By Professor Terry Sheppard (auth.)

In contemporary years the significance of extruded alloys has elevated end result of the decline in copper extrusion, elevated use in structural purposes, environmental effect and diminished power intake. There have additionally been large technical advances. this article presents entire insurance of the metallurgical, mathematical and functional beneficial properties of the process.

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**Extra resources for Extrusion of Aluminium Alloys**

**Example text**

Flow takes place in region 2 as if velocity discontinuities fonned the triangle BX02 and in region 4 as if velocity discontinuities fonned the triangle BC04 • Streamlines are thus parallel to BX and BC in regions 2 and 4 respectively. The velocity vectors in regions 2 and 4 are constant on lines through 02 and 04. (a) (b) Fig. 5 Axisymmetric upper bound (a) physical field; (b) hodograph. 35 36 I I CONTINUUM PRINCIPLES L -_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _~ The best upper-bound solution will minimize the expression for the internal rate of energy dissipation: .

9(a» in a less compressive stress state than the flow lines L2 and L3 (Fig. 9(b». If the forces resulting from that distribution were allowed to operate, they would promote flow towards the less compressed axial line, thus generating a void at the end of the ram stroke producing the well-known 'piping' defect. Because the absolute pressure and the hydrostatic gradient are both greater in the direct extrusion mode this defect is more likely to be observed in that mode. We must conclude that FEM solutions are, in fact, upper-bound solutions and require experimental verification if they are to be utilized to model the practical extrusion process.

Thus, general reductions of the critical mesh when sticking friction obtains is imperative in order to ensure that the gradients of the strain rate are spatially confined within very few elements, otherwise the resulting internal out of balance forces readily become unbounded producing deficient tool reactions (and overall pressures). Both maximum strain rate loci agree with the predictions of slip-line field theory. A mean strain rate for the extrusion process can be calculated by averaging along the cylindrical surface defined by the median radial line of the 3 x 3 element Gauss points.