Theoretical Solution of Linear Hardening Elastic-plastic Deformation Length for a Roll Formed Channel

Determination of the deformation length is one of the first steps in roll forming design. Roll forming industries are very interested in explicit simple relationsfor prediction the deformation length without using trail-and-error methods at workshop or time consuming finite element simulations. In this paper، elastic properties and work-hardening behaviour of the strip are considered in addition to geometric specifications of a channel section in order to study the strip deformation. Some relations are introduced for the deformation work consumed during the longitudinal stretching of the flange and the transverse bending of the bend line for a linear hardening elastic-plastic strip. Finally، a relation are developed for the deformation length. Theoretical results show that the forming angle، the flange length and the Young’s modulus increase the deformation length and the strip thickness، the initial strength and the tangential modulus at the elastic-plastic range decrease the deformation length. The Poisson’s ratio has no effect on the deformation length. However، the bend radius to the strip thickness ratio increases the deformation length. The elastic properties and work-hardening behaviour result in a deformation length which is shorter than the rigid–perfectly plastic deformation length which was proposed by Bhattacharyya.