2.3.1 Extrusion ratio
In conventional extrusion the extrusion ratio R is defined as:
= (2.1)
where is the area of the container cross section, is the cross sectional area of the extrudate.
2.3.2 Plastic strain and strain rate
The effective strain, ̅, obtained by integration is a logarithmic function. Therefore, the effective strain in direct extrusion is usually approximated as the fractional sectional area and is defined in an elementary notation as:
ε = = (2.2)
which ignores any inhomogeneity on the extrudate section.
The rate of straining is also an important parameter and very difficult to determine due to the complex flow pattern in the deformation zone. The material undergoes a rapid acceleration as it passes through the deformation zone. Therefore a mean equivalent strain rate, ̅̇ , is useful both for preliminary determination of the flow stress and a rapid way to determine possible limit of the equipment. After extensive optimisation of the upper bound solution, Castle and Sheppard (1976a) and Tutcher (1979) suggested the following equation for the mean equivalent strain rate
̅̇ = 6 2 ( + )( + )
3− 3 (2.3)
where a, b, c and d are constants, is the container diameter, is the extrudate diameter, is the ram speed and is the semi-angle of the deformation cone. Of
course more accurate calculation may be obtained when using FEM.
2.3.3 Friction
Generally hot extrusion of aluminium alloys is performed without lubricants.
However a small amount of graphite based grease is sometimes used on the face of the die and dummy block. This is because the surface is a very important feature of the product and is formed from the interior of the billet by the shear occurring in the conical zone adjacent to the die known as the dead metal zone (Sheppard 1999a, p.10).
Friction in aluminium extrusion is a complex and still not fully understood phenomenon (Nakamura et al. 1997; Nakamura et al. 2003; Schikorra et al. 2007;
Wagener and Wolf 1994). The environment of hot extrusion (i.e. high pressure, high temperature and complicated material flow) prevents efficient investigation of the frictional interfaces.
In direct extrusion (with a flat die) the friction occurs at four interfaces: (a) container-billet, (b) die bearing-material, (c) dead metal zone-material, and (d) dummy block-billet. In indirect extrusion there is a similar upsetting stage in the beginning as in direct extrusion whilst there is no friction on the container-billet surface during the extrusion process because of the lack of relative movement between them. On the other three interfaces frictions still exist.
At commencement of extrusion the ram contacts the billet interface producing a frictional force at that location. Further ram travel upsets the billet into the container and the billet surfaces make first contact only at the highest points of the billet surface. Subsequently due to increasing pressure the contact area is increased.
The high points start to deform and the concentrated mechanical energy required to overcome frictional resistance is converted into heat energy. This eventually
leads to sticking friction between the container and the billet and extrusion proceeds by shearing along the container wall. The thickness of the shearing layer was calculated as of an order of 40-100 (Jowett et al. 2000; Sheppard 1999a, p.49). At the bearing-extrudate interface friction in the die land can further increase the extrudate’s temperature, which contributes to the surface quality of the extrusion (Peng and Sheppard 2004; Saha 2004 ). This temperature change is also one of the influencing factors for recrystallisation in the extrudate. At the dead metal zone-material the material experiences intermetallic friction that defines the dead metal zone semi-angle (Saha 2000, p.8). Due to the relatively small flow of material and the shearing of the discard, the dummy block-billet surface does not significantly influence the extrudate quality.
2.3.4 Extrusion pressure
Since the first attempt based on the assumption of uniform deformation by Siebel and Fangmeir (Sheppard 1999a, p.29) the study of pressure during aluminium extrusion has been extensively reported (Flitta and Sheppard 2002; Jo et al. 2003;
Lou et al. 2008). The pressure required for the process is the principal consideration in the selection of an extrusion press. The pressure can vary depending on: the alloy and its condition, the extrusion ratio, diameter and length of the billet, initial temperatures of the billet and tooling, ram speed and the shape of the extrudate (Castle and Sheppard 1976b; Sheppard 1993; Sheppard 1999a, p.143-144; Sheppard and Wood 1980).
2.3.5 Heat transfer and temperature
Heat transfer is one of the most the important phenomena to consider in extrusion as it defines the temperature parameter. This is one of the process variables which should be controlled. Temperature rise and distribution have been investigated by many researchers (Duan and Sheppard 2002a; Libura et al. 2000; Lou et al. 2008;
Mollerbernd et al. 1996; Zasadzinskii and Misiolek 1988). In general it has been shown that variations in temperature are mainly due to the extrusion ratio and ram speed. The flow stress and therefore the pressure will be reduced if the temperature is increased. However there is a risk of localised incipient melting with high ram velocity.
Heat transfer occurs throughout the extrusion process from the initial stage of homogenisation to the following extrusion stage, during which heat transfers to the die (from the billet) and air (from the extrudate), until the stage of stretching and finally at the stage of solution treatment and ageing (Castle and Sheppard 1976b;
Chenot et al. 1996; Sheppard and Wood 1980). The heat generation and heat transfer occurring during the extrusion are critical because they define the exit temperature of the extrudate. The temperature distribution over the extrudate leaving the die is important for product quality (dimensional stability, structural factors and extrusion defects) and die life (wear and performance). Castle (1992) and Sheppard (1999b) divided the heat balance between the following processes:
• Heat generation due to plastic deformation;
• Heat generation due to friction at the container-billet, dead metal zone-material and die land-zone-material interfaces;
• Heat exchange between the billet and the tooling (container, pressure pad and die land).
Approximately 90-95% of the mechanical energy is transformed into heat.
Therefore the heat generation rate per unit volume, ̇ , can be written as follows:
̇ = ̇ (2.4)
where is the heat generation efficiency (0.90 ≤ ≤ 0.95).