Twisting of sheet metals C. H. Pham, S. Thuillier and P. Y. Manach Univ. Bretagne-Sud, EA 4250, LIMATB, F-56100 Lorient, France Abstract. Twisting of metallic sheets is one particular mode of springback that occurs after drawing of elongated parts, i.e. with one dimension much larger than the two others. In this study, a dedicated device for drawing of elongated part with a U-shaped section has been designed on purpose, in order to obtain reproducible data. Very thin metallic sheet, of thickness 0.15 mm, has been used, so that the maximum length of the part is 100 mm. Two different orientations of the part with respect to the tools have been chosen: either aligned with the tools, or purposefully misaligned by 2°. Several samples were drawn for each configuration, leading to the conclusion that almost no twisting occurs in the first case whereas a significant one can be measured for the second one. In a second step, 2D and 3D numerical simulations within the implicit framework for drawing and springback were carried out. A mixed hardening law associated to von Mises yield criterion represents accurately the mechanical behavior of the material. This paper highlights a comparison of numerical predictions with experiments, e.g. the final shape of the part and the twisting parameter. Keywords: Twisting; Ultra-thin metallic sheet; Finite element simulation; Experiments PACS: 62.20.fq,81.05.Bx,81.70.Bt INTRODUCTION Within the framework of deep drawing of thin metallic sheets, springback has arisen a wide and still up-to-date interest both from industrial and academic viewpoints. Indeed, the change of shape of a part from the ideal shape just after drawing, still within the tools, and the final one after removing the tools, remains difficult to predict accurately. In order to investigate springback on simplified geometries, compared to real industrial parts, rails with a U-shaped section have been considered, and springback is mainly dealt as a 2D phenomenon related to the opening/closure of the section, e.g. [1, 2, 3]. Twisting is another deformation mode that occurs when dealing with elongated parts, when considering 3D spring- back [4, 5]. It is related to torsion of the drawn part around the highest dimension. It is sometimes referred to as an unstable deformation mode, because after springback, the part seems to have two positions, a stable twisted one and another one, closer to the shape before springback than the previous one. By applying human force on the twisted part, it can be possible to reshape it back to the alternative position. From an experimental point of view, twisting is very challenging because a lot of data were obtained on industrial-type parts, with the longest dimension of the order of the meter. These data is usually very dispersed and for the same process parameters, material and geometry, very different values for the twisting parameter can be obtained. Such scatter seems to arise from dispersion related to the process, like the blank alignment with the tools. Twisting corresponds to an unwanted rotation gradient of the 2D sections of an extruded part, and its magnitude is usually characterized by the disorientation angle between the two end sections [6, 7]. Twisting has been usually evidenced and investigated for parts of length around 1 m. Depending on the material and the geometry, twisting parameter, defined as the ratio of the disorientation angle over the distance in-between the two sections, can reach values up to 25°.m -1 . This phenomenon is observed on parts exhibiting non-symmetry along the greatest length and obtained for example by extruding a symmetric section along a curved line [8] or a non-symmetric section along a line [5]. However, from industrial records [9], twisting can be obtained even for symmetric 2D section extruded along a straight line (U-shaped rails). Moreover, a large dispersion is obtained for twisting parameter corresponding to the same conditions. It seems therefore interesting to derive an experimental database leading to stable results, in order to validate finite element predictions of twisting. This article recalls experimental results obtained on the twisting of a U-shaped rail, presented in details in [10, 11].
Transcript
Twisting of sheet metals
C. H. Pham, S. Thuillier and P. Y. Manach
Univ. Bretagne-Sud, EA 4250, LIMATB, F-56100 Lorient, France
Abstract. Twisting of metallic sheets is one particular mode of springback that occurs after drawing of elongated parts, i.e.with one dimension much larger than the two others. In this study, a dedicated device for drawing of elongated part with aU-shaped section has been designed on purpose, in order to obtain reproducible data. Very thin metallic sheet, of thickness0.15 mm, has been used, so that the maximum length of the part is 100 mm. Two different orientations of the part with respectto the tools have been chosen: either aligned with the tools,or purposefully misaligned by 2°. Several samples were drawn foreach configuration, leading to the conclusion that almost notwisting occurs in the first case whereas a significant one canbemeasured for the second one.
In a second step, 2D and 3D numerical simulations within the implicit framework for drawing and springback were carriedout. A mixed hardening law associated to von Mises yield criterion represents accurately the mechanical behavior of thematerial. This paper highlights a comparison of numerical predictions with experiments, e.g. the final shape of the partandthe twisting parameter.
Keywords: Twisting; Ultra-thin metallic sheet; Finite element simulation; ExperimentsPACS: 62.20.fq,81.05.Bx,81.70.Bt
INTRODUCTION
Within the framework of deep drawing of thin metallic sheets, springback has arisen a wide and still up-to-dateinterest both from industrial and academic viewpoints. Indeed, the change of shape of a part from the ideal shape justafter drawing, still within the tools, and the final one afterremoving the tools, remains difficult to predict accurately.In order to investigate springback on simplified geometries, compared to real industrial parts, rails with a U-shapedsection have been considered, and springback is mainly dealt as a 2D phenomenon related to the opening/closure ofthe section, e.g. [1, 2, 3].
Twisting is another deformation mode that occurs when dealing with elongated parts, when considering 3D spring-back [4, 5]. It is related to torsion of the drawn part around the highest dimension. It is sometimes referred to as anunstable deformation mode, because after springback, the part seems to have two positions, a stable twisted one andanother one, closer to the shape before springback than the previous one. By applying human force on the twisted part,it can be possible to reshape it back to the alternative position. From an experimental point of view, twisting is verychallenging because a lot of data were obtained on industrial-type parts, with the longest dimension of the order of themeter. These data is usually very dispersed and for the same process parameters, material and geometry, very differentvalues for the twisting parameter can be obtained. Such scatter seems to arise from dispersion related to the process,like the blank alignment with the tools.
Twisting corresponds to an unwanted rotation gradient of the 2D sections of an extruded part, and its magnitudeis usually characterized by the disorientation angle between the two end sections [6, 7]. Twisting has been usuallyevidenced and investigated for parts of length around 1 m. Depending on the material and the geometry, twistingparameter, defined as the ratio of the disorientation angle over the distance in-between the two sections, can reachvalues up to 25°.m−1.
This phenomenon is observed on parts exhibiting non-symmetry along the greatest length and obtained for exampleby extruding a symmetric section along a curved line [8] or a non-symmetric section along a line [5]. However, fromindustrial records [9], twisting can be obtained even for symmetric 2D section extruded along a straight line (U-shapedrails). Moreover, a large dispersion is obtained for twisting parameter corresponding to the same conditions. It seemstherefore interesting to derive an experimental database leading to stable results, in order to validate finite elementpredictions of twisting.
This article recalls experimental results obtained on the twisting of a U-shaped rail, presented in details in [10, 11].
Twisting does not occur when the blank is correctly aligned with the drawing tools. However, a disorientation of 2° ofthe blank relative to the tools (die and punch) leads to a twisting parameter of 11 °.m−1. In this work, 2D and 3Dnumerical simulations of the process were carried out in order to compare the predicted values with the experiments.
MATERIAL AND EXPERIMENTS
The studied material is an austenitic stainless steel provided by Arcelor-Mittal company of AISI 304 type (X4CrNi18-9). The material is supplied as cold rolled sheets of 0.15 mm thickness, in coils of 28 mm width in a shining annealedfinal state. The tool dimensions are given in Fig. 1. The very thin sheet was chosen in order to be able to reproduce,over a maximum length of 100 mm, a significative twist of the part, in order to improve the stability of the measures.Typical dimensions were obtained by using a scale factor of 1/10th compared to values found in the literature. Blankdimensions are 28×100 mm2. The device allows to accurately control the initial position of the sample, either alignedor misaligned at an angle of 2° with respect to the longitudinal axis of the tools. The radii of the die and the punch areboth 0.5 mm. The gap between these tools is 0.17 mm which leadsto a constant gap between the sheet and the toolsof 0.01 mm during the test.
FIGURE 1. Tool dimensions and visualization of the blank disorientation with respect to the die and punch
Both the initial blank and the resulting part geometry were measured with a 3D laser scanner. The scanner is fixedon a 3D measuring machine and its displacement along the length of the sample is controlled by the machine. Thewhole surface in contact with the die was scanned using a lineof laser light. The scanner digitally captures the outsideshape and a data-point cloud was created. This data was post-treated with a dedicated software (Polygonia) and thepoint coordinates of three sections were output, one in the middle of the sample and the two others at the ends. Apost-treatment program was developed within the Scilab environment, in order to have an automatic calculation of thesection parameters for 2D springback and the twisting magnitude.
The twisting parameter has been calculated for several samples in both the aligned and misaligned cases. Threeseries of tests were performed, and in-between each series,the device was unsettled and then later re-settled onthe machine, inducing somehow different initial configurations. Moreover, the first series was conducted on virginsamples, i.e. without tensile pre-strain, whereas the two following ones were performed on pre-strained samples inorder to straighten the blank. Fig. 2 clearly shows that the twisting parameter is significantly higher for the misalignedcase than for the aligned one. Moreover, it should be emphasized that there is no overlapping of the values for thetwo cases, as they are below 5°.m−1 or above 10°.m−1 respectively, meaning that twisting is clearly influenced bythe misalignement of the blank with respect to the tools. An average twisting parameter of 13.5°.m−1 is found formisaligned blanks, which is much higher than the mean value (3.1°.m−1) calculated for the aligned blanks. Thedispersion of the results was shown to depend on the difference of springback of the sections. Indeed, the radius ofcurvature of the walls was measured and some differences occur even for the same configuration. Indeed, a sliding ofthe blank along the width direction was evidenced, and thereexists a strong correlation between this sliding magnitude
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FIGURE 2. Twisting parameter for the aligned and misaligned configurations
and the radius of curvature of the wall, leading to differenttwisting parameter.
For the given dimensions (blank length of 100 mm and drawing depth of 7 mm) and material (sheet of stainless steelof 0.15 mm thickness) no twisting is obtained when the blank is initially aligned with the tools, within the uncertaintyof the measuring system. However, a slight misalignment of 2° of the blank with the tools lead to a reproducibletwisting parameter of 11°.m−1 over 8 experiments.
NUMERICAL SIMULATION
Input data
Numerical simulations in 2D plane strain and 3D were carriedout within the implicit scheme, using Abaqussoftware. An elasto-plastic model based on a mixed hardening (combining two terms, as implemented in standardin Abaqus) associated to von Mises yield criterion gives a good description of the mechanical behavior of the materialboth in tension and simple shear; isotropic hardening is modeled with Voce equation. Parameters of this model aregiven in Table 1. Fig. 3 shows that the kinematic contribution to the hardening is significant and well-described withthe model. Young’s modulus and Poisson’s ratio were taken equal toE = 200 GPa andν = 0.3 respectively.
TABLE 1. Material parameter for the mixed hardening, identified fromtensile and simple shear tests
As a first step, 2D simulations were performed, in order to evaluate whether the non-symmetry of the 2D sectioncould induce any rotation of the section after springback. Indeed, from the experiments and in the misaligned case, thesections are no longer symmetric with respect to the tools (punch and die), there is a shift along the width directionof maximum value 1.75 mm. 2D simulations within plane strainassumptions were performed both for the symmetricand non-symmetric cases. Four node elements with reduced integration were used, with three layers of elementsin the thickness and a size of 0.08 mm along the sample width. Friction coefficient of 0.18 was used. The punchdisplacement is set to 7 mm, the blankholder force is equal tothe recorded experimental value; after drawing, the
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FIGURE 3. Experimental and numerical prediction of the stress level in tension and simple shear.
TABLE 2. Curvature radius of the wall, comparison between experimental and pre-dicted values
Non-symmetric/Misaligned short 15.3 17.1 28.4/29.5Non-symmetric/Misaligned long 16.8 17.9 28.6/27.9
middle node is pinned and tools are removed. Numerical profiles are post-treated in the same way as experimentalones, in order to calculate data related to the 2D springbackand rotation of the section.
2D springback of the section is usually quantified by introducing angles characteristics of the orientation of thebottom with the wall and the wall with the flange, as well as thecurvature radius of the wall [1]. It was shownthat between the two orientation cases considered in this study, the most significant variation was recorded on thecurvature radius [10]. Table 2 shows the comparison betweenexperimental values and predicted ones. It can be seenthat the longer the flange is, the higher is the curvature radius, meaning that the wall remains straighter. A relative gapof 2% between symmetric section and the shifted one is found in experiments whereas it goes up to 4.5-5% for the2D simulation. Moreover, the rotation between the bottom line of the asymmetric case and the symmetric one is equalto 1.08°, which would lead to a maximum twisting parameter of21.6°.m−1. Such a high value could be explained bythe plane strain assumption, leading to an overestimation of the twist because all the sections rotate by the same anglewhich is not the case in experiments.
3D numerical simulation was also performed, using solid shell elements. Elements in the area that will flow overthe die radius have a size of 0.1 mm whereas in the center the size has been increased to 0.5 mm. 100 elements areused along the sample length. Both aligned and misaligned configurations were considered. After drawing, the centralnode in the part bottom is pinned and springback occurs by tool removal. The final shape for the misaligned case isshown in Fig. 4. Sections were also post-treated as for experiments and parameters characteristics of the geometrywere calculated (Fig. 5). Curvature radius of the wall is also given in Table 2. A twisting parameter of 24.9°.m−1
was predicted for the misaligned case. Further work should be performed to ascertain the 3D predictions, e.g. byinvestigating the influence of the anelasticty during unloading and elastic deformation of the tools [12].
FIGURE 4. 3D simulation and final deformed shape after drawing and springback
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FIGURE 5. Comparison of the two end sections, from experiments and 3D numerical simulation (left) section 1 (right) section 3
CONCLUSIONS
This work presents a comparison between experimental and simulated results concerning twisting (during springback)of elongated parts. From a previous study, it was established that U-shaped rails in stainless steel sheets exhibit a twistwhen the blank is misaligned by 2° with respect to the tools. The twisting parameter is 11°.m−1. Numerical simulationsin 2D plane strain and 3D were carried out in order to compare the predicted twist magnitude with experiments. Asan input of the finite element simulation, parameters of a mixed hardening were identified from tension and simpleshear tests. Associated to von Mises yield criterion, an accurate description of the mechanical behavior is obtained.2D simulations show that when the blank is shifted from a symmetric position compared to the tools, a rotation of thesection is predicted. In 3D, the same conclusion can be drawn, however there are discrepancies between the predictedfinal geometry and the experimental profile, leading o an overestimation of the twisting parameter.
ACKNOWLEDGMENTS
The authors are grateful to the French Ministry of Educationand Research (via the University of South Brittany) forthe financial support given to C.H. Pham for carrying out his PhD.
REFERENCES
1. I. Ragai, D. Lazim, and J.A. Nemes,J. Mater. Process. Technol.166, 116–127 (2005).2. P. Chen, and M. Koç,J. Mater. Process. Technol.190, 189–198 (2007).3. B. Tang, G. Zhao, and Z. Wang,Int. J. Mater. Forming1 169–175 (2008).4. H. Watari, and O. Hiroshi,J. Mater. Process. Technol.80-81, 225–231 (1998).5. A. Andersson,J. Mater. Process. Technol.16, 301–307 (2007).6. M. Lee, D. Kim, C. Kim, M. Wenner, and K. Chung,Int. J. Plast.21 915–953 (2005).7. H. Li, G. Sun, G. Li, Z. Gong, D. Liu, and Q. Li,Mater. Design32, 3272–3279 (2011).8. M. Takamura, M. Sakata, A. Fukui, T. Hama, Y. Miyoshi, H. Sunaga, A. Makinouchi, and M. Asakawa,Int. J. Mater. Form.3
131–134(2010).9. S. Thuillier, P.Y. Manach, Excellence and Control for Automotive Opening Parts, industrial contract with competitiveness pole
ID4CAR (restricted diffusion, in French)10. C.H. Pham, S. Thuillier, and P.Y. Manach, submitted inJ. Mater. Process. Technol.(2013).11. C.H. Pham, S. Thuillier, and P.Y. Manach, "Vrillage de tôles ultra-minces après emboutissage " inproceedings 21eme Congrès
Français de Mécanique, Bordeaux France 26-30 août 2013 (in French)12. N. Iwata, H. Tutamori, N. Suzuki, and A. Murata,R D Review of Toyota CRDL39 (2004).
