An Approximate Method of Estimating the Yield of a Strip Under Tension Cut by Serrated Surfaces on Opposite Faces

In view of the well-known disparity between predictions from temper rolling models and measured values from rolling mills, there is a need to obtain a better understanding of the effect of roll asperities on the yielding characteristics of the rolled strip. This paper models a roll with asperities as a rigid body with a regular serrated surface and the rolling process as an indentation, and uses the plane strain model and slip-line theory to determine the critical pressure that is required to yield the strip throughout the thickness beneath the tips of the asperities. The strip is also under lateral tension at both ends. The emphasis of the paper is the effect of the lateral tension and the thickness of the strip on the critical pressure. For the case when the indenting surface has sharp teeth, the critical pressure can be found in close form. For the case when the indenting surface has blunt teeth, a robust approximate scheme for estimation of the critical values that does not require extensive computation is given and this scheme can be used in an on-line control process. It is found that when the tooth angle is smaller than a critical angle, the sharper the tooth, the lower the average critical pressure needed to make the strip yield. When the tooth angle is larger than the critical angle, then the blunter the tooth, the lower the pressure that is needed. The effect of the asperities is to reduce the critical pressure and it is found that this effect is more pronounced for thin strips than for thick strips. The lateral tension reduces the critical pressure further. These findings give some implications for the rolling of metal sheets.