Dynamic answer analysis of sintering pieces in thermic-structural coupled condition.

Ciupitu, Ion ; Dumitru, Nicolae ; Ghercioiu, Jeni 等

1. INTRODUCTION

In this work our purpose is to analyze cast iron, iron and copper powders mixtures.

The studied material is a mixture of iron, cast iron and copper metallic powders. This type of material can be included in the group of composite materials with special features such as high hardness and good plasticity.

The mixture of iron powder and cast iron powder ensures a structure with a good wear strength (established by the hard cast iron particles) and a good plasticity (ensured by the high amount of iron powder in the mixture).

Moreover, a uniform structure can be obtained by creating a good homogenous mixture, consisting of hard grains included in a strong fundamental structure. In this way, the result is a material with good wear strength properties, (Southern Methodist University USA).

2. SINTERING OF POWDER MIXTURES

The [empty set]10 mm samples, used for the characterization of powders mixtures pressability were sintered. The sintering process was performed into [10.sup.-1] torr vacuum precincts and introduced into electric oven with a maximum heating temperature of 1200[degrees]C. The samples were sintered at a temperature of 1150[degrees]C, according to the diagram in figure 2, with low-duration isotherm landings at every 200[degrees]C. The sintered samples were measured, the results being shown in figure 1 a, b, c.

[FIGURE 1 OMITTED]

3. MODELING WITH FINITE ELEMENTS

Assume a simple polynomial variation of temperature within each element. Write the polynomial in terms of the unknown values of the element nodal temperatures:

T = [{N}.sup.T] x {[T.sub.e]} (1)

Where [{N}.sup.T] = row vector elements of shape or interpolate ion functions, and {[T.sub.e]} is a vector of element nodal temperatures. The shape functions are functions of x, y, and z.

Calculate the thermal gradients and thermal flux in each element in terms of the element nodal temperatures.

{L}T = [B] x {[T.sub.e]} = {a} = thermal gradient vector (2)

where [{L}.sup.T] = [[partial derivative]/[partial derivative]x [partial derivative]/[partial derivative]y [partial derivative]/[partial derivative]z]

The [B] matrix is calculated by differentiating the shape functions: [B] = [{L}.sup.T] x [N]

The flux vector,{q}, is given by:

{q} = -[D] x {L} x T = -[D] x [B] x {[T.sub.e]} = -[D] x {a} (3)

Where [D] is the matrix of thermal conductivity properties.

Substituting the assumed temperature variation into the integral equation and noting that each term is multiplied by the virtual temperature and hence that term cancels on both sides, yields.

The equation can be written in simplified form as:

[C] x {[??]} + ([[K.sup.m]] + [[K.sup.d]] + [[K.sup.c]]){T} = {[Q.sup.f]} + {[Q.sup.c]} + {[Q.sup.g]} (4)

Where the subscript "e" has been dropped and it is understood that these matrices apply at the element level. [C]=specific heat matrix (energy storage) [[K.sup.m,d,c]] = contributions to thermal conductivity due to mass transport of heat, diffusion and convection, respectively. [[Q.sup.f,c,g]} = contributions to the nodal flows from flux, convection, and internal heat generation, respectively.

Where,

[C] = [[integral].sub.vol] [rho]c x [{N}.sup.T] x {N} x d x (vol) (5)

[[K.sup.m]] = [[integral].sub.vol] [rho]c(N} x [{v}.sup.T] x [B] x d x (vol) [[K.sup.d]] = [[integral].sub.vol][[B].sup.T] x [D] x [B] x d x (vol) (6)

[[K.sup.c]] = [integral] [h.sub.f] x [{N}.sup.T] x {N} x {[T.sub.e]} x d x ([S.sub.3]) (7)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

{[Q.sup.g]} = [[integral].sub.vol] [??]{N} x d x (vol) (10)

Note, [[K.sup.m]] is not symmetric. If mass transports of heat effects are included, a more computer-intensive, unsymmetrical equation solver must be employed. The system equations are formed by assembling the element contributions

where,

[C] x {[??]} + [K] x {T} = {Q} (11)

[C] = [[summation].sup.n.sub.i=1] [[C].sub.i][K] = [[summation].sup.n.sub.i=1][[K.sup.m,d,c]].sub.i] (12)

{Q} = [[summation].sup.n.sub.i=1]{[Q.sup.f,c,g]} + {Q} applied nodal flows (13)

n = number of elements.

4. MODELING USING FINIT ELEMENT OF THE HEAT TRANSFER FOR A SINTERED POWDERS PART

In order to simulate the behaviour of sintered parts during the sintering process were mainly covered the following steps.

The geometrical construction of the part model; identifying and defining the material properties; definition of finite elements; the definition of contour conditions and loadings for each heat transfer mode (convection, conduction or radiation) processing of nonlinear analysis and diagrams drawing of time variation.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

5. CONCLUSIONS

1. The density of the pressed and sintered samples decreases with the increase of cast iron content in the mixtures (high density at a 5% cast iron content);

2. The density of the sintering samples increases with the increase of the time of maintenance at sintering temperature (better density at t = 120 min.)

3. By mechanical experiments it was made a data base.

By processing this data base using mathematical models there were identified the necessary material properties used in finite elements analysis in dynamic condition of the piece.

We looked after modelling the thermal transfer in transitory condition for the sintering process.

This paper's purpose is to identify the dynamic answer using strains and deformations distribution analysis.

6. REFERENCES

Bodea, M., Bicsak, E. & Jumate, N. (2002). A software program for computer modeling of powder elaboration process, Acta Tech. Napocensis 45 (2002), pp 507-512

Ciupitu, I. (2000). Studies concerning the use of powder metallurgy in devices construction, Universitaria Printing House, Craiova, pp 58 - 99

John A. Schreifels. (2005). Thermodynamics of Surface, George Mason University, Science & Tech. Dept., www.gmu.edu

Mehrota, S.P. (1981). Mathematical modelling of gas atomization process for metal powder production, part 2, Powder Metall.Int., 13, pp 132-135

***Research Center for Advanced Manufacturing. (2003). Basic fluid mechanics behind the formation of high speed water jets, School of Engineering, Southern Methodist University USA, 2003