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					                                      22nd DANUBIA-ADRIA Symposium
                                 on Experimental Methods in Solid Mechanics

                                            September 28 - October 1, 2005
                                          MONTICELLI TERME / PARMA - ITALY


                             Pavel Macura, Prof. Ing. DrSc, Michal Keller, Dipl. Ing.
  Department of Elasticity and Strength of Materials, Faculty of Mechanical Engineering, VŠB-Technical University
                         Ostrava, 17. listopadu 15, 708 33 Ostrava – Poruba, Czech Republic.


The paper is devoted to the experimental stress analysis
in the zone of plastic deformation with attention
focused on practical application at solving the states of
stress at forming, especially at flat and pass rolling.
The trials for analytical solution of this problem are
complicated due to the non-linear character of the
relationship between the strains and stresses in the zone
of plastic deformation. Another serious problem
emerging with the analytical solution is the complex
character of boundary conditions at contact areas of the
formed material with the forming tools.

Applied methods and instruments
                                                                    Fig. 2: The isochromatic lines at mill rolls
For this reason new experimental-calculating method
was derived for solution of the stress fields which
would enable to analyze the strain field experimentally,
by means of some photoplastic methods, whereby the
tensor stress field is then evaluated analytically on the
basis of some of the theories of plasticity.
The strain measurements were performed on a new
transmission-reflection polariscope of own design
(Fig. 1). The polariscope enables the measurements in
through light at mill rolls (Fig. 2) or at rolling stocks
(Fig. 3), in reflected light and in through and reflected
light together (Fig. 4).

                                                                  Fig. 3: The isochromatic lines at rolling stock

                                                             The formed specimen is prepared of a low-modulus
                                                             optic-active resin and is deformed by relevant forming
                                                             tools. The specimen is placed between the polarization
                                                             filters of polariscope and the obtained courses of
                                                             isoclinic and isochromatic lines are recorded by means
                                                             of camera and they are the background for evaluation
                                                             of strain field. By calculation of the static conditions of
    Fig. 1: The transmission-reflection polariscope          equilibrium using the method of difference in shear
                                                             (Fig. 6), oval-circle-oval (Fig. 7), square-rhombus-
                                                             square (Fig. 8), the rolling of sheet pile (Fig. 9) etc.
                                                             were investigated.

     Fig. 4: The interference lines at through and
                     reflected light                               Fig. 7: The grooving series oval-circle-oval
stresses with application of the sequence-approach
method (Fig. 5) we can determine the components of
the stress tensor in all points of the formed specimen.
Here, a program was elaborated for calculation and the
whole evaluation is run on a computer.

                                                               Fig. 8: The grooving series square-rhombus-square

    Fig. 5: The curve of hardening and procedure of
                   numerical solution

The obtained tensor stress fields were shown plotted by
means of the equiscalar levels of the principal stresses
as well as by the equiscalar levels of both the shear
stress intensity Sτ and the intensity of shear strains Sγ.

                                                                          Fig. 9: the rolling of sheet pile


                                                             The results provide qualitative and even quantitative
                                                             picture of the uneven distribution of strain and stress in
                                                             material at the course of forming process. It is also
                                                             possible to determine the fields with active tensile and
                                                             compressive principal stresses as well as the course of
                                                             contact stress between the formed material and the
                                                             forming tools. The results serve for optimizing the
                                                             forming processes.

        Fig. 6: The rolling at two-arc oval pass

The application for pass rolling

This method was applied for solution of problems by
pass rolling. The grooving series of square-oval