity polycrystalline Ni were investigated using micro-tensile specimens [8]. Li et al. [9] successfully formed micro-arrayed deep drawn parts fabricated from Ni-Co/GO (graphene oxide) nanocomposite foils.
The micro-bending of foils is a fundamental materials test to underpin strain gradient plasticity theories [10]. Micro-bending experiments of brass foils were conducted and the results demonstrated obvious size effects on the springback angle, i.e., the normalized bending moment increased with the reduction of foil thickness [11]. To analyze the flow stress size effect, a simplified constitutive model was proposed, which took into account the plastic strain gradient hardening, and was applied to predict

Experimental Materials
Cu/Ni clad foils with a thickness of 100 µm and a thickness ratio of Cu to Ni of 1.25:1 were employed as the testing materials in this research. The detailed manufacturing process of Cu/Ni clad foil is that Cu and Ni plates had initially 1.5 mm thickness approximately, and then it was rolled down to 0.1 mm after three rolling steps. After each rolling step, the clad foils were annealed in 500~600 • C. The length of the rectangle specimens is 20 mm and the width is 5 mm. The specimen cross-section along the rolling direction (RD) was observed under a microscope, as shown in Figure 1.
To eliminate the work hardening and improve the forming ability, the specimens were annealed at 600 • C, 700 • C, and 850 • C for 1 h, respectively. Microstructures of the billets along RD at different annealing temperatures are shown in Figure 2. Complete recrystallization occurred in both copper and nickel layers after annealing. The annealed grains are equiaxed. The grain sizes of the copper and nickel layers are obtained from the rolling direction and measured by the linear intercept method. The component thicknesses were measured by SEM (MERLIN Compact, Carl Zeiss AG, Heidenheim, Germany). The grain sizes and thicknesses of each component of the billet are listed in Table 1. The grain sizes of copper and nickel layers increase with the annealing temperature. The thickness of the interface layer increases with the annealing temperature. In contrast, the thickness of copper and nickel layers decreases accordingly with the annealing temperature. annealing temperatures are shown in Figure 2. Complete recrystallization occurred in both copper and nickel layers after annealing. The annealed grains are equiaxed. The grain sizes of the copper and nickel layers are obtained from the rolling direction and measured by the linear intercept method. The component thicknesses were measured by SEM (MERLIN Compact, Carl Zeiss AG, Heidenheim, Germany). The grain sizes and thicknesses of each component of the billet are listed in Table 1. The grain sizes of copper and nickel layers increase with the annealing temperature. The thickness of the interface layer increases with the annealing temperature. In contrast, the thickness of copper and nickel layers decreases accordingly with the annealing temperature.

Experimental Setup
The setup of the micro V-bending experiment and three rigid punches with different bending angles are shown in Figure 3. Three punch angles are expressed by P1 (α1 = 60°, θ = 120°, r = 0.1 mm), P2 (α2 = 90°, θ = 90°, r = 0.1 mm), P3 (α3 = 120°, θ = 60°, r = 0.1 mm), which are shown in Figure 3d. α is bending angle, θ is punch angle, and α + θ = 180°. r is punch fillet radius.   Table 1. The grain sizes of copper and nickel layers increase with the annealing temperature. The thickness of the interface layer increases with the annealing temperature. In contrast, the thickness of copper and nickel layers decreases accordingly with the annealing temperature.

Experimental Procedure
The diagram of the V-bending process is shown in Figure 4. Square rubber with a thickness of 10 mm was put into the closed die. Then a clean clad foil was put in the center of the rubber, which can reduce the measurement error after springback. The punch was placed vertically into the die and touched lightly with the foil. All the V-bending experiments were carried out on an electronic universal testing machine (INSTRON 5967, Instron LTD, Boston, MA, USA). The punches were pressed down at a velocity of 2 mm/min, and the fully bent specimens were obtained. Five specimens were tested under the same process parameter to verify the repeatability of experiments. Then the specimens were placed in different ways to repeat the experiment. The placement of Cu/Ni means that Cu layer is closed to the punch, and the placement of Ni/Cu means that Ni layer is closed to the punch. The profile of the bent specimens was obtained under a stereoscopic microscope and the thickness was obtained under a microscope (OLYMPUS DSX510, Olympus Corporation, Tokyo, Japan). The bending angle and foil thickness reduction after springback were measured by an electronic ruler in the microscope, and the effects of different experimental parameters on the quality of flexible die micro V-bending were analyzed. At least 5 points or specimens were used to measure the thickness or bending angle. The

Experimental Procedure
The diagram of the V-bending process is shown in Figure 4. Square rubber with a thickness of 10 mm was put into the closed die. Then a clean clad foil was put in the center of the rubber, which can reduce the measurement error after springback. The punch was placed vertically into the die and touched lightly with the foil.

Experimental Procedure
The diagram of the V-bending process is shown in Figure 4. Square rubber with a thickness of 10 mm was put into the closed die. Then a clean clad foil was put in the center of the rubber, which can reduce the measurement error after springback. The punch was placed vertically into the die and touched lightly with the foil. All the V-bending experiments were carried out on an electronic universal testing machine (INSTRON 5967, Instron LTD, Boston, MA, USA). The punches were pressed down at a velocity of 2 mm/min, and the fully bent specimens were obtained. Five specimens were tested under the same process parameter to verify the repeatability of experiments. Then the specimens were placed in different ways to repeat the experiment. The placement of Cu/Ni means that Cu layer is closed to the punch, and the placement of Ni/Cu means that Ni layer is closed to the punch. The profile of the bent specimens was obtained under a stereoscopic microscope and the thickness was obtained under a microscope (OLYMPUS DSX510, Olympus Corporation, Tokyo, Japan). The bending angle and foil thickness reduction after springback were measured by an electronic ruler in the microscope, and the effects of different experimental parameters on the quality of flexible die micro V-bending were analyzed. At least 5 points or specimens were used to measure the thickness or bending angle. The All the V-bending experiments were carried out on an electronic universal testing machine (INSTRON 5967, Instron LTD, Boston, MA, USA). The punches were pressed down at a velocity of 2 mm/min, and the fully bent specimens were obtained. Five specimens were tested under the same process parameter to verify the repeatability of experiments. Then the specimens were placed in different ways to repeat the experiment. The placement of Cu/Ni means that Cu layer is closed to the punch, and the placement of Ni/Cu means that Ni layer is closed to the punch. The profile of the bent specimens was obtained under a stereoscopic microscope and the thickness was obtained under a microscope (OLYMPUS DSX510, Olympus Corporation, Tokyo, Japan). The bending angle and foil thickness reduction after springback were measured by an electronic ruler in the microscope, and the effects of different experimental parameters on the quality of flexible die micro V-bending were analyzed. At least 5 points or specimens were used to measure the thickness or bending angle. The bent specimen are shown in Figure 5, where (a) shows the outline of the specimen bent by the punch die of 60 • , 90 • , and 120 • , and (b) shows the specimen bent by the three kinds of punches. The Cu and Ni layers are not separated during the bending process because the strong interface of the Cu and Ni is formed during cold rolling and annealing. The Cu and Ni layers are constrained by the interfacial diffusion, mechanical occlusion, and metallurgical bonding. bent specimen are shown in Figure 5, where (a) shows the outline of the specimen bent by the punch die of 60°, 90°, and 120°, and (b) shows the specimen bent by the three kinds of punches. The Cu and Ni layers are not separated during the bending process because the strong interface of the Cu and Ni is formed during cold rolling and annealing. The Cu and Ni layers are constrained by the interfacial diffusion, mechanical occlusion, and metallurgical bonding.

Effect of Bending Angle
The experimental results of Figure 6 show that the springback angle increases significantly when the bending angle decreases from 120° to 60° using the same annealed specimens and placement mode. This is because the bending deformation zone is divided into an elastic zone, elastoplastic zone and plastic zone [4], as shown in Figure 7. Under a certain relative bending radius, the length of the deformation zone and the springback accumulation increase with the increase of bending angle, which leads to an increase of springback. The diagram of the different bending angle is shown in Figure 8a. In order to analyze the characteristics of bending deformation more intuitively, a finite element model was established. The bending process was simulated by the dynamic display algorithm and displacement loading. Finally, the deformation degree at different bending angles can be seen by the equivalent strain distribution, as shown in Figure 8b. When the bending angle is 120° because the guide of the die is not long enough and the rubber has a certain elasticity, the punch is not stable during the downward pressing process and the springback angle fluctuates greatly. This is consistent with the results in the references [13,15,17].

Effect of Bending Angle
The experimental results of Figure 6 show that the springback angle increases significantly when the bending angle decreases from 120 • to 60 • using the same annealed specimens and placement mode. This is because the bending deformation zone is divided into an elastic zone, elastoplastic zone and plastic zone [4], as shown in Figure 7. Under a certain relative bending radius, the length of the deformation zone and the springback accumulation increase with the increase of bending angle, which leads to an increase of springback. The diagram of the different bending angle is shown in Figure 8a. In order to analyze the characteristics of bending deformation more intuitively, a finite element model was established. The bending process was simulated by the dynamic display algorithm and displacement loading. Finally, the deformation degree at different bending angles can be seen by the equivalent strain distribution, as shown in Figure 8b. When the bending angle is 120 • because the guide of the die is not long enough and the rubber has a certain elasticity, the punch is not stable during the downward pressing process and the springback angle fluctuates greatly. This is consistent with the results in the references [13,15,17]. bent specimen are shown in Figure 5, where (a) shows the outline of the specimen bent by the punch die of 60°, 90°, and 120°, and (b) shows the specimen bent by the three kinds of punches. The Cu and Ni layers are not separated during the bending process because the strong interface of the Cu and Ni is formed during cold rolling and annealing. The Cu and Ni layers are constrained by the interfacial diffusion, mechanical occlusion, and metallurgical bonding.

Effect of Bending Angle
The experimental results of Figure 6 show that the springback angle increases significantly when the bending angle decreases from 120° to 60° using the same annealed specimens and placement mode. This is because the bending deformation zone is divided into an elastic zone, elastoplastic zone and plastic zone [4], as shown in Figure 7. Under a certain relative bending radius, the length of the deformation zone and the springback accumulation increase with the increase of bending angle, which leads to an increase of springback. The diagram of the different bending angle is shown in Figure 8a. In order to analyze the characteristics of bending deformation more intuitively, a finite element model was established. The bending process was simulated by the dynamic display algorithm and displacement loading. Finally, the deformation degree at different bending angles can be seen by the equivalent strain distribution, as shown in Figure 8b. When the bending angle is 120° because the guide of the die is not long enough and the rubber has a certain elasticity, the punch is not stable during the downward pressing process and the springback angle fluctuates greatly. This is consistent with the results in the references [13,15,17].

Effect of Annealing Temperature
The effect of the annealing temperature on the springback of Cu/Ni clad foils during flexible die micro V-bending process is shown in Figure 9. It is obvious that the springback increases with the annealing temperature. The annealing temperature determines the grain size. The higher the annealing temperature is, the larger the grain size is. On the one hand, the proportion of grain in the surface layer increases with the increase of grain size, and the strengthening effect is more obvious. On the other hand, inhomogeneous microstructure and complex boundaries make the deformation process difficult and then lead to an increase of springback in the case of the specimen with large grain size [17,22]. In the case of the specimen with large grain sizes, inhomogeneous microstructures and complex boundaries make the deformation process difficult and then lead to an increase of springback.

Effect of Annealing Temperature
The effect of the annealing temperature on the springback of Cu/Ni clad foils during flexible die micro V-bending process is shown in Figure 9. It is obvious that the springback increases with the annealing temperature. The annealing temperature determines the grain size. The higher the annealing temperature is, the larger the grain size is. On the one hand, the proportion of grain in the surface layer increases with the increase of grain size, and the strengthening effect is more obvious. On the other hand, inhomogeneous microstructure and complex boundaries make the deformation process difficult and then lead to an increase of springback in the case of the specimen with large grain size [17,22]. In the case of the specimen with large grain sizes, inhomogeneous microstructures and complex boundaries make the deformation process difficult and then lead to an increase of springback.

Effect of Annealing Temperature
The effect of the annealing temperature on the springback of Cu/Ni clad foils during flexible die micro V-bending process is shown in Figure 9. It is obvious that the springback increases with the annealing temperature. The annealing temperature determines the grain size. The higher the annealing temperature is, the larger the grain size is. On the one hand, the proportion of grain in the surface layer increases with the increase of grain size, and the strengthening effect is more obvious. On the other hand, inhomogeneous microstructure and complex boundaries make the deformation process difficult and then lead to an increase of springback in the case of the specimen with large grain size [17,22]. In the case of the specimen with large grain sizes, inhomogeneous microstructures and complex boundaries make the deformation process difficult and then lead to an increase of springback.

Effect of Placement Mode
From Figure 10, it can be observed that the springback angles for specimens under different annealing temperature and bending angles are larger when using Ni/Cu instead of Cu/Ni. Except for the specimen annealed at 600 °C and bent under 120° punch angle, the effect of placement on springback is different. Because of that, the elastic modulus of Cu is lower than that of Ni. When Ni is placed under Cu, the transverse stress of the transition layer after bending is compressive stress, which is slightly larger than that of the outer layer [24][25][26]. The stress neutral layer moves to the inner Ni layer and the bending moment increases. When using Ni/Cu, the transverse stress of the transition layer after bending is slightly less than that of the inner layer, and the stress neutral layer is still in the transition layer. The stress neutral layer is close to the geometric center of foil thickness and the bending moment decreases. The transverse stress distribution of S11 (normal stress along the length direction) is shown in Figure 11. The bending moment of Ni/Cu is larger than that of Cu/Ni thus the former springback is larger than that of the latter. Therefore, if the ratio of Ni to Cu increases, the position of the stress neutral layer will be more different and the springback angle will be larger when using Ni/Cu.

Effect of Placement Mode
From Figure 10, it can be observed that the springback angles for specimens under different annealing temperature and bending angles are larger when using Ni/Cu instead of Cu/Ni. Except for the specimen annealed at 600 • C and bent under 120 • punch angle, the effect of placement on springback is different. Because of that, the elastic modulus of Cu is lower than that of Ni. When Ni is placed under Cu, the transverse stress of the transition layer after bending is compressive stress, which is slightly larger than that of the outer layer [24][25][26]. The stress neutral layer moves to the inner Ni layer and the bending moment increases. When using Ni/Cu, the transverse stress of the transition layer after bending is slightly less than that of the inner layer, and the stress neutral layer is still in the transition layer. The stress neutral layer is close to the geometric center of foil thickness and the bending moment decreases. The transverse stress distribution of S11 (normal stress along the length direction) is shown in Figure 11. The bending moment of Ni/Cu is larger than that of Cu/Ni thus the former springback is larger than that of the latter. Therefore, if the ratio of Ni to Cu increases, the position of the stress neutral layer will be more different and the springback angle will be larger when using Ni/Cu.

Analysis of Thickness Variation at Fillet
The thickness of the bent specimen was measured and it can be found from Table 2 that the thickness of the foil decreases when the annealing temperature is 850 °C and the placement is Ni/Cu. In order to analyze and observe the thickness deformation more accurately, the finite element simulation result was analyzed, which is shown in Figure 12. According to the results of experiments and simulations, thickness thinning increases with the increase of bending angle and deformation degree. It can be found from Table 2 and Figure 12 that the thickness (corner position or deformation region) of the clad foil decreases when the annealing temperature is 850 °C and the placement is Ni/Cu. The thickness thinning increases with the increase of the bending angle. However, the

Analysis of Thickness Variation at Fillet
The thickness of the bent specimen was measured and it can be found from Table 2 that the thickness of the foil decreases when the annealing temperature is 850 • C and the placement is Ni/Cu. In order to analyze and observe the thickness deformation more accurately, the finite element simulation result was analyzed, which is shown in Figure 12. According to the results of experiments and simulations, thickness thinning increases with the increase of bending angle and deformation degree. It can be found from Table 2 and Figure 12 that the thickness (corner position or deformation region) of the clad foil decreases when the annealing temperature is 850 • C and the placement is Ni/Cu. The thickness thinning increases with the increase of the bending angle. However, the thickness of the Cu/Ni clad foil treated by the same annealing process increases with the increase of bending angle, as shown in Table 3. This is consistent with the air bending experimental results in reference [28]. When the softer layer is bent towards the punch, the clad foil may become thicker. This is because of that the transverse compressive stress is dominated when the Cu layer is located inside, which increases the thickness of the clad foil, as shown in Figure 13. thickness of the Cu/Ni clad foil treated by the same annealing process increases with the increase of bending angle, as shown in Table 3. This is consistent with the air bending experimental results in reference [28]. When the softer layer is bent towards the punch, the clad foil may become thicker. This is because of that the transverse compressive stress is dominated when the Cu layer is located inside, which increases the thickness of the clad foil, as shown in Figure 13.

Conclusions
Cu/Ni clad foils with a thickness of 100 µm were selected as the experimental materials in the research. To investigate the influence of processing and material parameters on springback of micro

Conclusions
Cu/Ni clad foils with a thickness of 100 µm were selected as the experimental materials in the research. To investigate the influence of processing and material parameters on springback of micro V-bending of clad foils, the micro-bending experiments using flexible die were carried out and the characteristics of stress and strain were analyzed. The reasons for the variation of fillet thickness were analyzed. The following conclusive remarks can be drawn from the study: (1) The bending angle has a significant effect on the bending process of clad foils, and the springback decreases with the increase of the bending angle. The reason is that the bending moment and elastic rebound are lower when using the small bending angle. The springback angle increases with the increase of annealing temperature. This is because of that the microstructure becomes inhomogeneous as the annealing temperature increases.
(2) The effect of placement on the bending process of clad foil is not significant. However, the springback of Ni/Cu is slightly higher than that of Cu/Ni. The difference in the bending moment results from the movement of the neutral layer. When using Ni/Cu, the neutral layer moves inward more significantly, resulting in a larger bending moment.
(3) The bending moment of the cross-section in the bending process is the superposition of the bending moment of the inner and outer sheet metals. The bending moments of each component are divided into the bending moment in the elastic zone and in the plastic zone. The curvature radius of the neutral layer of the clad foil after unloading is obtained by the relationship between bending moment and curvature variation.
(4) The thickness of the clad foil decreases along the fillet of the punch when using Cu/Ni. The thickness of the clad foil increases when using Ni/Cu. The reason is that the transverse compressive stress is dominated when the stronger Ni layer is inside.