**1. Introduction**

Improving the competitiveness of engineering products related to enhancement of extrusion technologies using computer modelling of the material behaviour that allows production of high-quality products (Aliev et al., 2001; Favrot et al., 1997, Ryabicheva, 2012).

It is well known that a wide range of complex-shaped parts with flanges and spherical cavities are applied in machine-building and operating at variable loadings and high wear conditions. This is why the mentioned parts are produced of compact materials by various types of extrusion. The extrusion techniques are less used for production parts from powder materials due to presence of residual porosity and density variation. The extrusion technologies for parts with spherical cavities producing in the automotive industry have studied insufficiently. Production of parts may be carried out using various deformation schemes by selection the optimal initial shape and porosity of billets, as well as the deformation temperature. The most common process flowsheet for parts from powder materials is the scheme involving pressing of billet (compact), sintering and subsequent final stamping to obtain the necessary accuracy and density (Ryabicheva et al., 2011).

Finite element simulation is the most effective way for determination of optimal process variables of forming operations. However, simulation of extrusion of porous billets from powder materials with taking into account dependences of mechanical properties from porosity, thermal and strain rate deforming conditions does not allow to estimate the conver‐ gence of finite element method (Awrejcewicz et al., 2004; Awrejcewicz & Pyryev, 2009). Mathematical formulation of the nonlinear coupled thermal plasticity problem makes necessary implementation of advanced solution methods for systems of linear algebraic equations (Awrejcewicz et al., 2007).

© 2014 Ryabicheva and Usatyuk; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This work aims on improvement a quality of automotive parts based on a theoretical analysis of the stress-strain state, temperature fields and density distribution during radial-direct extrusion of porous powder billets.

θ - is the porosity;

*ρ*¯ =1−*θ*- is the relative density;

by Skorokhod V.V. (Skorokhod, 1973):

where γ - is the shape changing rate.

where W - is the equivalent strain rate:

wq

(Skorokhod, 1973; Shtern et al., 1982; Segal et al., 1994):

by the expression (Shtern et al., 1982; Segal et al., 1981):

m - is the parameter characterizing the degree of imperfection of the contacts in the powder billet and defining different resistance of a porous body during its testing in tension and compression. The rate of volume change resulting from the plastic deformation is presented

where σ0 - is the flow stress of hard phase, which is a function of accumulated deformation

A flow stress of hard phase may be expressed as the function *<sup>σ</sup>* <sup>=</sup>*σ*<sup>0</sup> <sup>+</sup> *<sup>K</sup><sup>ω</sup>* 0.5, where K - is the hardening coefficient. The rate of accumulating deformation in hard phase of porous body was determined on the basis of postulate of uniqueness of the dissipation function formulated

> 22 2 (1 ) <sup>1</sup> 1 1

*e m m*

 y

*m m e*

æ ö + + =- + ç ÷

+ + è ø

The value of accumulated deformation ω is renewed by solving of differential equation

, *<sup>d</sup> <sup>W</sup> dt* w

<sup>1</sup>−*<sup>Θ</sup> <sup>ψ</sup><sup>e</sup>* <sup>2</sup> <sup>+</sup> *φγ* <sup>2</sup>

The finite element method presented as a series of procedures has used for determination of distributions of stress and strain intensity, as well as density in the volume of porous billet. The first procedure is triangulation of plastically deformed body or transition from a contin‐ uum billet to its finite element counterpart. Such simulation requires implementation of

*<sup>W</sup>* <sup>=</sup> <sup>1</sup>

extremal requirement for the functional (Shtern et al., 1982, Segal et al., 1981):

g

s

+ (2)

Computer Modelling of Radial-Direct Extrusion of Porous Powder Billets

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

121

,

= (4)

. (5)

(3)

 y

y

2 <sup>0</sup> 2(1 ) 2 (1 ) ~ , *m m m*

ω and is determined by a hardening curve of powder material at uniaxial tension.

+ +

*e p*

y
