A study on the buckling behaviour of strips and plates with residual stresses

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 global 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 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 across the strip width, the flatness index and the wave height can be determined by using a specialized finite 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 flat on the measuring table. Above this limit the strip lying on the table exhibits post-bucking deformations. In the latter case, the wave height increases with strip thickness and intensity of residual stresses.