Quantification of quenching stresses and heat transfer

Quenching

stresses

and heat transfer

QUANTIFICATION

OF QUENCHING

Ann. Chim. Sci. Mat, 1998, .23, pp. 143-146

STRESSES AND HEAT TRANSFER

F. OSTERSTOCK, F. TANCRET, 0. VANSSE, U. KUTSCHERA* ISMRA, Laboratoire d’Etudes et & Recherches sur les Materiaux (LERMAT), Cedex, France * IWW-TU CLAUSTHAL, D. 38678 Clausthal-Zellerfeld, Allemagne

URA 1317 CNRS. 14050 Caen

Summarv: The Vickers indentation technique has been used to freeze-in the amplitude of the thermal stressesappearing during quenching and to evaluate the effective coefficient of heat transfer. The later varies from 4000 W/m’K to 16000 W/m2K in the case of water at RT (lOO°C < AT < 2lO”C), and from 400 W/m*K to 800 W/m*K in.tbe case of a low viscosity silicon oil (200’C < AT < 550°C). Resume: Evaluation auantitative des contraintes et transfer& themiaues oendant la tremDe. La technique de l’indentation Vicken a ete utilisee pour geler Petat des contraintes thermiques et Cvaluer le coefficient de transfert thermique pendant la trempe. Ce demier varie de 4000 W/m2K a 16000 W/m2K darts le cas de l’eau a temperature ambiante (lOO°C
I. INTRODUCTION The quenching of ceramics gives rise to transient thermal stresses,whose maximum damages the sample if the temperature difference is higher than the critical value, AT,. The thermal stress is then put equal - to the rupture stress for calculating, more or less accurately, the effective value of the coefftcient of heat transfer, h. In order to improve this accuracy the controlled flaw technique, as resulting from hardness indentations, has been used. (1) (2) (3). For this, the residual contact stresses are removed, so that only catastrophic failure, at temperature differences depending on flaw size, could be observed. However it has been shown that if these residual stresses are not relieved a preliminary stage of stable extension of the indentation radial cracks takes place during post-indentation mechanical or thermal loading (4) (5). This property has also been used for defining the relative increase of radial crack length during quenching as an indicator for ranking thermal shock severities (6), or to investigate the relative thermal shock resistances of different batches of a given material in the stage of research and development (7). In the present work the stable extension of the radial is analysed quantitatively. The absolute value of their length, or their relative increase, during quenching is then enabled to quantify the maximum value of the thermal transient stress during quenching at temperature differences less than the critical one, ATc. A continuous description of the coefficient of heat transfer as a function of the initial temperature of the quenching sample is then opened. This starts with the definition of the Biot number in comparing the maximum of the transient stress, occurring in real conditions, with that which would occurs if the coefficient of heat transfert would be infinite. Renrints : F. OSTERSTOCK, Laboratoire d’Etudes et de Recherches sur les Materiaux (LERMAT) CNRS, URA 13 17, 6 boulevard du Mar&ha1 Juin, 14050, Caen Cedex, France.

144

F. Osterstock

2. PRINCIPLE.

EXPERIMENTALS

AND

et al.

RESULTS

The state and behaviour of as-indented or post-loaded median-radial cracks are described by (4) (5): K, = ~r.P.c;“”

I11

Or

K, = xr.P.f3’2

+ U,h (my’2

PI

respectively. The radial crack length, c, and c, are the initial and actual values, whereas P is the indentation load and oti the post-indentation applied thermal stress. The constants, x and (nn)‘” are related to the amplitude of the residual contact stressesand to the shape of the indentation flaw (I), and are .assumed as independent of the indentation load. It is assumed that during the quenching process, the increase of the actual radial crack length, c, accompanies that of the thermal transient stress, o,,,, and ceases to extend as soon as its maximum has been exceeded. The length of the radial cracks after quenching has thus frozen-in the value of the maximum of the thermal transient stress, The later can be quantified in replacing Kc in [eq. 21 by the expression written in [eq. I]. In previous works (6) (7) the relative increase in radial crack length, c/c,, as a function of indentation load, and for given quenching conditions has been proposed. In writing: + crfi (XC2C)"2 [3] or xVP.(c,3’2 - c-3’2) x,.p.c0-3’2 = x~.P.cY~~” yields if only one indentation load is considered:

=oe (7tRc)“2

u* = x,P.(c,3’2 - c-3’2)/(71Qc)“2 or after having made the ratio c/c, to appear, following expression for the thermal stress:

[41

El

WI

Figure 1: The convection phenomenon as it takes place during quenching an alumina sample, heated to 550°C, into a low viscosity silicon oil (20 mm% at 25°C). The photographs are separated by time steps of 0.5 sec. It may thus be remarked that an almost steady state of convective heat transfer arises only after 1.5 seconds.

Quenching

stresses

and heat transfer

145

Quenching a given material, or submitting a ceramic to a thermal shock results in actual cases in a convective heat transfer by the quenching medium. This is illustrated in the four photographs off&. It is difficult to decide whether natural on forced convection takes places. However the approach proposed above allows an experimental deduction of the maximum of the thermal transient stress. The experimental values of oh are then compared to those which would arise in the case of an ideal (infinite value of the coefficient of heat transfer) thermal shock i.e. o = cc.E.AT. The ratio oJa.E.AT quantifies then the thermal shock damping function f(p). Analytical expressions can be found in the literature (8) (9). It depends on the Biot number, p = rh/h, where a, E, k and r, are respectively the thermal expansion coefficient, the Young’s modulus, the thermal conductivity and the characteristic dimension of the sample. Atier having deduced the Biot number, p. the effective coefficient of heat transfer, h, was calculated in using the values of r and k, the later being that the temperature of the sample before quenching.

2 1.6 1.2 0.8 0.4 0

Figure 2: Increase in length of the Vickers indentation crack during successive quenches with stepped temperature differences. In the case of water quenching the size of the alumina sample was (4 x 8 x 60 mm3). For that of silicon oil quenching samples of dimensions (6 x 12 x 60 mm’) were also used. Their thickness, in mm, is indicated in the circles. The indentation loads are indicated iq Newton.

II 15 ‘-. _5E -3 -3

WATERlRmm

Al203 (AF995) Silicon oil at RT

r--0

0

‘0

.--J+

0 8d*

ae-

*H

,,‘gt

-I-=

.// T&.&/-“ 0 + ' 50 0

ATc ;3;

Temp 1

l

.+’

.-1

100

.A c /

200"250

Furnace

l

350

Temprature

tot

1

)

4

550

Figure 3: Variation of the effective coefficient of heat transfer during quenching into water or low viscosity silicon oil, both at room temperature. As the quenching temperature increases, it tends rapidly towards those already deduced in the case of water from the classical approach. The increase observed in the case of silicon oil is to be explained by the decreasing viscosity as the interface temperature increases.

146

F. Osterstock

et al,

The mirror polished alumina samples (AF 995) with sizes of 4 x 8 x 60 or 6 x 12 x 60 mm3 were fitted with three indentations on each large side, and the initial length, c,, was measured. After heatin& they were horizontally dropped into the quenching bath with the indented surfaces perpendicular to the surface of the bath. Afterwards it was reheated to a stepped higher temperature up to the difference in quenching temperature inducing the stage of instable crack extension (10) (11). This occurs for c > 2.52 c,. The increase in length of the radial cracks as a function of the successive and increasing thermal shocks is as expected (figure 2). Each point represents the mean of the three indentations. For the case of oil the effective coefficient of heat transfer, E, increases smoothly with quenching temperature (figure 3) and from 400 W/m*K to 800 W/m’K. These values are varies are in the range of those observed for equivalent oils in the same temperature range. Data for water quenching obtained by the same method are also plotted and tend towards those deduced from classical thermal shock resistance measurements. 3. CONCLUSION The indentation techniques applied to thermal shock investigations allows to determine the effective coefficient of heat transfer as a function of temperature. However for investigating a large domain of temperature a proper choice of polycrystalline ceramics and indentation loads must be made. this is due to the fact that the accuracy of the thermal stressmeasurement increase with the ratio c/c, - 2.5. 4. REFERENCES (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

PETROVIC J.J., I. Am. Ceram. Sot., 1983,s (4), 277-283. FABER K.T., HUANG D.D. and EVANS A.G., J. Am. Ceram. Sot., 1981,fi (5), 296-301. SAADAOUI M., OLAGNON C. and FANTOZZI G., J. Mat. Science Letters, 1996,5,64-66. LAWN B.R., EVANS A.G. and. MARSHALL D.B, J. Am. Ceram. Sot., 1980,@ (9), 574-581. ANSTIS G.R., CHANTIKUL P., LAWN BR. and MARSHALL D.B., J. Am. Ceram. Sot., 1981,a (9), 533-538. OSTERSTOCK F., Mat. Science Eneing, 1993 I-7A168 4 l-44. OSTERSTOCK F., MONOT J., DESGARDIN G. and MORDIKE B.L., J. Eur. Ceram. Sot., 1996,l&, 687-694. KINGERY W.D., J. Am. Ceram. Sot., 1955,% (I), 3-15. BECHER P.F., LEWIS III D., GARMAN K.R. and GONZALES AC., Ceram. Bull., 1980, s (5), 542-48. KUTSCHERA U., “Untersuchung des Thermoschockverhaltens einer A1203 - Keramik Anhand des Vickerseindruckverfahrens”, Studienarbeit, May 1996, TU Clausthal. (11) VANSSE O., “Etude du choc thermique sur une ahunine en vue de la ditermination du coefficient de hansfert thermique pendant la trempe”, DEA, Universitb de Caen, 1996.