Short-Crack Fracture Toughness of Silicon Carbide

Sarbjit Kaur, Raymond A. Cutler, and Dinesh K. Shettyw

Department of Materials Science and Engineering, University of Utah, Salt Lake City, Utah 84112

The fracture toughness of four different silicon carbides wasmeasured using single-edge precracked beam (SEPB) andindentation/strength techniques. Two were development gradeswith similar microstructures and chemistries, and yet exhibiteddifferent fracture modes. The grade that exhibited a predomi-nantly intergranular fracture had an SEPB fracture toughness(6.4 MPaOm) 88% higher than the one that showed primarily atransgranular fracture (3.4 MPaOm). The higher fracturetoughness was associated with a modest increase in averagestrength (25%), although there was a significant increase in theWeibull modulus (11–32). Fracture toughness at short cracklengths was assessed by an indentation method that usedfracture strengths, crack lengths at fracture, and a new methodof estimating the constant d that characterizes the residual driv-ing force of the plastic zones based on the stable growth of theindentation cracks from the initial (c0) to the instability (c�)lengths. The results showed a rising crack-growth-resistancebehavior for the grade exhibiting intergranular fracture, whilethe grade showing transgranular fracture had a flat crack-growth resistance. Tests on two commercial grades of siliconcarbide showed similar behaviors associated with the respectivefracture modes.

I. Introduction

PROCHAZKA’S discovery1 that boron and carbon promote thesolid-state sintering of SiC allowed its widespread use for

wear and erosion applications requiring good corrosionresistance.2,3 Other uses for SiC are based on its high thermalconductivity,4 electrical conductivity,5 low thermal expansion,6

and low specific gravity.7 This material, which fractures trans-granularly due to clean grain boundaries, has low fracturetoughness (2.5–3 MPaOm) and no R-curve behavior.8 Cutlerand Jackson9 used a liquid phase from Y2O3 and Al2O3 to sintera fine-grained SiC with a fracture toughness of 4 MPaOm. Chiaand Lau10 sintered SiC using AlN and Y2O3, which resultedin a material with a high toughness (8–10 MPaOm) and apronounced R-curve behavior upon annealing. The R-curvebehavior resulted from the intergranular fracture promoted byyttrium aluminate at triple junctions. Padture11 added a-SiCseeds to b-SiC powder to promote the growth of elongateda-SiC grains and R-curve behavior in the presence of a yttriumaluminate liquid.12 Researchers at Berekley8,13,14 used Al, B, andC as additives to sinter SiC and achieved a long-crack toughnessof 9 MPaOm with a strong R-curve behavior. Kim et al.15 hotpressed unseeded b-SiC using Y2O3 and Al2O3 as sinteringadditives. Annealing of these hot-pressed materials changedthe grain shape and produced an R-curve behavior associatedwith grain bridging.

While there is still much focus on long-crack fracture tough-ness, it has long been realized that properties such as strength16

and wear resistance17 are dependent on short-crack fracturetoughness. Measuring the extension of natural flaws is thepreferred method for measuring short-crack toughness andR-curves, but these data are sparse due to the difficulty in mak-ing these measurements.18 Short-crack toughness is oftenassessed from cracks produced by indentation,19 but scatter inthe data20 and lack of agreement with long-crack toughnessvalues21 are common problems. Silicon carbides with a hightoughness often have coarse grains and exhibit intergranularfracture and multiple cracking around indents.22 Strengthdistributions can provide an insight into R-curve behavior,with an increase in the Weibull modulus being exhibited bymaterials with R-curves.23,24 Kruzic et al.25 suggested that theearly part of an R-curve provides the greatest insight incorrelating with natural cracks, explaining why silicon nitridecan have high strength and high toughness.

Recent work on SiC has shown that a wide variety of micro-structures are possible by changing the sintering additives andgrain-boundary chemistry.26 It is now possible to change thelong-crack fracture toughness by a factor of two withoutsignificant differences in grain size or shape. This paper presentsresults on two pressureless-sintered silicon carbides with nearlyidentical microstructures and a slight difference in chemistry.The main difference between the materials is the amount ofintergranular fracture. The purpose of this paper is to comparethe fracture strengths, long-crack fracture toughness, andshort-crack fracture toughness as a function of crack length ofthe two silicon carbides to understand what advantages, if any,are gained by the change in fracture mode and the resulting in-crease in the long-crack fracture toughness. Two commerciallyavailable SiC grades are compared with the experimentalmaterials.

II. Experimental Procedures

Four SiC materials were evaluated in this study. Material N,sold under the trade name SiC–N (Cercom, Inc., Vista, CA), is ahot-pressed, state-of-the-art armor material, which uses AlN tolimit grain size.27 Material P, marketed as PS-5000 (MorganAM&T, St. Mary’s, PA), is an excellent pressureless-sinteredSiC based on traditional boron and carbon sintering aids.Grades A and B (Ceramatec, Inc., Salt Lake City, UT) areexperimental SiC materials made with Starck UF-15 SiC andproprietary sintering additives, but similar chemistries. Bothmaterials were processed identically by milling, freeze drying,pressing, and pressureless sintering, but the main differencebetween A and B was the amount of intergranular fracturethat was controlled by slight differences in the starting chemis-tries. Four-point bend test specimens (3 mm� 4 mm� 45 mm)were machined from all four materials by cutting and grindingwith a 320 grit diamond wheel as specified in ASTM StandardC-1161-02C.28

The density was measured using the Archimedes method.Polished surfaces were etched by different methods to revealtheir microstructures. Material N was thermally etched at15401C for 1 h in flowing argon, while material P was etchedwith a modified Murakami solution29 at 751C for 15 min. The Aand B materials were plasma etched by evacuating and backfilling with 400 mtorr of CF4-10% O2 and etching for 10 min.

M. Hofmann—contributing editor

This work was financially supported at Ceramatec under SBIR contract DAAD17-03-C-0036 for the Army Research Laboratory with Dr. Jane Adams as the technical monitor.

wAuthor to whom correspondence should be addressed. e-mail: d.shetty@utah.edu

Manuscript No. 25082. Received August 5, 2008; approved October 12, 2008.

Journal

J. Am. Ceram. Soc., 92 [1] 179–185 (2009)

DOI: 10.1111/j.1551-2916.2008.02829.x

r 2008 The American Ceramic Society

179

The mean grain sizes were measured by the line-interceptmethod, where the multiplication constant was 1.75 based onthe slightly elongated grain shape.30 Four hundred to sixhundred grains were measured for each material to obtain amean grain size. The lengths and widths of the three most elon-gated grains in each of five micrographs were used to estimateaspect ratios. The fracture mode, defined by the fraction of thecrack path covered by intergranular fracture, was determinedfrom polished and etched side surfaces of single-edge precrackedbeam (SEPB) bars.31 Fracture surfaces of the SEPB specimenswere also examined in a scanning electron microscope to assessthe fracture mode.

Rietveld analysis32,33 was used to estimate the weight percentsof SiC polytypes present in the sintered specimens using X-raydiffraction patterns collected in the 201–801 2y range, with a stepsize of 0.021 and a counting time of 4 s/step.

A microhardness tester (Leco model LM-100, St. Joseph, MI)was used to measure Vickers (HV1) and Knoop (HK1) hardnesson polished specimens at a load of 9.8 N. Reported hardnessvalues are the means of five measurements, with error bars rep-resenting two standard deviations.

Flexural strength was measured on 15 bars (3 mm�4 mm� 45 mm) using a 40 mm support span, a 20 mmloading span, and a crosshead speed of 0.5 mm/min.28 Themaximum likelihood method was used to estimate the Weibullmodulus (m) and the characteristic strength (sy) by fitting thetwo-parameter Weibull distribution function to the measureddata. Young’s modulus was measured in flexure using straingauges.

Long-crack fracture toughness was measured using the SEPBmethod,31 using black ink to mark the crack front.34 For eachmaterial, the reported fracture toughness is the mean of fourtests, with error bars representing two standard deviations.

Short-crack fracture toughness was measured using themultiple Vickers indentation method.35 The tension surfacesof four-point bend specimens were polished to a 1 mm finish,indented with a Vickers indenter at three locations (at the centerand at two locations 5 mm from the center so that all threeindents were within the inner span). Indents were aligned so thatone of the diagonals of the indents was normal to the beam axis.The indentation loads ranged from 2.5 to 300 N. The loadingrates were varied from 1 to 6.5 N/s for increasing indentationloads. The peak load was maintained for 30 s. To minimizesubcritical growth of the cracks, a thin layer of mineral oil wasspread on the tensile surface before indenting. The bars wereloaded to failure in four-point flexure with a thin layer of oilagain spread on the tensile surface. Fracture initiated from oneof the three Vickers indentation cracks, while the remaining twoshowed stable growth to a critical size, c�, the semi-axis of a semi-elliptical surface crack measured on the surface. The specimenswere inspected after tests to verify that fracture initiated at oneof the indents. Instability crack lengths, c�, were measured on theremaining two indents of each bar. At each indentation load,measurements on six indents were used to calculate the meanvalues of co, the as-indented crack length, and c�. Fracturetoughness as a function of instability crack length, KR(c

�),was calculated using the following equation36,37:

KRðc�Þ ¼ dE

H

� �1=2P

c�3=2þ Yðc�Þsf

ffiffiffiffiffic�p

(1)

where d is a nondimensional constant dependent on the indentergeometry, Poisson’s ratio, and the nature of the plastic zoneproduced by indentation, E is the elastic modulus, H is theVickers’s hardness at the indentation load, P, Y(c�) is a stress-intensity coefficient that accounts for free surface and stress-gradient effects, and sf is the fracture stress. Different values forthe constant d have been proposed in the literature. Anstiset al.19 proposed an average value, d5 0.01670.004, forceramics based on experimental calibration of indentationdata with long-crack fracture toughness measurements. Based

on theoretical considerations, Shetty et al.38 showed that theresidual crack-driving force of the plastic zone can be modeledin the extremes as that of a rigid wedge (d5 0.014) or a constantforce (d5 0.023). In the more general case, the plastic zone actsas a spring with a crack-opening force that reduces with far-fieldapplied stress.39 In this case, the residual force of the plastic zoneand, therefore, d, decrease with increasing far-field appliedstress. Clearly, estimation of fracture toughness from indenta-tion data is nontrivial. The error associated with such estimatescan be particularly large if based on as-indented crack lengths,c0, when d has the strongest influence on the estimated fracturetoughness. For these reasons, we used only the instability cracklengths and fracture stresses for estimating short-crack fracturetoughness using Eq. (1). The value of d was estimated by a newprocedure outlined here. First, it is noted that the appliedcrack-driving force, Ka(c), adopts a form similar to Eq. (1):

KaðcÞ ¼ dE

H

� �1=2P

c3=2þ YðcÞs

ffiffifficp

(2)

The value of d and the first term in Eq. (2) determine thedegree of stable growth of an indentation crack from c0 toc� before its instability. The instability condition at c5 c� isdefined by the following equations40:

Kaðs; c�Þ ¼ KRðc�Þ (3)

dKa

dcðs; c�Þ ¼ dKR

dcðc�Þ (4)

One method of estimating d is to match the instability cracklength, c�, measured in the experiments with that defined by Eqs(3) and (4). However, such a procedure requires a priori knowl-edge of the R-curve and the function, KR(c). To overcome thisdilemma, we used an iterative calculation method to estimated from c�. First, we assumed that the material had a flat-crack-growth resistance. For this case, the instability condition takesthe following form:

dKa

dcðsf ; c

�Þ ¼ 0 (5)

Equations (5) and (2), then, define the following initial valuefor d:

d ¼ sfc�2

3P

H

E

� �1=2

Yðc�Þ þ 2c�dY

dcðc�Þ

� �(6)

The average value of d calculated from Eq. (6) for differentindentation loads was used to calculate the fracture toughness ofthe material, KR(c

�), using Eq. (1). If the data showed increasingfracture toughness with increasing crack length, the followingempirical equation was fitted to the rising-crack-growth resis-tance or R-curve:

KRðcÞ ¼ K1 � ðK1 � K0Þ exp �c

l

� �(7)

In Eq, (7), KN is the plateau fracture toughness at long cracklengths, K0 is the crack-initiation toughness, and l is a scalingparameter for crack length. The crack-instability condition, Eq.(4), was then used to define a new value of d using the following

180 Journal of the American Ceramic Society—Kaur et al. Vol. 92, No. 1

equation:

d ¼sfc�2

3P

H

E

� �1=2

Yðc�Þ þ 2c�dY

dcðc�Þ

� �

� 2

3

H

E

� �1=2c�

5=2ðK1 � K0ÞPl

exp � c�

l

� � (8)

Equation (8) was used iteratively to calculate d, fracturetoughness from Eq. (1), and the empirical R-curve parametersof Eq. (7) until two consecutive values of theR-curve parametersdiffered by o1%, an arbitrarily selected error. Typically, threeor four iterations were required to achieve this convergence.

The stress-intensity coefficient, Y(c�), is a function of theaspect ratio of the semi-elliptical crack, a/c, where a is the semi-axis normal to the surface, the relative depth of the crack, a/w,where w is the thickness of the beam and the mode of loading(tension or bending). Raju and Newman41,42 have calculatedY(c�) as functions of these variables for both uniform tensionand bending by finite-element analysis (FEA). To use their re-sults, however, one needs to know the aspect ratio of the semi-elliptical crack and how the aspect ratio changes during stablegrowth from c0 to c�. Studies of shapes of surface cracks grownstably in fatigue in bending indicate that the aspect ratio de-creases approximately linearly with the relative crack depth43,44:

a

c¼ 1� a

w(9)

Values of Y(c�) were calculated for different values of c�, theaspect ratio defined by Eq. (9) and the relative crack depth usingthe FEA results of Raju and Newman.41,42 The followingequation was developed as an empirical fit to the numericalresults:

Yðc�Þ ¼ 0:2139þ 1:0770w

wþ c�

� �(10)

Equation (10) was used to calculate both Y and the derivativedY/dc in Eqs. (6) and (8).

III. Experimental Results and Analyses

(1) Properties of Silicon Carbides

Table I lists the densities, SiC polytypes, grain sizes, and thegrain-aspect ratios of the four materials. The densities of thefour materials ranged from 3.12 to 3.21 g/cc. For materialsA and B, these represent 97% of the densities achieved in hotpressing of identical compositions. Silicon carbide A was slightlydenser than B. The microstructures used to quantify the grainsize, aspect ratio, and percent intergranular fracture are shownin Fig. 1. The grain sizes of the four materials varied from 2.4 to4.5 mm, with materials A and B having similar grain sizes. Themicrostructure ranged from primarily equiaxed grains formaterial N to more elongated grains for the other three materi-als. Materials A and N showed mostly intergranular fracture,

whereas materials B and P fractured primarily transgranularly.The fracture surfaces (Fig. 2) and Vickers indents (Fig. 3) showeda more transgranular fracture mode for material P comparedwith composition B. Clean grain boundaries in SiC result intransgranular fracture, which is typical of materials sintered withboron and carbon. The fine grain size and segregation of Al andO to grain boundaries result in the high amount of intergranularfracture for SiC–N45 that is characteristic of SiC densified withAlN.46 While all four materials had primarily the 6H polytype,materials A and B had much more 4H than materials N and P.The polytypes present in A and B were similar.

Table II lists the Young’s moduli, fracture strengths, SEPBfracture toughness values, percent intergranular fracture, andhardness of the silicon carbides. Material N had the highestYoung’s modulus and B had the lowest modulus, consistentwith the density data. Material N had the highest strength of 566MPa, while P had the lowest strength of 385 MPa. Materials Aand B had intermediate strengths, with A having a higherstrength than B. Table II shows that material A had a signifi-cantly higher Weibull modulus as compared with the other threematerials. Because A and B materials were processed in an iden-tical manner using the same grade of SiC powder and similaradditives, it was expected that they would have similar process-ing flaws. The modest increase in the strength of A comparedwith B was disappointing based on their SEPB toughness values.This fact, coupled with the higher Weibull modulus of materialA, suggested that R-curve behavior could be the reason for thelower than expected increase in its strength.18 SEPB toughnessmeasured for the four materials varied, with material P having

Table I. Densities, Phases, Grain Sizes and Grain AspectRatios of the Silicon Carbides

Grade Density (g/cc)

Polytypes (w%)

Grain size (mm) Aspect ratio4H 6H 15R

A 3.1470.01 31.8 56.6 9.4 3.770.1 5.071.0B 3.1270.01 33.9 54.6 11.5 3.670.4 3.870.6N 3.2170.01 2.7 93.3 4.0 2.470.2 2.570.4P 3.1670.01 18.5 75.7 5.8 4.570.4 3.971.7

Fig. 1. Microstructures of the four grades of silicon carbides.

Fig. 2. Fracture surfaces of the four grades of silicon carbides.

January 2009 Short-Crack Fracture Toughness of Silicon Carbide 181

the lowest toughness of 2.5 MPam1/2 and A having the highesttoughness of 6.4 MPam1/2. Material P was the hardest, withlittle difference between the Vickers hardness of the other threematerials.

(2) Vickers Indentation and Strength Degradation

The degradation of the fracture strengths of the silicon carbidesas functions of the load in Vickers indentation is shown in thelog–log plots of Fig. 4. The fracture strengths of the unindentedspecimens are plotted on the y-axis (P5 1 N) for comparison.The indentation strengths decreased approximately linearly withthe indentation loads on the log–log plots. The slopes of theplots were approximately�0.3 for materials P and B. A slope of�0.33 is expected for materials with a crack-length-independentfracture toughness, KIc.

47 In contrast, materials A and N exhib-ited slopes of �0.24 and �0.25, respectively. A slope o�0.33 isoften due to R-curve behavior.48

(3) Short-Crack Fracture Toughness from IndentationStrengths and Instability Crack Lengths

Figure 5 shows plots of fracture toughness calculated using Eq.(1) as functions of the instability crack length, c�. For each ma-terial, the value of d was estimated by the iterative calculationprocedure described earlier. The calculations did not show anysignificant dependence of d on the indentation load or the initialcrack length. Therefore, the average values of d were calculatedfor the four silicon carbides and are listed in Table III. It is ev-ident that values of d required to correctly account for the stablegrowth of cracks from c0 to c� for all the silicon carbides arelow, with values ranging from 0.004 to 0.0081. There was anapproximate linear correlation of d with c�/c0, with material Nexhibiting the lowest values and material B the highest values.

Silicon carbides A and N showed clear evidence of increasingfracture toughness with increasing crack lengths or R-curvebehaviors, while grades B and P showed no increase in fracturetoughness with increasing crack length. These results were con-sistent with our expectations based on the indentation strength-indentation load plots of Fig. 4. The arrows on the right in Fig. 5indicate the average SEPB fracture toughness of the materials.

The SEPB fracture toughness was consistent with the short-crack (indentation) fracture toughness for materials P, B, and A.Material N was an exception in that the indentation toughnesswas higher than the SEPB value. Possible reasons for the anom-alous behavior of material N will be addressed in the discussionsection.

Table III also lists the R-curve parameters, l, K0, and KN,obtained by fitting Eq. (7) to the fracture toughness data. Formaterial A, fracture toughness ranged from K05 4.3MPaOm toKN 5 6.8 MPaOm, while the corresponding values for materialN wereK0 5 3.2 MPaOm and KN5 6.1 MPaOm. For materialsB and P, there was no evidence of R-curve behavior and the flatlines drawn in Fig. 5 represent the average values.

(4) Analyses of Indentation Strengths from R-Curves

To assess the self-consistency of the method used for calculatingshort-crack fracture toughness from indentation strengths, theR-curves (Eq. (7)) fitted to the short-crack toughness were, inturn, used to calculate indentation strengths. For this purpose,the crack-driving force for the indentation crack defined by Eq.(2) was plotted on the same plot as an R-curve defined by Eq.(7). An example of such a plot for material A is shown in Fig. 6.The applied stresses required to satisfy the fracture instabilityconditions of Eqs. (3) and (4) were assessed by selecting a valueof s for which the Ka(c) curve was tangent to the KR(c) curve.The stresses calculated in this manner are plotted in Fig. 4 assolid lines. It can be seen that the calculated indentationstrengths are consistent with the measured strengths.

IV. Discussion

Significant advances have been made in the sintering and densi-fication of silicon carbide in the last 20 years. It is now possibleto densify silicon carbide by pressureless sintering to near the-oretical density either by solid-state or by liquid-phase sinteringmechanisms using appropriate additives. Silicon carbide solid-state sintered with B and C additives offers excellent corrosion

Fig. 3. Hardness impressions and cracks produced by Vicker’s inden-tation at 1 kg load.

Table II. Young’s Moduli and Mechanical Properties of Silicon Carbides

Grade E (GPa) sf (MPa) syw (MPa) mz KIc (MPaOm) % intergranular fracture HK1 (GPa) HV1 (GPa)

A 41271 505756 535 15.6 6.470.5 82 18.070.4 22.270.3B 40171 411737 458 9.5 3.470.2 20 18.070.4 21.670.3N 44875 566786 605 8.6 4.670.2 88 20.470.1 23.070.8P 41673 385758 410 8.5 2.570.2 12 19.370.3 24.670.5

wCharacteristic strength (63.2% probability of failure). zWeibull modulus using maximum likelihood method.

Fig. 4. Fracture strengths as functions of Vickers indentation load forthe four grades of silicon carbides. Solid lines are based on calculations.

182 Journal of the American Ceramic Society—Kaur et al. Vol. 92, No. 1

resistance, but it has modest mechanical properties due topredominantly transgranular fracture. Liquid-phase-sinteredsilicon carbides, on the other hand, are poor in corrosionresistance, but are amenable to control of microstructure,grain-boundary chemistry, degree of intergranular fracture,and, therefore, their mechanical properties. The two develop-ment grades introduced in this study, A and B, have only smallamounts of liquid forming additives that supplement theirsintering, which is believed to be primarily solid state. Thesetwo silicon carbides have nearly identical microstructures, butsignificantly different mechanical properties due to differences intheir grain-boundary chemistries. Silicon carbide A has higherfracture strength, fracture toughness, and Weibull modulus ascompared with silicon carbide B despite their similar micro-structures. The enhanced mechanical properties of A are due toincreased amount of intergranular fracture induced by a smallchange in the sintering additives that influence the grain-bound-ary chemistry.

Silicon carbide A exhibited an SEPB fracture toughness of 6.4MPaOm. This represents an increase of 88% over that of B (3.4MPaOm) brought about by an increase in the amount of inter-granular fracture from 20% to 82%. However, this increase inlong-crack toughness did not translate into a corresponding in-crease in the fracture strength. The fracture strength of siliconcarbide A (505 MPa) was only 23% higher than that of siliconcarbide B (411 MPa). Fractography on both materials A and Bshowed that strength-controlling flaws were 450 mm. Anattempt was made to see whether the strength-controlling flawscould be reduced in size by filtering the slips through a 25 mmfilter. The resulting materials showed essentially the same SEPBtoughness (6.570.1 MPaOm for A compared with 3.370.2MPaOm for B) with modest increases in strength (567720 MPafor A compared with 436745 MPa for B). This was despitethe fact that fractography revealed smaller flaws as a result offiltering of the slip. The Weibull modulus of A (31.9) was stillhigh compared with B (11.0), as shown in Fig. 7. Both of theseresults are consistent with R-curve behavior for material A. It isalso interesting to note that the ratio of the fracture strengths of

materials A and B processed by filtering the slip (1.3) is approx-imately the same as the ratio of the short-crack toughness at acrack size of 50 mm (1.35). This confirms the fact that it is theshort-crack toughness that determines the fracture strength ofmaterials that exhibit R-curve behavior.

Ideally, short-crack toughness should be assessed by measur-ing the loads and lengths of cracks initiated at intrinsic flawsthat normally control fracture stresses of ceramics. Such mea-surements, although demonstrated in a limited number of cases,are difficult for two reasons. First, only cracks initiated atsurface flaws can be measured. This limits measurements tothose ceramics where bulk defects and flaws are less severe thansurface defects. Second, as shown recently by Kaur et al.,40

stable growth of cracks due to rising crack-growth resistanceoccurs only when the crack-initiation resistance (K0) is lowcompared with the plateau resistance (KN). Specifically, therequirement is K0/KNo0.2. This is satisfied only in a limitednumber of ceramics that have strongly rising R-curve due toprocess-zone development.

To avoid the difficulties in measuring cracks initiated at‘natural’ flaws, cracks produced by indentation have beenused in fracture research. There are two advantages in using

Fig. 5. R-curves for silicon carbides calculated from indentationfracture strengths and instability crack lengths. Arrows on the rightside show single-edge precracked beam data.

Table III. Indenter Constant and R-Curve ParametersEstimated by the Iterative Calculation Procedure

Grade d l (mm) K0 (MPaOm) KN (MPaOm)

A 0.0062 273 4.3 6.8B 0.0081 — 3.5 3.5N 0.004 246 3.2 6.1P 0.007 — 2.7 2.7

Fig. 6. Crack-driving force and crack-growth-resistance plots illustrat-ing fracture instability.

Fig. 7. Weibull plots for silicon carbides A and B made with slips fil-tered through a 25 mm screen before processing.

January 2009 Short-Crack Fracture Toughness of Silicon Carbide 183

indentation cracks. The lengths of the cracks can be controlledby the indentation load. Secondly, the crack-driving force due tothe plastic zone decreases with increasing crack length. Thiscauses an indentation crack to grow stably under an appliedfar-field load before it becomes unstable at a critical cracklength. This allows measurements of fracture toughness andR-curves over a range of crack lengths. These advantages are,however, negated by the difficulty in formulating the residualdriving force of the plastic zone. As pointed out before, theplastic zone should strictly be modeled as a spring and the springforce is a function of the elastic (E) and plastic (H) properties ofthe material, the geometry of the indenter, and the relative sizesof the plastic zone and the crack.39 This is equivalent to sayingthat d in Eqs. (1) and (2) is a function of crack size. Assumptionof a constant d during crack growth is clearly an approximation.The value of d in Eqs. (1) and (2) determines the degree of stablegrowth of cracks and the calculated fracture toughness. We haveused a new method for estimating an average value of d for eachmaterial by matching the measured crack length at instabilitywith a theoretically expected value at the point of instability ortangency. This method appears to work well for the three siliconcarbides, A, B, and P, in the sense that the plateau toughness(KN) for the indentation cracks is close to the SEPB toughnessand the measured indentation strengths are consistent with theshort-crack toughness. Material N was an exception. The pla-teau value of the short-crack toughness was much higher thanthe SEPB value. The reason for this anomalous behavior ofmaterial N is not clear. It is possible that a mechanism that canpotentially relax the residual driving force of the plastic zones,such as, for example, lateral cracking, may be operative in thismaterial.

V. Conclusions

The mechanical properties of silicon carbide (strength, fracturetoughness, and Weibull modulus) can be significantly improvedby controlling the amounts of sintering additives and grain-boundary chemistry without altering the microstructure. Theimprovements are obtained from an increased amount ofintergranular fracture.

A high amount of intergranular fracture produces high long-crack fracture toughness and a high Weibull modulus, but onlya modest increase in the fracture strength. This is believed to bedue to a rising crack-growth-resistance (R-curve) behavior atshort crack lengths brought about by grain bridging.

Measurements of short-crack toughness pose severalchallenges. A method proposed in this paper for assessing theconstant d based on the amount of stable growth of the inden-tation cracks provides consistency between the plateau values ofthe short-crack toughness and the SEPB values.

Acknowledgments

Lyle Miller of Ceramatec performed XRD measurements and Shane Verhoefhelped with some of the density and strength measurements. Technical discussionswith Marc Flinders and Darin Ray were insightful.

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