An upper bound solution for deformation field analysis in differential velocity sideways extrusion using a unified stream function. (15th June 2022)

• Record Type: Journal Article
• Authors: Zhou, Wenbin; Shi, Zhusheng; Lin, Jianguo; Dean, Trevor A.
• Is Part Of: International journal of mechanical sciences. Volume 224(2022)
• Publication Date: 2022-06-15
• Subjects: Sideways extrusion -- Strain rate -- Strain inhomogeneity -- Flow field -- Curved profile -- Upper-bound theorem; Mechanical engineering -- Periodicals; Génie mécanique -- Périodiques; Mechanical engineering; Maschinenbau; Mechanik; Zeitschrift; Periodicals; 621.05
• DOI: 10.1016/j.ijmecsci.2022.107323
• Languages: English
• ISSNs: 0020-7403

Abstract

Highlights: An analytical model for flow and deformation behaviour in DVSE is developed. Eccentricity ratio is independent of flow line shape parameter and material hardening. The model closely captures the flow lines obtained under different test conditions. The model well predicts the field distributions of effective strains and strain rates. Abstract: An analytical model providing a detailed description of the material flow and deformation behaviour of extruded curved profiles produced by the novel differential velocity sideways extrusion (DVSE) process, has been developed on the basis of a unified stream function and the upper bound theorem. Plasticine experiments and finite element (FE) modelling were carried out to validate the proposed analytical model. The derived streamline equation contains a shape parameter n describing the degree of curvature of a flow line and the coordinate parameters x 0 and y 0 defining entering and leaving positions respectively of the flow line, from the plastic deformation zone (PDZ). The analytical model was able to closely model the material flow eccentricity ratio ξ (the relative amounts of work-piece material entering the deformation zone from two opposing directions), and flow lines obtained from experiments under different velocity ratios and extrusion ratios. The predicted value of ξ was found to be independent of n value and hardening of the material. The n value was found to increase from the corner near the die orifice to the corner around the dead material zone (DMZ). In addition, the n value increased with the increase of extrusion ratio and ratio of velocities of the two opposing extrusion rams, which enabled the representation of a decreased area of DMZ and more localised PDZ containing 1–99% accumulated effective strain. The predicted field distributions of the localised effective strain rate in the PDZ and inhomogeneous effective strain in the extrudates were consistent with FE modelling results. Graphical abstract: Image, graphical abstract