Temperature field in EDM of ceramics composites.

Opran, Constantin ; Blajina, Olvidiu

1. INTRODUCTION

Technical ceramics is characterized (Dumitras, & Opran, 1994) as a composite type engineering material, with more than one fragile phase, discretely crystalline, or amorphous. It is obtained in a solidification and forming technological process, at high temperatures and pressures where the resulting material should be, at least, 30% of crystalline structure (Spur, 1889).

Ceramic composite represents a hole material system, anisotropic and non-homogenous, made of two or more various materials, with on purpose made interfaces (Schneider, 1991). There are two main phases of the material: the matrix and the reinforcing element (Vaia & Wagner, 2004).

In this paper an electro-conductive composite ceramic is studied. It is made of two refractory materials: one electrical non-conductive ([Al.sub.2][O.sub.3]) and one electrical conductive (TiC). They are made of the ceramic phase--[Al.sub.2][O.sub.3], whose size is 3 urn, the metal phase--TiC, whose size is 5 urn and the binder--Zr[O.sub.2]. As the percent of TiC is from 30% up to 45% and the maximum binder percent is 1% it results that the [Al.sub.2][O.sub.3] percent is the biggest (all results in 100%). The studies were carried out on [Al.sub.2][O.sub.3] + 30%TiC, conventionally named [E.sub.c]C[C.sub.s]-[Al.sub.2][O.sub.3]/TiC.

2. METHODOLOGY

The fundamental principle of the massive electrode electrical discharge machining by shape copying (EDM-[S.sub.m][C.sub.o]) is that of the controlled erosion of the material, as result of the controlled electrical discharges between the part and the electrode, within a dielectric fluid environment (Opran, 1997).

A schematic model of EDM-[S.sub.m][C.sub.o] for [E.sub.c]C[C.sub.s]-[Al.sub.2][O.sub.3]/TiC is made in Figure 1. The microscope images of the sample part, are shown in Figure 2, before (2.a) and after (2.b) EDM, using: [i.sub.e] is the electric current intensity ([i.sub.e] = 3.13 A); [t.sub.i] is the impulse time ([t.sub.i] = 6 [micro]s); [t.sub.0] is the pause time ([t.sub.0] = 190 [micro]s).

Obtaining a mathematical model of the temperature distribution field, by considering the inter-dependences of the electrical discharge process factors (energy distribution within part, electrode, dielectric, plasma channel and pressure ball limits) is possible only if some specific assumptions are made:

* the part is considered to be continuous, heterogeneous and isotropic, as an elastic environment under thermal shock;

* the interactions of the material, dielectric and their constituents are ignored;

* the resultant thermal flux toward the ceramic material is considered to be a semi-infinity solid;

* the intensity of thermal flux Q(x, t) acts as a non-linear filed, depending on time t and point's position x;

* the thermal flux radius [r.sub.t], acts like a non-linear field;

* there is a thermal influenced semi-spherical zone, within the material, whose radius is [r.sub.t];

* the detached zone, resulting from EDM thermal shock is determined by the position of the isotherms of temperature;

* the reference surface is always situated between two subsequent electrical discharges, so as the isotherms for detaching of material refers to the new resulting surface of the previously discharge;

* because of the fact that the thermal extension coefficient a differs for the considered components, [Al.sub.2][O.sub.3] and TiC, while electrical discharging, there do appear an oscillatory spatial residual contractions and stress field;

* the oscillatory spatial residual contractions field determines the micro-fractures, micro-cracking and has a role in their propagation and in detaching of material, by fragmentation, on EDM thermal shock.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

The heat distribution, within the considered granular [Al.sub.2][O.sub.3]/TiC material, is according to Cattaneo law (Schneider & Petzov, 1996):

[tau]dQ(x,t)/dt + Q(x,t) = -k grad([theta]-[[theta].sub.0])(x,t) (1)

where: t is the time of a singular electrical discharge process [[micro]s]; Q(x, t)--the thermal flux intensity variation, as function of time and of three-dimensional vector x; k--the thermal conductivity of material [W/mm[degrees]K]; 90[[theta].sub.0]--the initial temperature of material, [[theta].sub.0] = 293[degrees]K; [theta]--the temperature of material at time t [[degrees]K]; [tau]--the relaxing time, when a stationary thermal flux is set into the material [[micro]s].

3. MATHEMATICAL MODEL OF THE TEMPERATURE DISTRIBUTION FIELD

The constitutive equations for ceramic composite ([E.sub.c]C[C.sub.s]) are the equations of a material with the properties: granular, thermo-viscous-elastic, linear integral type, symmetrical axial, isotropic, submitted to a thermal high tide and having finite speeds of the heat propagate like wave inside the material.

The simplified constitutive equations, that determine the thermal field intensity, are the following (Opran et al., 2007):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

where: s is the time variable; 0 index is the initial state at time [t.sub.0] (the beginning of a singular electro-erosion discharge).

According to the balance equation of the energy, resulted through the application of the classic equation of the energy law, we obtain the equation writed in cylindrical coordinates:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

It verifies the following:

* the initial condition:

([theta] - [[theta].sub.0]) (r, z, 0) = 0 (4)

* the boundary conditions:

([theta] - [[theta].sub.0]) ([r.sub.t], 0, t) = 0 (5)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

where: [v.sub.[theta]] is the thermal wave speed; Q(t)-the thermal field in time interval [0, [t.sub.c]].

Finally, we find the following solution of the equation (3):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (8)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (9)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)

If checking the above obtained model, for real experimental conditions [k.sub.0] = 20 W/mm[degrees]K; [v.sub.[theta]] = 0.22; [r.sub.t] = [10.sup.-5] m; [tau] = [10.sup.-14] s; [[alpha].sub.0] = 8 x [10.sup.-6]/[degrees]K), the result is ([theta]-[[theta].sub.0])(0, 0, [10.sup.-6]) < 3 x [10.sup.-5][[degrees]K], meaning different from zero.

4. CONCLUSION

In practice, the electrical discharge machining represents an efficiently procedure for the getting ceramics composites ([E.sub.c]C[C.sub.s]) parts, according to the prescribed technical conditions.

The technical ceramics composite [Al.sub.2][O.sub.3]/TiC were studied and the machining procedure considered was massive electrode electrical discharge, by shape copying EDM-[S.sub.m][C.sub.o]. The displacement of thermal field in EDM-[S.sub.m][C.sub.o] determines the terms machining and the machining results.

The constitutive equation is specific for the answer of the material to EDM. There was determined a mathematical model of the temperature distribution field in EDM-[S.sub.m][C.sub.o], as function of thermal flux radius, thermal influenced zone radius, radial direction of machined part and time. The model has been check by using values suitable for real conditions.

The results of the researches presented in this paper allows the determination of the optimal machining parameters and obtaining processed surfaces with superior quality and precision, in according of the market requirements.

5. REFERENCES

Dumitras, C. & Opran, C. (1994). Prelucrarea materialelor compozite, ceramice si minerale, Ed. Tehnica, Bucharest, Romania

Opran, C. (1997). Cercetari privind prelucrarea prin electroeroziune a unor materiale ceramice, Doctoral Thesis, University Politehnica of Bucharest, Romania

Opran, C.; Blajina, O. & Iliescu, M. (2007). Researches on mathematical modelling of process functions regarding thermal spray technology of the polymer nanocomposites products, Annual Scientific Journal of Ovidius University, Mechanical Engineering Series, Vol IX, Tom I, pg. 13-22, Ovidius University Press, ISSN 1224-1776, Constanta, Romania

Schneider, A & Petzov, G. (1996). Thermal shock and thermal fatigue behaviour of advanced ceramics, Kluwer Academic Publishers Group, Netherlands

Schneider, S. (1991). Ceramics and glasses, Engineered Materials Handbook, Vol. 4, ASM International, ISBN 087170-282-7, USA

Spur, G. (1989). Keramikbearbeitung, Carl Hanser Verlag Munchen Wien, ISBN 3-446-15620-8

Vaia, R. & Wagner, D. (2004). Framework for nanocomposites, Materialstoday, November 2004