Fracture toughness of pressureless sintered silicon carbide: A comparison of Klc measurement methods

Ceramics International 13 11987) 159-165

Fracture Toughness of Pressureless Sintered Silicon Carbide: A Comparison of KIL M e a s u r e m e n t Methods Gilles O r a n g e , * Hidehiko Tanaka~ and G i l b e r t Fantozzi* * Groupes d'Etudes de M~tallurgie Physique et de Physique des Mat~,riaux (UA CNRS 34l) INSA de Lyon--Brit. 502, 69621 Villeurbanne Cedex, France. l National Institute of Research in Inorganic Materials I-1 Namiki, Sakura-Mura, Niihari-gun, Ibaraki-ken, T 305 Japan. (Received 23 March 1987; accepted 5 May 1987)

Abstract: Four different Kt¢ measurement methods, all of them using small bars, were compared, The materials studied in this paper were pressureless sintered :~- and fl-SiC. K~¢ values obtained by the direct crack measurement method depended on the indentation load. The single edge notched beam method yielded a higher value than others. Indentation strength bending and chevron notched beam methods showed almost the same K~¢ values: both methods measured K~c with a sharp crack as controlled defect. Effect of notch width was observed on single edge notched beam specimens as the strain rate and span length dependence on chevron notched beam specimens; chevron notched beam K~¢ values were also strain rates and span length dependent. Influence of the temperature was also studied. The fracture toughness of sintered SiC increases at high temperature (1350~C, in air).

1 INTRODUCTION

Mechanics, in mode I loading, at the critical point of crack propagation. Many methods are proposed for the K~c measurement and it cannot be said that the different resulting values are in perfect agreement. In fact, since KIt is only controlled by the material characteristics it must be independent of experimental methods. Another problem is the use of test methods that employ samples of simple geometry on the usual testing machines and which can be used at high temperature: this point is quite important in the case of ceramic materials. In this investigation, four different methods for measurement of KIt are compared, namely direct crack measurement (DCM), indentation strength by bending (ISB), single edge notched beam (SENB) and chevron notched beam (CVNB) methods. These methods require only small bar samples and need a usual bending machine (other methods such as

Recent intensive investigations have greatly improved the properties of ceramic materials and new families of ceramics have been developed for engineering applications. The brittleness of the ceramics, however, is still recognized as one of the problems which will limit structural applications of these materials. Fracture toughness is an important parameter to determine quantitatively the material's fracture resistance to crack initiation and/or propagation. So, the exact evaluation of this parameter is an important step in the fields of Research and Development. In K~c experiments, we have to measure the stress corresponding to the propagation of a macroscopic sharp crack of well controlled dimensions; K~¢ values are calculated in the case of Linear Elastic Fracture 159

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160

Gilles Orange, Hidehiko Tanaka, Gilbert Fantozzi

compact tension (CT), double cantilever beam (DCB) etc .... are not very suitable for ceramic materials). The materials studied here are pressureless sintered :~- and/?-silicon carbides (SIC). In the DCM and ISB methods, the indentation loads varied; notch depth and size (tip-radius) were varied in the SENB method; different strain rates (i.e. cross-head speed) and span dimensions (inner and outer loading points distance) were used in the CVNB method. The high temperature K~¢ values were also measured and compared with the room temperature fracture toughness. The results are discussed on the basis of Linear Elastic Fracture Mechanics: sintered SiC is a typical brittle material with very pure grain boundaries. No soft secondary phases have to be considered along the grain boundary, even at high temperature. The process zone around the crack tip, where different dissipative energy mechanisms can operate (plasticity, microcracking, etc.), is very small and is therefore neglected in the discussion.

~- b--- c

--Pa ~--

Fig. i. Vickers indentation fracture system.3 a: half diagonal of indent,b: deformation zone, c: radius ofcrack, P: indentation load, Pr: force which opens the crack, a,: rcsidual compressive stress by deformation, H: hardness and E: Young's modulus. Kt¢ by DCM was calculated according to the equation of Anstis et al. 1 or Lawn et al.: 2 K1¢ = O'O16( E / H ) t /2 . ( P / c 3/2) (1) and Ku¢ by ISB with the equation of Chantikul et a[.: 3 Kj~ = 0 . 5 9 ( E / H ) l/s . (a.

2 EXPERIMENTAL

PROCEDURE

Two kinds of pressureless sintered SiC samples were prepared. One was 7-SIC, with 6 H as the main polytype. Another was /?-SIC, of 3C type. Both were sintered by the additions of boron and carbon. The basic properties are listed in Table 1. The samples used here were rectangular bars (3 ~ 4 x 4 x 40mm3). The tension surface of the sample bars was carefully polished with 1 #m diamond paste and nylon cloth. Vickers indentations were carried out by V-tester (Wolpert Testwell). The indentation loads were selected from 0-5 to 30 kg (DCM and ISB methods). After indentation, samples (ISB method) were tested by a 4-point bending test with 7 (inner)-24 (outer) span (mm) and 0 . 1 m m m i n -1 cross-head speed (Schenck-Trebel). Table 1.

Sample

=-SIC /Y-SiC

Polytype

6H 3C

Pr

p1/3)3/,l.

(2)

where: E = e l a s t i c modulus, H = hardness, P = applied indentation load and a = fracture strength after indentation, c = c r a c k length, around the indenter. The scheme of the Vickers indentation crack system 3 is shown in Fig. 1. The straight-through (SENB) and chevron (CVNB) notches were machined with a diamond saw of small thickness. Notched samples were tested by a four-point bending test (7 x 2 4 m m span), with a cross-head speed of 0 - 1 m m m i n -1. For SENB, different diamond saws were used with 0"35 mm, 0-15 mm and 0-075 mm thickness; the ratio of notch depth to sample height varied from 0-1 to 0"6. For CVNB, one notch geometry was adopted: the angle of the chevron was 52 °, and geometrical parameters were ~o =0-1 and ~1 =0"9; two diamond saws were used: 0.35mm and 0-15mm thickness. CVNB specimens were tested with different span

Properties of = and /Y-SiC

p (g per cm 3)

E (GPa)

H (GPa)

G* (MPa)

v*

3-07 3.07

381 368

20 23

500 697

0.16 0.13

p--Density. E= Young's modulus by grind sonic method. H = Hardness by Vickers indentation. = Strength. v = Poisson's ratio. * The data were obtained from the manufacturers.

161

Fracture toughness of pressureless sintered silicon carbide Table 2.

K,¢ measured by SENB and CVNB methods at room temperature (0-1 mmmin-~; 0.35mm notch width)

Sam,pie

SENB

a/W

=-SIC

,6-SIC

CVN8"

Kic

~o

~1

Kc

( M N/m 3/2)

(ao/W)

(a,/W)

( M N/m 3/2)

0"22 0-44 061

406 4'53 4.03

0.1 5

0.92

3"09

0'12 022 0-40 0-60

3.51 3"98 4.1 7 4.28

0.11

0.96

3"44

a The angle of the chevron notch is 52L

,1

L.

0

I Ld L _.I.I CVNB

SENB

dimensions (7 x 2 4 m m and 10 x 35 mm), and with different cross-head speed ( 0 . 1 m m m i n -~ and 0 - 0 0 1 m m m i n - t ) . K,c was calculated from the following equations. Notation in the equations can be referred to in Table 2. Ktc by SENB: 4 Kl¢ = a. Y. a u2

(3)

where a = notch depth; a = fracture stress; Y = geometrical parameter; and Y = 1-99 - 2.47(a/W) + 12.97(a/W) 2 - 23.17(a/W) 3 + 24"80(a/W) 4 O=

that at room temperature (7 x 2 4 m m span; 0-1 mm min-~ cross-head speed). Temperature was maintained for 25 min at 1350°C before testing; all tests were performed in air. Indentation methods were not applied at high temperature; they are not suitable because the crack configuration can be modified (crack healing). The residual stress induced by indentation would relax at high temperature, and the calculation would become ambiguous. 3 RESULTS

AND

DISCUSSION

3. 1 K~c by D C M and ISB methods K,¢ values obtained by D C M and ISB methods at room temperature are shown in Fig. 2 and Fig. 3, respectively. The indentation loads less than 0-5 kg do not make macroscopic cracks around the indent. In the bending test, these samples were not always broken at the indented flaws. The indentation loads

3P(Lo -- L i) 2Bw2

L o = 2 4 m m ; L~ = 7 m m where L o, L~ is outer and inner span; B is specimen width; and W is specimen height (Figure in Table 2). Kz~ by C V N B was calculated according to Munz's slice model: s

DIRECT CRACKMEASUREMENT

,-,

3 -/k--~

K,¢ = (Pmax/BWU2). (3"08 + 5"00c~o + 8"33~) x ((L o - L~)/W)(1 + O'O07(LoLJ W2) u2)

x ((~l - %)/(1 - %))

0w

__

2

(4)

where eo = ao/W, cq = a l / W . F o r K,¢ determination at high temperature two methods, S E N B and C V N B , were used. The experimental procedures were just the same as

0

a-SIC

•

p-SIC

5 INDENTATION

Fig. 2.

I i0

H

t 30

LOAD (KG)

K~c by the DCM method versus indentation load.

162

Gilles Orange, Hidehiko Tanaka, Gilbert Fantozzi

assumptions/approximations of (i)-(v). a, b, c, P and Pr parameters are defined in Fig. 1. For the ISB method, 3 a component induced by the applied stress should be added into eqn (3):

INDENTATION STRENGTHBY BENDING

•

v

O

,~

-8

""'~

K = X r P / ¢ 3/2 + (/~¢)1,'2

8

2

0 I

I

5

(6)

where fl = geometric constant. Equation (6) has a m a x i m u m value of C m corresponding to the Kc valuel At the critical condition:

a-SiC

~-SIC

I

I0

II

I

ff m =-- 3 K¢14(lZ~Cm) ll2

30

INDENTAHON LOAD (KG)

Fig. 3. K~: by the ]SB method versus indentation load.

higher than 30 kg were not suitable for making a controlled flaw: the sintered SiC materials were too brittle to bear such indentation loads. Apparent K~¢ values were measured as 2-63"5 M P a x / ~ . There is seemingly little difference in Kt¢ between zt and/3-SIC. The DCM method did not show a constant value at low indentation loads, but measured Kt¢ tends to quite constant values as the indentation load increases (~z-SiC: K,¢ --- 2'8 MPa x / ~ ; /3-SIC: K,~ = 2-6 MPa x//-m). In the ISB method, K~c increased slightly with the indentation load, but the fact that a constant K~¢ value can be obtained by this method should be considered (K,~ = 2"8 MPa x / ~ for both s-SiC and

&SIC). For ceramics, Evans et al. 6 proposed the basic relation of the D C M method; Anstis et al., 1 Chantikul et al., 3 Lawn et al. 2 and Niihara et al. 7 considered the DCM method more precisely. According to Lawn et al., radial cracks open during unloading, after indentation, due to the residual stress around the plastic zone. K~ is given for DCM as: K,¢ = X ' r P / C 3/2

(5)

where X r is a constant. The equation is deduced by using the following assumptions: (i) K¢ ~" Pr/c 3/2, K¢ and crack opening load. (ii) Pr-=-b2%, crack opening load and residual stress. (iii) ab -- E(a/b) 3, residual stress and deformation zone. (iv) a/b ~ (H/E) t/2, deformation zone and material constant. (v) H-,- P/a 2, Vickers relation. Equation (5) then becomes eqn (1) by using the

with Cm =

(4Xr P I K e ) z/3

(7)

It can be seen that eqn (7) can be reduced to eqn (2). The assumption is made that each indentation test induced the same stress field which is shown by eqns (5), (6) and (7). The relations (i)-(iii) may be applied strictly to the Vickers indentation crack system, because the different equations assume linear elastic relations. The relation (iv) is an analogy of a spherical cavity under an internal stress. Considering that the ISB method gave a constant value which is independent of P, the relation (iv) about the plastic zone can be applied safely. Then, the dependence of the Kt¢ value measured by DCM is attributed to the over--or under--estimation of radical crack length. There is a tendency in DCM to measure the smaller cracks at lower indentation loads. But the results show that with 5-10 kg indentation loads, K,¢ values measured by DCM and ISB agree very well in both SiC materials.

3.2 K~c by SENB and CVNB methods The values of K~¢ obtained at room temperature by SENB and CVNB methods in standard conditions (notch width of 0.35 mm; 4 point bending test with a 7 x 2 4 m m span; 0-1 mm/min) are listed in Table 2. KIc was measured as 4 " l - 4 . 5 M P a x / m for e-SiC, 3.5-4-3MPax/-m for fl-SiC by SENB; and 2-8-3-6 MPa ~ for s-SiC, 3"1-3"9 M P a x / ~ for flSiC by CVNB. There seems to be no significant difference between e and/3-SIC. KI¢ by SENB seemed to depend on the notch depth and showed a large value when a/w is around 0-4. In the CVNB method, materials have to present a controlled crack propagation before reaching the maximum load. a With standard conditions, it was not possible to detect macroscopic stable crack

Fracture toughness ~/-pressuretess sintered silicon carbide Table 3.

Sample

~-SiC

//-SIC

163

Effect of span dimensions and cross-head speed on K,,; measured by t h e CVNB m e t h o d (angle = 52-; 0"15 mm n o t c h w i d t h )

K,: (CVNB) MN./m 32)

Cross-head speed (mm rain-')

Span=7 ×24

0.1 0-001

3.02 3-10

2.85 2.70

0.1 0-001

3.50 3-20

3.20 2.72

propagation on the stress-strain curves during tests: a lower strain rate has to be used to induce a controlled fracture mode. Different conditions of span (4 point bending) and cross-head speed were studied: results are reported in Table 3. At constant span dimension, the K~ values decreased for fl-SiC whereas they remained quite constant for ~-SiC as the cross-head speed was reduced. F o r both strain rate conditions (0-1 mm rain - i and 0.001 mm rain - 1),/<~ values decreased as the span length increased. Deviation to linearity at the fracture point was observed on load-displacement curves only in large span condition ( 1 0 x 35ram). In fi-SiC, a small deviation was detected only at very low cross-head speed (0001 m m m i n - 1 ) . For a-SiC, deviation was observed even at 0'1 m m m i n - t ; at low cross-head speed (0-001 m m m i n - ~ ) ; the specimen's fracture mode is controlled by a stable crack propagation. According to the chevron method theory, 8 these measured values in controlled fracture mode conditions can be considered as close estimations of the material fracture toughness (Kj¢ = 2.7 M P a x/m, for both =t and fl-SiC). The S E N B method yielded higher values than CVNB. This is due to the difference of the crack tip geometry: the fracture starts from the machined notch in SENB whereas the crack tip is naturally sharp in C V N B when the fracture occurs. As we can observe from Table 2 and Table 3, the C V N B method is not dependent on the notch width, and the same Kl¢ values are obtained for both 0-15 mm and 0-35 turn notch width. In SENB, fracture stress depends on both crack nucleation or initiation and propagation. Machining of the notch can also induce residual stresses and/or crack blunting effect. These two effects lead to an apparent increase of KK¢ in S E N B (Table 2). If we consider the effect of the notch width, i.e. the crack tip geometry, A.'~ values seem to be quite constant as the tip radius is lowered from 0.2 mm to

Span=10x35

0-1 mm (except for very small radii). In Table 4, K~ doesn't decrease as the notch width is redticed and on the contrary seems to increase at smallest notch width (0"08 ram). This effect is not well nnderstood and can be explained by the strong dependence on microstructure. In the case of large notch width, blunting stresses have to be released, in the case of too small notch width, a crack has to be initiated, and in both cases apparently the K~ values are overestimated. The C V N B method seems to be more adequate: a natural sharp crack initiates and propagates to some extent prior to fracture (with large span conditions, and quite low strain rate). In this sense, K~ by the C V N B method reflects only the propagation of a natural sharp crack. This interpretation is confirmed by the fact that K~¢ by indentation methods ( D C M and ISB) is closely equal to K~ by CVNB. The identation can produce as sharp a crack as m CVNB. As a result, the C V N B method seems to be the best suited among the different methods studied. This method can avoid the problem of the crack geometry and can be used at high temperature. The ISB method is restricted only to the room temperature toughness measurement of brittle materials. 3.3 K~c values at h i g h t e m p e r a t u r e The results are given in Fig. 4 where high temperature K~ values are compared with those at room Table 4.

Effect of n o t c h w i d t h on K~c measured by SENB m e t h o d

Sample

>SiC #-SIC

Notch width (mm) 0-08

0.15

035

402 4-32

3-70 3.75

4.53 4.17

164

Gilles Orange, Hidehiko Tanaka, Gilbert Fantozzi

t

~L330°C 1330~C

E

RT

~

Q

~- 2 ~:!:!

N

o

3. EII~U S S-Z~IB

CilKX

3

SZV

2739

A-SIC

ES

CV~IB

Fig. 4. Comparison of K~¢at room temperature and at high tcmpcrature (1350~C) by the SENB and CVNB methods. temperature. SENB method showed higher values than CVNB. K,~ increased at 1350°C (in air) for both :t and/3-SIC, using both SENB and C V N B methods. The increase in K~¢ from r o o m temperature to 1350':C is about 4% in a-SiC and 20-30% in/~-SiC: /~-SiC showed larger increases than a. The high temperature increase of K,¢ can be explained by considering the microstructure of each material and the fracture mode. Figures 5 and 6 show the microstructure and fracture surfaces of a and /3-SIC at r o o m t e m p e r a t u r e and 1350°C. Sintered a-SiC is made of spherical and h o m o geneous size distributed grains, fl-SiC is constructed by the composite structure of large elongated grains and small spherical grains. In Fig. 6, the r o o m temperature and high temperature fracture surfaces are compared. The fracture surfaces at r o o m temperature are observed to be flat and the crack propagated dominantly by the transgranular fracture mode. :t-SiC does not show a difference between ambiant and high temperature fracture. On the other hand,/3-SIC tends to be broken with a rougher surface at high temperature than at room temperature. Figure 6(D) is a typical example of a fracture surface in/I-SiC at high temperature. Then the total fracture energy, ;,~, may be written as: 7, =

+

+

(8)

where: 7,~=transgranular fracture energy, ;,~g= intergranular fracture energy, x = ratio of trans. to intergranular fracture and q5 = factor of crack deflection ( < 1). In the sintered SiC with B and C additives, x seems to be nearly 1 and the dependence on temperature is not significant.

Fig. 5. Microstructure of (A) :~ and (B) fl-SiC. Surfaces are etched by Murakami's reagent. It is considered, from our study, that the factor of crack deflection, 05, depends on the microstructure. At room temperature, both SiC materials behaved as a brittle fracture: 4~should be same in a-SiC and/3SiC. At high temperatures, ~b is larger in/3-SIC than in a-SiC: the crack plane has to deflect m u c h more along the elongated grains than along the spherical grains. The intergranular force contributes to the total fracture energy more effectively in /3-SIC. Therefore, the K,c increased in /3-SIC at high temperature. CONCLUSION The fracture toughness, K~, of a and/3-SIC materials was measured by D C M , ISB, SENB and C V N B methods. K~c by D C M depended on the indentation load. The ISB m e t h o d showed quite constant values of K~c. The SENB m e t h o d measured larger K~c values than C V N B and other methods; these

165

Fracture toughness o f pressureless sintered silicon carbide

Fig. 6.

Fracture surfaces at room temperature and 1350°C. (A) :~-SiC at room temperature, (B) at 1350°C. (C) fl-SiC at room temperature, (D) at 1350'~C.

values are d e p e n d e n t on the n o t c h tip g e o m e t r y , the s p a n length, a n d the s t r a i n rate. In c o n trolled fracture m o d e conditions, the C V N B m e t h o d s h o w e d s i m i l a r K ~ v a l u e s to D C M a n d I S B m e t h o d s . T h e r e was no a p p a r e n t difference in Kt¢ values b e t w e e n ~ a n d /3-SIC at r o o m t e m p e r a t u r e . K~¢ increased at high t e m p e r a t u r e (1350°C, in air) a n d /~-SiC s h o w e d larger increases in K ~ at these t e m p e r a t u r e s . T h e c r a c k deflection c o n t r i b u t e s to a large e x t e n t to the total f r a c t u r e e n e r g y at h i g h temperatures.

2.

3.

4. 5.

ACKNOWLEDGEMENTS 6. This w o r k was d o n e u n d e r the p r o g r a m m e o f Science and T e c h n o l o g y C o o p e r a t i o n b e t w e e n F r a n c e a n d J a p a n s u p p o r t e d by the t w o g o v e r n m e n t s .

7.

REFERENCES 8. I. ANSTIS, G. R., CHANTIKUL, P., LAWN, B. R. and MARSHALL, D. B., A critical evaluation of indentation

techniques for measuring fracture toughness: I, direct crack measurements, J. Amer. Ceram. Soc., ($4 (1981), 533. LAWN, B. R., EVANS, A. G. and MARSHALL, D. B., Elastic/plastic indentation damage in ceramics; The median/radial crack system, J. Amer. Ceram. Sot., 63 (1980), 574. CHANTIKUL, P., ANSTIS, G. R., LAWN, B. R. and MARSHALL, D. B., A critical evaluation of indentation technique for measuring fracture toughness: II, strength method, J. Amer. Ceram. Soc., 64 (198l), 539. BROWN, W. F. and STRAWLEY, J. E., Plane strain crack toughness testing of high-strength mctallic materials, A S T M STP, 410 (1967), 13. MUNZ, D. G., SHANNON, J. L. and BUBSEY, R. T., Fracture toughness calculation from maximum load in four point bend test of chevron notch specimens, Int. J. Frac., 16 (1980), RI37. EVANS, A. G. and CHARLES, E. A., Fracture toughness determinations by indentation, J. Amer. Ceram. Soc., 59 (1976), 371. NIIHARA, K., MORENA, R. and HASSELMAN, D. P. H., Indentation fracture toughness of brittle materials for palmquist cracks, in Fracture Mech. of Ceramics, Vol. 5, R. C. Bradt, A. G. Evans, D. P. H. Hassetman and F. F. Lange (eds), Plenum Press, New York, 1983, pp. 97-106. SHIH, T. T., An evaluation of the chevron V-notched bend bar fracture toughness specimen, Eng. Frac. Mech., 14 (4) (1981), 821.