EXPERIENCES WITH CRUCIFORM SAMPLE TO CHARACTERIZE ANISOTROPY PLASTICITY AND HARDENING FOR STEEL SHEET

Transcription

1 Proceedings of the 5th International Conference on Integrity-Reliability-Failure, Porto/Portugal July 2016 Editors J.F. Silva Gomes and S.A. Meguid Publ. INEGI/FEUP (2016) PAPER REF: 6204 EXPERIENCES WITH CRUCIFORM SAMPLE TO CHARACTERIZE ANISOTROPY PLASTICITY AND HARDENING FOR STEEL SHEET Hugo Folgar Ribadas 1(*), Miroslav Urbánek 1, Radek Procházka 2, Jan Džugan 2 1 Computer Modeling Department, COMTES FHT a.s., Průmyslová 995, Dobřany Czech Republic 2 Mechanical Testing Department, COMTES FHT a.s., Průmyslová 995, Dobřany Czech Republic (*) hfolgar@comtesfht.cz ABSTRACT One of the most used processes in industry is sheet metal forming. In order to get more information about the process and reduce the trial and error method for making the tools, there are series of numerical simulation programs based on FEM which are adjusted for such a task. One of the main pre-requisite for good results is the material data. Metal sheets are anisotropic with defined hardening. To obtain reliable data close to actual stress strain status during the deep drawing process, which is mainly multi-axial and subjected to large strains, we need to perform multiple material tests. Classically, hydraulic bulge tests of circular specimen, uniaxial tensile test, internal pressure tests of tubular specimen, throughthickness compression tests using stack specimen are performed [1]. Another possible approach is the use of the biaxial test. Biaxial test was normalized in order to obtain the yield surface based on the work of Kuwabara [2], [3]. This approach is limited to small strains and the main advantage/disadvantage is the evaluation based on the equivalent cross section. The way to measure the limit strain diagram through biaxial test sample with a cross-shaped is summarized in the article [4] and [5], where a number of approaches are mentioned. The cruciform specimen could be used as well for FFLD (fracture forming limit diagram) evaluation. For the initial measurement and testing of this procedure at COMTES FHT, a combination of two hydraulic actuators with both force and displacement control was used. Deformation field measurements were performed with the use of ARAMIS DIC system. FEM simulation of the deformation field in cruciform specimen using FEM model was subsequently performed in order to obtain detailed information about the material behaviour. Own cruciform shape specimen was optimized using FEM simulations in order to achieve a uniform as well as maximum deformation in the central region and not in the shoulder area. Different shapes have been numerically tested with the aim to use it for small thickness sheets assessment. An interesting cruciform shape was designed by Mitukiewicz [6], using ribs, which increase the strength in the arms without affecting the centre of the cruciform specimen. The Mises and Hill 48 will be used in the yield characterization process, some other criteria are planned to be evaluated as well. Keywords: Biaxial test, sheet metals, cruciform sample, FEM simulation. -81-

2 Topic_B: Experimental Mechanics INTRODUCTION The material selected for this experimental work is the DC01 steel. This steel alloy is usually applied for deep-drawn applications, commonly used in home-appliance industry (fridges, cookers...). The nominal thickness of the sheets evaluated is 1.5mm. Table 1 - DC01 steel alloy chemical composition Material name C Mn P S N Al DC For the characterization of the anisotropy plasticity and hardening behaviour of the selected material, the tests used were the uniaxial tensile test (for each direction related to the rolling direction), the stack test and the multiaxial test using the cruciform sample. MATERIAL MODEL Nowadays, FE simulation is an essential tool for testing and developing new parts for industrial environments, resulting in a significant reduction in expensive experimental costs. However, FE predictions are highly dependent on accurate descriptions of the material s mechanical behaviour, the selected constitutive model as well as the input data used for its calibration. Therefore, trying to create the appropriate description for the DC01 steel sheet, the following material model was selected to describe as accurately as possible the material behaviour based on the hardening law and the yield criteria. Yield criteria The Von Mises is the most widely used yield criteria, but it is only describing isotropic metallic materials. One of the most implemented yield criteria is the one proposed in 1948 by Hill [7], that is the first orthotropic yield criterion. In order to obtain a balance between the accuracy of the model and parameter identification costs, most of the advanced yield criteria are using a set of seven or eight experimental values. Usually, six input values are used for parameter identification: the three yield stresses (σ 0, σ 45, σ 90 ) and the three r-values (ratio between the strain in the width and the thickness) obtained from uniaxial tensile tests (performed with orientations of 0, 45 and 90 to the rolling direction), calculated using the formula: = ( ) = ( ) However, these six experimental values are insufficient to calibrate recent advanced yield criteria as BBC2008 [8]. The additional values needed, are commonly the balanced biaxial stress (σ b ) (measured from bulge test or equibiaxial tensile test) and the balanced strain ratio r b -value (gained from stack test and the equibiaxial tensile test)[9]. For the definition of our material model, we will use the balanced biaxial strain ratio (r b ) obtained from the stack test and the biaxial test. The balanced biaxial strain ratio r b -value can -82-

3 Proceedings of the 5th International Conference on Integrity-Reliability-Failure be calculated comparing the strain in two directions (rolling direction and transverse to rolling direction) and using the formula: = Hardening law In order to define the hardening behaviour of the metallic sheet we decided to use the Swift hardening law. In the model of Swift law, three material constants, strength coefficient (K), strain-hardening exponent (n) and initial strain (ε 0 ) should be estimated by curve fitting the measured true stress-strain data before necking to the following equation: = ( ) UNIAXIAL TENSILE TEST The first step of the evaluation process has been the measurement of the tensile test in three directions (0, 45 and 90 ) related to the rolling direction (Fig.1). Three tensile tests have been performed for each direction using the universal testing machine Zwick Roel 250kN. The strain measurements of the tests have been performed by Digital Image Correlation (DIC) method [10] with the use of ARAMIS system [11]. The system is using two cameras that enable optical 3D strain measurements. The elastic and plastic behaviour of the material was obtained after the evaluation of the tests. Fig. 1 - Sample directions related to the rolling direction The mechanical properties evaluated from the uniaxial tensile test are the engineering strain (e) and engineering stress (s), these properties are obtained directly from measurements: = = Finally the flow stress behaviour has been obtained rcalculating the true strain (ε) and true stress (σ). These parameters calculated directly from the engineering parameters before the necking and with an extrapolation after it. = (1 ) = (1 ) -83-

4 Topic_B: Experimental Mechanics We calculate these parameters for each direction (0, 45 and 90 ) to obtain the flow stress curves before necking, the flow stress beyond necking point can be extrapolated to fit the force-displacement curve. The flow stress curves are shown in the Figure 2: Fig. 2 - Flow stress curves for each direction After the calculation of the true stress-strain we fitted the constants for the Swift hardening law for the rolling direction curve (0 ), obtaining the following parameters: Table 2 - Swift model parameters K ε 0 n Fig. 3 - Swift model fitted to the tensile test -84-

5 Proceedings of the 5th International Conference on Integrity-Reliability-Failure The anisotropy parameters have been calculated after the initialization of the straining and before the necking of the specimen. The results obtained after the evaluation of the uniaxial tensile tests are: Table 3 - Anisotropy parameters gained from uniaxial tensile tests σ 0 [MPa] σ 45 [MPa] σ 90 [MPa] r 0 [-] r 45 [-] r 90 [-] STACK TEST To complete the characterization of the anisotropy model it is necessary to obtain another parameter in order to create a material model more reliable for advanced yield criteria. This parameter is the balanced biaxial strain ratio r b -value that is obtained from the disk compression test (stack test), the bulge test or the biaxial test. To obtain this parameter the stack test has been performed, using disks of 25mm diameter and stacking a total of 10 disks [12]. To conserve the anisotropy properties, the disks were piled considering the rolling direction. To reduce the friction between the stacked specimen and the compression plates of the tool, a Teflon-foil acting as a solid lubricant is placed at each end of the specimen. Fig. 4 - Compression stack test sample During the test, the force was gained from the universal testing machine Zwick Roell 250kN and the strain and displacement values were gathered by another DIC method using MERCURY system [13]. Two independent cameras were arranged with an angle of 90 to each other, one of them in the rolling direction and the other one perpendicular to the rolling direction. With this setup it was possible to cover more than the half lateral surface and to measure the strain in the rolling direction and in the transversal direction. -85-

6 Topic_B: Experimental Mechanics Fig. 5 - Compression and force and strain distribution during stack test Using the formula previously described we have obtained the value r b = gathering the strain values of the central disks of the pile, where the strain field is homogeneous. MULTIAXIAL TEST CRUCIFORM SAMPLE The last test performed to complete the characterization of the anisotropy model was the multiaxial test with the cruciform sample. At the beginning, this test was performed using a combination of two hydraulic pistons with both strength and deformation control. Deformation field measurements were performed with ARAMIS system [8]. With the material model previously described it was possible to create a detailed simulation of the deformation field in the cruciform using FEM model and the commercial code MARC- MENTAT [14]. This allowed us to develop a geometry model where the maximum strain was located in the central part of the sample, where it was possible to see the equibiaxial tensile strain. Fig. 6 - Cruciform simulation and eq. plastic strain at reference points To eliminate the issues in the usage of two hydraulic pistons, extensively simulations have been performed to optimize the length of the arms and reduce the moments created in the sample. With current settings we could perform the equibiaxial tensile test and some nonlinear path loads. The used model and results can be seen in the following picture. It is also possible to appreciate that the main prerequisite of having the highest strain level in the central part is maintained: -86-

7 Proceedings of the 5th International Conference on Integrity-Reliability-Failure Fig. 7-3D model of the two pistons machine setup For the equibiaxial tensile test, linear hydro-motor INOVA with maximum displacement of ±100 mm and force 20 and 25 kn was used. ARAMIS system was used for the strain measurements, with lenses 100 mm. The 3D measurement was enabled with the use of two cameras in angles of 25. The measured space was 100x85 (mm). The test was performed with speed 0.05mm/s and frame acquisition was carried out with 10Hz frequency. During the testing process, our equipment has upgraded to four servo-hydraulic pistons with load capacities of 25, 50, 150 and 250 kn (Figure 8). The behaviour of the specimens under multiaxial tension-compression was conducted with multiaxial testing system INOVA (2D planar testing) which employs four servo-hydraulic cylinders with load capacities of 25, 50, 150 and 250 kn. Servo-controlled hydraulic testing machines provide effective piston stroke of 200/250 mm and allow velocities of up to 1.0 m/s. Fig. 8 - Left: two pistons machine setup. Right four pistons machine setup The major and minor strains were acquired using the ARAMIS system in the central point (point 0 in figure 9) of the cruciform sample, so it has been possible to obtain the ratio between these two strains as it is possible to see in Figure 9. Three tests were carried out for the equibiaxial tensile test and two more for the uniaxial tensile test Figure 10. The results obtained for the uniaxial and equibiaxial test can be seen in the Fig. 11. Comparing the values of major and minor strain of the equibiaxial test, the value r b = has been obtained, calculated for the region of straining before fracture, using the cruciform specimen. This value differs from the one obtained in the stack test. This is due to different conditions during the tests: friction is a big influence in the stack test and in the equibiaxial, the sample is not tested in the complete thickness due to complex geometry of the sample. -87-

8 Topic_B: Experimental Mechanics Fig.9 - ARAMIS measurement of the cruciform specimen Fig a) Equibiaxial samples b) Uniaxial samples -88-

9 Proceedings of the 5th International Conference on Integrity-Reliability-Failure Fig Major and minor strain for Equibiaxial and Uniaxial test Some another tests like uniaxial, biaxial and non linear strain paths have been performed using this setup and DC01 steel sheet, but this paper will only analyze the results obtained for the equibiaxial tensile test. To verify that the material model created is presenting an accurate behaviour, a comparison between the simulation and the equibiaxial test has been performed. For the comparison, a section at the centre of the geometry was selected in the direction of the rolling direction. Fig. 12 -Section and Major Strain distribution -89-

10 Topic_B: Experimental Mechanics The distribution of the major and minor strain through the section has been plotted at different time stages. It is possible to see that the simulation predicts well the major and minor strain distribution through the section, showing the correct tendency and difference between both strains. Fig Major and minor strain distribution through the section RESULTS In order to calculate the yield locus for the DC01 steel sheet, the BBC2008 yield criterion was used [8]. The material parameters used as in put in the BBC2008 identification procedure [15] are the previously calculated: Three Yield stresses for each direction (σ 0, σ 45, σ 90 ) Three r-values (r 0,r 45,r 90 ) Balanced biaxial stress (r b ) The calculated BBC2008 yield locus is shown in Figure 14. There are three identification cases; with 4, 6 and 7 parameters; for the BBC2008 yield criterions plotted on the yield locus graph. It is possible to see that definition with fewer coefficients fail to describe the behaviour of the metal sheet, overestimating the strength in the biaxial area. Adding the biaxial plasticity parameters provides better accuracy of the model. Henceforth, the model used will be described with 7 parameters. -90-

11 Proceedings of the 5th International Conference on Integrity-Reliability-Failure Fig Yield locus for different anisotropy parameters definition With this parameter configuration it is possible to represent the planar distribution of the uniaxial yield stress and the anisotropy coefficients. Fig Planar distribution of the uniaxial yield stress and anisotropy coefficients Using the yield criteria (7 parameters model) and the coefficients obtained with the Swift model, it is possible to obtain a calculation of the FLD for the DC01 material model using the BBC2008 procedure. The results are shown in the following picture: -91-

12 Topic_B: Experimental Mechanics Fig Calculation of the FLD for DC01 steel sheet CONCLUSION From the obtained results, it can be concluded that the material parameters provided by the tensile tests, the stack test and the multiaxial test are important for an accurate prediction of the Yield surface. It is possible to see that in the absence of the biaxial plasticity characteristics (identification with only 4 or 6 parameters) overestimates the strength stress in the biaxial area of the yield locus. Therefore the model is more accurate than the simple anisotropy model. This material model will be used by [16] in further investigations with the multiaxial testing machine (already with 4 pistons setup). The paper deals with the prediction and improvement of the FLD diagrams using the cruciform specimen and non linear strain path. ACKNOWLEDGMENTS This paper was created by project Development of West-Bohemian Centre of Materials and Metallurgy No.: LO1412, financed by the MEYS of the Czech Republic. -92-

13 Proceedings of the 5th International Conference on Integrity-Reliability-Failure REFERENCES [1]-Vegter H., An Y.: Mechanical Testing for Modeling of the material behavior in forming simulation, Numisheet 2008, Interlaken, Switzerland. [2]-ČSN ISO [3]-Deng N., Kuwabara T., Korjolis Y.P.: Cruciform specimen design and verification for constitutive identification of anisotropic sheets, Experimental Mechanics (2015). [4]-Zidane I., Guines D., Leotoing L., Ragneau E.: Development of an in-plane biaxial test for limit curve (FLC) characterization of metallic sheets, Measurement Science and Technology, 21,(2010) 1-11 [5]Liu W., Guines D., Leotoing L., Ragneau E.: Identification of sheet metal hardening for large strains with an in-plane biaxial tensile test and dedicated cross specimen, International Journal of Mechanics Sciences, (2015), [6]-Mitukiewicz G., Glokowski M.: Cruciform specimen to obtain higher plastic deformation in a gauge region, Journal of Materials Processing Technology, 227 (2015) [7]-Hill R., A theory of the yielding flow of anisotropic metals, Proc. Roy. Soc. A193 (1948) [8]-Comsa D.S., Banabic D., Plane/stress zield criterion for highly-anisotropic sheet metals, Numisheet 2008, ed. P. Hora, Interlaken, 2008, p [9]-Khalfallah A., Alves J.L., Oliveira M.C., Menezes L.F., Influence of the characteristics of the experimental data set used to identify anisotropy parameters. Simulation Modelling Practice and Theory, 53(2015)15-44 [10]-Sutton, M., Digital and Image Correlation: Principle Developments and Applications for Parameter Estimation, University of South Carolina. [11]-GOM: ARAMIS System [Online]

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