Transient effects in the quasi-static and dynamic internal inversion and nosing of metal tubes

The plastic deformation mechanisms of metal tubes during quasi-static noting and internal inversion are analysed. Rigid-plastic analyses which incorporate an assumption of full conformity between the deforming tube and the forming die predict accurately the nosing load-displacement curve. Details of the deformation processes during internal inversion are examined using the non-linear facilities of the finite-element code ABAQUS. The early stages of the forced inversion characteristic are more complex than for nosing, with different deformation modes dominating the behaviour at different times. Each of these is also examined using rigid, perfectly plastic models. The quasi-static behaviour is used to provide insight into features of the load pulses generated during dynamic/impact loading of the tubes. The peak impact loads can only be assessed through a full dynamic analysis since inertial effects strongly influence the magnitude of the dynamic loads. It is shown that measured dynamic force pulses for both nosing and internal inversion can be accurately predicted using appropriate finite element models and the source of the high dynamic force peaks in inversion is discussed. It has been found both experimentally and numerically that the steady-state inversion force is lower under dynamic loading conditions than under quasi-static loading. A simple analytical model provides an explanation for this and highlights the importance of the ratio of the mass of the striker to that of the inverted portion of the tube in this phenomenon.