On feasibility of roll-stamp forming variable-sectional metal channels

Sheet metal channels with variable sections or local features have been widely used in automobile and construction industries, and novel forming techniques, such as flexible roll forming process, flexibly reconfigurable roll forming process, Deakin’s flexible forming facility, and chain-die forming recently have been developed to manufacture those channels. In this paper, the feasibility of chain-die forming technique to manufacture channels with variable sections is systematically investigated through experiment and finite element simulation by taking 6 types of channel products as demonstration, including three variable-width and three variable-depth profiles. The forming process of the channels shows a combination of roll forming and stamping, and this roll-stamp mode has great potential in manufacturing a wide variety of channels with variable cross-sections. The formability for roll-stamp forming variable-depth channels is evaluated through finite element simulation and forming limit diagram. The roll-stamp mode can be discomposed into roll forming longitudinally and stamping vertically, and can achieve a reduction in forming load by the maximum of 33.9% compared with the conventional stamping in forming the flange step product. The forming direction sensitivity of the variable-width feature is discussed from the aspect of web arch height development.


Introduction
Metal channel products of variable cross-sections and with local features such as steps, dimples, and grooves have been widely used in automotive and construction industries, as demonstrated in Fig. 1, and demands on those long channels aroused progresses in sheet metal forming technologies in the past two decades.
Stamping has been the most commonly used techniques for sheet metal forming. However, large-tonnage stamping presses are required when forming long channel parts. In the past one decade, gradual forming techniques have been increasingly used in manufacturing of channel products, especially with the increasing of sheet metals' strength. The cold roll forming has shown high efficiency and low cost in producing high-strength thin-walled channel parts [1], in which steel strip is gradually bended by a series of rolls installed at the tandems along the longitudinal direction [2], as schematically shown in Fig. 2a [3]. Roll forming can achieve continuous production of diverse length without changing dies and loading/unloading. Meanwhile, it requires a lower machine capacity [4], and has the ability to form small radius [5,6]. However, the products ideally suitable for the traditional roll forming have to be of constant cross-sections.
In order to fabricate products with variable crosssections, several novel sheet metal forming techniques were developed, such as flexible roll forming (Fig. 2b) [10,11] and flexibly reconfigurable roll forming process Kaijun Lu and Zhenye Liang contributed equally to this work.  [8]. In the flexible roll forming process, by controlling the roll stands both axially and rotationally, variable cross-section profiles can be manufactured as the forming rolls move along a complex trajectory [12]. Groche et al. [13] studied the feasibility of the flexible roll forming process and influence of geometrical and material parameters through numerical analyses and experiments. Yu et al. [14] simulated the flexible roll forming of a side door beam, and studied the longitudinal bow and edge wave defects in the flexible roll forming. Kim et al. [15] investigated the influence of flexible roll forming mode on longitudinal bowing, and found that smaller initial bending angle and higher bending angle increment are helpful to decrease the longitudinal bowing in flexible roll forming. Rezaei et al. [16] tried to find a cost-effective method to reduce the web warping in flexible roll forming. Different bend curves, circular, quantic, linear, fractional, and Bezier, were comparatively designed, and the linear bend curve was found to be able to reduce the web warping height most significantly. Woo et al. [17] analyzed three types of width variable channels in the flexible roll-formed samples-trapezoid, concave, and convex-and found that edge wave and longitudinal bow cannot be alleviated simultaneously. Based on the wrinkling limit diagram in terms of stress triaxiality, Kasaei [18] developed a method for wrinkling prediction in flexible roll forming, and analyzed the effect of geometric parameters and material properties on wrinkling defect. In the flexibly reconfigurable roll forming (FRRF) process, a sheet metal is formed by several pairs of small-diameter rollers with various gaps bending the sheet both longitudinally and transversely [8]. The FRRF can achieve various 3D curved surfaces, but the curvature is usually small and Schematic diagrams of a roll forming process [3], b flexible roll forming process [7], c flexibly reconfigurable roll forming process [8], and d Deakin's flexible forming facility (DFFF) [9] (a) the typical products are utilized in the ship building and construction industries [19]. The difficulty in flexible roll forming processes planning and machine designs limited their application [20]. Meanwhile, most variable cross-section profiles ideal for flexible roll forming are constant in height, and their cross-sections are usually of U-section with wide web and low sidewall height. Therefore, a new flexible roll forming technique, Deakin's flexible forming facility, was further developed to deform more complex shapes, as schematically depicted in Fig. 2d [9]. In that process, the pre-cut sheet metal is held between the top and bottom dies and then moves back and forth being deformed by the forming rolls. Chain-die forming was developed as another gradual forming technique. It was originally proposed as an alternative to the conventional roll forming, aiming at reducing the longitudinal strain and enabling a smoother forming processes by a pair of virtual rolls with a very large radius to enlarge the deformation zone [21]. The forming mechanism is practically realized by discrete die blocks assembled on the perimeter of a track board, as shown in Fig. 3, and the die blocks are attached to the chain links and move forward with the rotary track driven by the gear. The top and bottom die blocks are engaged one after another and enable a gradual deformation process. If all the die blocks are designed as a same cross-section, the chain-die forming works as a conventional roll forming process. The comparison between chain-die forming and roll forming of advanced high-strength steels (AHSS) indicates that the chain-die forming has the advantage of achieving more bending deformation in one pass, with less end-flare and longitudinal bow [2]. Theoretically, if die blocks with transitionally varied sections are used, channels with variable sections could be formed. Furthermore, some local features, such as steps, dimples, and grooves, can be formed by the die blocks with corresponding features [22]. In this sense, the sheet metal is formed incrementally along both the longitudinal direction and vertically stroke direction, and fulfills a combined function of roll forming and stamping. Up to now, the researches on chain-die forming are mainly on U and hat channels with constant cross-section. The feasibility of chain-die forming in realizing the "roll while stamp" mode to form channels with variable cross-sections has not been systematically studied.
In this work, six representative channels of variable cross-sections are designed and then formed by the rollstamp mode realized by chain-die forming. Finite element simulation is used to facilitate deformation analysis of the sheet metals. The comparison between the roll-stamp and stamping is carried out in terms of deformation characteristics and forming loads. The characteristic of roll-stamp process is further discussed by analyzing the deformation processes of typical cross-sections. The main novelty of the present work is to systematically investigate the feasibility of forming variable cross-sectional channels via the chain-die forming, and shed light on the roll-stamp combined mode in the gradual sheet metal forming processes.

Base channel
A hat channel with a constant section and length of 100 mm, as shown in Fig. 4, is used as a base component. Different local features and variable-sectional characteristics, including steps, dimples, and grooves, will be added on the web, sidewall, and flange of the base component. The cross-section variants of interest here generally can be divided into two major categories, the variablewidth and variable-depth. The variable-width are mainly realized on the sidewalls, and the variable-depth on the web and flanges. Note that all contours of profiles involved in this paper are of first derivative continuity.

Experimental setup
A lab-scale roll-stamp (chain-die forming) machine used for the experiments is presented in Fig. 4. The radius of the forming area on each track board is 35 m, while the length of each die block is 36 mm. Figure 4 also shows the engagement and the separation of the discrete die blocks, indicating the gradual forming process. The linear velocity of the die blocks is set to 70 mm/s. The development of forming loads is acquired by National Instruments (NI) cDAQ-9171 and recorded by LabVIEW. The geometry of the formed samples is acquired by using the ATOS scanner. The initial sheet metals are electrochemically etched with circle grids before forming, and the GMAS strain measurement system is used to obtain the plastic strain of the test samples.
QP1180 plates of 1.2-mm thickness produced by Baosteel are used in the roll-stamp forming experiments. The basic mechanical properties of the QP1180 plate are listed in Table 1 [2].

Finite element modeling
The finite element (FE) models for the metal channels with variable sections are established by using ABAQUS/ standard to numerically analyze the forming processes. A variable-width channel is used to demonstrate the FE modeling, as shown in Fig. 5. The dimensions of the designed dies are the same as in experiments and a half model is considered due to symmetry. The sheet metal is discretized into 5 layers of eight-node linear brick elements with reduced integration (C3D8R). Three pairs of die blocks are modeled as discrete rigid surfaces by 4-node 3-D bilinear rigid quadrilateral (R3D4) elements and the assembling clearances between the die blocks are determined according to the dimension of the track board. An angular velocity of 0.002 rad/s around the X-axis is assigned to realize rotation of die blocks. The Coulomb friction model is used and the friction coefficient is 0.1 [24].
The von Mises yield criterion and Chaboche nonlinear kinematic hardening model with 3 back stress components are used to describe the hardening behavior of the QP1180 materials. The Chaboche model with von Mises yield function is described as And where and ′ are stress tensor and stress deviators respectively, X and X ′ are the back stress and stress deviators respectively, is the size of yield surface, and and ISO are the initial yield stress and isotropic hardening stress respectively.
The back stress X is the sum of components X i .
(  Table 1 Mechanical properties of QP1180 from Baosteel [2] Note: t , thickness of the specimen; y , 0.2% offset yield strength; UTS , ultimate tensile strength; e u , uniform elongation (engineer strain at maximum tensile load); e t , total elongation (engineer strain at fracture); E , Young's modulus. where X and Ẋ are back stress components and back stress increment rate components respectively. c i and i are kinematic hardening constants. ̇ and ṗ are plastic strain rate and accumulated equivalent plastic strain rate respectively. The isotropic hardening component is expressed as [2] (3) where Q is the saturation stress; b is the saturation rate of isotropic hardening stress; and p is the accumulated plastic strain. The kinematic hardening component is the summation of three back stresses and is controlled by six parameters c i and i (i = 1, 2, 3). The fitted coefficients adopted from a previous study are listed in Table 2 [2].

Roll-stamp forming of variable-width channels
The variable-width here refers to the variation on the sidewall, while the web and flange remain unchanged. The variable-width channel is further categorized into three types, the concave, the convex, and the S-shape (the combination of the concave and  Table 2 The fitted coefficients of Chaboche model for QP1180 [2] Note: C i and γ i (i = 1, 2, 3) are kinematic hardening constants; Q is the saturation stress; b is the saturation rate of isotropic hardening stress. convex), as illustrated in Fig. 6. Three different sets of geometric parameters are assigned for each variable-width profile, numbered as #1, #2, and #3, as listed in Table 3. Theoretically, deformation will become increasingly large from #1 to #3. Figure 7 shows the formed variable-width samples. No fracture occurs. The dimensional accuracy, i.e., the difference between deformed and expected configurations, is listed in Table 4. The average forming accuracy is about 2.08% without any die compensation, which shows the success in roll-stamp forming variable-width channels.

Roll-stamp forming variable-depth channels
The variable-depth refers to the variation in the web and flanges. Here, the variable-depth characteristics include three types, dimple, flange step, and web step, as illustrated in Fig. 8. Three different sets of design parameters are assigned for each variable-depth channel, numbered as #1, #2, and #3, as listed in Table 5, indicating increasing deformation extent from #1 to #3. Figure 9 shows the roll-stamped variable-depth samples. The feasibilities of roll-stamp forming for variabledepth channels are experimentally proved. Fracture occurs on the dimple #3 and web step #3. The measured h for the deformed samples is listed in Table 6, with an average deviation of 11.99% without any die compensation.

Discussion
The characteristics of roll-stamp forming will be discussed in four aspects: the forming pattern, the forming load, the influence of forming direction, and the main deformation mode. Figure 10 schematically shows the combination of roll forming and stamping, where 6 die blocks are used to better understand the relationship between the two forming modes. Figure 10 shows deformation of sheet metal and the movement of dies. In roll forming, the steel blank is fed and bended by the rolls one after another; in stamping, the blank is simultaneously stamped by an integrated die moving vertically. In roll-stamp, the blank is fed in by the die blocks as in roll forming, and then is stamped by die blocks but in different strokes step by step, as illustrated in Fig. 11. Since the virtual rolling radius is extremely large, each pair of die blocks can be regarded as a stamping die pair mounted on a slightly inclined plane. Furthermore, the inclination angle is so small that the die blocks can be simplified as a series of progressive dies. In this regard, the roll-stamp forming could be decomposed into roll forming and stamping. Figure 12 further illustrates the evolution of the abovementioned six cross-sections in 5 specific deformation moments of roll-stamp forming. Each column represents the evolution of a cross-section, while each row shows the deformation difference between the cross-sections along the longitudinal direction. Figure 12 indicates that during the roll-stamp forming process, a sheet metal is deformed gradually and mainly by bending, and the forming of different cross-sections is performed in an asynchronic way. A schematic overview  on deformation in roll-stamp forming is further presented in Fig. 13. The cross-section of the sheet metal is bended gradually in the vertical direction, as in stamping. The web is firstly bended into a curve (stage A) and then pressed downward with the upper die until the apex of the arc reaches the lower die (stage B). The material flows from the flange regions to the sidewall regions from stage A to the intermediate stage B with a nearly constant web's shape, and then, the material flows out with the reverse bending of the web region from stage B to the finish stage.

Combination of roll forming and stamping
In the longitudinal section, the blank is formed gradually in the longitudinal direction as in a roll forming process but with very large rolls. A detailed evolution of the end section is shown in Fig. 14. From step 1 to step 7, though the end region does not contact with corresponding die blocks, its arch is gradually formed in compatibility to the front region. In the key step 7, the blank's end is clamped by corresponding die blocks for the first time, and the shape of arch is determined at the highest height and largest curvature. From step 7 to step 11, the arch is pressed down with an almost constant shape, while the sidewall is gradually formed.
The deformation in the front region induces deformation in the subsequent region that repeats the deformation of the previously deformed region. The induced deformation is mainly located in the web region, as shown in Fig. 15. Figure 15 shows that all keystone points of web arches in all sections are forced to fall on a nearly straight line, causing a deeper keystone point position and a larger curvature in the subsequent region. The curve of the web arch in section E is determined in the key step where the blank starts being engaged by the upper and lower die. Figure 16   on the first intersection point between the upper and the lower die, as shown in Fig. 17. Figure 17 shows that with the increase of the blank length, the position of the endpoint in the key step remains constant, while the line of the keystone points lies down with the shift of the first upper die block from block C to block A, leading to the rise of the arch's height from h c to h A .
The growth of the arch height is mainly induced by the impact from the former region, which is similar to the roll forming process. Figure 18 shows the evolution of the arch height with the increase of the blank length, indicating that the roll-stamp forming can be considered a transitional form between stamping and roll forming.
In summary, the sheet metal is pressed in the vertical direction and fed in the longitudinal direction during the roll-stamp forming process, and these two integrated motions enable formation of a more complex cross-section than that formed in a typical roll forming process.

Forming load
The forming load evolution of one die block is shown in Fig. 19a, while the forming load evolutions of six die blocks are shown in Fig. 19b. Though all die blocks share the same load evolution, the phase difference between them is inevitable.
When the forming load of one die block reaches the maximum in a moment, the asynchrony of all die blocks leads to a saturated and much smaller total forming load (sum of six die blocks), as illustrated in Fig. 20. In contrast, the evolution of forming load in conventional stamping process could be represented by the curved "6 × Die lock 1." Therefore, the maximum forming load is obviously reduced in the rollstamp process.
To compare roll-stamp forming and stamping, FE models for stamping of the channels are additionally established. The material properties, meshing strategies, and contact conditions are the same as the roll-stamp FE models. In the stamping FE models, the lower die blocks are fixed, and the upper die blocks move together downward to deform the sheet metal.
The calculated maximum forming loads for roll-stamp forming, stamping, and experimental measurements are presented in Table 7 and Fig. 21. The measured maximum forming load for the variable-depth channels is about 30% higher than those of the variable-width ones, and this discrepancy results from the different deformation modes. The major deformation in forming the variable-width channels is bending, whereas stretching deformation takes a large proportion when forming the variable-depth channels. It also can be found that by taking advantage of the progressive deformation in the rollstamp forming, the maximum forming load is greatly reduced in comparison with stamping. The maximum forming load of roll-stamp forming processes is lower than the stamping processes for the presented channels by 7.03 ~ 33.90%. Therefore, a relatively lower machine capacity is needed for the roll-stamp forming process, especially for high-strength channels. Table 7 shows that a larger forming load is required when roll-stamp forming the variable-depth channels due to the local stretching deformation. The insufficient stiffness of the present roll-stamp machine leads to the  inadequate deformation and the dimension deviations, as listed in Table 6, which was discussed by Qian et al. [24].

Transversal flow of material
Previous analysis indicates that the material flow during the forming process can be divided into three steps, as shown in Fig. 22. Firstly, the material flows from the flange region to the web region to bend the web region from a line segment into an arch; secondly, the material flows from the root of the flange region to the adjacent sidewall region while the web region is pressed downward simultaneously with a nearly constant shape; and finally, the arch of the web region is bended inversely into a line segment when its "keystone" reaches the lower die, and the material flows out from the web region to the sidewall and the flange region. Obviously, the material flows smoothly in the bending and pressing step, while in the inverse bending step, the flow is easily blocked with the sidewall trapped in the die clearance. The forming feasibility can be evaluated by the length of web, or more simply, the height of the web arch.  The arch height is defined as the height difference between the keystone point and the endpoint. The former one is determined by the front upper die block, while the latter one is determined by the subsequent lower die block, indicating that the arch height in the subsequent region is easily influenced by the inconsistency of the section shape between the front region and the subsequent region, especially for the variable section channels, as shown in Fig. 23.
In this section, the influence of forming direction on the flow of material and the deformation of the variable-width and variable-depth channels is discussed. Starting from relatively wider end is defined as the positive forming direction, and starting from the narrow end to wide is defined as the negative direction, as schematically shown in Fig. 24. Figure 25 shows that with the vertical press of the upper die, the curvature and the arch height of the web region firstly increase and then tend to be stable. Three blanks are  Figure 26 illustrates the impact of the forming direction on the variable-width channels. Compared with the narrow cross-section, the arch height of wide section's web is relatively larger, leading to a deeper position of keystone point and more redundant material staying in the web region. When the variable-width product is formed in the positive direction, the deformation in the front wide section region induces a deeper keystone point position in the subsequent region, which implies more severe deformation than forming a uniform sectional product. Moreover, the residual material in the web region has difficulty in flowing out when the web arc is flattened, with the sidewall trapped in the die clearance.
However, when the channel is formed in the negative direction, the deformation in the front wide section region induces a shallower keystone point position in the subsequent region, which implies slighter deformation than forming a uniform sectional product, as illustrated in Fig. 27.
A more detailed description on the evolution of arch height is shown in Fig. 28. The web region in the subsequent region is slightly affected by the front region. The residual material in the subsequent narrow region increases when formed in the positive direction, while the residual material in the subsequent wide region is reduced in the negative direction, leading to a better formality for the variable-width channels. Starting from relatively shallower end is defined as the positive forming direction, and starting from the deep end to shallow is defined as the negative direction, as schematically shown in Fig. 29. Figures 30 and 31 illustrate the influence of the forming direction on the web step variable-height channels.
When the variable-height product is formed in the positive direction, the keystone point line slides down with the axial slop web region, leading to a deeper position of keystone point and more redundant material staying in the web region, as shown in Fig. 30. However, when the channel is formed in the negative direction, the deeper web position in the front region induces a much deeper keystone point position in the subsequent region, leading to more residual material and more severe bending deformation in the web region than positive direction, as shown in Fig. 31. Figures 32 and 34 illustrate the influence of the forming direction on the flange step variable-height channels. When the variable-height product is formed in the positive direction, though the keystone point line proceeds from a same point, it tips slightly more upward with the rise of the flange, leading to slighter deformation in the web region than the uniform section, as shown in Fig. 32.
Though the key section, in which the upper punch intersects with the lower die in the vertical direction for the first time, changes with the rise of the flange, it has no effect on the arch height in the subsequent region. Figure 33 illustrates that the angle between the first and the last upper die block is constant when the trajectory curvature is constant, and the arch height in the subsequent region is also constant as below: When the variable-height product is formed in the negative direction, as the flange level falls, the keystone point line tips slightly downward, leading to a little more residual material in the web region, as shown in Fig. 34.
A more detailed description on the evolution of web curvature is shown in Fig. 35. The keystone point line is mainly determined by the axis shape in the web region, while it is slightly impacted by the changes in the flange region. For web step variable cross-section channels, though the residual material in web region increases when formed in (6) h u = l blank * tan u = l blank * tan vh = h vh     the positive direction is better than the negative direction, the difference between them is quite small.
In summary, the transversal flow of material is mainly determined by the residual material in the subsequent web region, which is greatly impacted by the axial web step and slightly impacted by the axial flange step or the width of the web. Figure 36 illustrates the deformation in roll-stamp forming variable-width channels, where three deformed stages for concave, convex, and S-shape channels are respectively plotted, representing the initial contact between die blocks and sheet metal, an intermediate stage and the maximum stroke stage.

Bending and stretching deformation
Take the deformation of the lead end as an example, the cross-section of the channel is bended in the vertical direction and the material flows from the flange to the web region. It is found that the deformation pattern of the cross-section is similar to stamping process. Meanwhile, different sections in the longitudinal direction are sequentially deformed, and the previously deformed regions exert constraint on the deformation of the following sections, which is similar to the roll forming process. It is also noted that bending is the major deformation for variable-width channels, and the transition region experiences a limited stretching/ compression. Meanwhile, compared with flexible roll forming, the curvature of the transition region is much larger because the deformation is primarily dominated by bending rather than rolling, referring to Kasaei et al. [7], and the flange can be formed easily. In summary, the experiments and the numerical analysis indicate that variable-width channels can be gradually deformed through the roll-stamp forming process, and a transition region with larger curvature could be realized. Figure 37 shows the deformations of roll-stamp forming variable-depth channels with dimple, flange step, and web step, respectively. Similar to the variable-width channels, the deformation is a combination of stamping and roll forming. It is also found that relatively large stretching deformation exists at the web region for channels with dimples and web steps, which is the major source of the fractures. Compared with the flexible roll     According to Figs. 36 and 37, bending and stretching both occur in roll-stamp forming variable channels, while large stretching deformation primarily exists at the web region for channels with dimples and web steps. Figure 38 shows that the seam between web and sidewall is firstly formed by transversal bending in steps 1-2, and then stamped downward in steps 3-5 for most channels. However, for web step channels, the seam is stretched from an approximately straight line to a step curve in steps 3-5, leading to relatively large axial stretching deformation.     The measured plastic strains near the cracks are extracted for all the deformed samples and put into the forming limit diagrams of the QP1180 alloy (FLD, provided by Baosteel), as depicted in Fig. 39. It shows that the strain increases from #1 to #3. Figure 39a and b signify that the strains, especially the axial stretching strain for dimple #3 and web step #3, exceed the forming limits, consistent to the fracture in the experiments.

Conclusions
In this work, the feasibility of roll-stamp forming metal channels with variable sections is systematically evaluated through experiments and FE analysis. Six variablewidth and variable-depth channels are roll-stamp formed and studied. The following conclusions can be drawn. Fig. 37 Deformation processes of roll-stamp forming variabledepth channels: a dimple, b flange step, c web step, where 1st, 2nd, and 3rd represent the initial contact stage, intermediate stage, and the maximum stroke stage respectively Fig. 38 Web-sidewall intersection seems' evolution of variable section channels 1. The forming of metal channels with variable sections by the roll-stamp mode is evaluated by experiments and FE analysis. The experimental results indicate the good feasibility of roll-stamp in manufacturing variable-width and variable-depth channels. 2. The roll-stamp forming mode is a combination of roll forming and stamping, from the view of longitudinal and vertical motion respectively. The deformation induced by longitudinally feeding is mainly located in the subsequent web region, which is greatly affected by the axial web step and slightly impacted by the axial flange step or the width of the web, leading to forming feasibility difference between two forming directions. 3. The FE results indicate that a smaller forming load is achieved by roll-stamp technique compared with stamping, with a maximum reduction rate of 33.9% for the 100-mm-length AHSS channels studied. 4. Bending and stretching both occur in roll-stamp forming variable channels, while large stretching deformation primarily exists at the web region for channels with dimples and web steps, which is the major cause of the fracture.

Declarations
Ethical approval This work does not contain any ethical issues or personal information.