COMPARISON OF DIFFERENT SHEET METAL BENDING TEST SETUPS BY MEANS OF FINITE ELEMENT SIMULATIONS

COMPARISON OF DIFFERENT SHEET METAL BENDING TEST SETUPS BY MEANS OF FINITE ELEMENT SIMULATIONS Leopold Wagner, Christian Walch, voestalpine Stahl GmbH

INHALT 03 Summary 04 01. Introduction 05 02. Materials and Methods 05 03. Results and Discussion 08 04. Variation of sheet thickness 09 05. Variation of device geometry 10 06. Conclusions 11 07. References

3 SUMMARY Bending of sheet metal is among the main processes used in sheet metal forming and is used for material characterization of sheet metal as well. Different test setups have been proposed and standardized, e.g. bending into a V-shaped die or bending on supporting rolls. These two test methods have been investigated by means of finite element simulations for two different steel grades, exhibiting high (DP800HD) and low strain hardening potential (CP1200), and a multitude of different bending ratios and setup geometries. Bending strains were higher for CP1200 than for DP800HD. A distinct strain affected localization zone of 1.5 times sheet thickness was formed for CP1200, irrespective of the actual bending radius, whereas the bending strains were more distributed for DP800HD. Punch-sheet liftoff could be depicted in the simulations for CP1200, with a gap peaking at a bending ratio of 3.0-4.0 at 90 bending angle. The neutral fiber was shifted towards the inner radius for all investigated setups, with an increasing shift as the bending ratio decreased. For a constant bending ratio the bending strains, relative gap as well as relative neutral fiber shift slightly increased with increasing sheet thickness. This could be explained by incomplete scaling, as the device geometry was not altered. Increasing roll diameter or die width decreased bending strains, gap and neutral fiber shift for roll bending and V-bending, respectively. Altered geometry incomplete scaling or altered device geometry had larger effects on CP1200. Thus the setup geometry has to be considered for comparison of bending test results as well. Keywords: AHSS, bending test, finite element simulations, gap formation

4 01 Introduction Bending is among the main processes used for sheet metal forming and has established itself as a method for material characterization as well. Typically, a desired inner sheet radius r i to sheet thickness t ratio (bending ratio r i /t) and/or a bending angle are prescribed in material specifications only. Different bending test setups and devices have been proposed and some of these also standardized [1-4]. Among them, guided bending into a V-shaped die using a similarly shaped stamp (V-bending) as well as free bending on support rolls using a bending sword or mandrel (roll bending) are most commonly applied. These setups differ in their geometric boundary conditions during the respective bending deformation. Roll bending as stated above leaves the sheet free to deform between the mandrel and the support rolls. Depending on the geometry, the sheet can typically be bent to bending angles > 160. The final shape (e.g. bending angle) during V-bending is determined by the shape of the V-shaped die, and especially during the final phase of the bending deformation the sheet is largely in contact with the die and the stamp. However, most standards do not restrict the device geometries of the bending test setups, e.g. roll diameters, die widths and opening angles [1-4]. The strains due to bending can assuming the validity of the Bernoulli hypothesis (i.e. the cross sections of the sheet remain plane and perpendicular to the neutral fiber and the neutral fiber remains in the sheet center) solely be estimated from the bending ratio r i /t. Typically, the inner sheet radius r i is assumed to be equivalent to the tool radius r TOOL. Whereas this assumption is reasonable for mild or high strength steels, it does not hold for advanced high strength steel (AHSS) grades with low strain hardening capacity. Here, a gap is formed as the sheet lifts off from stamp or mandrel during bending [5-6]. This results also in r i < r TOOL, leading to increased strain in a zone of strongly localized deformation. Thus from here on r i denotes the actual inner sheet radius and r TOOL is the nominal tool radius. Since the sheet thickness is also prone to changes during bending the initial thickness is referred to as t 0 whereas the actual thickness during the bending test is denoted t. Herein we investigate the differences in bending strains, resulting from differences between V- and roll bending test setups, by means of finite element simulations only. The setups are compared for a range of bending ratios. In addition, the respective device geometries, i.e. the width of the V-shaped die and the support roll diameter, as well as the sheet thickness are varied for a constant bending ratio. As stated above materials exhibiting low strain hardening capacities are of interest when it comes to gap formation. For comparison a steel grade with distinct strain hardening capacity was investigated as well.

5 02 Materials and Methods The above mentioned influence of the strain hardening behavior was studied by choosing the materials accordingly. To depict high strain hardening potential, a dual-phase steel grade with increased ductility, i.e. CR440Y780T-DH (DP800HD), was chosen. The low strain hardening behavior was investigated by means of a complex-phase steel grade, namely CR900Y1180T- CP (CP1200). Their plastic behavior was assumed to be isotropic (von Mises) with isotropic hardening. The strain hardening behavior has been determined by means of uniaxial tensile and hydraulic bulge tests and fitted by a modified El-Magd function [7], re-written in the form: = + ( - 0 )(1-e -c eq) n 0 +k eq with the respective material parameters given in Table 1. steel grade 0 [MPa] [MPa] c [-] n [-] k [MPa] CP1200 1000 1330 59.43 0.40 15 DP800HD 500 940 14.50 0.75 0.75 Table 1: Parameters for the modified El-Magd flow stress curves of the two investigated steel grades. The simulations were conducted using ABAQUS/Explicit 6-14.4. Assuming a sufficient sample width, the plane strain condition in the center of the sample was simulated in 2D only. Friction was applied between sheet and V-shaped die as well as between sheet and stamp during V-bending, and between sheet and mandrel for roll bending ( = 0.15). The frictionless contact between sheet and supporting rolls during roll bending depicts situation of support rolls being free to rotate during the bending process. 03 Results and Discussion The strains during bending were evaluated in terms of strain in the sheet plane normal to the bending axis XX. Since the plane strain condition in the middle of the specimen was simulated only, XX on the surface is equal to the major strain which corresponds to measurable strains in an experiment at this position. The strains were extracted along the outer sheet contour as well as distribution through the sheet thickness. A shift of the location of XX = 0 with respect to the initial neutral fiber at = 90 y NF90 towards the inner sheet contour was determined. The inner curvature i = 1/r i was determined from the inner contour of the sheet y i (x i ), which was fitted by B-splines from the simulation results. r i was then related to the actual sheet thickness t and an actual bending ratio r i /t was calculated. The bending angle was not calculated according to standardized formulas (e.g. [1,3]), but directly determined from the analysis as the angle

6 between the two legs of the sheet outside the bending device. The gap formation was quantified as the distance between the stamp or mandrel and the sheet and reported for = 90 as well y GAP90. Variation of r TOOL /t 0 The tool radius for V-bending and roll bending setups was varied in the range of r TOOL = 0.5, 1.5, 2.25, 3.0, 3.75, 4.5, 6.0, 7.5 and 10.5 mm with t 0 = 1.5 mm, i.e. r TOOL /t 0 values of 0.33, 1.0, 1.5, 2.0, 2.5, 3.0, 4.0, 5.0 and 7.0. The width of the V-shaped die was 50 mm, its opening angle 90. The roll bending setup had a roll diameter of 30 mm and a distance between the supporting rolls according to [1-2,4]. Examples of the resulting strain distributions for the two investigated steel grades being bent using the two different bending setups are shown in Figure 1. * * Figure 1: Equivalent plastic strain P,eq (von Mises) distribution during roll bending (top row) and V-bending (bottom row) of CP1200 (left) and DP800HD (right) at = 90 for t = 1.5 mm, r TOOL /t 0 = 2.0; gap formation is visible for CP1200 with y GAP,90 as the distance between the bending tool and the sheet (*). The corresponding strain distributions on the outer sheet contour are shown in Figure 2. Obviously the maximum strain decreases with increasing r TOOL /t 0 (Figure 3a). The maximum strains tend to be a little higher for V-bending than for roll bending for DP800HD, while for CP1200 the situation is inconclusive. The strains are more distributed for DP800HD as compared to CP1200, which exhibits low strain hardening. There, a bending affected zone of approximately 1.5 times the sheet thickness is formed almost irrespective of the actual r TOOL (Figures 1&2). It can also be seen that for V-bending using small r TOOL the final shape of the DP800HD sheet is coined between stamp and die after the actual r i remained larger than r TOOL almost throughout the entire bending deformation (Figure 1).

7 Gap formation could be observed during V- and roll bending for both steel grades, although for DP800HD it was not severe and occurred only during roll bending at > 130. Gap formation, characterized by the actual bending ratio r i /t (Figure 3b) and the distance between sheet and tool at = 90, y GAP,90 (Figure 4a) are shown with respect to the nominal bending ratio r TOOL /t 0. It can be seen that, while as mentioned before it is small for DP800HD, for CP1200 there is a distinct increase of y GAP,90 with increasing r TOOL /t 0 until values of 3.5-4.0, a range where also r i /t falls short of r TOOL /t 0 (Figure 3b). For r TOOL /t 0 < 1, coining suppresses gap formation for CP1200. For small r TOOL /t 0, r TOOL fits the r i formed by the combination of t 0, device geometry and strain hardening behavior. Then for larger the r TOOL /t 0 the strains are no longer high enough to trigger the strain localization responsible for gap formation. The neutral fiber is shifted towards the inner radius for V- and roll bending of both investigated materials (Figure 4b). An increasing y NF,90 is observed as the bending ratio decreases. In general this shift is higher for CP1200 than for DP800HD. Figure 2: Total strain xx distribution along the outer sheet contour x OUT (0 = sheet center) during roll bending (top row) and V-bending (bottom row) of CP1200 (left) and DP800HD (right) at of 90 for t = 1.5 mm and varying r TOOL.

8 Figure 3: Maximum bending strains XX,max (a) and bending ratio r i/t (b) at = 90 for roll (R) and V-bending (V) of CP1200 and DP800HD using different r TOOL/t 0 ratios (t = 1.5 mm) 04 Variation of sheet thickness For r TOOL /t 0 = 3.0 the sheet thickness t 0 was varied from 1.0 to 1.5 and 2.0 mm for V- and roll bending of both materials. A constant r TOOL /t 0 would imply that the resulting strains should be identical for all thicknesses, i.e. there is geometrical similarity. However, the device geometry was not altered, resulting in incomplete scaling of the setups. Thus XX,max, actual r i /t, specific y GAP,90 ( y GAP90 /t) as well as the specific neutral fiber shift y NF,90 ( y NF90 /t) did not remain constant (Figures 5-6). However, considerable changes could only be found for CP1200. There XX,max, y GAP90 /t and y NF90 /t increased with increasing t 0 whereas the actual r i /t decreased with increasing t 0. The higher strain hardening of DP800HD seems to render this steel grade less prone to the incomplete scaling issue. Figure 4: Gap y GAP,90 (a) and neutral fiber shift y NF,90 (b) at = 90 for roll (R) and V-bending (V) of CP1200 and DP800HD using different r TOOL/t 0 ratios (t = 1.5 mm)

9 Figure 5: Maximum bending strains XX,max (a) and bending ratio r i /t (b) at = 90 for roll (R) and V-bending (V) of CP1200 and DP800HD for different sheet thicknesses (r TOOL/t 0 = 3.0). 05 Variation of device geometry As seen above XX,max, actual r i /t, y GAP,90 as well as y NF,90 seem to be affected by the device geometry, which is not prescribed in the applied bending test standards [1-2,4]. So to further investigate this effect, the die width of the V-bending setup, w, was varied from 30 to 50 and 70 mm and roll diameter of the roll bending setup, D, was varied from 20 to 30, 50 and 100 mm for t 0 = 1.5 mm and r TOOL /t 0 = 3.0. Again, geometry changes resulted in a less pronounced effect on the results for DP800HD as compared to CP1200. (Figures 7-8), where XX,max, y GAP,90 as well as y NF,90 increased with decreasing w or D. Figure 6: Specific gap y GAP,90/t (a) and specific neutral fiber shift y NF,90/t (b) at = 90 for roll (R) and V-bending (V) of CP1200 and DP800HD for different sheet thicknesses (r TOOL/t = 3.0).

10 Figure 7: Maximum bending strains XX,max (a) and bending ratio r i /t (b) at = 90 for roll (R) and V-bending (V) of CP1200 and DP800HD for different device geometries, i.e. die width w and roll diameter D (t = 1.5 mm, r TOOL/t 0 = 3.0). Figure 8: Gap y GAP,90 (a) and neutral fiber shift y NF,90 (b) at = 90 for roll (R) and V-bending (V) of CP1200 and DP800HD for different device geometries, i.e. die width w and roll diameter D (t = 1.5 mm, r TOOL/t = 3.0).

11 06 Conclusions The influence of bending test setup parameters on bending strains and gap formation has been studied by finite element simulations for two different steel grades (high and low strain hardening). Regarding bending strains, the expected increase with decreasing bending ratio could be depicted. Gap formation occurred mainly for low strain hardening steel grades. It had a maximum for bending ratios being high enough to avoid coining and low enough to still trigger the necessary strain localization. Testing increasing sheet thicknesses for a constant bending ratio results in increased bending strains and gap formation if the tests are performed using an unaltered device geometry. The bending strains and gap formation are influenced by the choice of the size of the bending device. Increasing device geometries, such as die widths of roll diameters, may decrease bending strains as well as gap formation. Especially steel grades with low strain hardening capacity are prone to sheet thickness and device geometry changes. In the light of these results, care has to be taken when comparing results of sheet metal bending tests. If any quantitative conclusions are to be drawn, the setup geometry has to be considered for comparison as well. The presence of gap formation has to be taken into account when comparing results from the same setup for steel grades showing different strain hardening behavior. As presented above, the actual inner sheet radius might no longer coincide with the nominal tool radius. 07 References [1] EN ISO 7438: Metallic materials Bend test, European Committee for Standardization (CEN), 2005. [2] ASTM E290-13: Standard test methods for bend testing of material for ductility. ASTM International, 2013. [3] VDA 238-100: Plate bending test for metallic materials, Verband der Automobilindustrie (VDA), 2010. [4] Japanese Industrial Standard JIS Z 2248: Metallic materials Bend test, Japanese Standards Association, 2006. [5] Larour P, Hackl B, Leomann F, Benedyk K: Bending angle calculation in the instrumented three-point bending test. In: Proceedings of the IDDRG 2012, November 25-29, 2012, Mumbai, India. [6] Larour P, Hackl B, Leomann F: Sensitivity analysis on the calculated bending angle in the instrumented bending test. In: Proceedings of the IDDRG 2013, June 2-5, 2013, Zurich, Switzerland. [7] El-Magd E, Gese H, Tham R, Hooputra H, Werner H (2001) Fracture criteria for automobile crashworthiness simulation of wrought aluminum alloy components. Mat.-wiss. u. Werkstofftech., 32:712-724.