*Steel Res. Int.* **76**, 327-335, 2005

### A STUDY ON THE BUCKLING BEHAVIOUR OF STRIPS AND PLATES WITH
RESIDUAL STRESS

F.D. Fischer¹, N. Friedl², A. Noé³ and
F.G. Rammerstorfer&sup4;

¹Institute of Mechanics, Montanuniversität Leoben,

Leoben, Austria

²CAE Simulation & Solutions, Vienna, Austria

³BWG Bergwerk- und Walzwerk-Maschinenbau,
Duisburg, Germany

&sup4;Institute of Lightweight Design and Structural
Biomechanics,

TU Wien,
Vienna, Austria

**Abstract** -
During and after rolling or flattening of metal strips and plates the
permissible deviations from flatness are described by the permissible absolute
wave height and the flatness index.
Both values can be determined on a measuring table while the material is not
subjected to gobal tension.
Because this procedure is expensive, time-consuming and allows measurement
only at discrete positions along the strip length, on-line flatness measuring
systems are used which can detect the distribution of longitudinal tensile
stresses distributed along across the strip width allowing for the calculation
of the flatness index.
This value does not always agree with the value obtained directly by measuring
on the table even when the measurement of the longitudinal tensile stress
distribution operates perfectly.
It can be shown that the measurement of the tensile stress distribution does
not give a direct indication on the wave height in the tension-free state
determined on the measuring table.
To explain the relationship between tensile stress distribution in the strip
and the flatness measurement on the measuring table, the buckling behavior is
analysed both with and without dead load for simple symmetrical residual stress
distributions resulting, e.g. from the rolling process.
Based on the knowledge of the distribution of the longitudinal residual
stresses acroess the strip width, the flatness index and the wave height can be
determined by using a specialized fintie element model.
If the direct measurement is performed under action of dead load, large
differences between the directly and indirectly obtained flatness index are
observed.
Below a certain limit of the intensity of the residual stress distribution the
strips and plates lie flag on the measuring table.
Above this limit the strip lying on the table exhibits post-buckling
deformations.
In the latter case, the wave height increases with strip thickness and
intensity of residual stresses.

(hjb,050427)