BENCHMARK 1 Hole Expansion of A High Strength Steel Sheet

Transcription

1 BENCHMARK 1 Hole Exansion of A High Strength Steel Sheet Chair: Toshihiko Kuwabara (Toko Universit of Agriculture and Technolog, Jaan) Co Chair: Tomouki Hakoama (RIKEN, Jaan) Members: Taiki Maeda (Toko Universit of Agriculture and Technolog, Jaan) Chiharu Sekiguchi (Toko Universit of Agriculture and Technolog, Jaan) October 2, 217 Revised on December 12, Overview The objective of this benchmark (BM1) is to redict the deformation and ture of a dual hase steel sheet (1.2 mm thickness) with a tensile strength of 98 MPa (DP98) subjected to hole exansion. A circular blank with a central hole (3 mm diameter) fabricated using a wire electrical discharging machine is used to erform hole exansion forming to a set deth with a circular unch (1 mm diameter), see Fig. 1. Formed arts will be sectioned to measure thickness strain along the hole edge as well as along the three radial directions: (RD), 45 (DD), and 9º (TD) from the rolling direction of the test samle. Additional arts will be formed to failure, and the location and timing of the failure will be identified. These measurements will be used to evaluate numerical redictions of the results submitted b benchmark articiants rior to the Numisheet 218 Conference. Fig. 1 A secimen after hole exansion forming. Material: cold rolled ultralow carbon steel sheet. The unch and die geometr used is the same as that used in this benchmark, see Fig EXPERIMENTAL PROCEDURE 2.1 Blank material and material data DP98 (1.2 mm thickness) is considered for this benchmark. Large blanks are trimmed to circular blanks with a diameter of 215 mm. A detailed material characterization for the test 1

2 samle is shown in Section 4 of this document, which includes the uniaxial and biaxial tension test data. The data are also available in a searate Excel file (BM1_Material Data) to allow analsts to use their own data fitting algorithms and/or emlo alternate material model otions. 2.2 Hole Exansion Forming Figure 2 shows the exerimental aaratus used for the hole exansion forming. The unch was 1 mm in diameter and the die and unch rofile radii were 15 mm. The initial hole diameter was d 3 mm, fabricated at the center of a circular blank using a wire electrical discharging machine. The eriher of the blank was clamed using a triangular draw bead with a diameter of 195 mm. The interface between the blank and unch head was lubricated with Vaseline and.3 mm thick Teflon sheet, while no lubricant was alied to the interfaces between the blank and the die/blank holder. The blank was clamed using a hdraulic (a) (b) (c) (d) Fig. 2 Exerimental aaratus for hole exansion exeriment. (a) Schematic illustration of the die geometr and secimen used for the hole exansion exeriment. All dimensions are in millimeters. (b) Geometr of the male and female beads. (c) Lower die and unch. (d) Setu of a secimen; the center of the secimen is coaxial with that of the unch as it is guided b a clindrical block that stands at the unch center. 2

3 clinder, and the blank holding force was aroximatel 8 kn (revised on December 12, 217). The unch seed was aroximatel.1 mm/s, and the forming was terminated when the unch stroke reached 15 mm. After the hole exansion forming, the sheet thickness along the radial lines at (RD), 45 (DD), and 9 (TD) from the RD, as well as along the hole edge, was measured using a micrometer with a minimum readout of.1 mm. 3. BENCHMARK REPORT All results must be reorted using the benchmark reort temlate, BM1_Reort.xlsx, 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. 3.1 General descrition Please fill out the information: A. Benchmark articiant Name, affiliation, address, e mail, hone number and fax number B. Simulation Software Name of the FEM code, general asects of the code, basic formulations (imlicit or exlicit), element/mesh technolog, te of elements, element adativit information, number of elements (or initial and final number of elements if adativit is used), contact roert model and friction formulation Simulation Hardware CPU te, CPU clock seed, number of cores er CPU, number of CPUs, arallel or shared rocessing, main memor, oerating sstem and total CPU time C. Material model Yield function/plastic otential, Hardening rule, Stress Strain Relation, and Failure Model D. Remarks 3.2 Calculated results Please fill out the information: (1) Punch force (kn) vs. unch stroke (mm) u to and a bit beond the oint of maximum load. The zero mm unch stroke is defined at the osition when the secimen is just in contact with the unch with zero interface force. (2) Logarithmic thickness lastic strain z at a ositon of S 2 mm distant from the hole edge in the original blank vs. circumferential coordinate (degree in the original blank), see Fig. 3, at a unch stroke of 15 mm. (3) Logarithmic thickness lastic strain z vs. S (mm), at a unch stroke of 15 mm, for 3

4 the three radial directions: RD, DD and TD of the original blank, see Fig. 4. (4) Punch stroke at the redicted onset of ture (within.1 mm recision) (5) Location of the redicted onset of ture, ( (degree), S (mm)), in the original blank. Fig. 3 Definition of the circumferential osition,, for the reort of logarithmic thickness lastic strain rofile along the hole edge. is defined to be zero at the RD. Fig. 4 Definition of the ositon S (mm) from the hole edge in the original blank for the reort of the logarithmic thickness strain rofile along the three radial directions: RD, DD and TD 4. UNIAXIAL AND BIAXIAL TENSION TESTS 4.1 UNIAXIAL TENSION DATA Tensile tests are erformed in ever fifteen degrees, i.e.,, 15, 3, 45, 6, 75, and 9, inclined from the rolling direction (RD) of the test samle. The strain rate is aroximatel s. Stress strain curves and r values are measured. 4

5 Figure 5(a) and (b) shows the lastic work based roof stresses,.2(w) and 1.(W), and the r values measured from the uniaxial tensile tests erformed ever 15 from the RD..2(W) and 1.(W) are defined as the uniaxial tensile stress at an instant when the same lastic work er unit volume is consumed as that at a tensile strain of.2 and.1, resectivel, in the RD, see Aendix. The r values were measured at a nominal tensile strain of.1. These data are rovided in a searate Excel sheet (BM1_Material Data). Plastic-work-based roof stress.2(w), 1.(W) /MPa (W).2(W) Angle from rolling direction / r - value Average Angle from rolling direction / (a) (b) Fig. 5 Mechanical roerties measured using uniaxial tension tests: (a).2(w) and 1.(W) and (b) r values. The marks show an average of two secimens for each tensile direction. Figure 6 shows the nominal stress N vs. nominal strain N curves for, 45, and 9. The number of secimens are two for each tensile direction. The data for the N N curves are rovided in a searate Excel sheet in file BM1_Material_Data.xlsx. Figure 7 shows the true stress vs. logarithmic lastic strain for, 45, and 9, comared with those aroximated using Swift s ower law. The arameters of Swift s ower law are determined for a strain range of.2 u, u is the logarithmic lastic strain giving the maximum tensile force. The data for the curves are rovided in a searate Excel sheet in file BM1_Material_Data.xlsx. Logarithmic lastic strain comonents in the thickness ( T ), width ( W ), and longitudinal ( L ) directions in the localized necking area of tured secimens are also measured for, 45, and 9, see Fig. 8. T is determined b directl measuring the thickness at the ti of the ture surface using a tool microscoe in an accurac of.1 mm. W is determined using a DIC sstem just outside of the localized neck. L is calculated as T W. The data for T, W, and L are rovided in a searate Excel sheet in file BM1_Material_Data.xlsx. 5

6 Nominal stress N /MPa Exerimental #1 Exerimental #2 Maximum stress Nominal stress N /MPa Exerimental #1 Exerimental #2 Maximum stress Nominal strain N Nominal strain N (a) (b) 45 Nominal stress N /MPa Exerimental #1 Exerimental #2 Maximum stress Nominal strain N (c) 9 Fig. 6 Nominal stress vs. nominal strain curves for, 45, and 9 True stress /MPa True stress /MPa Exerimantal #1 Exerimantal #2 4 Swift's ower low 2 =1525(-.9+ ).12 /MPa (for =.2 ~.83) Logarithmic lastic strain True stress /MPa Exerimental #1 Exerimental #2 4 Swift's ower low 2 =1481(-.12+ ).12 /MPa (for =.2 ~.81) Logarithmic lastic strain (a) (b) 45 6 Exerimental #1 Exerimental #2 4 Swift's ower low 2 =1522(-.14+ ).11 /MPa (for =.2 ~.84) Logarithmic lastic strain (c) 9 Fig. 7 True stress vs. logarithmic lastic strain curves, comared with those aroximated using Swift s ower low

7 Fig. 8 Schematic diagram for the measurement of for a tensile secimen in the RD ( ). T and W. The ictures were taken 4.2 BIAXIAL TENSION DATA The secimen geometr used in the biaxial tension tests and a method of determining a contour of lastic work are given in Aendix. Figure 9 shows the stress oints that form the contours of lastic work associated with the reference lastic strain of (a).2 and (b).1; 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 than 1% of the flow stress. The maximum value of, for which the work contour has a full set of stress oints measured using cruciform secimens, was.12. The values of the stress oints forming the work contours are rovided in a searate Excel sheet (BM1_Material Data). Figure 9 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 exonent of a 6, the value ticall suggested for BCC metals. The material DP DP /.75 =.2 Exerimental.5 von Mises r-hill '48.25 Yld2-2d (a = 6) / =.1 Exerimental von Mises r-hill '48 Yld2-2d (a = 6) x / x / (a) (b) Fig. 9 Measured stress oints forming the contour of lastic work at (a).2 and (b).1, comared with those theoretical ield loci calculated using the von Mises, Hill 48, and the Yld2 2d ield functions.

8 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 uniaxial tensile flow stress measured at an angle from the RD, resectivel, and r b and b are the ratio of the lastic strain rates, /, and the flow stress at a balanced x biaxial tension, resectivel, associated with a articular value of. The values of i ( i 1~8) are rovided in a searate Excel sheet (BM1_Material Data). The material arameters of the Hill '48 ield function were determined using the r, r 45, and r 9. Figure 1 comares the directions of the lastic strain rates, measured at.2 and.1, 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 for each stress ath is rovided in a searate Excel sheet (BM1_Material Data). Direction of lastic strain rate / DP98 45 x =.2 Exerimental von Mises r-hill '48 Yld2-2d (a = 6) Loading direction / (a) Direction of lastic strain rate / DP98 45 x =.1 Exerimental von Mises r-hill '48 Yld2-2d (a = 6) Loading direction / (b) Fig. 1 Directions of the lastic strain rates measured at (a).2 and (b).1, comared with those calculated using the von Mises, Hill 48, and the Yld2 2d ield functions. APPENDIX: METHOD OF BIAXIAL TENSION TEST A1 Secimen geometr Figure A1 shows the geometr of the cruciform secimen used in the biaxial 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. A1 (Hanabusa et al., 21 and 213). 8

9 Fig. A1 Geometr of the cruciform secimen and the strain measurement ositions used in the biaxial tensile tests A2 Measurement of contours of lastic work Seven linear stress aths, x : 4:1, 2:1, 4:3, 1:1, 3:4, 1:2, and 1:4, are alied to the secimens using a servo controlled biaxial tensile testing machine develoed b Kuwabara et al. (1998), where x and are the true stress comonents in the RD and TD of the test 4 1 samle, resectivel. The von Mises strain rate is aroximatel 5 1 s. Details of the testing rocedures are given in ISO (214). Contours of lastic work in the stress sace (Hill and Hutchinson, 1992; Hill et al., 1994) are measured to identif a roer material model for the test samle, see Fig. A2. First, the true stress vs. logarithmic lastic strain curve ( curve) is measured from the uniaxial 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. Next, 9 W W =W x +W (a) (b) Fig. A2 Schematic diagrams for the data analsis of the biaxial tension test. (a) A method for determining the stress oints forming a contour of lastic work. (b) The definitions of arctan( / ) and x W x x W x x x W W. arctan( / x ) 9 W W x W X x

10 the stress oints that give the same lastic work as W are determined from the biaxial tension test data and the uniaxial tension test data in the TD. Consequentl, these stress oints form a contour of lastic work associated with stress sace. x in the first quadrant of the Moreover, the direction of the lastic strain rate, arctan( / x), is measured for each linear stress ath with a loading angle of arctan( / x ), 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 biaxial stress tests with cruciform secimen using numerical method. Steel Research Int. 81 (9), Hanabusa, Y., Takizawa, H., Kuwabara, T., 213. Numerical verification of a biaxial tensile test 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 axial load. Int. J. Solids Struct. 31, Hill, R., Hutchinson, J.W., Differential hardening in sheet metal under biaxial loading: a theoretical framework. J. Al. Mech. 59, S1 S9. ISO 16842: 214 Metallic materials Sheet and stri Biaxial 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 biaxial tension. J. Mater. Process Technol. 8 81, 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,