A radial direction

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					A Drop-weight High-speed Tensile Testing Instrument
            1)*            1)             2)                 2)        2)                1)
O.K. Demir , C. Becker , S. Seuren , H. Voswinckel , G. Hirt , A.E. Tekkaya

 Institute of Forming Technology and Lightweight Construction, TU Dortmund, Dortmund / Germany; 2) Metal Forming Institute, Aachen
University, Aachen / Germany

* Corresponding author: E-mail address:; Tel.: +49 321 755 5238

The abstract can be ten lines at maximum. A 3-dimensional finite element simulation of free electromagnetic tube compression was per-
formed with the aim of predicting wrinkle formation. Staggered coupling was applied between the electromagnetic and mechanical parts of
the problem. The full problem was modelled since the wrinkle formation does not represent any symmetry in circumferential direction. The
initial geometric imperfections of the tube were measured and included in the model to trigger buckling. The deformed geometry with the
wrinkles could be predicted accurately.

Keywords: Cold forging, Electromagnetic tube compression, Wrinkling

                                                                      measurements, and random values were used for n. Equa-
Introduction                                                          tion (1) reveals that the tubes were crushed and the result-
                                                                      ing shapes were very complex to simulate accurately. The
   Electromagnetic tube compression is the reduction of               correspondence with the experimental results was better
tube radius due to the application of radial electromagnetic          when a mandrel was used, especially at high energy values,
forces. The material may buckle under the increasing                  when the tube was more ironed on the mandrel.
circumferential compression during the inward motion,
which causes wrinkles on the final product.                           Experimental Setup
   In a homogenously compressed body geometric or mate-
rial imperfections trigger buckling. However, inadequacy                 Simulations were conducted using explicit finite element
of the simulation tools or harsh assumptions avoided good             method. The algorithmic setup for the represented frame-
correspondence with the experimental results. The aim of              work was derived in principal axes using Equation (1) and
the present study is to calculate wrinkles in free electro-           implemented. With two materials, namely 100Cr6 and
magnetic tube compression by a coupled 3-dimensional                  Cf53 respectively, the effects of process parameters, such
finite element simulation.                                            as friction, semi-cone angle and reduction ratio on damage
                                                                      accumulation zones and intensities were investigated.
State of the Art                                                      Following Gao et al. (1999), Chrysler chevron free produc-
                                                                      tion curve was utilized. The process geometry and the
   In electromagnetic forming, a highly damped alternating            location of the selected dimensions on the Chrysler curve
current is sent through a coil in tens of microseconds. This          are given in Fig. 1.
current creates a counter current in the workpiece. The
repulsive forces between the two currents form the work-
piece. A tube is placed inside a solenoid for the electro-
magnetic compression.
   Kirkpatrick and Holmes (1988a) calculated wrinkling of
tubes under radial explosive loading by means of finite
element method and shell elements. They showed the im-
portance of including the correct initial geometrical imper-
fections in wrinkle prediction.
   Kirkpatrick and Holmes (1988b) measured the magnetic
flux during electromagnetic tube compression experiments
and calculated the magnetic pressure vs. time from the
flux. The tube was modelled with solid elements, one in
thickness direction. The initial imperfections were repre-
sented by an initial displacement perturbation given by

       W     an cos  n  n  ,                    (1)

  where  is the hoop angle, n is the mode number, an is
the amplitude of the displacement perturbation, and n is             Figure 1. Martensite fraction formed in cold rolling in (a)
the phase angle. an was calculated with regard to roundness           various steel grades, (b) in EN 1.4318.

Simulation Results                                                 stated by Bergmann and Weidig (2007) in their review
                                                                   paper on modelling of EMF. Second, if the calculation is
  Valls et al. (2007) assumed that the local governing             going to be used only for small strains, for instance, in case
equations collected so far can be reduced, particularly for        of calibration processes. Höhling (2000) simulated calibra-
the chosen yield criterion, making use of the substitution,        tion processes uncoupled, owing to this assumption. Simu-
n =  / an , and exploiting the condition of collinear flow       lation of tube compression cannot be classified into both
                                                                   groups and demands a coupled calculation. The possible
and the trial Kirchhoff stress tensor, finally, representing
                                                                   methods are:
the hardening/softening function.
                                                                    Eulerian method
  Table 1 gives the parameters used for the 10x20 mesh
(10 elements in radial direction and 20 elements in longi-          Lagrangian method
tudinal direction), which uses a 4-node axisymmetric ther-          Arbitrary Lagrangian-Eulerian method
mally coupled quadrangular element with bilinear dis-
placement and temperature interpolations. For the central          Discussion
damage deterioration method (hereafter damage triggering
type 1), an initial nonzero damage held, smoothly varied             In order to monitor variable distributions through path
over a certain length, is introduced at the central zone.          plots along the radius for isotropic and orthotropic cases,
Accordingly, the regions numbered with n = 1, 2, 3, 4, 5 in        four paths are defined. These are located at top and bottom
Fig. 1a are deteriorated by an initial damage of D = 2(1-n) x      surfaces with an orientation of 0° and 90° with respect to
10-6. The rest of the domain has zero initial damage.              the x-axis. A similar method was also applied by Lobaugh
                                                                   (1975). Fig. 1b shows the effect of damage on equivalent
Table 1. Chemical analysis of the investigated steel (in           plastic strain distribution for isotropic and orthotropic
mass %).                                                           cases.
EN Steel Grade      EN Strength Class   Rp0.2 / Rm - ratio
      1.4318              +C700                      0.55
      1.4301              +C700                      0.70
                                                                     The achievement of flow curves obtained using the de-
      1.4404              +C850                      0.90
                                                                   veloped drop-weight instrument and the proposed method-
      1.4301             +C1000                      0.80          ology is satisfying. In addition, the instrument has the
      1.4318              +C700                      0.65          important advantage of being simple and cheap.

   Inspired by these two methods, we propose two addi-             Acknowledgement
tional necking triggering methodologies, which rely on the
imposed conditions on the damage held over the problem               The authors would like to thank the German Research
domain. Accordingly, either the elements at the central            Foundation (DFG) for its financial support.
band are deteriorated by a slight initial appropriately se-
lected damage value, or the ones at the boundary bands are         References
assigned to non-increasing and zero damage.
                                                                   Kirkpatrick, S.W., Holmes, B.S., 1988a. Structural re-
   Mechanical Properties. Tensile tests were performed to             sponse of thin cylindrical shells subjected to impulsive
study mechanical properties. For each condition, three                external loads, AIAA Journal 26, p. 96-103.
parallel specimens were examined. The mean values of               Kirkpatrick, S.W., Holmes, B.S., 1988b. Nonlinear conti-
experimental results are given in Table 1. More impor-                nuum mechanics and oxidation of intermetallics, 2nd
tantly, the acquisition rate (10 s) of displacement data is          Edition, Wiley-VCH.
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                                                                   Gao, X.C., Kang, D.C., Meng, X.F., Wu, H.J., 1999. Expe-
plastic transition. As a result, the velocity, force, strain and
                                                                      rimental research on a new technology-ellipse spinning.
strain rate values (thus, the obtained flow curves) are inac-
                                                                      Journal of Materials Processing Technology 94 (2-3),
curate until a certain time value is reached (50 s can be
                                                                      p. 197-200.
mentioned as a rough estimation).
                                                                   Valls, I., Maikranz-Valentin, M., Cook, N.H., 2007. New
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  Modified mechanical properties. The method described
                                                                      10th Internal Conference on Cutting Methods, April 16-
here is not suitable for determining the Young’s modulus
                                                                      19, Paris, France, p. 25-32.
and yield strength of the material. The reasons are, first of
                                                                   Bergmann, K., Weidig, U., 2007. Fabrication d’une Pièce
all, that the gage length elongation calculated from the
                                                                      en Acier de Microstructure Multi-Phase. In: Moderne
weight displacement is not accurate enough for such a
                                                                      thermomechanische Prozessrouten beim Formhärten,
                                                                      Stahlinstitut VDEh, Düsseldorf, p. 115-135 (in
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                                                                   Höhling, O., 2000. Numerical and experimental study of
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coil current that is creating the forces damps out before a           hot stamping, M.Sc. thesis, TU Dortmund.
significant WP move. This assumption was used in many              Lobaugh, L.E., Gallo, T.S., 1975. US Patent 3,948,013.
early modelling efforts of EM sheet metal forming as                  Cold forged steel grating, 7 May.