A novel approach for the edge rolling force and dog-bone shape by combination of slip-line and exponent velocity field

This study presents a new mathematical model for edge rolling force and dog-bone shape using the combination of slip-line and exponent velocity field. The slip-line field of the dog-bone area is drawn out based on the deformation characteristics of edge rolling and the maximal depth of dog-bone zone is determined. Then a new exponent velocity field and corresponding strain rate field which satisfy kinematically admissible condition are proposed to analyze the edge rolling force based on upper bound approach. The upper bound solutions of dog-bone shape and rolling force are obtained by minimizing the total power which contains the internal plastic power, frictional and shear powers. The effects of reduction rate, initial thickness and roll radius on dog-bone shape size and edge rolling force are discussed. The results obtained by the combined solution in this paper are compared with measured data in strip hot rolling field and finite element method (FEM) simulation results, and a good agreement is found.