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A Method to Compare the Thermal Shock Resistances and the Severity of Quenching Conditions of Brittle
Solids
F. Osterstock, B. Legendre
To cite this version:
F. Osterstock, B. Legendre. A Method to Compare the Thermal Shock Resistances and the Severity of Quenching Conditions of Brittle Solids. Journal de Physique III, EDP Sciences, 1997, 7 (3), pp.561- 574. �10.1051/jp3:1997143�. �jpa-00249601�
A Method to Compare the Thermal Shock Resistances and the Severity of Quenching Conditions of Brittle Solids
F. Osterstock (*) and B. Legendre
ISMRA-LERMAT (*"), 6 boulevard du Mardchal Juin, 14050 Caen Cedex, France
(Received 6 Alarch 1996, revised i October 1996, accepted 16 December1996)
PACS 65.70.+y Thermal expansion and density charges; thermomechamcal effects PACS 62 20.Mk Fatigue, brittleness, fracture, and cracks
PACS.81 70 Fy Nondestructive testing: optical methods
Abstract. The thermal shock behavior and resistance of brittle materials are mostly in-
vestigated through the determination of a critical quenching temperature difference, ATC. This
technique, however, needs a large number of, almost, identical samples and is thus poorly adapted
to products being in the stage of research and development In order to overcome this difficulty, the indentation technique has been used m this work. The residual contact stresses, created during indentation, permit a stage of stable extension of the indentation cracks under the action of further stressing The relative increase of radial crack length as a function of Vickers inden-
tation load, c/co us P, is taken as a criterion, or indicator, of relative thermal shock resistance,
or of the severities of quenching conditions. This is validated, first in quenching materials whose
empirical ranking is well established, and second in varying parameters of the Biot number.
Finally, are two batches of a functional ceramic compared The proposed criterion reflects the
competition between the toughness of the quenched material, as an intrinsic property, and the thermal transient stresses, as a consequence of the physical properties of both the quenched sam- ple and the quenching medium Possibilities for extending the developed approach towards a
more accurate description of quenching phenomena and stress states such as to refine theoretical models are discussed.
R4sum4. La ddtermination d'une difldrence de tempdrature critique, ATC, est la technique
la plus souvent utilisde dans l'dtude de la rdsistance et du comportement au choc thermique
des matdnaux fragiles. Elle ndcessite cependant un grand nombre d'dchantillons, presque iden- tiques et est donc peu adaptde aux produits dans le stade de recherche et ddveloppement. Afin de lever cet obstacle, la mdthode de l'indentation de duretd est utilisde dans ce travail L'in- dentation crde des contraintes rdsiduelles de contact qui permettent une extension stable des fissures d'indentation pendant une sollicitation ultdrieure. L'accroissement relatif de la longueur des fissures radiales en fonction de la charge d'indentation Vickers, c/co us. P, est ainsi proposd
comme critAre, ou indicateur, de la rdsistance relative au choc thermique ou de la sdvdritd des
conditions de trempe Ce critAre est validA, premiArement en trempant des matAriaux dont la rd-
sistance relative est dtabhe et deuxiAmement, en faisant varier des paramAtres du nombre de Biot.
Finalement, nous comparons deux cdramiques fonctionnelles Le critAre proposd rend compte de la rdsistartce h la fissuration du matdriau, en tant que propridtd intrinsAque, et de la contrainte
thermique transitoire rdsultant des propridtds physiques h la fois de l'dchantillon et du milieu de trempe Nous dvoquons finalement les possibilitds d'utiliser cette ddmarche aux fins d'une
description prdcise du phdnomAne de trempe et des contraintes qui en rdsultent, pour afliner les modAles existants.
(* Author for correspondence ("*) UPRESA CNRS 6004
© Les #ditions de Physique 1997
Introduction
The thermal shock resistance of brittle materials is most usually investigated by the determi- nation of a critical temperature difference of quenching, ATC For this purpose, the stepwise
increase of the quenching temperature difference looks for the detection of a sudden drop of the retained strength being then used for defining it. Models describing this loss of strength
have been proposed by Kingery [Ii, Buessem [2) and Hasselman [3]. The two former propose the creation of surface flaws under the action of the thermal transient stress, whereas the latter
investigated the conditions for unstable and stable extension of pre-existing microcracks.
However, the size of the initial, or extended, flaws obeys a statistical distribution. This makes the accurate determination of ATC quite impossible. A transition range is rather ob-
served, in which the retained strength decreases smoothly with increasing AT [4, 5]. Statistical approaches may thus yield a qualitative description of thermal shock damage but remain un- able to accurately quantify the thermal stress responsible for it. The combination of acoustic emission with the observation by scanning electron microscope [6,ii shows that microcracks appear at values of AT less than ATC. The drop of the retained strength is explained by their
coalescence. Quantitative studies such as the velocity of ultrasonic waves detected the change
of the elastic characteristics as a result of microcracking at the surface of the sample [8] The
amount of the latter [as separately been measured by
a gas absorption technique [9].
These approaches involve a destructive method, needing a large number of samples with
homogeneous and reproducible microstructures. Also does a number of uncontrolled physical factors enter into the process of heat transfer. They are thus not really suited for investigating
structural or functional ceramics which are in the stage of research and development. The value of ATC varies with the size of the samples [10, Iii, the quenching medium [12], its temperature [13] or the height from which the samples are dropped into the bath [14]. The experimental
data should thus be worked out carefully, because poorly known experimental parameters may false the conclusions. As an example, the boiling of water or the formation of a vapor layer
varies strongly with the temperature at the interface and with the state of the sample surface
finishing [15]. In that respect, a bath of liquid metal, in which heat transfers by conduction,
was used such as to avoid the boiling phenomena [16). The contact between a metal rod and the hot sample was also used but the interface was not perfect and its thermal resistance was
modelized by convection [17].
Consequently, methods have been developed with the aim to define more accurately the maximum of the thermal transient stress. For this purpose, the controlled flaw technique has been put to work [18~19]. Within this method, a flaw, larger than the pre-existing microcracks and of defined size and geometry, is introduced by hardness indentation onto the surface of the
sample. Evans et al. [20] used additionally acoustic emission in order to detect fracture and the time taken by the thermal stress to reach its maximum value. Afterwards, Faber et al [21]
indented disks in their center but polished them such as to remove the indentation residual
stresses. More recently [22,23], the indentation technique was also used to ditect R-curve
effects within the frame of a model taking into account the time dependence of the thermal
stress during quenching [24, 25]. These approaches, however, aim all to describe the damage,
in considering unstable crack extension, possibly preceded, and followed, by stable stages at
temperature differences larger than ATC.
in the present work, use is made of the existence of the residual indentation stresses which
provoke the formation of radial cracks. Their occurrence has been analyzed by Lawn, Evans and Marshall [26], and the possibility to evaluate the toughness of the indented material from
the length of the induced crack described by Anstis, Chantikul et al. [27,28]. The residual indentation stresses allow, when a stress is furtheron applied, a stage of stable extension of the
indentation cracks before catastrophic extension occurs. Its analysis may yield a criterion for thermal shock damage and resistance [29] It will be derived and then checked, first in repro-
ducing empirically the ranking of well known thermal shock resistance of different materials,
and secondly that of the severity of quenching conditions. This occurs without the knowledge
of the heat transfer parameters. Finally, the proposed method will be applied to the thermal shock resistance of functional ceramic compounds in the R & D stage and be discussed in view of their microstructure.
Background and Analysis
The cracks induced by the contact of a Vickers indenter with the surface of a brittle material
are described by the median-radial system [26]. The radial cracks, visible on the surface of
a polished sample, are distinguished from the median cracks growing beneath the indenter tip. Typical examples are shown on the photographs of Figure I. The proposed sequence for
the formation of the median-radial crack system is depicted in Figure 2. During loading, the circular median crack forms beneath the indenter tip. During unloading, the residual contact
stresses become effective and permit the formation of the radial cracks. The well-developed
median-radial crack sfstem is than considered to be in equilibrium between the residual opening force and the toughness of the material.
This is written as:
Kr
= xrPcj~/~. II
The length co, of the radial cracks after indentation is defined for a given indenter-indented material couple and a given indentation load. xr is a constant, given by:
j~ 1/2
Xr " l~r (fi) 12)
~r depends on indenter geometry, whereas (E/H)~/~ makes evidence of the elasto-plastic char- acteristics of the indented material Because the radial cracks are the only ones visible on the surface of a polished sample, the following will concentrate on them. Finally is the median- radial crack system assumed to be in mechanical equilibrium after the removal of the indenta- tion load.
If now a thermal stress, ath is applied, the median-radial cracks will extend iii equilibrium
with the toughness, Kc, of the material. The principle of superimposition of the stress intensity
fields yields then:
Kc = xrPc~~/~ + ath(~Qc)~/~ (3)
Where c > co is no~N. the actual length of the propagatiiig crack. The term ath (~Qc)~/~ gives
the stress intensity factor induced by the stress applied, on a semi-elliptical surface crack. Q
is a constant depending on its geometry IQ = 4/~~ for a half penny crack). Figure 3 gives an
illustration of it. Rewriting equation (3) describes the applied stress as a function of indentation
load, actual crack length and toughness as:
~~h j~(1/2 ~
$)
l~~
The solution of ~~~~
= 0 defines the maximum of the applied stress, ath, and the actual crack
length, cm. dc
$$3 _,-,'~ fi~~
~fii~~,~ll"'( ~_
Fig 1. Typical examples of indentation crack systems in the glass-ceramic- a) Optical photograph
of the radial cracks (ST3; 98 N). b) SEM fractography (ST3, 30 N) where the median, radial and lateral cracks appear clearly
- j-
~~
~
~'
,
~fl
' ', ,'
',
loading unloading
Fig. 2. The two main steps of the formation of the semi-elliptical crack system (doted line) At
full load the contact (Boussinessq) tensile stresses have reached their maximum value and the median
crack is formed. At complete unloading the contact stress field has disappeared, whereas the residual central opening force extends the radial cracks
Between co and cm, i e. during the initial stage of loading, crack extension is stable. Beyond
cm, it becomes unstable. As a matter of illustration, ath us. c, curves are plotted in Figure 4.
They have been calculated using arbitrary values of xr (xr
= I) and KIC (KIC " 4 MPa@).
The increasing parts correspond to the stage of stable crack extension.
, c,crack
~~'~~~~~'~ 'l~~~~~"~9
uilibriumonditions
Kc
zfr, P,
fih ~~,/~
1
Fig. 3 Sketch of the radial cracks (see Fig. la) and definition of the parameters m view of equi- librium conditions for the as-indented state or under the action of an applied mechanical or thermal stress.
applied stress,MPa
5N
20N
K,~z~mPa~m
level of thermal stress c~
200N
radial crack
0 1000 2000 3000
Fig. 4 Stable (increasing) and unstable (decreasing) branches of the extension of Vickers indenta- tion radial cracks under the action of an applied stress The value of the indentation load is given on
the top of each curve The extension for a given level of applied stress is the thick part of each line
(Xr " 1).
The level of the thermal stress applied to the indentation flaw is also shown in Figure 4 by
the dotted horizontal line. A value of 58 MPa has been arbitrary chosen because it would correspond to that of am for
an indentation load of100 N. Within this scheme and for inden-
tation loads lower than 100 N, this line cuts the increasing branches corresponding to stable
crack extension at length c. For an indentation load higher than 100 N, crack extension be-
comes inevitably unstable if this stress would be reached. This can be deduced from the curve
corresponding to an indentation load of 200 N.
Thus for a given stress levelincreasing values ofthe ratio c/co as a function ofindention loads
P, appear. This is illustrated in Figure 5. Difserent values of thermal stress and toughness of
the material have been considered. The rate of increase of c/co with P depends strongly on
relative Increase in radial crack length,c/c~
imPa~m
~ffPa~m; 2k6 MPa
0 5 10 indentation load,P IN
Fig. 5. Comparative effects of toughness and given applied stress on the relative increase in length of the radial cracks from Vickers indentations, as a function of indentation load
the level of thermal stress for a given toughness, or on the toughness of the indented materials for a given applied stress The limiting value of cm/co
" 2.52 corresponds to the onset of
uncontrolled crack extension under inert environment. Beyond it, experimental data become unreliable [28] and below it the thermal stress have been frozen-in by stable crack extension.
The stage of stable extension of the radial cracks which is addressed here differs basically from that studied in recent developments [23-25,30]. The latter are principally concerned, first with the decrease of the thermal tensile stresses as one moves toward the core of the quenched sample, and secondly with the possible existence of an increasing crack resistance curve.
The possibility to freeze-in the maximum value of the thermal transient stress at tempera- ture differences less than zhTc is thus offered. The latter is due to both the thermomechanical
characteristics of the quenched sample and the coefficient of heat transfer of the quenching
medium. It is compared to the sample's toughness and results in the definition of the relative increase of radial crack length with indentation load as a indicator For a range of defined in- dentation loads, the rates of increase say how different materials resist against given quenching conditions, or inversely ho~N. far, in using a given material, the quenching conditions are more
or less severe. As a such, the rate of increase may be related indirectly to the fourth parameter
of thermal shock resistance [31]
The maximum value of the transient thermal stress, ath is given by:
where:
a, E and v are respectively the thermal expansion coefficient, the Young's modulus and the Poisson's ratio of the quenched material;
AT is the quenching temperature difference;
f(fl) is a damping function describing real quenching conditions with respect to ideal ones for which the Biot number would be infinite.
Table I. Main characteristics of the investigated samples.
Material Samples Porosity Toughness Young
MPa GPa
VM-ST3 Rectangular bar amorphous 0
4 x 8 x 16 mm3 SENB
4 x10 x 60 mm3
Rectangular bar 0 1.3 83
4 x 8 x 16 mm~ multiphased SENB
4 x10 x 60 mm~
r~ 5 > 0.5
r~ 3.00 405
4 x 8 x 16 mm3 SENB
Disk A-10 16 0.24
25 mm x5 B-1.5 19 0.70
Indentation
The Biot number measures the importance of the surface heat transfer as compared to
internal conduction heat transfer [32]. It, thus, reflects the severity of the thermal shock and helps to describe the temperature gradient, which builds up. It is given as:
fl =
~ (6)
with:
r characteristic dimension of the sample. It represents a mean free path for heat flow and is often taken as the ratio of volume over external surface [10,15];
h coefficient of heat transfer at the sample-quenching medium interface;
k thermal conductivity of the quenched sample
Several empirical expressions for f(fl) are proposed in the literature [1,10, iii. They are dependent on the geometry of the sample. They may be considered as normalized values of the quenching stress with respect of the ideal stress, as it would of arise from an infinite value of fl.
Now, if one of these parameters is changed, difserent maxima of the thermal stresses arise.
They are frozen-in by ratio c/co as a function of the indentation load P. In the following, this analysis will be verified first in submitting materials ha~-ing a well established ranking of thermal shock resistance to a given thermal shock. In a second step, will, for a given material, the temperature difserence, quenching medium or the size and shape of the sample, be changed.
Finally will samples of a functional ceramic in the R & D stage be compared and the results be discussed in view of the microstructures.
Materials and Experimental Procedures
Four difserent materials have been used: a glass-ceramic (ST3) and its precursor (VM-ST3),
two sintered polycrystalline ceramics: a sintered dense a-silicon carbide (SN-SiC) and porous
high-Tc superconductors, "YBaCUO"'. Their available physical characteristics are listed in Table I
The V~f-ST3 is a very brittle fluorydric glassy compound. It is used as a precursor for the ST3 material. The latter is obtained after a dedicated heat-treatment [33j, such as to
Provoke crystallization and improve markedly the thermal shock resistance, principally through
