BENCHMARK 2 Cup Drawing of Anisotropic Thick Steel Sheet

Transcription

1 BENCHMARK 2 Cu Drawing of Anisotroic Thick Steel Sheet Chair: Co Chairs: Member: Tomokage Inoue (Aisin AW Industries co.,ltd., Jaan) Hideo Takizawa (Nion Institute of Technolog, Jaan) Toshihiko Kuwabara (Toko Universit of Agriculture and Technolog, Jaan) Shuna Nomura (Toko Universit of Agriculture and Technolog, Jaan) October 2, OVERVIEW This benchmark (BM2) investigates the deformation and fracture of a hot rolled steel sheet (2.8 mm thickness) with a tensile strength of 44 MPa subjected to dee drawing and embossing (see Fig. 1). An aismmetric cu with an outer diameter of 2 mm is fabricated b dee drawing a circular blank with a diameter of 246 mm. This is a model aroimating a real automotive art, for which it is required to redict the dimensional accurac of the outer diameter within.2 mm and the timing of fracture of the die height within 1 mm, b using finite element analses (FEA). The main objective of this benchmark is to assess the influence of material models and quantif the influence of different numerical modelling techniques that affect wrinkling, sringback, and fracture rediction. Numerical techniques include the finite elements used, integration rules, imlicit or elicit code analsis, and contact and friction models. This benchmark involves the following three tasks: Task 1 Predict the height and cross sectional shae of the drawn cu after sringback Task 2 Predict the number and locations of wrinkles when no blank holding force is alied to the blank Task 3 Predict the die height at which the blank fractures at the ae of the center boss Fig. 1 Drawn cus obtained from reliminar eeriments for Task 1 (left) and Task 3 (right). 1

2 2. EXPERIMENTAL PROCEDURE 2.1 Blank Material and Material Data Hot rolled steel sheet with a tensile strength of 44 MPa (SAPH 44 in Jaanese Industrial Standard) Thickness: mm Blank diameter: mm (cut from a large as received sheet using laser machining) Material roerties: see Section 4 of this document, which includes the uniaial and biaial tension test data for the test material. The data are also available in a searate Ecel file, BM2_Material_Data.ls, to allow analsts to use their own data fitting algorithms and/or emlo alternate material model otions. 2.2 Descrition of Forming Oerations This benchmark involves three tasks and each task has its own objective. This section describes the forming oeration for each task. Task 1. Predict the height and cross sectional shae of the drawn cu after sringback Figure 2 shows the setu of the tools used for Task 1. The die moves downwards with constant velocit of 1 mm/s to form cu wall. The strier alies a force of 5 kn to the blank. It is ket constant during the forming using knockout clinders. (a) Fig. 2 Setu for the oeration of Task 1 (a) at an initial stage and at the bottom center of the die. 2

3 Fig. 3 Schematic reresentation of the tools used in the oeration of Task 1 Figure 3 shows the geometr and dimensions for the tools used in Task 1, with a blank of 246 mm in diameter. The lifter alies a blank holding force (BHF) of 7 kn to the flange area of the blank. It is ket constant during the oeration using the lifter ins suorted b hdraulic clinders. The 2.5 mm high rojection attached to the lifter revents the total BHF from concentrating on the blank edge immediatel before it is drawn into the die hole. NOTE: The thickness of the samle is 2.8 mm (higher than the rojection height). Therefore, a blank holding force of 7 kn is constantl alied to the flange area during the drawing rocess. It is noted that the uer surface of the strier contacts the die bottom near or at the bottom dead center of the die, see Fig. 2, to al a larger contacting force to the cu bottom. This rocess is effective to suress the sringback of the cu. Friction coefficient (recommended):.15 Note: Lubricant with a mass densit of.97 g/cm 3 and a viscosit coefficient of Pa s is alied to the surfaces of the blank, strier, unch, die, and lifter. Task 2. Predict the number and locations of wrinkles when no blank holding force is alied to the blank Figure 4(a) shows the geometr and dimensions for the tools used in Tasks 2 and 3, with a blank of 246 mm in diameter. It is noted that the lifter is not used in Tasks 2 and 3, and that the unch shae is changed to have a center boss with a height of 14 mm. The die moves downwards with constant velocit of 1 mm/s, u to a height of H=23.2 mm above the bottom dead center of the die, as shown in Fig. 4. 3

4 (a) Fig. 4 Schematic reresentation of the tools used in the oeration of the Tasks 2 and 3 The strier alies a force of 5 kn to the blank. It is ket constant during the oeration using knockout clinders, see Fig. 2. Friction coefficient (recommended):.15 Task 3. Predict the die height at which the blank fractures at the ae of the center boss The tools used in Task 3 are the same as those used in Task 2, see Fig. 4. The die moves downwards with constant velocit of 1 mm/s to form cu wall and center boss until fracture occurs at the ae of the center boss. It is noted that the uer surface of the strier ma contact to the die bottom near or at the bottom dead center of the die, as shown in Fig BENCHMARK REPORT All results must be reorted using the benchmark reort temlate, BM2_Reort.ls, which can be downloaded from the conference website. The file must be submitted b March 1, 218, on the website under the Benchmark Reort Submission tab on the right sided menu. The data file for the blank can be downloaded in DXF and IGES format from the conference website: blank.df and blank.igs. The data file for the die geometr used in Task 1 can be downloaded in DXF and IGES format from the conference website: tools_task1.df and tools_task1.igs. The data file for the die geometr used in Tasks 2 and 3 can be downloaded in DXF and IGES format from the conference website: tools_tasks2 3.df and tools_tasks2 3.igs. 4

5 3.1 General Descrition A. Benchmark Particiant Name, affiliation, address, e mail, hone number and fa number B. Simulation Software Name of the FEM code, general asects of the code, basic formulations (imlicit or elicit), element/mesh technolog, te of elements, number of elements (or initial and final number of elements if adativit is used), contact roert model and friction formulation C. Simulation Hardware CPU te, CPU clock seed, number of cores er CPU, number of CPUs, main memor, oerating sstem and total CPU time D. Material Model Yield function/plastic otential, Hardening rule, Stress Strain Relation, and Failure Model (strain based, stress based or Polar Forming Limit Diagram (FLD) used) E. Remarks 3.2 Calculated Results Figure 5 shows the aes of material anisotro, RD and TD, and the forming direction in relation to the global coordinate sstem (X, Y, Z) in BM2. Fig. 5 The aes of material anisotro, RD and TD, and the forming direction in relation to the global coordinate sstem (X, Y, Z) in BM2 5

6 Task 1. Predict the height and cross sectional shae of the drawn cu after sringback (1) Plot of Forming force (kn) vs. Press stroke (mm), see Fig. 6(a). The forming force is defined as the sum of the z ais comonents of the die force (the reaction force alied to the die from the material) and the strier force (the reaction force alied to the strier from the material). Note: In our reliminar eeriment, the forming force at the bottom dead center of the die was in between 1,8 to 2, kn. (a) Fig. 6 (a) Schematic of Forming force vs. Press stroke curve. Die force and strier force generated during the cu drawing (2) Plot of the cross sectional rofiles (z coordinate vs. Radial coordinate) of the cu after sringback, measured from the center oint of the inner surface (unch side) of the cu along the rolling direction (RD), 45 degree direction (DD), and the transverse direction (TD) of the blank. The zero z coordinate is defined at the center of the inner surface of the cu, see Fig. 7. The measurement ositions should be in.5 mm increments on the original blank. Fig. 7 Measurement method for a cross sectional rofile of the cu after sringback 6

7 (3) Plot of cu height (mm), measured around the circumference from the RD to 36, reorted in 5 increments or less. The measurement oint for the cu height should be at the center of the wall thickness, see Fig. 8. The zero height is defined at the lowest bottom surface of the cu after sring back. Fig. 8 Measurement method for cu height after sringback Task 2. Predict the number and locations of wrinkles when no blank holding force is alied to the blank Drive the die u to a height of H=23.2 mm above the bottom dead center of the die, as shown in Fig. 9(a). Then, reort the calculated results: (a) (c) Fig. 9 Measurement method for the cu wall shae with wrinkles. 7

8 (1) Plot of the radial coordinate, R, of the inner surface of the cu wall (with wrinkles) after sringback, measured around the circumference from the RD to 36, reorted in the increments of the mesh size used in the FEA, see Fig. 9. The measurement osition for the R should be at a height of 25 mm from the center of the inner surface of the cu base, see Fig. 9(c). (2) The number of wrinkles (the local maimum of R) of the cu wall (3) An isometric view of the inner surface of the cu after sringback, as shown in Fig. 1, in BMP or JPEG or PNG format. Fig. 1 Isometric view of the inner surface of the cu after sringback. It is noted that the cu shae in this figure shows no wrinkle because the FEA is erformed as a two dimensional aismmetric roblem, and the resulting cross sectional cu shae is just etended to an isometric view. Task 3. Predict the die height at which the blank fractures at the ae of the center boss (1) Plot of the Minimum thickness, T, at the ae of the center boss vs. the Die height, H, from the bottom dead center of the die, as shown in Fig. 11. (2) Identification of the value of H, with accurac of.1 mm, at which fracture is redicted to occur at the ae of the center boss. Fig. 11 Measurement method for the develoment of the minimum thickness at the ae of the center boss with die height 8

9 4. MATERIAL DATA 4.1 Uniaial Tension Uniaial tensile tests are erformed in ever fifteen degrees, i.e.,, 15, 3, 45, 6, 75, and 9, from the rolling direction (RD) of the test samle. The strain rate is aroimatel /s. Stress strain curves and r values are measured. Figure 12(a) and shows the variation of YE and r values with, where YE is defined as an average flow stress for a strain range of.2 YE, where YE is the logarithmic lastic strain corresonding to the end oint of the ield elongation. The r values were measured at a nominal tensile strain of.1. These data are rovided in a searate Ecel sheet in file BM2_Material_Data.ls. Plateau stress YE /MPa 4 35 r - value SAPH Angle from rolling direction / Angle from rolling direction / (a) Fig. 12 Mechanical roerties measured using uniaial tensile tests: (a) YE and r values. The mark shows an average of two secimens for each tensile direction. Figure 13 shows the tensile true stress logarithmic lastic strain curves for, 45, and 9, comared with those aroimated using Swift s ower law. The arameters of Swift s ower law are determined for a strain range of YE u, where YE is the logarithmic lastic strain corresonding to the end oint of the ield elongation, and u is that giving the maimum tensile force. The data for the curves are rovided in a searate Ecel sheet in file BM2_Material_Data.ls. 9

10 True stress /MPa SAPH44 ( ) True stress /MPa E. #1 E. #1 E. #2 2 E. #2 1 Swift's ower law Swift's ower law =763( ).179 /MPa 1 =752( ).184 /MPa YE =35.6 /MPa YE =36.7 /MPa Logarithmic lastic strain Logarithmic lastic strain (a) SAPH44 (45 ) 45 True stress /MPa SAPH44 (9 ) 3 E. #1 2 E. #2 Swift's ower law 1 =756(-.41+ ).179 /MPa YE =366.8 /MPa Logarithmic lastic strain (c) 9 Fig. 13 Tensile true stress vs. logarithmic lastic strain curves comared with those aroimated using Swift s ower law frac frac Logarithmic lastic strain comonents in the thickness ( T ), width ( W ), and longitudinal frac ( L ) directions in the localized necking area of fractured secimens are also measured for frac, 45, and 9, see Fig. 14. T is determined b directl measuring the thickness at the ti of the fracture surface using a tool microscoe in an accurac of.1 mm. frac W is determined b directl measuring the change in the gauge length (5 mm) in the width Fig. 14 Schematic diagram for the measurement of for a tensile secimen in the RD ( ). frac T and frac W. The ictures were taken 1

11 direction, using a tool microscoe in an accurac of.1 mm. frac L is calculated as frac frac frac frac frac T W. The data for T, W, and L are rovided in a searate Ecel sheet in file BM2_Material_Data.ls. 4.2 Biaial Tension Figure 15 shows the geometr of the cruciform secimen used in the biaial tension tests. The stress measurement error is estimated to be less than 2% when using the cruciform secimen with the geometr and strain measurement ositions as shown in Fig. 15 (Hanabusa et al., 21 and 213). Fig. 15 Geometr of the cruciform secimen and the strain measurement ositions used in the biaial tensile tests Seven linear stress aths, : 4:1, 2:1, 4:3, 1:1, 3:4, 1:2, and 1:4, are alied to the cruciform secimens using a servo controlled biaial tensile testing machine develoed b Kuwabara et al. (1998), where and are the true stress comonents in the RD and 4 1 TD of the test samle, resectivel. The von Mises strain rate is aroimatel 5 1 s. Details of the testing rocedures are given in ISO (214). Contours of lastic work in the stress sace and the directions of the lastic strain rates are measured; see Aendi for the method of measuring a contour of lastic work. These data are used to identif a roer material model for the test samle (Hill and Hutchinson, 1992; Hill et al., 1994), see Section In Plane Uniaial Comression and Combined Tension Comression In lane uniaial comression and combined tension comression tests are erformed to measure the stress oints forming contours of lastic work and the directions of the lastic 11

12 strain rates for the linear stress aths of : 1: and : 1, and : 1: 1 and 1:1, resectivel. Regarding the geometr of the secimen and the tools used in these tests, see Kuwabara (214). 4.4 Measured Data for Contours of Plastic Work and Directions of Plastic Strain Rates Figure 16 shows the stress oints that form the contours of lastic work associated with the reference lastic strain of (a).1 and.5; the stress values are normalized b the associated with each work contour. Each data oint reresents an average of the data measured from two secimens; the difference between these two measured data was less True stress /MPa SAPH44 =.1 Eerimental Yld2-2d (a =6) von Mises r -Hill'48 (a) True stress /MPa True stress /MPa SAPH44 =.5 Eerimental Yld2-2d (a =6) von Mises r -Hill' True stress /MPa Fig. 16 Measured stress oints forming the contour of lastic work at (a).1 and.5, comared with those theoretical ield loci calculated using the von Mises, Hill 48, and the Yld2 2d ield functions. 12

13 than 1% of the flow stress. The maimum value of, for which the work contour has a full set (nine) of stress oints measured using cruciform secimens, was.5. The values of the stress oints forming the work contours are rovided in a searate Ecel sheet in file BM2_Material_Data.ls. Figure 16 also includes the theoretical ield loci based on the von Mises (von Mises, 1913), Hill s quadratic (Hill, 1948), and the Yld2 2d ield function (Barlat et al., 23; Yoon et al., 24) with an eonent of a 6, the value ticall suggested for BCC metals. The material arameters i ( i 1~8) of the Yld2 2d ield function were determined using r, r45, r 9, and r, and b /, 45 /, 9 /, and b /, where r and are the r value and tensile flow stress measured at an angle from the RD, resectivel, and r and b b are the ratio of the lastic strain rates, /, and the flow stress at a balanced biaial tension, resectivel, associated with a articular value of. The values of i ( i 1~8) are rovided in a searate Ecel sheet in file BM2_Material_Data.ls. The material arameters of the Hill '48 ield function were determined using the r, r 45, and r 9. Figure 17 comares the directions of the lastic strain rates, measured at.1 and.5, with those calculated using selected ield functions. The Yld2 2d ield function with a 6 is consistent with the measured data, while those redicted b the von Mises and Hill 48 ield functions deviate slightl from the measured data. The value of measured for each stress ath is rovided in a searate Ecel sheet in file BM1_Material_Data.ls. Direction of lastic strain rate / SAPH44 =.1 Eerimental Yld2-2d (a =6) von Mises r -Hill'48 Direction of lastic strain rate / SAPH44 =.5 Eerimental Yld2-2d (a =6) von Mises r -Hill' Loading direction / Loading direction / (a) Fig. 17 Directions of the lastic strain rates measured at (a).1 and.5, comared with those calculated using the von Mises, Hill 48, and the Yld2 2d ield functions.

14 APPENDIX: METHOD OF MEASURING A CONTOUR OF PLASTIC WORK Figure A1 shows a schematic diagram for the measurement of a contour of lastic work. First, the true stress vs. logarithmic lastic strain curve ( curve) is measured from the uniaial tension test for the RD, and is selected as the reference data for work hardening; the lastic work er unit volume W associated with selected values of are determined. Net, the stress oints that give the same lastic work as W are determined from the biaial tension test data and the uniaial tension test data in the TD. Consequentl, these stress oints form a contour of lastic work associated with in the first quadrant of the stress sace. 9 W W W W W X W W W =W +W (a) Fig. A1 Schematic diagrams for the data analsis of the biaial tension test. (a) A method for determining the stress oints forming a contour of lastic work. The definitions of arctan( / ) and arctan( / ). W Moreover, the direction of the lastic strain rate, arctan( / ), is measured for each linear stress ath with a loading angle of arctan( / ), to check whether the normalit flow rule is established for the work contour. References Barlat, F., Brem, J.C., Yoon, J.W., Chung, K, Dick, R.E., Lege, D.J., Pourboghrat, F., Choi, S.H., Chu, E., 23. Plane stress ield function for aluminum allo sheets art 1: theor. Int. J. Plasticit 19, Hanabusa, Y., Takizawa, H., Kuwabara, T., 21. Evaluation of accurac of stress measurements determined in biaial stress tests with cruciform secimen using numerical method. Steel Research Int. 81 (9), Hanabusa, Y., Takizawa, H., Kuwabara, T., 213. Numerical verification of a biaial tensile test 14

15 method using a cruciform secimen. J. Mater. Processing Technol. 213, Hill, R., A theor of the ielding and lastic flow of anisotroic metals. Proceedings of the Roal Societ of London A193(133), Hill, R., Hecker, S.S., Stout, M.G., An investigation of lastic flow and differential work hardening in orthotroic brass tubes under fluid ressure and aial load. Int. J. Solids Struct. 31, Hill, R., Hutchinson, J.W., Differential hardening in sheet metal under biaial loading: a theoretical framework. J. Al. Mech. 59, S1 S9. ISO 16842: 214 Metallic materials Sheet and stri Biaial tensile testing method using a cruciform test iece. Kuwabara, T., Ikeda, S., Kuroda, T., Measurement and analsis of differential work hardening in cold rolled steel sheet under biaial tension. J. Mater. Process Technol. 8 81, Kuwabara, T., 214. Biaial Stress Testing Methods for Sheet Metals. In Comrehensive Materials Processing, Van Tne, C. J., Ed., Elsevier Ltd., Vol. 1, von Mises, R., Mechanik der festen Korer un lastich deformablen Zustant. Göttingen Nachrichten, math. hs. Klasse, Yoon, J.W., Barlat, F., Dick, R.E., Chung, K., Kang, T.J., 24. Plane stress ield function for aluminum allo sheets art II: FE formulation and its imlementation. Int. J. Plasticit 2,