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Available online at www.sciencedirect.com

Wear 264 (2008) 770–774

Correlation between surface fatigue and microstructuraldefects of cemented carbides

Fjodor Sergejev ∗, Irina Preis 1, Jakob Kubarsepp 2, Maksim Antonov 3

Department of Materials Engineering, Tallinn University of Technology, Ehitajate tee 5, 19086 Tallinn, Estonia

Accepted 13 February 2007Available online 15 June 2007

bstract

The main aim of the present theoretical work is to determine numerical dependence between the geometrical parameter of maximum area oftructural defect

√areamax (proposed by Y. Murakami, 1983) and surface fatigue of cemented carbides. The proposed relations allow making pre-

ictions of surface fatigue properties of cemented carbides (WC-Co hardmetals—with 10 wt% Co and 15 wt% Co binder; TiC-based cermets—with2 wt% Fe/8 wt% Ni and 16 wt% Fe/14 wt% Ni binder) in conditions of sliding, rolling contact and impact cycling loading.

Pores are considered being equivalent to small defects. Three comparative defects conditions are distinguished: surface pores, pores just belowree surface and interior pores. The Vickers hardness of the binder (as mainly responsible for the fracture mechanism of hardmetals and cermets,

ue to porosity) is presumed to be the basis of such an assumption.

The estimate of this prediction has been done by analyzing the pore sizes using the statistics of extremes. The lower limit of fatigue strength andurface fatigue life can be correctly predicted by estimating the maximum occurring pore size in a critical material volume.

2007 Elsevier B.V. All rights reserved.

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eywords: Cermets; Hardmetals; Surface fatigue; Murakami model

. Introduction

Surface cracks and defects, which are most likely to be foundn many structures in service such as pressure vessels, pipelineystems, off-shore structures and aircraft components, have beenecognized as a major origin of potential failure for such compo-ents. The study of fatigue crack propagation from such defectsas been an important subject during recent decades.

Powder metallurgy materials such as hardmetals and cermets

re most widely used as tool materials in machining and formingpplications. These materials are best known for their excellenttrength-wear resistance combination. Wear resistant cementedarbides tend to contain inward and superficial natural structural

∗ Corresponding author. Tel.: +372 620 3355; fax: +372 620 3196.E-mail addresses: fjodor.sergejev@ttu.ee (F. Sergejev), ipreis@ttu.ee

I. Preis), Jakob.Kubarsepp@ttu.ee (J. Kubarsepp), Maksim.Antonov@ttu.eeM. Antonov).1 Tel.: +372 620 33 55; fax: +372 620 31 96.2 Tel.: +372 620 20 07; fax: +372 620 31 96.3 Tel.: +372 620 33 58; fax: +372 620 31 96.

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pp

043-1648/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.wear.2007.02.024

efects, pores, non-metallic inclusions or inhomogenities, etc.heir existence is crucial for most mechanical properties andaterial selection, and unfortunately cannot be totally excluded

y current technologies.Based on the experimental fact that the crack shape of propa-

ating surface cracks in a plate under cyclic tension, bending orombined loading is approximately semi-elliptical, a theoreticalodel with two degrees of freedom is proposed for prediction of

he fatigue crack growth [1,2]. This model permits to conjecturehe size and location of the surface and subsurface cracks thatccur during cyclic loading.

Present work is based on these assumptions and aimed atinking the geometrical parameter of maximum area of struc-ural defect

√areamax (proposed by Y. Murakami, 1983) [3],

nd surface fatigue parameters for cemented carbides. Hertzianontact theory and Palmqvist model for indentation surfaceracks were applied for numerical evaluation of subsurfacerack location (depth) and number of impact cycles to failure

Nf, fatigue life).

The proposed equations are hypothetical and have not beenroved experimentally so far, but are based on the previouslyublished studies on steels, ceramic materials and glasses [4–7].

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F. Sergejev et al. / W

. Theoretical backgrounds

Contact between two solid bodies under cyclic stressing andolling with impacts is described with Hertzian theory of fractureechanics. This method can be used for evaluations of sur-

ace residual stress levels in brittle materials like WC-Co andiC-Fe/Ni also. This gave an idea to combine Hertzian contactpproach with the Palmqvist indentation theory. As a result webtained a computational technique for surface crack geometryvaluation and surface fatigue life prediction for heterogeneousaterials, containing hard phases (WC, TiC).The Murakami approach for microstructure analysis with a

roposed geometrical parameter of maximum area of structuralefect

√areamax and extreme value statistics were incorporated

o make the prediction more precise and correct. This method cane used for prediction of fracture toughness also. No additionalatigue or other tests are required.

.1. Fracture by Hertzian contact (indentation)

The problems of contact between two non-conforming bodiesith circular shape (rolling bearings, gears, wheel-on-rail, etc.)ere first solved by Hertz and generally referred to as Hertzian

ontacts [8]. One of the uses of Hertzian indentation is to deter-ine number and sizes of surface flaws. Here we consider the

urface with large number of small cracks then the stress fieldround contact area (in our case indentation) will encompass aarge number of ring cracks, outside the contact path, of radius,see Fig. 1. Then d can be found as [5]

=(

3PR

4E∗

)1/3

, (1)

here P is the load on the indenter, R the indenter radius and E*

s the equivalent Young’s modulus.As we know ν1, ν2 and E1, E2 are the Poisson’s and Young’s

oduli for the indenter and substrate, respectively, then E* can

e determine from

1

E∗ = 1 − ν21

E1+ 1 − ν2

2

E2. (2)

Fig. 1. EHD contact pressure distribution [9,10].

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64 (2008) 770–774 771

hen the maximum pressure under the contact pmax is [5]

max = 3P

2πd2 =(

3

2π

)(P)1/3

(4E∗

3R

)2/3

. (3)

n the other hand, the mean contact pressure pmean during thempact of an indenter in the Hertzian region [8] is equal to

mean = FN

πc2 , (4)

here FN is the maximum normal force and c is the maxi-al scar that corresponds to the elastic and plastic deformation

c = cel + cpl) [6].This is the normal condition for mechanical elements (gears,

earings) when the contacting surfaces are separated by a thinubricant film (Elastohydrodynamic lubrication:EHD or EHL).

.2. Fatigue life prediction

Fatigue limit was defined by Murakami as the threshold stressor crack propagation and not the critical stress for crack initia-ion [3].

This leads to the fact that cracks/defects are present in theicrostructure of the hardmetals or cermets. Several relation-

hips are available for prediction of the lower bound of scatterf fatigue limit (σf) and fracture toughness (KIc) which are basedn the Vickers hardness (HV) and maximum inclusion areageometrical parameter of maximum area of structural defect

areamax) and uniform tensile/compressive stress (σ0) values:

σf=1.43HV+120(√

area)1/6 , ΔKth=1.43(HV+120)

(√area

)1/3,

KIc = 0.5σ0

√π√

area. (5)

hese equations are proposed for surface defects. For otherefects, just below surface and interior defect, the coefficient.43 must be replaced by 1.41 and 1.56 correspondently [3].

Then for surface defects with previously evaluated Murakamiarameter

√areamax (defect size) [3] and fatigue limit lower

ound (σf) values [11,12]. It is possible to find the total accu-ulated energy Ei in the material as a function of the number of

mpact cycles, calculated from

i=3σfπR3

[2

3−

( c

R

)2√

1 −( c

R

)2+2

3

(1− c

R

)2]

, (6)

he strain energy release rate (G) for the propagation of therack with given parameters to the controlled dimensions cane found from

Ic =√

E × G

2 . (7)

1 − ν

inally, the surface fatigue life Nfs (number of impact cycles toailure) can be predicted by extracting the strain energy releaseate G from the total accumulated energy Ei, while the fracture

772 F. Sergejev et al. / Wear 264 (2008) 770–774

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Fig. 2. Geometry for elliptic-crack models [13].

f surface is in the elasto-plastic deformation regime

fs = Ei

G. (8)

rediction of number of cycles to failure in the cyclic impactegime gives us the practical knowledge (critical in materialelection in conditions of rolling contact and impact cyclic load-ng) about material surface behavior at prescribed conditions.

.3. Indentation crack geometry

Fracture toughness analyses for brittle materials generallyssume that indentation precracks have the classic half-pennynd radial/median geometries. However, there is no compellingvidence that this is universal. Serial sectioning of indentationracks often reveals a surface-localized, Palmqvist crack geom-try [7,13].

Fig. 2 shows a schematic of the radial/median and Palmqvistrack limiting geometries, which were produced by Vickersndentation.

The subsurface lateral cracks are orthogonal to the radial andalmqvist cracks and can intersect them. Usually two lateralracks can be observed—primary and secondary (in the case oflasses and ceramics, see Fig. 3) [13].

wta

ig. 3. The schematic representation of the shapes for subsurface indentation cracks

ig. 4. Schematical drawing showing the evaluation of surface and subsurfacerack configuration development with time [7].

Secondary lateral cracks cannot be taken into consideration.he primary lateral cracks are the only ones that can cause crit-

cal damage of the surface. Their propagation gives way forurface fatigue debris formation. The mechanism of such fail-re is schematically shown in Fig. 4. This situation is generalor rolling contacts. Crack openings at early (D1) and later (D2)tages of crack propagation are indicated.

The increase of number of fatigue cycles as compared to crackrowth depths has shown that indentation cracks not only changeheir geometries (preserving their elliptical behavior), but alsoend to grow into the substrate material, increasing radically14].

In the further investigation we assume that cracks propagaterom surface and subsurface defects, and are elliptical.

. Results and discussion

Specimens used for application of Murakami approach

ere produced through conventional press and sinter powder

echnology, according to ASTM B406. The main structural char-cteristics and mechanical properties are given in Table 1.

for different indentation loads (1, 2, 3, 4,. . ., n, are the test number) [13].

F. Sergejev et al. / Wear 264 (2008) 770–774 773

Table 1Chemical composition and mechanical properties (Vickers hardness HV, transverse rupture strength RTZ, Young’s modulus E, Poisson’s ratio ν) of cemented carbides

No. Grade Carbide (wt%) Binder (wt%) Binder composition structure HV (GPa) RTZ (GPa) E (GPa) ν

1 H10 90 10 Co (W) 1.31 2.2 540 0.232 H15 85 15 Co (W) 1.13 2.9 600 0.233 T70/14 70 30 Fe + 14Ni austenite 1.27 2.4 410 0.234 T60/8 60 40 Fe + 8Ni martensite-bainite 1.11 2.3 395 0.22

Table 2Calculated surface fatigue life results and employed parameters of cemented carbides

No Grade Total accumulated energy, Ei (J) Surface fatigue life, Nfs cycles Maximum pressure pmax (N/mm2) Mean pressure pmean (N/mm2)

1 H10 27,093 1.069 × 107 26.79 11.942 H15 35,636 1.291 × 107 21.92 12.053 26.00 11.074 22.33 10.04

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T70/14 27,085 7.063 × 106

T60/8 28,269 8.089 × 106

All materials were produced at the Powder Metallurgy Lab-ratory of Tallinn University of Technology.

.1. Computation of surface fatigue life

According to the evaluation method described in Section 2.2nd taking into consideration results of the Murakami modelpplication for the same materials for prediction of the lowerimit of the fatigue strength it can be proposed that the surfaceatigue life of WC-hardmetals and TiC-Fe/Ni cermets can bequated as

fs = EEi

0.25(1 − ν2)σ20

√π√

area. (9)

alculated results for the studied materials are given in Table 2.he radius of indenter R is equal to 10 mm, and indentation loadis 10 N for every material. The surface fatigue life means that

t the given loads, with an indenter of given radius, crack prop-gation up to the maximum size (critical size) for wear debrisormation will be achieved after the predicted number of cycles.

The combination of knowledge about surface fatigue crackrowth and debris formation will allow prediction of the serviceife of hardmetals and cermets in conditions of cyclic loading andolling contact, like in metal forming and blanking applications.

.2. Surface fatigue crack geometry

The predicted crack profile almost perfectly overlaps with aemi-ellipse crack shape (see Fig. 5), as it was shown by Linnd Smith [1,2,14]. For all four materials we got very similarurface crack depths and geometries (c = 0.199–0.212 mm) foronditions described above.

That is why we assume that the primary lateral crack will beocated at almost the same depth, around 0.125–0.128 mm from

he contact surface. This prediction cannot be accurate if otherubsurface defects are present that are closer to the contact area.n case of “pure” conditions the depth of the crack has to beithin the prediction limits.

ig. 5. Comparison of typical semi-ellipse crack with predicted crack shapeH10).

As mentioned above, several lateral cracks can appear underyclic loading. This condition gives a reason to predict morehan two lateral cracks, but in this case the number of cracksill be dependent on the loading force.

. Conclusions

. A new numerical technique is developed for the predictionof surface fatigue properties of cemented carbides. The pro-posed equation for evaluation of the surface fatigue life Nfwhich correlates with geometrical parameter of maximumarea of structural defect

√area, is in the agreement with

previously reported results.. This numerical technique can be used for cemented carbides

for prediction of the surface fatigue life and crack geometry.. The proposed method does not need additional fatigue tests.

Only few mechanical properties and structure parametersmust be known.

. To obtain correct and reliable results: loading force (F),indenter radius (R), mechanical properties (E, ν, HV), geom-etry of contacting parts and the size of structural defects(pores) must be taken into consideration.

. Unfortunately, this method is not yet proved by experiments,

but is based on surface fatigue observations and studies ofWC-Co, ceramic and glass, described in literature. Thesematerials behave very similar to cermets, as they are verybrittle.

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74 F. Sergejev et al. / W

cknowledgments

This work was supported by The Estonian Ministry of Sci-nce and Education and The Estonian Science Foundation grant-505.

eferences

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