58249834 hardness vs rupture

International Journal of Refractory Metals & Hard Materials 23 (2005) 119–127

www.elsevier.com/locate/ijrmhm

Correlation of transverse rupture strength of WC–Co with hardness

Zhigang Zak Fang *

Department of Metallurgical Engineering, University of Utah, 135 S. 1460 East, Room 412, Salt Lake City, Utah 84112, USA

Received 10 September 2004; accepted 26 November 2004

Abstract

The transverse rupture strength (TRS) of WC–Co composites is often loosely viewed as an equivalent of ‘‘toughness’’ which

increases as hardness decreases in the industry. The results of this study, conducted using a controlled group of WC–Co samples

with consistent TRS values, suggest a different correlation between the TRS and hardness of WC–Co composites. It was shown that

TRS is closely related to the hardness and facture toughness. Within a hardness range of 800 <Hv < 1500 kg/mm2, TRS appears to

first increase and then decrease as the hardness increases. It reaches a peak value at Hv � 1300 kg/mm2. While in the past TRS of

WC–Co has been used as a indicator of porosities of WC–Co materials, the result of this study is understood on the basis that these

samples are porosity-free because most products of WC–Co today contains very little (if any) porosity owing to modern advances in

processing technologies. When the effect of porosity is negligible, TRS is determined by intrinsic mechanical properties which are

dependent of microstructure and compositions. The relationship between TRS and hardness and the fracture toughness is explained

by a qualitative model based on the work hardening and flow stress of the cobalt binder phase.

� 2004 Elsevier Ltd. All rights reserved.

Keywords: Cemented tungsten carbide; Hardmetal; TRS; 3-point bending; Fracture toughness; Cermets

1. Introduction

One of the most frequently used mechanical proper-

ties of cemented tungsten carbide (WC–Co) composites

is their transverse rupture strength (TRS) [1–3]. Thereare several reasons for its popularity in practice. First

of all, TRS is very sensitive to porosity levels [4]. When

porosity level is high, TRS values will be not only poor

but also very inconsistent. Therefore, it has historically

being used as an indicator of the quality of sintered

WC–Co materials in manufacturing. Today, however,

due to advances in manufacturing technologies in the

industry in the past two decades, the majority of com-mercial WC–Co materials are essentially porosity free.

While TRS continues to be an effective metrics of the

quality of cemented tungsten carbide products, it is

0263-4368/$ - see front matter � 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ijrmhm.2004.11.005

* Corresponding author. Tel.: +1 801 581 8128; fax: +1 801 581

4937.

E-mail address: [email protected]

more a true reflection of intrinsic properties of the

WC–Co composites when porosities are negligible. The

intrinsic strength of WC–Co composite is functions of

cobalt content, grain size, carbon balance, and other

chemical composition and microstructure factors.Secondly, because of its sensitivity to pores and other

defects, TRS is often also viewed as a measure of

‘‘toughness’’ by application engineers as well as metal-

lurgical engineers. When a WC–Co composite contains

significant porosity, the strong correlation between its

TRS and the fracture toughness is easily understood.

The pores are viewed as existing defects, of which the

critical size is related to critical stress and the fracturetoughness by KIc ¼ Arr

ffiffiffiffiffi

acp

[5,6], where ac is the critical

defect size, rr is the rupture strength, and A is a geome-

try related constant. But when the porosity level is very

low or negligible, the relationship between TRS and the

fracture toughness is not so straight forward. In fact,

it has been shown that strength reaches an asymptotic

value as the defect size, a, becomes equal or less than

mailto:[email protected]

1000

1500

2000

2500

3000

3500

4000

84.00 86.00 88.00 90.00 92.00 94.00

Hardness, HRa

TRS

(N/m

m2 )

1st manufacturer 2nd manufacturer

Fig. 2. TRS vs. hardness based on handbook values.

120 Z.Z. Fang / International Journal of Refractory Metals & Hard Materials 23 (2005) 119–127

the size of a characteristic value [7]. Further, the flexural

strength and fracture toughness are completely different

concepts in the context of solid mechanics. TRS is a sta-

tic tensile property while the fracture toughness is a

measure of the resistance of a material to crack propaga-

tion. The relationship between them must be examinedaccordingly.

A notion that has historically been quoted by appli-

cation engineers in the industry is that TRS is inversely

proportional to hardness of WC–Co materials. TRS in-

creases when hardness decreases within a range and this

trend plateaus when Hv < 1200 kg/mm2 as illustrated in

Fig. 1 [8,9]. According to this trend TRS increases with

cobalt content so long as the tungsten carbide grain sizesare held constant, because hardness decreases when co-

balt content increases. This relationship depicted by Fig.

1 is called into question when an extreme case with pure

cobalt metal is considered. Because cobalt metal has

much lower modulus compared to WC, the TRS of

WC–Co composite must decrease when the cobalt con-

tent becomes so high that the effect of cobalt metal in

the composite becomes dominant. This implies thatTRS will decrease when the hardness is lower than a

threshold value. The question is what is this threshold

value? There is no published study available to-date in

this regard. This uncertainty about the relationship be-

tween TRS and hardness is further illustrated by Fig.

2 which plots data of TRS vs. hardness of commercial

grades published in the Handbook of Hardmetals [10].

All data plotted in Fig. 2 are straight WC–Co gradescontaining no other additives. Although the data set

Fig. 1. Conventional view of the relationship between the TRS and

hardness of cemented tungsten carbide as illustrated in Ref. [7].

from the 2nd manufacturer shows a slight increasing

trend of TRS with decreasing HRa, the scatter of the

data at any given Hv is as wide as the entire data range

of TRS. When the data sets of both manufacturers are

combined, it is even more difficult to discern a trend be-

tween TRS and Hv. In short, Fig. 2 suggests a cloudycorrelation between TRS and hardness. These may be

explained by two categories of reasons: First, the cloud-

iness can be partially attributed to porosities because

these data are presumably collected before the wide

spread use of sinter-HIP technology. The second possi-

bility is that there are no simple correlations between

TRS and hardness. The dependence of TRS test values

on porosity and specimen preparations has been exten-sively studied and reported [11–13]. This study attempts

to shed light on this issue by focusing on the correlation

of TRS with intrinsic mechanical properties including

the hardness and the fracture toughness. The analysis

of the correlation is possible only when the porosities

of specimens are extremely low and the effects of poros-

ities are negligible.

This study examines interrelationships between TRS,hardness, and fracture toughness using a controlled

group of samples with varying cobalt content and grain

sizes. The relationships between the TRS, hardness, and

fracture toughness are analyzed based on the flow stress

and work hardening of cobalt during 3-point bending

tests. The dependence of TRS on microstructure param-

eters is inherent to its dependence on other intrinsic

mechanical properties.

2. Experimental

2.1. Design and selection of test matrix and samples

To understand the interdependence of TRS, hard-

ness, fracture toughness, and microstructure, it is impor-tant to isolate the effects of microstructure parameters

and the intrinsic correlation between the hardness and

TRS. A group of samples are designed with varying

hardness levels. Each hardness level is achieved by vary-

Z.Z. Fang / International Journal of Refractory Metals & Hard Materials 23 (2005) 119–127 121

ing grain sizes and cobalt content to obtain three differ-

ent types of microstructures, namely low Co content-

large grain size, medium Co-medium grain size, or high

Co-fine grain size. By comparing data from these sam-

ples, it is possible to resolve the effects of microstructure

and the effects of intrinsic mechanical properties such ashardness. If the effects of microstructure are dominant,

then for each hardness level that will be examined, the

TRS values will vary depend on their microstruc-

ture characteristics. If the effects of intrinsic mechani-

cal properties are dominant, then there will be a clear

correlation between TRS and hardness even when the

same hardness level can be achieved via different

microstructures.

2.2. Specimen preparations

Samples were fabricated using laboratory ball milling

method and sinter-HIP furnaces. Porosity is at mini-

mum level with porosity ratings at A02B00C00 or less

according to ASTM-B276-91. It is important to note

once again that porosity has strong influence on TRSvalues of WC–Co composite. But when porosity levels

are lower than detectable levels using conventional

methods, it is reasonable to assume the TRS values will

reflect the intrinsic mechanical properties of the material

which is the focus of this study.

TRS samples were prepared and measured following

ASTM-B406-90. All samples were ground to dimensions

using resin-bound diamond grinding wheels and surfacegrinders to achieve dimensional accuracy as well as good

Table 1

Data table

Sample # Co content Magnetic saturation

(emu/g)

Coercivity Hc Grain size

1 0.1520 23.5 52 3.07

2 0.1470 23 69 2.37

3 0.1674 25.8 72 2.07

4 0.1220 18.7 72 2.55

5 0.1627 26.2 83 1.83

6 0.1020 15.9 66 3.06

7 0.1032 16 69 2.91

8 0.1093 17.6 101 1.93

9 0.1452 22.6 98 1.68

10 0.0931 14.9 98 2.15

11 0.1057 16.2 122 1.63

12 0.0923 13.9 122 1.73

13 0.1090 17.4 112 1.74

14 0.0635 9.8 130 1.86

15 0.0818 13 142 1.57

16 0.0801 12.9 157 1.43

17 0.1024 15.8 208 0.97

18 0.0610 9.3 169 1.45

19 0.0591 9 210 1.18

20 0.1375 17.8 321 0.53

21 0.1030 14 352 0.57

22 0.0397 5.2 252 1.06

23 0.0627 10.1 268 0.91

surface finishes. Surface roughness of a specimen must

be Ra < 0.4 lm, or it was not used for this study. During

grinding the rate of material removal was carefully con-

trolled by using very slow feed rate to minimize the ef-

fects of compressive residual stresses. Ten samples of

each group were tested under controlled procedures.All data obtained had standard deviation below 5% ex-

cept for that when Hv > 1500 standard deviations

were > 15%. The fracture toughness was measured in

accordance with ASTM-B771 using the short-rod

method, tested on a TERRATEK FRACTOMETER.

Three samples were tested for each KIc data. The aver-

age was reported.

3. Results

Table 1 tabulates cobalt content, grain size, magnetic

saturation, coercivity, and all measured mechanical

properties. The cobalt contents and grain sizes of all sam-

ples in Table 1 are calculated based on density, magnetic

saturation, and magnetic coercivity data using empiricalequations that had been developed previously [14].

Although the cobalt content of a sample is determined

by its specification, actual cobalt content of a sintered

sample is also affected by sintering operations, carbon

content, and systemic errors. Therefore, the calculated

cobalt content reflects the true cobalt level of the sample.

The calculation of grain sizes using magnetic coercivity

data is also conducted using the empirical equations[10]. It is noted that the grain sizes and size distributions

(lm) MFP (lm) Hv (kg/mm2) KIc (MPa m1/2) TRS (MPa)

2.07 935 20.90 3250

1.48 1020 17.71 3215

1.75 1035 17.49 3429

1.07 1050 17.49 3229

1.44 1075 17.05 3554

0.91 1070 16.31 3015

0.88 1105 16.02 3547

0.65 1225 14.30 3802

1.02 1160 15.18 3836

0.54 1225 13.75 3781

0.52 1300 13.20 3919

0.43 1300 12.16 3912

0.59 1265 12.51 3671

0.24 1335 12.73 3602

0.31 1370 12.51 3153

0.27 1430 11.78 3236

0.29 1440 11.55 3353

0.18 1450 10.18 3133

0.14 1595 10.41 3712

0.29 1645 10.02 4271

0.17 1750 9.43 3705

0.07 1710 9.53 3464

0.12 1653 3174

Fig. 3. A optical micrograph of WC–10Co.


were also measured using commercial image analysis

software. No significant differences were found between

the two methods. A typical micrograph of these samples

is shown in Fig. 3. Special attentions were paid to exam-

ine porosities and abnormal grain growth. All samples

have porosity rated as A00B00C00 in accordance with

ASTM-B276. No abnormal large grains were present inthis group of samples.

Using these data, we will first reaffirm the dependence

of mechanical properties on microstructure parameters,

namely cobalt content, grain size, and the mean free

path (MFP) which have long been established in the

field. Then, the focus of our analysis will be on the rela-

tionship between TRS and fracture toughness and

hardness.

3.1. Dependence of mechanical properties on

microstructure

Microstructure parameters included in this study in-

clude cobalt content, grain size, and the mean free path

800900

100011001200130014001500160017001800

0.00 0.05 0.10 0.15 0.20

Cobalt content by weight

Har

dnes

s, H

v (K

g/m

m2 )

1.0 micron grain size 1.5 micron grain size2.0 micron grain size 3.0 micron grain sizeLinear (2.0 micron grain size) Linear (3.0 micron grain size)Linear (1.5 micron grain size) Linear (1.0 micron grain size)

(a)

Fig. 4. (a) Hardness and (b) fracture tough

between WC grains. Fig. 4 shows the variations of hard-

ness, fracture toughness as functions of cobalt content.

It is clear from Fig. 4(a) and (b) that the hardness

decreases while the fracture toughness increases as the

cobalt content increases. The correlations between the

hardness and fracture toughness and the cobalt contentare viewed by plotting Hv or KIc vs. Co content at vari-

ous constant grain sizes. The finer the grain sizes, the

higher the hardness, and the lower the fracture tough-

ness. Fig. 4(a) and (b), also shows the effects of grain

sizes, which are presented directly in Fig. 5. For any given

constant cobalt content, when the grain sizes are re-

duced, the hardness increases and the fracture toughness

decreases. This is consistent with the results in Fig. 4.Fig. 6 shows the variations of hardness and fracture

toughness as functions of mean free path (MFP). MFP

is a microstructure parameter that unifies the effects of

cobalt content and grain sizes for cemented tungsten

carbide materials. Fig. 6(a) and (b) clearly shows the

one-to-one correlations between the hardness and the

fracture toughness and MFP respectively. The liner or

near-liner relationship between KIc and MFP has beenshown in many previous studies [15–17]. Theoretical

models that attribute the most of the fracture energy

of WC–Co composites to the plastic deformation and

tearing of the cobalt phase are also well established

[18,19].

In order to study the relationships of TRS with Hv

and KIc, Fig. 6(c) plots TRS vs. MFP. It is clear that

the dependence of TRS on microstructure is drasticallydifferent from that of Hv and KIc vs. MFP. While it is

known (since Gurland�s work in the 1950s) that the

TRS of WC–Co increases with Co content (at constant

grain size) and with grain size (at constant cobalt con-

tent) up to a maximum and then decreases, the data of

the present work are not designed to examine the rela-

tionships of TRS vs. cobalt content and grain sizes di-

rectly. Rather, the key focus of the present study,

6

8

10

12

14

16

18

20

22

0.00 0.05 0.10 0.15 0.20

Cobalt content by weight

Frac

ture

Tou

ghne

ss, K

Ic, (

MPa

m1/

2 )

1.0 mic. Grain Size 1.5 mic. Grain size2.0 micron grain size 3.0 micron grain sizeLinear (1.0 mic. Grain Size) Linear (1.5 mic. Grain size)Linear (2.0 micron grain size) Linear (3.0 micron grain size)

(b)

ness as functions of cobalt contents.

(a) (b)

800

1000

1200

1400

1600

1800

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50Grain Size (µm) Grain Size (µm)

Har

dnes

s, H

v (K

g/m

m2 )

6%Co 8.5%Co10.5%Co 14.5%CoLinear (10.5%Co) Linear (8.5%Co)Linear (6%Co) Linear (14.5%Co)

6.00

10.00

14.00

18.00

22.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50

Frac

ture

Tou

ghne

ss, K

Ic (M

Pa

m1/

2 )

6% Co 8.5% Cobalt10.5% Cobalt 14.5% CobaltLinear (10.5% Cobalt) Linear (6% Co)Linear (8.5% Cobalt) Linear (14.5% Cobalt)

Fig. 5. (a) Hardness and (b) fracture toughness as functions of WC grain sizes.

800

1200

1600

2000

0.00 0.50 1.00 1.50 2.00 2.50

MFP (µm)

Vick

ers

hard

ness

, Hv

(Kg/

mm

2 )

5.00

7.00

9.00

11.00

13.00

15.00

17.00

19.00

21.00

0.00 0.50 1.00 1.50 2.00 2.50

MFP (µm)

Frac

ture

toug

hnes

s, K

Ic (K

g.m

1/2 )

2000

2500

3000

3500

4000

4500

5000

0.00 0.50 1.00 1.50 2.00 2.50

MFP (µm)

TRS

(MPa

)

(a) (b)

(c)

Fig. 6. (a) Hardness, (b) fracture toughness, and (c) TRS as functions of the MFP.


however, is to explore the relationship of TRS with

intrinsic mechanical properties including Hv and KIc,,

which is presented as follows.

3.2. Dependence of TRS on fracture toughness and

hardness

Fig. 7(a) and (b) shows the dependence of TRS on Hv

and KIc respectively. It is found that when

Hv < 1500 kg/mm2 TRS increases vs. hardness when

hardness is relatively lower; and it decreases vs. hardness

when hardness is relatively higher. Within this hardness

range, i.e. 900 < Hv < 1500 kg/mm2, TRS reaches a

peak value at Hv values between 1250 and 1300 kg/

mm2. Fig. 7(b) shows that the trend line of TRS vs.KIc is similar to TRS vs. Hv except for that it is in the

reverse direction of changes of hardness. This can be

understood based on the fact that the hardness and frac-

ture toughness is inversely related to each other as

shown in Fig. 8.

2800

3200

3600

4000

4400

800 1000 1200 1400 1600 1800

Hardness, Hv (kg/mm2)

TRS

(MPa

)

(a)

(b)

2800

3200

3600

4000

4400

8.00 10.00 12.00 14.00 16.00 18.00 20.00

Fracture toughness, KIc (MPa.m 1/2)

TRS

(MPa

)

Fig. 7. Correlations between TRS and (a) hardness and (b) fracture

toughness.

8.00

12.00

16.00

20.00

800 1000 1200 1400 1600 1800

Hardness, Hv (kg/mm2)

Frac

ture

toug

hnes

s, K

Ic

(MPa

.m1/

2 )

Fig. 8. Relationship between the hardness and fracture toughness.

2800

3200

3600

4000

4400

800 1000 1200 1400 1600

Hardness, Hv (Kg/mm2)

TRS

(MPa

)

Fig. 9. Correlations between TRS and hardness within 800 < Hv

< 1500 kg/mm2.


It is noted that when Hv > 1500, unfortunately, TRS

are rather scattered with relatively large standard devia-tions (>15%) and no certain trend can be deducted. TRS

of some of the samples with submicron size grains

reached values as high as 4200 MPa. The scatter of the

data of these samples is attributed to their uncertain

qualities with respect to porosities and specimen surface

preparations. These data in the very high hardness range

are therefore not included in the following analysis since

this paper focuses on the correlation of TRS with intrin-sic mechanical properties for which it is essential that the

effects of porosities and other possible defects from sam-

ple preparations are negligible.

Fig. 9 re-plots TRS vs. Hv when Hv < 1500 kg/mm2

with a trend-line imposed. Two key points can be de-

rived from the results in Figs. 7 and 9. First, Fig. 7(b)

demonstrates that although TRS and KIc are related,

the relationship is not a linear one-to-one correlation

which would suggest that one may use TRS as a mea-

sure of the fracture toughness. Contrary to that, the

Fig. 7(b) suggests that TRS is not equivalent to KIc.

Although it is understandable in layman�s terms that ifTRS is high, the material must be ‘‘tough’’, it could be

misleading for materials engineers to assume a higher

TRS would mean high fracture toughness.

Secondly, a new correlation is observed between TRS

and Hv within the range of 900 < Hv < 1500. This cor-

relation is clearly different from that of the Fig. 1. This

new correlation suggests that TRS is determined by the

hardness and fracture toughness of the material. Inother words, it measures a mechanical property that re-

flects combined effects of the hardness and fracture

toughness of the material. Considering that the trans-

verse rupture strength test is a three-point bending test

and a specimen fails under a critical tensile stress on

its surface, the dependence of its value on hardness is

logical. Its relation to the fracture toughness, which

has long been considered the factor that determinesTRS, should also be considered in the context of a flow

stress that is required to propagate a crack after the

crack is initiated. TRS is the maximum stress that is

encountered during a test.

It is noted here that the correlation as shown in Fig. 9

is absent in Fig. 2. As mentioned earlier, the cloudiness

of the data in Fig. 2 may be attributed to either no rela-

tionship between TRS and Hv or were strongly effectedby defect levels because they were collected before the

wide spread use of sinter-HIP technology. In light of

the correlation shown in Fig. 9, the latter is more likely

the case.

It should also be noted that the correlation in Fig. 9 is

rather qualitative than definitive. The effects of micro-

structure are embedded. In other words, for a same

hardness value, different microstructure characteristicsmay have contributed to the variations of TRS values.

However, it appears that the effects of hardness on

TRS is more dominant than that of the microstructure


provided the hardness is held constant for different

microstructures. In reality, the TRS vs. Hv correlation

line in Fig. 9 could be a band that defines a range of

TRS values for each given hardness value. However,

the general trend should still hold based on the data of

this study. Further work is needed to define the rangesof the band.

Fig. 10. Schematic illustrations of the relationships between ry,(reff.b � rb)(1 � CVw) and TRS vs. hardness respectively.

4. Discussion

The most significant result of this study is the corre-

lation between TRS and Hv as illustrated in Fig. 9.

TRS increases with hardness when Hv < 1200 kg/mm2,maximizes at Hv values of approximately 1300 kg/

mm2, and decreases with hardness when 1300 <

Hv < 1500 kg/mm2. This result challenges the conven-

tional view that TRS decreases as hardness increases

as illustrated by Fig. 1. This new relationship can be

understood by a qualitative model based on the work

hardening and flow stress of the cobalt phase.

As stated earlier, TRS is the tensile stress at which asample fails during a three-point bending test. It is

essentially a ‘‘tensile strength’’ property that should be

proportional to the tensile strength of the material. Dur-

ing an actual three-point bending test, a specimen would

experience plastic deformation, crack initiation, and

crack growth processes before fracture, even though

the plastic deformation of WC–Co is usually small and

difficult to detect when cobalt content is very low.Therefore, TRS is defined as the maximum flow stress

during the deformation, crack initiation, and crack

propagation processes before the specimen fractures.

Yield strength of WC–Co composite can be given by

the rule of mixture as

ry ¼ rbð1� CV wÞ þ rwCV w ð1Þwhere rb and rw are the in situ yield stress of Co and

WC respectively. Vw is volume fraction of WC. C isthe contiguity of WC grains defined by C ¼ Swc=wc

Swc=wcþSwc=co,

where Swc/wc and Swc/co are surface areas of WC–WCand WC–Co contacts respectively. C approaches the

maximum value of 1 when there is minimum amount

of cobalt binder phase and the minimum value of zero

if all WC grains are separated within the cobalt matrix.

In any conventional WC–Co composites, the dimen-

sion of cobalt phase between WC grains, which is mea-

sured by the mean free path (MFP), is in the order of

less than 2–3 l. The cobalt phase is constrained betweenthe WC grains. The plastic behavior of the cobalt phase

is thus significantly different from its bulk properties.

Specifically, the cobalt phase under such constraint is ex-

pected to work harden rapidly and exhibit much higher

flow stress than it would have been otherwise. Based on

these considerations, the flow stress by the rule of mix-

ture can be given as

r ¼ reff :b 1� CV wð Þ þ rwCV w ð2Þwhere reff.b is the effective flow stress of binder. Work

hardening of the composite is then

r� ry ¼ ðreff :b � rbÞ 1� CV wð Þ ð3Þor

r ¼ ry þ ðreff :b � rbÞ 1� CV wð Þ ð4ÞIn Eq. (3), the first term (reff.b � rb) represent the

work hardening of the binder phase under the constraint

conditions. The second term, (1 � CVw), represent

microstructure parameters, which is the effective volumefraction of cobalt phase taking into account the effects

of contiguity of WC grains. (1 � CVw) approaches zero

if the cobalt content becomes extremely low.

Eq. (4) shows that the overall flow stress is the sum of

the initial tensile yield strength of the material and the

contributions of work hardening. To understand the

relationship between TRS and Hv as depicted in Fig.

6, we examine the changes of ry and the work hardeningterm as functions of Hv respectively.

First, the hardness of the composite is proportional

to ry, Hv = 3ry [20]. Therefore, ry always contributes

to the continued increase of the overall flow stress as

hardness increases as shown schematically in Fig. 10.

But, the relationship between Hv and the second term

in Eq. (4) is dependent on two separate factors: the work

hardening of the binder and the microstructure. Since(reff.b � rb) measures the work hardening of the binder

which is independent of the cobalt content or the overall

hardness of the composite, it is reasonable to assume

that (reff.b � rb) term varies little when hardness in-

creases. The microstructure term 1 � CVw, though, is

a function of the cobalt content. Specifically, 1 � CVw

decrease dramatically when cobalt content is very low

as shown in Fig. 11. The contiguity, C, is calculatedemploying an empirical equation that can be obtained

by fitting experimental data from literature [5]

0.0

0.2

0.4

0.6

0.8

1.0

0.000.050.100.150.200.250.300.35

cobalt content by weight

(1-C

Vw)

Fig. 11. The effective volume fraction of cobalt binder (1 � CVw) as

the function of the cobalt content.


C ¼ 1:03 exp �5fð Þ ð5Þwhere f is the volume fraction of cobalt phase.

Since the hardness is inversely proportional to the

cobalt content, the relationship between the term

(reff.b � rb)(1 � CVw) and hardness may be schemati-

cally shown as in Fig. 10. Now considering that the

overall flow stress and TRS is the sum of the two terms,

TRS as a function of the hardness is the sum of the two

lines for ry and (reff.b � rb)(1 � CVw) respectively inFig. 10, which determines that TRS has a peak value

as a function of the hardness. At lower hardness ranges

(Hv < 1300), the sum of the two terms increases with

hardness, while at higher hardness range (1300–1500),

it decreases.

This model does not explain the data at Hv >

1500 kg/mm2. As it was pointed earlier, the data ob-

tained during this study within this hardness range istoo scattered to enable reliable analysis. Further work

is needed to produce consistent data and analysis.

But if we view the fracture process during TRS test-

ing as consisting of crack initiation and propagation

processes and assume the ideal case when the effects of

porosity is negligible, the crack initiation process will

dominates when the hardness is very high and the frac-

ture toughness is very low. Therefore the higher thehardness is, the higher the stress that is needed for crack

initiation and hence the higher the TRS.

5. Summary

The data and analysis of the present work demon-

strate that the transverse rupture strength of WC–Cocomposites is directly related to intrinsic mechanical

properties, namely hardness and fracture toughness,

when the effects of porosity are negligible. TRS should

not be used as a fracture toughness measure. The rela-

tionship between TRS and hardness is also not unidirec-

tional, rather it is complex. Within a range of

800 < Hv < 1500, TRS appears to first increase and then

decrease as the hardness increases. It reaches a peak

value at approximately Hv � 1300 kg/mm2. When hard-

ness is greater than 1500 kg/mm2, TRS values could

reach very high values, but the variations of TRS are

also high in the high hardness range. The dependence

of TRS on cobalt content, grain sizes, and other micro-structure parameters is embedded in its relation to the

hardness and fracture toughness.

Acknowledgements

The author acknowledges that this paper is partially

based on a poster presentation at Euro PM96. Theauthor is also grateful for many constructive comments

and suggestions made by Professor Silvana Luyckx and

Dr. Brian Roebuck. Several changes were made to the

original manuscript based on their view points.

References

[1] Gurland J. The fracture strength of sintered tungsten carbide–

cobalt alloys in relation to composition and particle spacing.

Trans Metall Soc AIME 1963;227:1146–50.

[2] Exner HE, Gurland J. A review of parameters influencing some

mechanical properties of tungsten carbide–cobalt alloys. Powder

Metall 1970;13:13–31.

[3] Gurland J, Bardzil P. Relations of strength, composition, and

grain size of sintered WC–Co alloys. Transactions AIME, J

Metals 1955:311–5.

[4] Chatfield C. Comments on microstructure and the transverse

rupture strength of cemented carbides. Int J Refrac Metals Hard

Mater 1985;4(1):60.

[5] Fischmeister HF. Development and present status of the science

and technology of hard materials. In: Viswanadham RK, Rowc-

liffe, DJ, Gurland J, editors. Science of Hard Materials. Proceed-

ings of international conference on science of hard materials,

August 1981. New York: Plenum. p. 1–42.

[6] Exner HE, Walter A, Pabst R. Fault distributions in brittle

materials. Mater Sci Engng 1974;16(3):231–8.

[7] Roebuck B. A model for the limiting strength of hardmetals.

J Hard Mater 1995;6:1–15.

[8] Almond EA. Deformation characteristics and mechanical prop-

erties of hardmetals. In: Viswanadham RK, Rowcliffe, DJ,

Gurland J, editors. Science of hard materials. Proceedings of

international conference on science of hard materials, August

1981. New York: Plenum. p. 517–61.

[9] Bonjour C, Stellram SA, Nyon S. New developments in cemented

carbide cutting tools. Wear 1980;62(1):83–122.

[10] Brookes KJA. World directory and handbook of hardmetals and

hard materials. UK: International Carbide Data; 1992.

[11] Roebuck B. The tensile strength of hardmetals. J Mater Sci

1979;14:2837–44.

[12] Roebuck B. Notched bend tests on WC–Co hardmetals. J Mater

Sci 1988;23:281–7.

[13] Roebuck B. Effect of testpiece geometry on the flexural strength of

representative hardmetals and cermets. In: Kneringer G, Rod-

hammer P, Wilhartitz P. Plansee AG, editors. Proceedings of the

14th Plansee Seminar, Reutte, vol. 2; 1997. p. 352–65.

[14] Fang Z, Eason JW. Nondestructive evaluation of WC–Co

composites using magnetic properties. The Int J Powder Metall

1993;29:259–65.


[15] Pickens JR. The fracture toughness of tungsten carbide–cobalt

Alloys as a function of microstructural parameters. Ph.D.

Dissertation. June 1977, Brown University.

[16] Laugier MT. A microstructural model for hardness in WC–Co

composites. Acta Metall 1985;33:2093–9.

[17] Sigl LS, Exner HE. Experimental study of mechanics of fracture

of WC–Co alloys. Metall Trans A 1987;18A(July):1299–308.

[18] Sigl LS, Fishmeister HF. On the fracture toughness of cemented

carbides. Acta Metall 1988;36:887–97.

[19] Ravichandra KS. Fracture toughness of two phase WC–Co

cermets. Acta Metall Mater 1994;42:143–50.

[20] Lee HC, Gurland J. On the hardness of cemented carbides. NSF

Hard Materials Research Workshop. June 1975, University of

Cincinnati.

58249834 hardness vs rupture

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