**3. Initial data for modelling**

Two variants of radial direct extrusion, which are different by a shape of initial billet, have been considered. The first variant of billet is the bushing with a hole and the second is the bushing with a hole and a spherical cavity in the upper butt end. The input data for simulation: the strain rate is 0.5 m/s, deformation temperature interval is 1100 - 900 °C, friction coefficient 0.2, initial porosity of powder billet is 15 %. The dimensions of billet for extrusion by the first variant: the outer diameter Dinit is 27 mm, hole diameter 9 mm, height 31 mm, diameter of forged piece 28 mm, flange diameter 30.8 mm, height 26 mm, hole diameter 8.5 mm, die preheating temperature 200 °C. Material of stamp is die steel 5HNV GOST 5950 - 2000. The finite element model of the billet-stamp system at the beginning and the end of the extrusion is presented in Fig. 1.

Analysis of the stress-strain state and temperature field were performed in sections of billet, as shown in Fig. 2. The effective method to reduce a non-uniformity of the stress-strain state during extrusion is formation of relieving cone-shaped cavity in the initial billet (Fig. 4). According to the recommendations (Ryabicheva et al., 2011), relieving cavity for reducing of significant non-uniformity of stress-strain state in the upper end of the billet has made. The simulation scheme is presented in Fig. 3. It was assumed for simulation that the cavity depth is equal to the radius of the sphere, the cone angle was equal to 15°, 30° and 40°.

**Figure 3.** The model of the billet-stamp system for extrusion of billet with a relieving cavity: (a) - is the starting posi‐

Computer Modelling of Radial-Direct Extrusion of Porous Powder Billets

http://dx.doi.org/10.5772/57142

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**Figure 4.** Drawings of initial porous powder billets: (a) - is the billet without relieving cavity; (b) - is the billet with re‐

**4. Computer simulation of radial-direct extrusion of forged piece with a**

Finite element simulation of extrusion of forged piece from cylindrical billet with a hole has shown clearly that maximum intensities of stress and deformation observed in the surface layers of the spherical cavity by sections of forged piece OA, OB and OC. These values were decreased gradually while increasing the distance from the surface of the forged piece (Fig. 5). The maximum values of the studied variables and dramatic non-uniformity of stress-strain

**spherical cavity and flange from cylindrical billet with axial hole**

Drawings of initial porous powder billets are presented in Fig. 4.

tion, (b) - is the extrusion stage.

lieving cavity.

**Figure 1.** The model of the billet-stamp system: (a) - is the starting position, (b) - is the extrusion stage.

**Figure 2.** The model of initial billet – (a), section of forged piece for analysis of the stress-strain state – (b).

**Figure 3.** The model of the billet-stamp system for extrusion of billet with a relieving cavity: (a) - is the starting posi‐ tion, (b) - is the extrusion stage.

Drawings of initial porous powder billets are presented in Fig. 4.

Analysis of the stress-strain state and temperature field were performed in sections of billet, as shown in Fig. 2. The effective method to reduce a non-uniformity of the stress-strain state during extrusion is formation of relieving cone-shaped cavity in the initial billet (Fig. 4). According to the recommendations (Ryabicheva et al., 2011), relieving cavity for reducing of significant non-uniformity of stress-strain state in the upper end of the billet has made. The simulation scheme is presented in Fig. 3. It was assumed for simulation that the cavity depth

is equal to the radius of the sphere, the cone angle was equal to 15°, 30° and 40°.

124 Computational and Numerical Simulations

**Figure 1.** The model of the billet-stamp system: (a) - is the starting position, (b) - is the extrusion stage.

**Figure 2.** The model of initial billet – (a), section of forged piece for analysis of the stress-strain state – (b).

**Figure 4.** Drawings of initial porous powder billets: (a) - is the billet without relieving cavity; (b) - is the billet with re‐ lieving cavity.
