The curling characteristics of static inside-out inversion of metal tubes

Abstract

The curling behavior of quasi-static inside-out inversion of tubes was analyzed using an energy method technique based on the critical condition for more precise design. (1) The first part is to derive the critical bending radius ρ ̄ c as a curling criterion to distinguish between curling and flaring on a conical die, in which the strain hardening exponent n and half-apex angle of die α have very marked effects on ρ ̄ c theoretically; however, the friction coefficient μ-dependence is not as great as the n. As a result, a much more satisfactory correlation between prediction and experiment is obtained and Kitazawa's study is a special case of this work. (2) The second part is to theoretically find the range of semicircular curling ( ρ ̄ min o < ρ ̄ o < ρ ̄ max o ) and the compressing load P of inversion in tube inversion with a quarter circle die. It appears that the material properties of the aluminum tubes used have little effect on the curling behavior of inversion. It is noted that factors μ and n obviously affect the position of semicircular curling of inversion but not its range size. On the other hand, n in contrast to μ affects significantly the compressing load. Good agreement between the theoretical prediction and experimental results is obtained for the compressing load, except in the case of the sharp fillet die radius for the strictly bending effect to be ignored in the prediction.