METAL FLOW DURING EXTRUSION OF NON-CIRCULAR SECTIONS

The paper presents the analysis of nature of metal flow during extrusion of non-circular sections and determining the relationship between extrusion force and geometrical parameters of extrudate (the shape of the extrudate). Experimental procedure was curried out for the simplest cases of non-circular profiles (triangle, square, rectangular) of various geometrical parameters. The extrusion load and punch displacement have been registered during experimental work. By determining parameters of metal plastic flow (the depth of plastic zone Lp and the dead zone angle sm) it has been shown the difference in nature of metal flow during extrusion product differing in non-circular sections. This differentiation results in the complex nature of flow consequential from change with circular section of the billet to non-circular section of extrudate. It has been shown that flow resistance can be different with regard to appearing configurations of deformation zones (the size and shape of plastic zone, dead and shear zones) and dependent from for example geometrical parameters of a die (shape and size of an die orifice).


Introduction
The possibility to obtain products of different shapes mainly from aluminium and aluminium alloys, e. g. in the aspect of complexity of the shape and thin-walled sections are difficult to determine with regard on insufficiently examined processes of deformation as well as the side of description of mechanical behaviour of the material (the change of structure and properties) and the technology (the selection and controlling the parameters of process).The wide use as well as production of shapes about with complex cross-sections creates the need conduct researches to make investigations including the analysis of structure of the material as well as its transformation in different temperature -velocity -force conditions.One of basic criteria to evaluate possibilities of forming in the process of plastic work are the amount of quantify of pressures and their distribution on contact surface from tool [1][2][3][4][5][6][7][8][9][10][11][12].Many factors influence on the magnitude of unit pressure.We can include the following for example: the properties of materials (physical, chemical, structure), the kinematics of movement of tools and of the material (the kind of extrusion process: direct and indirect extrusion), magnitude of relative strain and uniformity of their distribution, shape and dimensions of final material, friction conditions, temperature and heat balance of the process and strain rate.The extrusion force results in resistance of deformation of extrusion metal while being total effect of plastic resistance and flow resistance.The flow resistance can be different with regard to appearing configurations of deformation zones (the size and shape of plastic zone, dead and shear zones).The flow resistance dependent from for example geometrical parameters of a die (shape and size of an orifice die, height of bearing area).
The differentiation in size and shape of deformation in dependence on the shape of extrudate cross-section and extrusion load is especially visible in the case of extrusion of nonaxisymmetrical sections.This differentiation results in the complex nature of flow consequential from change with circular section of the billet on non-circular section of extrudate and various configuration of deformation zones (the size, shape and volume of plastic zone) to comparison with extrusion of axi-symmetrical cross-section extrudate.
The professional literature provides but little information about effect of geometry of crosssection extrudate on mechanics of metal flow and extrusion load [10][11][12][13][14][15][16][17][18].Considering the present state of research in this field [19 -23] we can say that in none of the researches studies so far any attempt has been made of an analytical approach to the problem of connecting the of nature of metal flow during extrusion of non-circular sections with the extrusion load.Limited attempts have been found to describe the relationship between the force characteristics of extrusion and of the nature of metal flow (geometrical parameters of plastic and dead metal zones).Evaluation of different mechanical behaviour of deformed material depended on shape and size of the cross-section of extrudate let to determine the relationship between extrusion force and geometrical parameters of product.Description of the type of complex flow (experimental investigations, modelling the process) let to determine proper parameters of the process.This work contains the results of experimental method of investigation of the character of metal plastic flow during extrusion of non-circular profiles.Results obtained will be used to modification of relationship that lets to calculate the extrusion load through introduction of the factor which determines dependence between extrusion load and the cross-sections of extrudate shape.

Experimental material and methods
The aim of the experimental work is analysis of nature of metal flow during extrusion of noncircular sections and determining the relationship between extrusion force and geometrical parameters of extrudate.Experiments were carried out at room temperature, the extrusion load and punch displacement have been recorded simultaneously.The material was extruded directly with the use of sectional flat and conical dies.The shape of the die orifices and the value of the used extrusion ratios  have been presented in Fig. 1.
The examined material was Pb 99.98 lead billets of a 36 mm diameter and 72 mm in length.During experimetal work it was possible to analyse the flow of the extruded metal with the help of visioplasticity method.For the visioplasticity technique a 1.5 x 1.5 mm square grid was inscribed on the meridian plane of the billet.In all cases the process was stopped after extrusion of 1/2 the initial billet length.plastic zones during extrusion product of non-circular cross-sections Fig. 5 show obtained results.
Main differences in the nature of plastic flow in dependence of the shape of the die orifices.The manner of flow effect on mean pressure and (total) extrusion load.From this point of view it is important to analyse the characteristic parameters of flow suchlike: shape and a volume of plastic zone, plane and axis symmetry, number of corners of cross-section shape etc.In the case of extrusion of triangle shape of the die orifice there is a lack of plane symmetry in cross-section of extruded product, which finds its reflection in irregular shape of deformation zone.Determining the depth of plastic zone and the value of the dead zone angle permitted for determining the configuration of deformation zone.Fig. 6 shows the effect of the shape of extrudate cross-section on the configuration of deformation zones.relationship between maximum extrusion load for different extrusion ratio and different shape of extrudate is presented in Fig. 7.
The consequence of formed configuration of plastic zones is the answer in a form of differential size of extrusion load in the case of extrusion different shapes at the same value .Furthermore, in case of non-circular sections shape and size of cross-section extrudate significantly influences on quantity of extrusion load, but none of introduced relationships for calculating of extrusion load does not contain an additional factor, which maybe called "shape factor".An example parameters which may be defined as a "shape factor" S f are proposed: circumference of the noncircular extruded cross-section (C ncs ) to circumference of a circle that has the same crosssectional area as the extruded section (C cs ) and circumference of the extruded cross-section (C es ) to circle circumscribed about a extruded section (C ces ).The aim of the continue investigations will be modification of a/m "shape factors" and introduction their to relationship for calculating of extrusion load of non-circular sections.

Conclusions
Based on the results in this study, the following can be concluded.1.By determining parameters of metal plastic flow (the depth of plastic zone L p , the height of the dead zone L sm , the value of dead zone angle  sm ) it has been shown the difference in nature of metal flow during extrusion product differing in non-circular sections.Parameters of metal plastic flow determine the shape and the region (volume) of plastic zone, which influences on the extrusion load directly.2. Shape complexity significantly influences on the extrusion load.The extrusion load is the lowest for the circular cross-section; it increases for the square, triangle and rectangle cross-sections respectively.The attribute which determines the shape of the extruded cross-section (e.g.number of corners, acute and obtuse angles in extruded shape, number of axes and planes of symmetry, thickness of walls of segments of profiles cross-sections) reflect in the influence of shape extruded on size of extrusion load.3. The identified deformation zone, their description and connection with the shape of extrusion product and extrusion load let to modify analytical relationship determining the extrusion load through introducing the "shape factor".It may improve designing such ones especially for more complicated cases of extrusion of non-circular profiles.

Fig. 6 Fig. 7
Fig.6 Configuration of plastic zones during extrusion of circular and non-circular sections