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Stamping of stringer sheets
Journal of Manufacturing Processes 36 (2018) 319–329
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Stamping of stringer sheets
T
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P. Groche, S. Köhler , S. Kern Institute for Production Engineering and Forming Machines (Technische Universität Darmstadt), Otto-Berndt-Straße 2, 64287 Darmstadt, Germany
A R T I C LE I N FO
A B S T R A C T
Keywords: Stringer sheet forming Stamping Buckling Simulation
Light-weight performance of load carrying structures can be increased through the use of bifurcations. Stringer sheets make use of this design principle. They consist of a base sheet with stiffening ribs or stringers. In this work the stringers are attached to the flat base sheet via laser welding and afterwards the part receives its targeted 3D shape in a subsequent forming process. While a larger height of the stringers is advantageous in terms of lightweight performance, it can lead to higher compressive stresses in concave areas of the part, causing buckling of the stringers. Previous studies made use of hydroforming for the manufacture of the 3D shaped stringer sheets. During hydroforming a side support to the stringers is given by the pressurized medium. Due to relatively long cycle times, it is not suitable for highly efficient mass production. Hydroforming also has shortcomings in the attainable geometries. This paper presents a new industrial-suited stringer sheet stamping process which is up to 20 times faster than current stringer sheet forming processes based on hydroforming. Furthermore, a numerical model allowing the prediction of stringer buckling is provided. Both, process and numerical model, are experimentally validated.
1. Introduction The performance in terms of weight and stiffness is a major evaluation criterion for many products, especially in the transportation sector. Every kilogram of material saved does not need to be produced, nor accelerated during product usage and recycled at the end of the product lifecycle [1]. Therefore, promising principles for lightweight design are sought after. Many successful technological solutions are inspired by nature and have been adopted by science [2], as evolution has optimized solutions under specific boundary conditions [3]. Loaded structures like shells, leaves or wings use bifurcations to reach the best strength to weight ratio while using minimal resources. Many technical products, e.g., roof tops or car body parts are created with the same intention. They also face the requirements of high stiffness, maximized resource efficiency and minimized efforts for manufacturing. Bifurcated structures provide the possibility to fulfill high stiffness requirements by using minimum material amount. Analytical investigations show an increase in the load carrying capacity to weight ratio up to 16.8 when comparing stringer sheets to non-bifurcated ones (see Fig. 1) [4]. Despite these opportunities for weight reduction, industrial applications of bifurcated sheet structures are rare. The main reason for that can be attributed to the lack of an efficient and economically feasible way to produce spatially curved, bifurcated sheet metal structures.
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Milling, for example, leads to an immense waste of up to 95% of the initial material [5], whereas processes like casting and extrusion, which are suitable for fabrication of these structures, go along with a vast energy consumption as well as inflexibility in terms of geometry and materials used [6]. One approach to increase the efficiency of sheet metal products is the use of tailored blanks [7]. These are semi-finished parts with locally differing properties like varying sheet metal thickness, material or coating. Beside tailored blanks made out of steel, other materials like aluminum [8] or magnesium [9] were investigated, too. An extended review of current possibilities of tailored blanks was given by Merklein et al. [7]. Tailored semi-finished parts introduce new challenges to forming processes. Kinsey et al. reported that the forming of tailor welded blanks (TWB), which consist of different materials or sheets with different thicknesses, requires new tooling concepts [10]. The weld line movement is an often investigated phenomenon in forming processes with TWB, because it has a significant influence on the thickness distribution throughout the sheet metal part. Mennecart et al. managed to reduce the weld line movement and therefore improving the thickness distribution in a deep drawing process by using a tailored tool. It consists of a segmented blank holder made from steel and reinforced polymer parts [11]. Heo et al. investigated the effects of draw beads on the weld line movement of TWB during a deep-drawing process, discovering that the weld line movement decreases for wider and
Corresponding author. E-mail address: [email protected] (S. Köhler).
https://doi.org/10.1016/j.jmapro.2018.10.025 Received 18 December 2017; Received in revised form 16 October 2018; Accepted 22 October 2018 1526-6125/ © 2018 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
Journal of Manufacturing Processes 36 (2018) 319–329
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Nomenclature
FEM FN γ hSt L l le m μ rb1 rb2 S t TWB TRB v w wcrit
Symbol b β δ Δb Δβ Δγ ΔhSt Δl Δt Δw Δxr E Fcrit,x FEA
Welding distortion Angle between stringer and base sheet Imperfection factor Imperfection due to the welding distortion Imperfection in the angle between stringer and base sheet Imperfection due to twist of stringer sheet in Y-direction Imperfection in the stringer height Imperfection in the base sheet length Imperfection in the sheet thickness of the stringer Imperfection due to initial waviness of the stringer X-distance between the origin of rb1 and rb2 Young’s-Modulus Critical load for stringer sheet with stringer height x Finite element analysis
Finite element method Blank holder force Twist of stringer sheet in Y-direction Stringer height Actual stringer edge length after forming Base sheet length Evaluation length Mass of the stringer sheet Friction coefficient Radius of the punch Radius of the drawing die Drawing depth Sheet metal thickness Tailor welded blanks Tailor rolled blanks Poisson Ratio Waviness of a stringer Critical waviness
Fig. 1. Advantages in stiffness of stringer sheets [4].
hydroforming. It is based on the process principle depicted in Fig. 3. A pressurized fluid fills the die cavity and presses the sheet metal into the die while the blank holder closes the die cavity and controls the flange movement [22]. The hydroforming process exhibits advantages with respect to interferences between stringers and tool as well as the support of the stringers. Disadvantages are the needed process time and restrictions concerning the feasible geometries. In the performed experiments the cycle time in hydroforming for one drawn part is close to one minute. Additionally, the geometry of the part needs a circumferential flange where no stringers can be placed, since stringers in the flange would cause leakage. To overcome these restrictions in both process time and feasible geometries, first steps towards forming of stringer sheets with solid tools through die-bending were conducted [24]. Slots for the stringer in the punch and the die allow a convex or concave bending operation, as it can be seen in Fig. 4.
higher draw beads [12]. Different thicknesses of tailor rolled blanks (TRB) or TWB result in a significantly higher tendency of leakage in hydroforming processes [13]. Leakage problems in hydro mechanical deep drawing of TWBs were reduced with segmented tool parts, which compensate the difference in thicknesses [14]. A blank holder with adapted thickness transition can balance the offset in conventional deep drawing [15]. Kopp et al. discoved that an elastic blank holder is more useful to prevent wrinkling errors in deep drawing of TRB than a blank holder made of steel [16]. Tailored blanks can also be used to extend process limits. By using TRB Meyer et al. were able to increase the drawing depth by 19% in deep drawing [17]. Mori et al. applied plate forging for local thickening of semi-finished parts in square cup deep drawing. In this way, they achieved an increase in drawing depth of 33% [18]. Tailor heat treated blanks use a local heat treatment (e. g. conducted with a laser) to improve parameters like formability [19] or optimize mechanical properties of a sheet metal product [20]. The last category of tailored blanks are patchwork blanks, which consist of multi-layer sheet metals [7]. Jalanesh et al. presented a way how two sheets can be connected and formed in one process step by the integration of a projection welding process into a deep drawing process [21]. Ertugrul and Groche [22] developed a process chain which contains the fabrication of bifurcations in plane sheet metal followed by a forming process that generates the intended 3D shape. The advantage of this process sequence lies in the avoidance of a complex 3D joining process. The bifurcation of a flat sheet is carried out by attaching stringers through laser welding as it can be seen in Fig. 2. Here, the stringer is connected to the base sheet by means of a concentrated heat input from the rear side of the base sheet. The subsequent forming process is mostly conducted by
Fig. 2. Laser welding of stringer sheets. 320
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further buckling or wrinkling criteria. Hutchinson summarized plastic buckling theories in his work [27]. He described the effect of imperfections on the buckling sensitivity with the help of calculated examples. Cao and Boyce presented an elastic-plastic wrinkling model for rectangular plates under different constraints like binder pressure [28]. They account for imperfections in the material by representing geometrical inaccuracies or material inhomogeneities with offset elements. This approach leads to an accurate simulative prediction of flange wrinkling in deep drawing. Wang and Cao provide an analytical model with a modified energy approach to predict and prevent side-wall wrinkling in sheet metal forming [29]. Their model is supported by a numerical sensitivity analysis and experimentally validated by Yoshida buckling tests. A further development of [28] is shown in [30]. It shows that the critical buckling stress and the wavelength of the buckles in flange wrinkling in sheet metal forming can be predicted analytically. A utilization of the bifurcation criterion in finite element method (FEM) is presented by Saxena and Dixit [31]. Here, flange wrinkling in circular and square cup drawing is predicted. Kim et al. utilize the bifurcation theory in FEM, too. They successfully predicted the initiation and growth of wrinkles in a cylindrical deep drawing process and found stable solutions in their finite element analysis (FEA) if the normalized element length is sufficiently small [32]. Kawka et al. simulated the wrinkling of conical cups in a deep drawing process [33]. They found a significant influence of the initial finite element mesh. However, their FEA simulations do not show a good agreement with the experimental results. Correia and Ferron presented an analytical and numerical study of wrinkling in deep drawing of anisotropic sheets [34]. A critical compressive stress is defined and used as a wrinkling criterion. The authors were able to predict the wrinkling behavior of experimental studies found in literature [35]. Banu et al. used shell elements with reduced integration to simulate the wrinkling and springback behavior of a rail shaped sheet metal that has analogies to the roof tile in Fig. 1 [36]. They achieved an acceptable quality of springback prediction. However, their FE model overestimates the wrinkling failure during the stamping process. Morovvati et. al used numerical simulations for the prediction of flange wrinkling in deep drawing of cups with multiple sheet layers. They observed a good agreement of numerical and experimental results [37]. Latest models even cover thermal aspects. Zheng et. al. presented a buckling model that uses the energy method and adopt a one-dimensional beam geometry assumption to predict flange wrinkling in hot deep drawing [38]. This model is suitable for higher forming temperatures. As can be seen from the current state of wrinkling models in sheet metal forming a strong focus is set to the utilization and improvement of the FE analysis, which is an important tool in industrial process design [39]. This work provides a numerical model for dimensioning feasible stringer sheet geometries in a new stamping process. It answers the question how flat stringer sheets can be formed with solid tools and
Fig. 3. Process principle of hydroforming of stringer sheets [23].
Fig. 4. Process principle of die-bending of stringer sheets [24].
Since sheet metal product geometries often require more complex forming conditions, a new stamping process for stringer sheets with solid tools is necessary to exceed the current process limits. This paper presents a highly productive forming process that meets the requirements for mass production of bifurcated structures. Compressive stresses in concave curvatures limit the maximum producible height of the stringers. They can lead to buckling failure of the stringer. The trend to thinner high strength sheet metals increases the relevance of this failure mode. Therefore, the reliable prediction of wrinkling/buckling process limits becomes crucial to design engineers. Several approaches have been proposed. In 1956, Senior analytically predicted the occurrence of flange wrinkling in deep drawing based on the stress strain curve of the material and the flange geometry [25]. He estimated the stability of the flange with the aid of the classical energy method. Buckling is expected in this approach if the energy stored in the wrinkled structure is smaller than the one of the flat state without wrinkles. Using a similar approach, Hill set up his theory of uniqueness and stability in elastic-plastic solids [26]. It is the basis of several
Fig. 5. Tool concept for stamping of stringer sheets with solid tools. 321
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future investigations. Two geometries are investigated in the present work. Both are depicted in Fig. 6. They represent “open” part geometries without circumferential flange but with stringers in the flange area. These geometries cannot be manufactured by hydroforming for the reasons given before. The two specimens differ in the number of stringers (one or two) and the sheet metal width (150 mm and 300 mm). The specimens have a length of 300 mm in the flat state after the laser welding process. The stringers are welded at 1000 W and a speed of 22 mm/s using an ytterbium fiber laser. The sheet metal thickness t is 1 mm for both the stringer and the base sheet. The material used is a deep-drawing steel DC 04. During the forming process the parts take on their targeted shape of a roof tile. The radii rb1 and rb2 are 30 mm while the X-distance between the origin of the two radii Δxr is 64.95 mm. The drawing depth S and the stringer height hSt are varied during the experiments (S = 20–40 mm; hSt = 5–10 mm). Inlay sheets are placed at the opposite side of the punch and the blank holder for the production of the part with one stringer. In this way, the same stamping tool can be used for both geometries and a comparable, symmetrical distribution of the blank holder force is guaranteed.
shows occurring process errors. The maximum producible stringer height without failure for different process setups will be determined. 2. Process design The experimental setup and numerical model are presented in this section. At first, the new tool concept for stamping of stringer sheets is explained. This is followed by an introduction of the investigated geometries and the process steps used. Afterwards, the observed process errors are discussed. A numerical model to predict one of the major appearing failure modes is presented at the end of the section. 2.1. Tool concept and specimen Fig. 5 shows the tooling concept for a stringer sheet stamping process. The concept is suitable for mass production on single-acting presses. The press used in the experimental investigation is a 2500 kN servo press with an integrated drawing cushion which allows for a maximum blank holder force of 400 kN. The tool consists of a punch, a blank holder, a drawing die and a counter punch. The punch and the blank holder have slots with a width of two millimeter in which the stringers are placed during the forming process. The blank holder is coupled with the drawing cushion of the press while the punch is fixed at the press table. The drawing die and the counter punch move together with the press ram. In the present work the drawing die consists of two straight edges with radii rb2 = 30 mm. The counter punch is linearly guided and suspended with pneumatic springs (the springs produce a combined maximum force of 10 kN). The active elements are easily exchangable, so that the geometry can be varied quickly for
2.2. Process steps This subsection details the process steps of the introduced stringer sheet stamping process. The procedure can be divided into four steps (see Fig. 7): I) The tool is open: The flat stringer sheet is placed in the tool so that the stringer is in the middle of the slot in the blank holder and the
Fig. 6. Geometry of specimen (semi-finished part; stamped part). 322
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Fig. 7. Process steps for stamping of stringer sheets.
punch. II) The tool closes: Drawing edges and counter punch move together in positive Y-direction until the contact with the stringer sheet is
established. III) The specimen is formed: Counter punch and punch remain at their position while the drawing edge and the blank holder move 323
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c) Bump in the base sheet: The stringer can produce a bump at the opposite side of the stringer sheet, especially if the force of the counter punch is not sufficient or the stringer misses the slot in the punch. This failure mode occurs more frequently when the stringer height is very large (hSt > 10 mm). d) Tearing of the stringer: This error can occur due to high positive strains in convex curvatures during the process. Brittle materials, high stringer heights and high blank holder forces can produce this failure mode. e) Collision of stringer and tool: If the accuracy of the insertion position or the geometry of the semi-finished part is not sufficient, the stringer misses the slot in the punch or the blank holder and collides with the solid tool surfaces. f) Tool marks in the stringer: Tool marks can occur in process step III) if the stringer moves in the punch slot at the edge of the punch or if the stringer is not parallel to the intended slot.
together in positive Y-direction. The counter punch presses the stringer sheet with a force of 10 kN against the punch and the blank holder force acts in negative Y-Direction towards the drawing edge. IV) The tool opens: At first, the drawing die and the counter punch move back into their starting point followed by the blank holder. The stamped stringer sheet can be removed. The cycle time for the investigated processes is about three seconds. 2.3. Process errors During the process steps described above, several errors can occur. Beside the typical deep drawing defects like wrinkling or tearing of the base sheet metal, the stringers can cause new failure modes which are depicted in Fig. 8: a) Buckling of the stringer: The stringer starts to buckle if the negative strains caused by a concave curvature in the stringer edge are too high. b) Failure of the welding seam: Inaccuracies in the welding process and tension peaks during the forming process in the welding seam can cause fracture at this position.
The process errors b–f) are mostly due to limitations of the used material or inaccuracies in the welding or forming process. However, the buckling of the stringer is strongly dependent on the stringer height and forming process parameters like the blank holder force or drawing depth. Buckling appears as a significant failure mode that affects
Fig. 8. Process errors during stringer sheet stamping and place of occurance. 324
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mechanical properties of the final part. The stiffness of a stringer sheet with a buckled stringer is not as high as the stiffness of a stringer sheet with the same stringer height without buckled stringers [24]. For that reason, this work focuses on the investigation of the buckling failure. A buckling criterion to detect and quantify this failure mode was proposed by Bäcker [40]. A waviness w is calculated with the straight connection le of two points on the stringer edge and the actual stringer edge length L (see Fig. 9) after the forming process:
w=
L − le le
the blank holder force. The semi-finished parts show an initial waviness (Δw) and deflections (Δb) due to the welding distortions. As the slot width of the tool is bigger than the sheet thickness, the insertion position of the semi-finished part can be twisted in Y-direction by a small angle (Δγ). Table 1 shows the values of the geometric imperfections of three semi-finished samples with different stringer heights that have been measured with an optical measuring system (GOM Atos III). For hSt, β, t and l the reference value used was the desired value. For w and b, the critical waviness wcrit and the length of the sheet l were selected as reference to determine the variation in percentages. Since γ is difficult to measure in the process, the maximum possible value, which is due to the slot width in the tool parts, was used. In the measured samples, the seven geometrical inaccuracies have an average deviation of 1.13% with regard to the particular target values. The modelling of all imperfections would be very time consuming, therefore, a useful method to model these irregularities is needed. Cao and Boyce provided a simple but valuable way to model similar imperfections in the prediction of the wrinkling behavior of rectangular plates under lateral constraints. Offset elements represent process and material imperfections in their work [28]. This approach is adapted to the stringer for the determination of the buckling error of the stringer in the stamping process. As it can be seen in Fig. 12, one row of elements is shifted in Z-direction by a predefined percentage of the sheet thickness t. This percentage is called imperfection factor δ. In front and behind the offset element row, there is a transition element row to compensate the offset. Here, elements that have a slight parallelogram shape in the X/Z-plane ensure a continuous meshing of the stringer. Without these transition element rows the meshing of the stringer would be unsteady. This would cause unwanted local effects such as stress peaks at the boundaries of the offset element row.
(1)
Bäcker set the critical waviness to wcrit = 0.002. If w exceeds a critical waviness wcrit the straightness deviation is higher than usual deviations caused by the welding process for the production of the semi-finished part and the stringer is called buckled [40]. Due to the fact that the buckling errors occur in concave curvatures of the stringer, the evaluation length le is set to the duplicated concave curvature radius rb1
le = 2rb1
(2)
2.4. Process simulation This section describes the numerical simulation. The stringer sheet stamping process needs to be modelled accurately especially concerning the buckling of the stringer. The FE analysis is carried out with Dassault Systèmes Abaqus 6.14 using an explicit solver. Due to symmetries in the set-up, a quarter model, which is shown in Fig. 10, is sufficient to describe the whole stamping process. The hexagonal “incompatible mode” element type C3D8I, which is optimized for bending analysis [41], is used. A mass scaling factor of 1000 is set to shorten simulation times. The element edge length is 1 mm in each direction. A convergence analysis proved these assumptions to be adequate. The tools are modelled as rigid bodies. The assumption of rigid bodies for the tool bodies in simulation is based on the statements of Neto et al. [42]. They conclude that the elastic modeling of tool bodies can increase the accuracy of deep drawing simulations, but that considerably longer calculation times are required. They therefore recommend the use of elastic tool bodies only in specific cases, e.g. if the stiffness of the tools is low, or high strength steels are formed [42]. This is not the case in this work. Nevertheless, to verify the assumption of rigid bodies in the die, the drawing depth S of three experimentally formed specimens was compared with that of the simulation. The deviations of the samples from the FEA results with rigid tools were below 1% (0.12–0.28 mm) relating to the total drawing depth S = 30 mm. This leads to the conclusion that the assumption of rigid tool bodies in the simulation is sufficiently accurate. Penalty contact is used with Coulomb´s friction law. Due to the fact that the investigated stamping process is a combination of deep drawing and bending, the friction coefficient is set to μ = 0.08 which is common in deep drawing [43] as well as bending [44] simulations. The material model for DC 04 has a flow curve represented by data points (see Fig. 10a), a Young’s-Modulus E = 210 GPa and a Poisson Ratio v = 0.3. The flow curve is determined from tensile tests and extrapolated using Ludwik’s approach [45]. An elaborate modelling of the weld line and the heat affected zones has little influence on the forming behavior of the rest of the part in the simulation of tailor welded blanks but it increases the calculation time significantly [46]. Hence a homogeneous material behavior is assumed in this work. However, imperfections of the specimen or the procedure of the process have to be considered. Especially geometrical inaccuracies can influence the buckling behavior significantly. Fig. 11 shows the most common imperfections. After the laser welding of the semi-finished parts, deviations in the stringer height (ΔhSt) and the angle between stringer and base sheet (Δβ) can be observed. The sheet thickness of the stringer is varying (Δt), as well as the base sheet length (Δl), both influencing the distribution of
3. Results and evaluation 3.1. Variation of imperfection factor This section compares the results of the numerical investigations with the experiments. Process parameters like the blank holder force FN or the drawing depth S were varied as well as the stringer height hSt and the number of stringers on the semi-finished part. The waviness w of the stringer in the concave curvature is evaluated. Each stringer height is tested three times and both concave curvatures of the drawn parts were considered in the evaluation. During the experiments, the specimens are lubricated manually using a drawing oil by Zeller + Gmelin (Multidraw PL 61). The simulations are carried out with an ideal modelled stringer (δ = 0%), an imperfection factor δ = 1%, which represents the observed irregularities, and δ = 10% for exaggerated imperfections.
Fig. 9. Stringer edge lengths L and le for the calculation of the stringer waviness w. 325
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Fig. 10. Simulation model (a) and material model (b).
Fig. 11. Geometrical imperfections of the semi-finished parts. Table 1 Measured imperfections in semi-finished stringer sheets. β [°]
Measured value
hSt [mm]
hSt = 5 mm hSt = 8 mm hSt = 10 mm target value/ reference (average) imperfection
4.957 89.59 7.935 90.11 9.923 90.05 hSt 90 0.81 % 0.21 % average = 1.13 %
t [mm]
l [mm]
w [−]
b [mm]
γ [°]
1.000 1.018 1.008 1 0.87 %
299.24 299.32 299.19 300 0.25 %
0.00007 0.00011 0.00013 0.002 (=wcrit) 5.17 %
1.789 0.969 0.917 300 (=l) 0.4 %
Due to the slot width, the maximum possible twist in the tool is Δγmax = 0.19°.
90° 0.21 %
process setup. It leads to the same critical stringer heights as the experiments. The simulations with δ = 0% are not able to model the buckling behavior realistically. Here, the predicted critical stringer height is always too high. An imperfection δ = 10% is obviously too high to model the process inaccuracies. An imperfection value of δ = 1% seems to be sufficient to meet the experiments. Fig. 13a), b) and d) show that an increasing drawing depth S leads to a decreasing critical stringer height. This is due to the fact that with increasing drawing depth the arch length of the concave curvature increases, too. This leads to a larger stringer sector with negative strains and therefore a higher risk for buckling. The influence of the blank holder force FN can be seen in Fig. 13a) and c). Like in hydroforming of stringer sheets [40] a higher blank holder force leads to higher feasible stringer heights without buckling failure. In his case, doubling FN allows for a stringer height up to 9 mm (FN = 400 kN). Due to process inaccuracies in the experimental investigations, the border between buckling free and buckled stringers is a transition area rather than a hard boundary [24]. Some stringers of the same stringer height hSt are already heavily buckled here, while others are only just beginning to buckle. This can lead to large variations in the waviness in this area, as can be seen for example in the values for hSt = 7 mm in Fig. 13a and d. In order to check the accuracy of the numerical model, the numerical and experimental waviness patterns of heavily buckled stringers are compared. In general, the results of the simulation agree with experiments, as the correct number of waves is predicted. This is illustrated by an example in Fig. 14.
Fig. 12. Modelling of imperfections.
Fig. 13 shows the results for the stringer waviness w depending on the stringer height hSt in different process setups for the geometry with one stringer. The waviness w increases with increasing stringer height hSt in every setup. Fig. 13a) illustrates the buckling limit in the concave curvature for FN = 200 kN and S = 30 mm. These values for the blank holder force and the drawing depth are in the middle of the operating window of the tool/press. The experiments show that hSt = 6 mm is a stringer height where three of six concave curvatures are buckling free. For hSt = 5 mm no stringer buckled and for hSt = 7 mm or higher, every stringer buckled. The simulations with δ = 0% showed buckling at a stringer height hSt = 8 mm whereas the simulations with δ = 1% predicted a buckling behavior which is within the range of variation of the experiments for every stringer height. For δ = 10% the estimated waviness for three out of four stringer heights is too high. Looking at the other setups confirms this behavior (see Fig. 13b–d). The values for 12 out of 15 simulations with δ = 1% meet the range of experimental values, whereas no value for δ = 0% and only three for δ = 10% are within this scope. Furthermore, the simulation with δ = 1% is able to predict the critical stringer height for each tested 326
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Fig. 13. Waviness of stringer for different parameters (numerical and experimental).
with only one stringer, which led to a symmetrical loading situation. The flow direction of the material of these stringer sheets is nearly parallel to the weld line. With a second stringer on the base sheet an additional lateral influence on the buckling behavior is present. The movement of the base sheet in Z-direction is not symmetrical on both sides of the stringer. It is assumed that this influence leads to an earlier buckling failure. The parallelism of both stringers is important for the correct insertion of the semi-finished part in the tool. The stringer position has to be precise in the welding process, too. If both stringers are not parallel to each other, the stringers do not hit the tool slot. That leads to a collision of stringer and tool. Fig. 15 shows a comparison of drawn parts with one stringer and with two stringers (S = 30 mm; FN = 200 kN). The simulations were carried out with an imperfection of δ = 1%. It can be seen that the numerical results for both parts reach nearly the same waviness values. The values for the stringer sheets with two stringers are constantly negligible higher compared to the values of the parts with one stringer only. The average waviness of the experimental investigation with one stringer is in the range of the error bars of the values of the sheet with
Fig. 14. Comparison of experimental and numerical waviness pattern.
3.2. Variation of number of stringers Here, the influence of a second stringer on the base sheet is evaluated. Now, the stringers are no longer in the Z-symmetry plane of the part. The results already shown were obtained with a stringer sheet 327
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The blank holder force introduces positive strains into the stringer and therefore reduces the risk of buckling. The number of stringers has no significant influence on the critical stringer height. In future work a lateral support will be developed to support the stringer during the process to prevent the risk of buckling and to increase the producible stringer height. Here, for example, a wedgeshaped punch slot can compensate for small geometric defects in the semi-finished parts and produce straightened stringers. In this way, the lightweight potential of the stringer sheet forming technology can be enlarged enormously. Declarations of interest None. Acknowledgements Fig. 15. Influence of the number of stringers.
The presented investigations were carried out within transfer project T7 of CRC 666 ‘Integral sheet metal design with higher order bifurcations’. The authors thank the German Research Foundation (DFG) for supporting the Collaborative Research Centre 666. References [1] Allwood JM, Cullen JM, Carruth MA, Cooper DR, McBrien M, Milford RL, et al. Sustainable materials: with both eyes open. Cambridge: UIT Cambridge; 2012. [2] Bar-Cohen Y. Biomimetics - using nature to inspire human innovation. Bioinspir Biomim 2006;1:1–12. [3] Knippers J, Speck T. Design and construction principles in nature and architecture. Bioinspir Biomim 2012;7. [4] Groche P, Köhler S, Husmann H, Kurpiers C. Erweiterung von Grenzen der Stegblechumformung, Wt Werkstattstechnik online. Heft 2017;10. [5] Shamsuddin KA, Ab-Kadir AR, Osman MH. A comparison of milling cutting path strategies for thin-walled aluminium alloys fabrication. Int J Eng Sci 2013;2:1–8. [6] Yoon H-S, Lee J-Y, Kim H-S, Kim M-S, Kim E-S, Shin Y-J, et al. A comparison of energy consumption in bulk forming, subtractive, and additive processes: review and case study. Int J Precis Eng Manuf Technol 2014;1:261–79. [7] Merklein M, Johannes M, Lechner M, Kuppert A. A review on tailored blanks Production, applications and evaluation. J Mater Process Tech 2014;214:151–64. [8] Kinsey B, Viswanathan V, Cao J. Forming of aluminum tailor welded blanks. SAE technical paper. 2001. [9] Bräunig S, Düring M, Hartmann H, Viehweger B. Magnesium sheets for industrial application. Magnesium: Proceedings of the 6th International Conference Magnesium Alloys and Their Applications. Geesthacht: Wiley Online Library; 2003. p. 955–61. [10] Kinsey B, Liu Z, Cao J. A novel forming technology for tailor-welded blanks. J Mater Process Tech 2000;99:145–53. [11] Mennecart T, Güner A, Ben Khalifa N, Hosseini M. Deep drawing of high-strength tailored blanks by using tailored tools. Materials 2016;9. [12] Heo YM, Wang SH, Kim HY, Seo DG. The effect of the drawbead dimensions on the weld-line movements in the deep drawing of tailor-welded blanks. J Mater Process Tech 2001;113:686–91. [13] Krux R, Homberg W, Kleiner M. Properties of large-scale structure workpieces in high-pressure sheet metal forming of tailor rolled blanks. Steel Res Int 2005;76:890–6. [14] Hétu L, Siegert K. Hydromechanical deep drawing of tailor welded blanks. Steel Res Int 2005;76:857–65. [15] Hirt G, Abratis C, Ames J, Meyer A. Manufacturing of sheet metal parts from tailor rolled blanks. J Technol Plast 2005;30. [16] Kopp R, Wiedner C, Meyer A. Flexibly rolled sheet metal and its use in sheet metal forming. Adv Mat Res 2005;6–8:81–92. [17] Meyer A, Wietbrock B, Hirt G. Increasing of the drawing depth using tailor rolled blanks - Numerical and experimental analysis. Int J Mach Tools Manuf 2008;48:522–31. [18] Mori K, Abe Y, Osakada K, Hiramatsu S. Plate forging of tailored blanks having local thickening for deep drawing of square cups. J Mater Process Tech 2011;211:1569–74. [19] Vollertsen F, Lange K. Enhancement of drawability by local heat treatment. CIRP Ann Manuf Technol 1998;47:181–4. [20] Meza-García E, Rautenstrauch A, Kräusel V, Landgrebe D. Tailoring of mechanical properties of a side sill part made of martensitic stainless steel by press hardening. ESAFORM 2016: Proceedings of the 19th International ESAFORM Conference on Material Forming 2016. [21] Jalanesh M, Miller A, Hehmann M, Spiekermeier A, Hübner S, Behrens BA. Processintegrated projection welding during deep drawing. Adv Mat Res 2016;1140:59–66. [22] Ertugrul M, Groche P. Hydroforming of laser welded sheet stringers. Key Eng Mater 2009;410–411:69–76. [23] Groche P, Bäcker F. Springback in stringer sheet stretch forming. CIRP Ann Manuf
Fig. 16. Process window for stamping of stringer sheets (rb1 = rb2 = 30 mm).
two stringers. So an influence of the number of stringers in this case cannot be stated.
4. Conclusions and outlook The feasibility of stamping stringer sheets as a highly productive alternative to a hydroforming process is proven. New geometries without circumferential flange are producible in industrial-suited cycletimes while new process errors can be observed. The buckling error of the stringer is predictable in numerical simulations. These are validated by experimental results for several process setups. Occurring inaccuracies of the stringers need to be modelled in numerical simulations to allow for a correct prediction of the buckling behavior of the stringers. An element row shifted by 1% of the sheet metal thickness in the concave curvature is sufficient to model process and geometrical imperfections. If this element offset is set too high, buckling occurs too early in the numerical simulation. The results of the experiments and the numerical simulations can be summarized in a process window (see Fig. 16). Here, the stringer height hSt is normalized with the sheet metal thickness t and the drawing depth S is normalized with the X-distance between the two curvatures Δxr. The ratio of S and Δxr is comparable to the bending angle in die bending [24]. The line for different blank holder forces FN is the critical stringer height hSt,crit. A stringer height below hSt,crit can be produced buckling free during the stamping process. Stringers with a height above hSt,crit have a high buckling risk, which increases with increasing stringer height. The critical stringer height decreases with increasing drawing depth and increases with a higher blank holder force. This is due to the fact that higher drawing depths lead to higher compressive stresses in the stringer, which is comparable to higher bending angles in die bending. 328
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Technol 2013;62:275–8. [24] Köhler S, Groche P, Baron A, Schuchard M. Forming of stringer sheets with solid tools. Adv Mat Res 2016;1140:3–10. [25] Senior BW. Flange wrinkling in deep-drawing operations. J Mech Phys Solids 1956;4:235–46. [26] Hill R. A general theory of uniqueness and stability in elastic-plastic solids. J Mech Phys Solids 1958;6:236–49. [27] Hutchinson JW. Plastic buckling. Adv Appl Mech 1974;14:67–144. [28] Cao J, Boyce MC. Wrinkling behavior of rectangular plates under lateral constraint. Int J Solids Struct 1997;34:153–76. [29] Wang X, Cao J. On the prediction of side-wall wrinkling in sheet metal forming processes. Int J Mech Sci 2000;42:2369–94. [30] Wang X, Cao J. An analytical prediction of flange wrinkling in sheet metal forming. J Manuf Process 2000;2:100–7. [31] Saxena RK, Dixit PM. Prediction of flange wrinkling in deep drawing process using bifurcation criterion. J Manuf Process 2010;12:19–29. [32] Kim J, Yoon JW, Yang D. Investigation into the wrinkling behaviour of thin sheets in the cylindrical cup deep drawing process using bifurcation theory. Int J Numer Methods Eng 2003;56:1673–705. [33] Kawka M, Olejnik L, Rosochowski A, Sunaga H, Makinouchi A. Simulation of wrinkling in sheet metal forming. J Mater Process Tech 2001;109:283–9. [34] Correia JDM, Ferron G. Wrinkling of anisotropic metal sheets under deep-drawing: analytical and numerical study. J Mater Process Tech 2004;155:1604–10. [35] Narayanasamy R, Sowerby R. Wrinkling behaviour of cold-rolled sheet metals when drawing through a tractrix die. J Mater Process Tech 1995;49:199–211. [36] Banu M, Takamura M, Hama T, Naidim O, Teodosiu C, Makinouchi A. Simulation of
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springback and wrinkling in stamping of a dual phase steel rail-shaped part. J Mater Process Tech 2006;173:178–84. Morovvati MR, Fatemi A, Sadighi M. Experimental and finite element investigation on wrinkling of circular single layer and two-layer sheet metals in deep drawing process. Int J Adv Manuf Technol 2011;54:113–21. Zheng K, Lee J, Lin J, Dean TA. A buckling model for flange wrinkling in hot deep drawing aluminium alloys with macro-textured tool surfaces. Int J Mach Tools Manuf 2017;114:21–34. Altan T, Lilly B, Yen YC. Manufacturing of dies and molds. CIRP Ann Manuf Technol 2001;50:404–22. Bäcker F, Bratzke D, Groche P, Ulbrich S. Time-varying process control for stringer sheet forming by a deterministic derivative-free optimization approach. Int J Adv Manuf Technol 2015;80:817–40. Abaqus analysis user’s manual, Dassault Systèmes (Abaqus). 2010. Providence, RI, USA. Neto D, Coër J, Oliveira M, Alves J, Manach P, Menezes L. Numerical analysis on the elastic deformation of the tools in sheet metal forming processes. Int J Solids Struct 2016;100:270–85. Till E, Berger E, Larour P. On an exceptional forming behaviour aspect of AHSS sheets. IDDRG 2008 International Conference, Olofström 2008. Traub T, Groche P. Experimental and numerical determination of the required initial sheet width in die bending. Key Eng Mater 2014;639. Ludwik P. Elemente der Technologischen Mechanik. Berlin: Springer-Verlag; 1909. Jiang HM, Li SH, Wu H, Chen XP. Numerical simulation and experimental verification in the use of tailor-welded blanks in the multi-stage stamping process. J Mater Process Tech 2004;151:316–20.
Contents lists available at ScienceDirect
Journal of Manufacturing Processes journal homepage: www.elsevier.com/locate/manpro
Stamping of stringer sheets
T
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P. Groche, S. Köhler , S. Kern Institute for Production Engineering and Forming Machines (Technische Universität Darmstadt), Otto-Berndt-Straße 2, 64287 Darmstadt, Germany
A R T I C LE I N FO
A B S T R A C T
Keywords: Stringer sheet forming Stamping Buckling Simulation
Light-weight performance of load carrying structures can be increased through the use of bifurcations. Stringer sheets make use of this design principle. They consist of a base sheet with stiffening ribs or stringers. In this work the stringers are attached to the flat base sheet via laser welding and afterwards the part receives its targeted 3D shape in a subsequent forming process. While a larger height of the stringers is advantageous in terms of lightweight performance, it can lead to higher compressive stresses in concave areas of the part, causing buckling of the stringers. Previous studies made use of hydroforming for the manufacture of the 3D shaped stringer sheets. During hydroforming a side support to the stringers is given by the pressurized medium. Due to relatively long cycle times, it is not suitable for highly efficient mass production. Hydroforming also has shortcomings in the attainable geometries. This paper presents a new industrial-suited stringer sheet stamping process which is up to 20 times faster than current stringer sheet forming processes based on hydroforming. Furthermore, a numerical model allowing the prediction of stringer buckling is provided. Both, process and numerical model, are experimentally validated.
1. Introduction The performance in terms of weight and stiffness is a major evaluation criterion for many products, especially in the transportation sector. Every kilogram of material saved does not need to be produced, nor accelerated during product usage and recycled at the end of the product lifecycle [1]. Therefore, promising principles for lightweight design are sought after. Many successful technological solutions are inspired by nature and have been adopted by science [2], as evolution has optimized solutions under specific boundary conditions [3]. Loaded structures like shells, leaves or wings use bifurcations to reach the best strength to weight ratio while using minimal resources. Many technical products, e.g., roof tops or car body parts are created with the same intention. They also face the requirements of high stiffness, maximized resource efficiency and minimized efforts for manufacturing. Bifurcated structures provide the possibility to fulfill high stiffness requirements by using minimum material amount. Analytical investigations show an increase in the load carrying capacity to weight ratio up to 16.8 when comparing stringer sheets to non-bifurcated ones (see Fig. 1) [4]. Despite these opportunities for weight reduction, industrial applications of bifurcated sheet structures are rare. The main reason for that can be attributed to the lack of an efficient and economically feasible way to produce spatially curved, bifurcated sheet metal structures.
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Milling, for example, leads to an immense waste of up to 95% of the initial material [5], whereas processes like casting and extrusion, which are suitable for fabrication of these structures, go along with a vast energy consumption as well as inflexibility in terms of geometry and materials used [6]. One approach to increase the efficiency of sheet metal products is the use of tailored blanks [7]. These are semi-finished parts with locally differing properties like varying sheet metal thickness, material or coating. Beside tailored blanks made out of steel, other materials like aluminum [8] or magnesium [9] were investigated, too. An extended review of current possibilities of tailored blanks was given by Merklein et al. [7]. Tailored semi-finished parts introduce new challenges to forming processes. Kinsey et al. reported that the forming of tailor welded blanks (TWB), which consist of different materials or sheets with different thicknesses, requires new tooling concepts [10]. The weld line movement is an often investigated phenomenon in forming processes with TWB, because it has a significant influence on the thickness distribution throughout the sheet metal part. Mennecart et al. managed to reduce the weld line movement and therefore improving the thickness distribution in a deep drawing process by using a tailored tool. It consists of a segmented blank holder made from steel and reinforced polymer parts [11]. Heo et al. investigated the effects of draw beads on the weld line movement of TWB during a deep-drawing process, discovering that the weld line movement decreases for wider and
Corresponding author. E-mail address: [email protected] (S. Köhler).
https://doi.org/10.1016/j.jmapro.2018.10.025 Received 18 December 2017; Received in revised form 16 October 2018; Accepted 22 October 2018 1526-6125/ © 2018 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
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Nomenclature
FEM FN γ hSt L l le m μ rb1 rb2 S t TWB TRB v w wcrit
Symbol b β δ Δb Δβ Δγ ΔhSt Δl Δt Δw Δxr E Fcrit,x FEA
Welding distortion Angle between stringer and base sheet Imperfection factor Imperfection due to the welding distortion Imperfection in the angle between stringer and base sheet Imperfection due to twist of stringer sheet in Y-direction Imperfection in the stringer height Imperfection in the base sheet length Imperfection in the sheet thickness of the stringer Imperfection due to initial waviness of the stringer X-distance between the origin of rb1 and rb2 Young’s-Modulus Critical load for stringer sheet with stringer height x Finite element analysis
Finite element method Blank holder force Twist of stringer sheet in Y-direction Stringer height Actual stringer edge length after forming Base sheet length Evaluation length Mass of the stringer sheet Friction coefficient Radius of the punch Radius of the drawing die Drawing depth Sheet metal thickness Tailor welded blanks Tailor rolled blanks Poisson Ratio Waviness of a stringer Critical waviness
Fig. 1. Advantages in stiffness of stringer sheets [4].
hydroforming. It is based on the process principle depicted in Fig. 3. A pressurized fluid fills the die cavity and presses the sheet metal into the die while the blank holder closes the die cavity and controls the flange movement [22]. The hydroforming process exhibits advantages with respect to interferences between stringers and tool as well as the support of the stringers. Disadvantages are the needed process time and restrictions concerning the feasible geometries. In the performed experiments the cycle time in hydroforming for one drawn part is close to one minute. Additionally, the geometry of the part needs a circumferential flange where no stringers can be placed, since stringers in the flange would cause leakage. To overcome these restrictions in both process time and feasible geometries, first steps towards forming of stringer sheets with solid tools through die-bending were conducted [24]. Slots for the stringer in the punch and the die allow a convex or concave bending operation, as it can be seen in Fig. 4.
higher draw beads [12]. Different thicknesses of tailor rolled blanks (TRB) or TWB result in a significantly higher tendency of leakage in hydroforming processes [13]. Leakage problems in hydro mechanical deep drawing of TWBs were reduced with segmented tool parts, which compensate the difference in thicknesses [14]. A blank holder with adapted thickness transition can balance the offset in conventional deep drawing [15]. Kopp et al. discoved that an elastic blank holder is more useful to prevent wrinkling errors in deep drawing of TRB than a blank holder made of steel [16]. Tailored blanks can also be used to extend process limits. By using TRB Meyer et al. were able to increase the drawing depth by 19% in deep drawing [17]. Mori et al. applied plate forging for local thickening of semi-finished parts in square cup deep drawing. In this way, they achieved an increase in drawing depth of 33% [18]. Tailor heat treated blanks use a local heat treatment (e. g. conducted with a laser) to improve parameters like formability [19] or optimize mechanical properties of a sheet metal product [20]. The last category of tailored blanks are patchwork blanks, which consist of multi-layer sheet metals [7]. Jalanesh et al. presented a way how two sheets can be connected and formed in one process step by the integration of a projection welding process into a deep drawing process [21]. Ertugrul and Groche [22] developed a process chain which contains the fabrication of bifurcations in plane sheet metal followed by a forming process that generates the intended 3D shape. The advantage of this process sequence lies in the avoidance of a complex 3D joining process. The bifurcation of a flat sheet is carried out by attaching stringers through laser welding as it can be seen in Fig. 2. Here, the stringer is connected to the base sheet by means of a concentrated heat input from the rear side of the base sheet. The subsequent forming process is mostly conducted by
Fig. 2. Laser welding of stringer sheets. 320
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further buckling or wrinkling criteria. Hutchinson summarized plastic buckling theories in his work [27]. He described the effect of imperfections on the buckling sensitivity with the help of calculated examples. Cao and Boyce presented an elastic-plastic wrinkling model for rectangular plates under different constraints like binder pressure [28]. They account for imperfections in the material by representing geometrical inaccuracies or material inhomogeneities with offset elements. This approach leads to an accurate simulative prediction of flange wrinkling in deep drawing. Wang and Cao provide an analytical model with a modified energy approach to predict and prevent side-wall wrinkling in sheet metal forming [29]. Their model is supported by a numerical sensitivity analysis and experimentally validated by Yoshida buckling tests. A further development of [28] is shown in [30]. It shows that the critical buckling stress and the wavelength of the buckles in flange wrinkling in sheet metal forming can be predicted analytically. A utilization of the bifurcation criterion in finite element method (FEM) is presented by Saxena and Dixit [31]. Here, flange wrinkling in circular and square cup drawing is predicted. Kim et al. utilize the bifurcation theory in FEM, too. They successfully predicted the initiation and growth of wrinkles in a cylindrical deep drawing process and found stable solutions in their finite element analysis (FEA) if the normalized element length is sufficiently small [32]. Kawka et al. simulated the wrinkling of conical cups in a deep drawing process [33]. They found a significant influence of the initial finite element mesh. However, their FEA simulations do not show a good agreement with the experimental results. Correia and Ferron presented an analytical and numerical study of wrinkling in deep drawing of anisotropic sheets [34]. A critical compressive stress is defined and used as a wrinkling criterion. The authors were able to predict the wrinkling behavior of experimental studies found in literature [35]. Banu et al. used shell elements with reduced integration to simulate the wrinkling and springback behavior of a rail shaped sheet metal that has analogies to the roof tile in Fig. 1 [36]. They achieved an acceptable quality of springback prediction. However, their FE model overestimates the wrinkling failure during the stamping process. Morovvati et. al used numerical simulations for the prediction of flange wrinkling in deep drawing of cups with multiple sheet layers. They observed a good agreement of numerical and experimental results [37]. Latest models even cover thermal aspects. Zheng et. al. presented a buckling model that uses the energy method and adopt a one-dimensional beam geometry assumption to predict flange wrinkling in hot deep drawing [38]. This model is suitable for higher forming temperatures. As can be seen from the current state of wrinkling models in sheet metal forming a strong focus is set to the utilization and improvement of the FE analysis, which is an important tool in industrial process design [39]. This work provides a numerical model for dimensioning feasible stringer sheet geometries in a new stamping process. It answers the question how flat stringer sheets can be formed with solid tools and
Fig. 3. Process principle of hydroforming of stringer sheets [23].
Fig. 4. Process principle of die-bending of stringer sheets [24].
Since sheet metal product geometries often require more complex forming conditions, a new stamping process for stringer sheets with solid tools is necessary to exceed the current process limits. This paper presents a highly productive forming process that meets the requirements for mass production of bifurcated structures. Compressive stresses in concave curvatures limit the maximum producible height of the stringers. They can lead to buckling failure of the stringer. The trend to thinner high strength sheet metals increases the relevance of this failure mode. Therefore, the reliable prediction of wrinkling/buckling process limits becomes crucial to design engineers. Several approaches have been proposed. In 1956, Senior analytically predicted the occurrence of flange wrinkling in deep drawing based on the stress strain curve of the material and the flange geometry [25]. He estimated the stability of the flange with the aid of the classical energy method. Buckling is expected in this approach if the energy stored in the wrinkled structure is smaller than the one of the flat state without wrinkles. Using a similar approach, Hill set up his theory of uniqueness and stability in elastic-plastic solids [26]. It is the basis of several
Fig. 5. Tool concept for stamping of stringer sheets with solid tools. 321
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future investigations. Two geometries are investigated in the present work. Both are depicted in Fig. 6. They represent “open” part geometries without circumferential flange but with stringers in the flange area. These geometries cannot be manufactured by hydroforming for the reasons given before. The two specimens differ in the number of stringers (one or two) and the sheet metal width (150 mm and 300 mm). The specimens have a length of 300 mm in the flat state after the laser welding process. The stringers are welded at 1000 W and a speed of 22 mm/s using an ytterbium fiber laser. The sheet metal thickness t is 1 mm for both the stringer and the base sheet. The material used is a deep-drawing steel DC 04. During the forming process the parts take on their targeted shape of a roof tile. The radii rb1 and rb2 are 30 mm while the X-distance between the origin of the two radii Δxr is 64.95 mm. The drawing depth S and the stringer height hSt are varied during the experiments (S = 20–40 mm; hSt = 5–10 mm). Inlay sheets are placed at the opposite side of the punch and the blank holder for the production of the part with one stringer. In this way, the same stamping tool can be used for both geometries and a comparable, symmetrical distribution of the blank holder force is guaranteed.
shows occurring process errors. The maximum producible stringer height without failure for different process setups will be determined. 2. Process design The experimental setup and numerical model are presented in this section. At first, the new tool concept for stamping of stringer sheets is explained. This is followed by an introduction of the investigated geometries and the process steps used. Afterwards, the observed process errors are discussed. A numerical model to predict one of the major appearing failure modes is presented at the end of the section. 2.1. Tool concept and specimen Fig. 5 shows the tooling concept for a stringer sheet stamping process. The concept is suitable for mass production on single-acting presses. The press used in the experimental investigation is a 2500 kN servo press with an integrated drawing cushion which allows for a maximum blank holder force of 400 kN. The tool consists of a punch, a blank holder, a drawing die and a counter punch. The punch and the blank holder have slots with a width of two millimeter in which the stringers are placed during the forming process. The blank holder is coupled with the drawing cushion of the press while the punch is fixed at the press table. The drawing die and the counter punch move together with the press ram. In the present work the drawing die consists of two straight edges with radii rb2 = 30 mm. The counter punch is linearly guided and suspended with pneumatic springs (the springs produce a combined maximum force of 10 kN). The active elements are easily exchangable, so that the geometry can be varied quickly for
2.2. Process steps This subsection details the process steps of the introduced stringer sheet stamping process. The procedure can be divided into four steps (see Fig. 7): I) The tool is open: The flat stringer sheet is placed in the tool so that the stringer is in the middle of the slot in the blank holder and the
Fig. 6. Geometry of specimen (semi-finished part; stamped part). 322
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Fig. 7. Process steps for stamping of stringer sheets.
punch. II) The tool closes: Drawing edges and counter punch move together in positive Y-direction until the contact with the stringer sheet is
established. III) The specimen is formed: Counter punch and punch remain at their position while the drawing edge and the blank holder move 323
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c) Bump in the base sheet: The stringer can produce a bump at the opposite side of the stringer sheet, especially if the force of the counter punch is not sufficient or the stringer misses the slot in the punch. This failure mode occurs more frequently when the stringer height is very large (hSt > 10 mm). d) Tearing of the stringer: This error can occur due to high positive strains in convex curvatures during the process. Brittle materials, high stringer heights and high blank holder forces can produce this failure mode. e) Collision of stringer and tool: If the accuracy of the insertion position or the geometry of the semi-finished part is not sufficient, the stringer misses the slot in the punch or the blank holder and collides with the solid tool surfaces. f) Tool marks in the stringer: Tool marks can occur in process step III) if the stringer moves in the punch slot at the edge of the punch or if the stringer is not parallel to the intended slot.
together in positive Y-direction. The counter punch presses the stringer sheet with a force of 10 kN against the punch and the blank holder force acts in negative Y-Direction towards the drawing edge. IV) The tool opens: At first, the drawing die and the counter punch move back into their starting point followed by the blank holder. The stamped stringer sheet can be removed. The cycle time for the investigated processes is about three seconds. 2.3. Process errors During the process steps described above, several errors can occur. Beside the typical deep drawing defects like wrinkling or tearing of the base sheet metal, the stringers can cause new failure modes which are depicted in Fig. 8: a) Buckling of the stringer: The stringer starts to buckle if the negative strains caused by a concave curvature in the stringer edge are too high. b) Failure of the welding seam: Inaccuracies in the welding process and tension peaks during the forming process in the welding seam can cause fracture at this position.
The process errors b–f) are mostly due to limitations of the used material or inaccuracies in the welding or forming process. However, the buckling of the stringer is strongly dependent on the stringer height and forming process parameters like the blank holder force or drawing depth. Buckling appears as a significant failure mode that affects
Fig. 8. Process errors during stringer sheet stamping and place of occurance. 324
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mechanical properties of the final part. The stiffness of a stringer sheet with a buckled stringer is not as high as the stiffness of a stringer sheet with the same stringer height without buckled stringers [24]. For that reason, this work focuses on the investigation of the buckling failure. A buckling criterion to detect and quantify this failure mode was proposed by Bäcker [40]. A waviness w is calculated with the straight connection le of two points on the stringer edge and the actual stringer edge length L (see Fig. 9) after the forming process:
w=
L − le le
the blank holder force. The semi-finished parts show an initial waviness (Δw) and deflections (Δb) due to the welding distortions. As the slot width of the tool is bigger than the sheet thickness, the insertion position of the semi-finished part can be twisted in Y-direction by a small angle (Δγ). Table 1 shows the values of the geometric imperfections of three semi-finished samples with different stringer heights that have been measured with an optical measuring system (GOM Atos III). For hSt, β, t and l the reference value used was the desired value. For w and b, the critical waviness wcrit and the length of the sheet l were selected as reference to determine the variation in percentages. Since γ is difficult to measure in the process, the maximum possible value, which is due to the slot width in the tool parts, was used. In the measured samples, the seven geometrical inaccuracies have an average deviation of 1.13% with regard to the particular target values. The modelling of all imperfections would be very time consuming, therefore, a useful method to model these irregularities is needed. Cao and Boyce provided a simple but valuable way to model similar imperfections in the prediction of the wrinkling behavior of rectangular plates under lateral constraints. Offset elements represent process and material imperfections in their work [28]. This approach is adapted to the stringer for the determination of the buckling error of the stringer in the stamping process. As it can be seen in Fig. 12, one row of elements is shifted in Z-direction by a predefined percentage of the sheet thickness t. This percentage is called imperfection factor δ. In front and behind the offset element row, there is a transition element row to compensate the offset. Here, elements that have a slight parallelogram shape in the X/Z-plane ensure a continuous meshing of the stringer. Without these transition element rows the meshing of the stringer would be unsteady. This would cause unwanted local effects such as stress peaks at the boundaries of the offset element row.
(1)
Bäcker set the critical waviness to wcrit = 0.002. If w exceeds a critical waviness wcrit the straightness deviation is higher than usual deviations caused by the welding process for the production of the semi-finished part and the stringer is called buckled [40]. Due to the fact that the buckling errors occur in concave curvatures of the stringer, the evaluation length le is set to the duplicated concave curvature radius rb1
le = 2rb1
(2)
2.4. Process simulation This section describes the numerical simulation. The stringer sheet stamping process needs to be modelled accurately especially concerning the buckling of the stringer. The FE analysis is carried out with Dassault Systèmes Abaqus 6.14 using an explicit solver. Due to symmetries in the set-up, a quarter model, which is shown in Fig. 10, is sufficient to describe the whole stamping process. The hexagonal “incompatible mode” element type C3D8I, which is optimized for bending analysis [41], is used. A mass scaling factor of 1000 is set to shorten simulation times. The element edge length is 1 mm in each direction. A convergence analysis proved these assumptions to be adequate. The tools are modelled as rigid bodies. The assumption of rigid bodies for the tool bodies in simulation is based on the statements of Neto et al. [42]. They conclude that the elastic modeling of tool bodies can increase the accuracy of deep drawing simulations, but that considerably longer calculation times are required. They therefore recommend the use of elastic tool bodies only in specific cases, e.g. if the stiffness of the tools is low, or high strength steels are formed [42]. This is not the case in this work. Nevertheless, to verify the assumption of rigid bodies in the die, the drawing depth S of three experimentally formed specimens was compared with that of the simulation. The deviations of the samples from the FEA results with rigid tools were below 1% (0.12–0.28 mm) relating to the total drawing depth S = 30 mm. This leads to the conclusion that the assumption of rigid tool bodies in the simulation is sufficiently accurate. Penalty contact is used with Coulomb´s friction law. Due to the fact that the investigated stamping process is a combination of deep drawing and bending, the friction coefficient is set to μ = 0.08 which is common in deep drawing [43] as well as bending [44] simulations. The material model for DC 04 has a flow curve represented by data points (see Fig. 10a), a Young’s-Modulus E = 210 GPa and a Poisson Ratio v = 0.3. The flow curve is determined from tensile tests and extrapolated using Ludwik’s approach [45]. An elaborate modelling of the weld line and the heat affected zones has little influence on the forming behavior of the rest of the part in the simulation of tailor welded blanks but it increases the calculation time significantly [46]. Hence a homogeneous material behavior is assumed in this work. However, imperfections of the specimen or the procedure of the process have to be considered. Especially geometrical inaccuracies can influence the buckling behavior significantly. Fig. 11 shows the most common imperfections. After the laser welding of the semi-finished parts, deviations in the stringer height (ΔhSt) and the angle between stringer and base sheet (Δβ) can be observed. The sheet thickness of the stringer is varying (Δt), as well as the base sheet length (Δl), both influencing the distribution of
3. Results and evaluation 3.1. Variation of imperfection factor This section compares the results of the numerical investigations with the experiments. Process parameters like the blank holder force FN or the drawing depth S were varied as well as the stringer height hSt and the number of stringers on the semi-finished part. The waviness w of the stringer in the concave curvature is evaluated. Each stringer height is tested three times and both concave curvatures of the drawn parts were considered in the evaluation. During the experiments, the specimens are lubricated manually using a drawing oil by Zeller + Gmelin (Multidraw PL 61). The simulations are carried out with an ideal modelled stringer (δ = 0%), an imperfection factor δ = 1%, which represents the observed irregularities, and δ = 10% for exaggerated imperfections.
Fig. 9. Stringer edge lengths L and le for the calculation of the stringer waviness w. 325
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Fig. 10. Simulation model (a) and material model (b).
Fig. 11. Geometrical imperfections of the semi-finished parts. Table 1 Measured imperfections in semi-finished stringer sheets. β [°]
Measured value
hSt [mm]
hSt = 5 mm hSt = 8 mm hSt = 10 mm target value/ reference (average) imperfection
4.957 89.59 7.935 90.11 9.923 90.05 hSt 90 0.81 % 0.21 % average = 1.13 %
t [mm]
l [mm]
w [−]
b [mm]
γ [°]
1.000 1.018 1.008 1 0.87 %
299.24 299.32 299.19 300 0.25 %
0.00007 0.00011 0.00013 0.002 (=wcrit) 5.17 %
1.789 0.969 0.917 300 (=l) 0.4 %
Due to the slot width, the maximum possible twist in the tool is Δγmax = 0.19°.
90° 0.21 %
process setup. It leads to the same critical stringer heights as the experiments. The simulations with δ = 0% are not able to model the buckling behavior realistically. Here, the predicted critical stringer height is always too high. An imperfection δ = 10% is obviously too high to model the process inaccuracies. An imperfection value of δ = 1% seems to be sufficient to meet the experiments. Fig. 13a), b) and d) show that an increasing drawing depth S leads to a decreasing critical stringer height. This is due to the fact that with increasing drawing depth the arch length of the concave curvature increases, too. This leads to a larger stringer sector with negative strains and therefore a higher risk for buckling. The influence of the blank holder force FN can be seen in Fig. 13a) and c). Like in hydroforming of stringer sheets [40] a higher blank holder force leads to higher feasible stringer heights without buckling failure. In his case, doubling FN allows for a stringer height up to 9 mm (FN = 400 kN). Due to process inaccuracies in the experimental investigations, the border between buckling free and buckled stringers is a transition area rather than a hard boundary [24]. Some stringers of the same stringer height hSt are already heavily buckled here, while others are only just beginning to buckle. This can lead to large variations in the waviness in this area, as can be seen for example in the values for hSt = 7 mm in Fig. 13a and d. In order to check the accuracy of the numerical model, the numerical and experimental waviness patterns of heavily buckled stringers are compared. In general, the results of the simulation agree with experiments, as the correct number of waves is predicted. This is illustrated by an example in Fig. 14.
Fig. 12. Modelling of imperfections.
Fig. 13 shows the results for the stringer waviness w depending on the stringer height hSt in different process setups for the geometry with one stringer. The waviness w increases with increasing stringer height hSt in every setup. Fig. 13a) illustrates the buckling limit in the concave curvature for FN = 200 kN and S = 30 mm. These values for the blank holder force and the drawing depth are in the middle of the operating window of the tool/press. The experiments show that hSt = 6 mm is a stringer height where three of six concave curvatures are buckling free. For hSt = 5 mm no stringer buckled and for hSt = 7 mm or higher, every stringer buckled. The simulations with δ = 0% showed buckling at a stringer height hSt = 8 mm whereas the simulations with δ = 1% predicted a buckling behavior which is within the range of variation of the experiments for every stringer height. For δ = 10% the estimated waviness for three out of four stringer heights is too high. Looking at the other setups confirms this behavior (see Fig. 13b–d). The values for 12 out of 15 simulations with δ = 1% meet the range of experimental values, whereas no value for δ = 0% and only three for δ = 10% are within this scope. Furthermore, the simulation with δ = 1% is able to predict the critical stringer height for each tested 326
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Fig. 13. Waviness of stringer for different parameters (numerical and experimental).
with only one stringer, which led to a symmetrical loading situation. The flow direction of the material of these stringer sheets is nearly parallel to the weld line. With a second stringer on the base sheet an additional lateral influence on the buckling behavior is present. The movement of the base sheet in Z-direction is not symmetrical on both sides of the stringer. It is assumed that this influence leads to an earlier buckling failure. The parallelism of both stringers is important for the correct insertion of the semi-finished part in the tool. The stringer position has to be precise in the welding process, too. If both stringers are not parallel to each other, the stringers do not hit the tool slot. That leads to a collision of stringer and tool. Fig. 15 shows a comparison of drawn parts with one stringer and with two stringers (S = 30 mm; FN = 200 kN). The simulations were carried out with an imperfection of δ = 1%. It can be seen that the numerical results for both parts reach nearly the same waviness values. The values for the stringer sheets with two stringers are constantly negligible higher compared to the values of the parts with one stringer only. The average waviness of the experimental investigation with one stringer is in the range of the error bars of the values of the sheet with
Fig. 14. Comparison of experimental and numerical waviness pattern.
3.2. Variation of number of stringers Here, the influence of a second stringer on the base sheet is evaluated. Now, the stringers are no longer in the Z-symmetry plane of the part. The results already shown were obtained with a stringer sheet 327
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The blank holder force introduces positive strains into the stringer and therefore reduces the risk of buckling. The number of stringers has no significant influence on the critical stringer height. In future work a lateral support will be developed to support the stringer during the process to prevent the risk of buckling and to increase the producible stringer height. Here, for example, a wedgeshaped punch slot can compensate for small geometric defects in the semi-finished parts and produce straightened stringers. In this way, the lightweight potential of the stringer sheet forming technology can be enlarged enormously. Declarations of interest None. Acknowledgements Fig. 15. Influence of the number of stringers.
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Fig. 16. Process window for stamping of stringer sheets (rb1 = rb2 = 30 mm).
two stringers. So an influence of the number of stringers in this case cannot be stated.
4. Conclusions and outlook The feasibility of stamping stringer sheets as a highly productive alternative to a hydroforming process is proven. New geometries without circumferential flange are producible in industrial-suited cycletimes while new process errors can be observed. The buckling error of the stringer is predictable in numerical simulations. These are validated by experimental results for several process setups. Occurring inaccuracies of the stringers need to be modelled in numerical simulations to allow for a correct prediction of the buckling behavior of the stringers. An element row shifted by 1% of the sheet metal thickness in the concave curvature is sufficient to model process and geometrical imperfections. If this element offset is set too high, buckling occurs too early in the numerical simulation. The results of the experiments and the numerical simulations can be summarized in a process window (see Fig. 16). Here, the stringer height hSt is normalized with the sheet metal thickness t and the drawing depth S is normalized with the X-distance between the two curvatures Δxr. The ratio of S and Δxr is comparable to the bending angle in die bending [24]. The line for different blank holder forces FN is the critical stringer height hSt,crit. A stringer height below hSt,crit can be produced buckling free during the stamping process. Stringers with a height above hSt,crit have a high buckling risk, which increases with increasing stringer height. The critical stringer height decreases with increasing drawing depth and increases with a higher blank holder force. This is due to the fact that higher drawing depths lead to higher compressive stresses in the stringer, which is comparable to higher bending angles in die bending. 328
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