A modified Marciniak–Kuczynski model for determining the forming limit of thin-walled tube extruded with initial eccentricity

Abstract

Thickness deviation in hoop direction is often observed in thin-walled extruded tubes, which is mainly due to the eccentric position of extrusion mandrel. This imperfection in thickness may result in different deformation pattern and consequently different formability. The influence of initial thickness deviation caused by extrusion eccentricity on deformation is investigated by FE analysis first. Radial expansion, hoop stress distribution, and change of cross-section during free hydro-bulging are analyzed. The maximum and minimum wall thicknesses are used to characterize the thickness deviation directly. A new definition of initial inhomogeneity coefficient in M–K model is proposed, and consequently a modified M–K model is proposed specially for tubes extruded with eccentricity. Controlled hydro-bulging test of AA6061-F extrusion is then carried out to verify the modified M–K model.It is shown that asymmetrical deformation tends to occur in free hydro-bulging process of aluminum alloy tubes extruded with initial eccentricity. Higher stress appears in the region with thinner thickness, and expansion occurs first. The original circular cross-section changes its shape to ellipse as hydro-bulging proceeds. The bigger the initial eccentricity is, the bigger the ellipticity of the deformed section. As the initial eccentricity is introduced in defining the initial inhomogeneity coefficient, the modified M–K model can be determined directly, without any requirement of experimental data. Based on the modified M–K model, the theoretical predictions of forming limit curves on the right side of FLD agree well with the experimental results determined by controlled hydro-bulging test.