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We investigate front end bending (FEB) behaviours of material that usually occur during flat rolling using the shape factor, defined as the ratio of the mean contact length to the mean thickness of a material for a given roll-bite profile (that is, a non-dimensional value composed of the incoming thickness of the material, its exit thickness, and the diameter of the work roll). In this study, we demonstrate that diverse values of FEB and its slope exist for a given shape factor. To determine a distinct value of FEB and its slope for a given shape factor, we introduce an additional non-dimensional parameter, geometric factor, defined as the ratio of the work roll radius to the incoming material thickness. It has been found that the geometric factor is much more sensitive to FEB behaviour than the shape factor. If one uses the shape factor and geometric factor together, a distinct value of FEB and its slope can be determined no matter what type of roll-bite profile is used in the flat rolling process.

A large-deformation constitutive model applicable to the calculation of roll force and torque in heavy-reduction rolling has been presented. The concept of the volume fraction of dynamically recrystallized grains, which depicts the flow stress softening correctly with the level of strain, strain rate and temperature has been newly introduced in the proposed model. The material constants required in the proposed model have been obtained by a series of hot-torsion tests.A laboratory-scale hot-plate rolling experiment, together with three-dimensional finite element analysis coupled with the proposed model, has been performed to investigate the accuracy of the proposed constitutive model. The soundness of the proposed model has been demonstrated through a series of finite element simulations with temperature and reduction changed.The finite element predictions of roll force based on the proposed model and the experimental results was shown to be in fair agreement whereas those based on the Misaka-Yoshimoto model, in which dynamic recrystallization was not considered, failed to predict the roll force precisely at heavy reduction. The results also revealed that, for a typical reduction, the flow stress softening effect was not observed during deformation, whereas the effect was considerable when the material underwent heavy reduction.

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Two sets of roll profiles were designed such that the roll surface outline is larger in the centre than at the end and vice versa (i.e. convex and concave roll profiles) to simulate positive bending and negative bending profiles in actual cold rolling. Pilot cold rolling tests were then performed to show how waviness of high-silicon steel (3.0 per cent Si) specimens occurs during cold rolling and leads to edge cracking. A finite-element analysis was carried out to examine stress distributions in the region of the specimen where edge cracking initiates during cold rolling. Results show that these specially designed roll profiles create waviness in the specimen, even though the ratio of width to thickness of the specimen used in this study is 10. (Generally, the width to thickness ratio of actual high-silicon steel strip is greater than several 100s.) It has been found that the convex roll profile, corresponding to positive bending in the actual cold rolling, generates waviness in the specimen centre and subsequently the edges of the specimen start fracturing locally due to tensile stress in the rolling direction produced by the waviness. Hence, the best way to avoid edge cracking in actual cold rolling mills is to suppress occurrence of waviness in the centre of the high-silicon steel strip by controlling the roll bending profile.