Theoretical and experimental studies of the external inversion process in the circular metal tubes

Abstract

This article introduces a new theoretical model of deformation and based on the energy method derives a new theoretical relation to predict the axial load versus the axial displacement during the external inversion process in the circular metal tubes. Several deformation mechanisms are assumed in the theoretical model: bending around circular hinge line, bending in normal to meridian direction and circumferential expansion. A total inversion process in the tubes is divided to three different stages versus the inversion angle, θ: 0⩽θ⩽π, π⩽θ⩽2π and after θ=2π. In each stage, the total dissipated energy is calculated by different deformation modes. The different strain components are calculated and based on the principle of energy conservation; some theoretical relations are derived to predict the instantaneous inversion force. Then, some circular brazen tubes are used in the external inversion tests with die radiuses of R=2.85mm and 4mm and diagrams of axial load versus the axial displacement are sketched. Comparison of the theoretical predictions and the experimental results shows a reasonable correlation. The theoretical relations can predict variations of the axial load versus the axial displacement of three considered stages during the whole inversion process with a good agreement. Comparison of the theoretical and experimental curves shows a better correlation in the horizontal part and position of start point of the inversion process with the die radius of R=4mm, comparing with the inversion process with the die radius of R=2.85mm. Also, the theoretical analysis shows that the absorbed energy and the axial load during the inversion process in the circular tubes depend on the wall thickness and diameter of the tube, tube material type, and the die radius.