A STUDY ON PDC DRILL BITS QUALITY

M. Yahiaouia,1, L. Gerbaudb, J-Y. Parisa, K. Delba, J. Denapea, A. Dourfayec

Abstract

The quality of innovating PDC bits materials needs to be determined with accuracy by measuring cuttingefficiency and wear rate, both related to the overall mechanical properties. Therefore, a lathe-type test devicewas used to abrade specific samples. Post-experiment analyzes are based on models establishing coupledrelations between cutting and friction stresses related to the drag bits excavation mechanism. These modelsare implemented in order to evaluate cutting efficiency and to estimate wear of the diamond insert. Fromhere, an original approach is developed to encompass cutting efficiency and wear contribution to the overallsample quality toward abrasion. Four main properties of PDC material were used to define quality factor:cobalt content in samples that characterizes hardness/fracture toughness compromise, other undesired phaseas tungsten carbide weakening diamond structure, diamond grains sizes and residual stresses distributionaffecting abrasion resistance.

Keywords: Drill bit, PDC cutters, wear rate, cutting efficiency, quality factor, XRD, tungsten carbide,cobalt, cobalt carbide, residual stresses.

1. Introduction

The main tools employed in the drilling industry are roller cone and drag bits. Roller cone bits work byimpact excavation and are currently used in hard rock formations because of a convenient wear resistance.Drag bits rather operate by shear mode in softer rock to medium hard formations. Nevertheless, they sufferfrom thermal abrasive wear and impact damage while drilling interbedded formations. As excavation rate isdirectly related to the overall cost, the drag bits using PDC (Polycrystalline Diamond Compact) cutters arereally attractive compared to roller cone bits. In fact, PDC bits could drill twice faster and longer than rollerbits even in hard formations [1]. Petroleum and hydrothermal investigations in deep geological formationslead to manufacturing new bits materials able to drill at higher temperature, in more abrasive and hardergeological fields. Such innovating materials, sintering processes and design, recently developed to improvedrill bits hardness and fracture toughness, also require new strategies in quality measurement. According tothe abrasive destructive mode of drag bits, quality can be defined by two main parameters: materials wearrate and excavation performance. Wear rate calculus by Archards model has been commonly used in severalworks to describe PDC/rock behavior [2]. Cutting efficiency evolution is closely linked to wear flat formationduring friction and it is initially determined by the sample depth of cut. The aim of this paper is to proposean objective quality criterion to clearly classify PDC cutters by considering drilling mechanisms and materialanalysis.

1Corresponding author. Ecole Nationale dIngnieurs de Tarbes,Adress: 47 avenue dAzereix 65016 Tarbes, France.Tel.: +33 5624 42700; fax: +33 5624 42708.E-mail address: malik.yahiaoui@enit.fr (M. Yahiaoui).

Preprint submitted to Elsevier March 19, 2012

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Author manuscript, published in "Wear 298-299 (2013) 32-41"

Nomenclature Back rake angle, deg Intrinsic specific energy, J m3 Cutting efficiency Friction coefficientx Cobalt mass content at distance x Cutting coefficientAc Cross-sectional area of cut, m2Af Wear flat area, m2D Diffusion coefficient, m2 s1E Specific energy, J m3F c Cutting stress component, NF f Friction stress component, NFN Total normal force, NF 0N Initial stress value, NFT Total drag force, NG Grinding ratioI Sum of maximum peak of all present phasesICoCx XRD maximum peak intensity of cobalt carbide phaseIdiamond XRD maximum peak intensity of diamond phaseIWC XRD maximum peak intensity of tungsten carbide phasek Wear rate, mm3 N1 m1L Excavation distance, mLT Excavation distance, mQ Quality factorR2 Coefficient of determinationt Time of diffusion, su Cutting capacity, mVC Cutter worn volume, m3VR Cut rock volume, m3Wm Cutter mechanical work, Jxi Diffusion transition position, mm

2. PDC samples

Six cutters coming from various manufacturers (referred from A to F) were selected to represent a largerange of physical properties. Cutters are made of a tungsten carbide cylinder surmounted by a diamond table(Fig. 1a). Material parts have a diameter of 13mm: the tungsten carbide cylinder has a height of 8mm andthe diamond layer is around 2mm thick. The diamond layer has a chamfer of 45 0.4mm or 45 0.7mmfor sample C. These cutters have been sintered by HPHT (i.e. High Temperature and High Pressure) at atemperature over 1400 C under a pressure near 5.5GPa (Fig. 1b) [3].

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(a)

Diamond powder

WC-Co

6 to 18%wt Co

HPHT sintering

over 1400 C and 5.5 GPa

Cobalt di"usion

Co

2 to 8%wt Co

Manufacturing Process

Chamfer

Acid dissolution

of cobalt phase

over 100 m

Interface

design

(b)

Figure 1: PDC cutter: (a) photography of a cutter; (b) manufacturing process of a cutter.

Tungsten carbide prismatic grains in a binder cobalt phase form the substrate part (Fig. 2a). The meangrain size of tungsten carbide is around 2m with minimum and maximum values observable under a micronand over 10 m (Tab. 1). SEM observations reveal aggregates of micro-metric diamond grains also surroundedby cobalt (Fig. 2b). Samples A, E and F have been exposed to a chemical post-treatment called leachingprocess [4]. This treatment removes interstitial cobalt grain boundaries on the diamond layer beyond severaltens of microns (Fig. 2c).

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(a) (b)

(c)

Figure 2: SEM images at 15 kV: (a) sample B tungsten carbide-cobalt part by secondary electron analysis;(b) sample B diamond part by backscattered electron analysis; (c) illustration by secondary electron andcolorized energy dispersive X-ray spectrometry (EDX) cartography of cobalt leaching for sample F.

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Table 1: Geometry and microstructural properties of PDC samples A to F measured by SEM image analysis.

PDCsamples A B C D E F

Transversalview

8.36.2mm

Sidediamondthickness

(mm0.05)2.1 1.3 1.6 2.1 1.7 1.8

Diamondmean

aggregatesize (m)

13.3 3.9min < 4.5max > 21.8

15.1 5.8min < 7.2max > 29.9

9.8 4.8min < 3.1max > 23.8

8.1 5.1min < 2.3max > 20.5

11.6 4.6min < 3.2max > 21.4

11.0 5.0min < 3.4max > 22.4

WC-Comean grainsize (m)

2.5 1.1min < 0.8max > 5.7

1.9 1.7min < 0.3max > 9.8

2.0 1.3min < 0.5max > 8.3

1.4 1.1min < 0.4max > 9.1

1.7 1.0min < 0.5max > 6.2

2.2 1.1min < 0.3max > 7.0

Leachingdepth (m) 70 4 / / / 100* 325 30

* not measured, manufacturer data.

The cobalt content in the diamond part comes from the migration of the metal during sintering. Com-monly, cobalt proportion can represent 6 to 18wt.% in tungsten carbide substrate and 2 to 8wt.% in thediamond part. The cobalt distribution in samples follows a distribution law that can be expressed as asolution [5] of differential equations from Ficks diffusion laws (Eq. 1).

(x) = (0 10)erfc

[1

2Dt (x xi)

]erfc

[ 1

2Dtxi

] + 10 (1)In this equation, (x) represents axial cobalt mass content from diamond face (where(x) = 0 ) to the

bottom of a sample in tungsten carbide part (where (x) = 10). D is the diffusion coefficient, t is the timeof diffusion and xi expresses diffusion transition position between PDC and WC-Co materials. This diffusiondistribution has been observed on all samples (Fig. 3) thanks to energy dispersive X-ray spectrometry(EDX) analyzes with Bruker XFlash 4010 detector. To perform semi-quantitative measurements, the detectorwas calibrated with an adhesive copper placed near samples before each observation campaign. For thesemeasurements, the seven samples have been longitudinally cut by electroerosion, polished and metalized withpalladium. The Jeol JSM-7000F field emission scanning electron microscope (SEM) was adjusted at 15 kVwith a working distance of 15mm. The electron beam intensity was set around 100 counts per second toenable a high speed analysis. The cobalt mass content distribution was evaluated along a line on sectionswith a resolution of 500 m.

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PD

C p

art

WC

-Co

pa

rt

(x)

Figure 3: EDX longitudinal measurement of cobalt content from diamond to tungsten carbide material forsample B.

EDX characterizations showed that all samples have similar cobalt content (0) around 3wt.% in thediamond material (Table 2). Whereas cobalt content of tungsten carbide (10) part can vary from 8 to17wt.%. The square root of D t is linked to sigmoidal cobalt content evolution. It permits to evaluatedispersion of the diffusion transition and metal ability to spread from tungsten carbide to diamond. Thediffusion coefficient of cobalt depends on diamond/WC grains size and on sintering temperature. At sinteringtemperatures, molten cobalt moves by capillarity through voids between diamond grains and with larger voids,which are directly associated with larger grain size, displacement of cobalt is favored [6]. Moreover, metalinfiltration in diamond structures increases with temperature as viscosity of molten cobalt decreases.

Table 2: Cobalt mean content and diffusion parameters obtained by EDX profiles analyzes for samples A toG (measurements of cobalt content exclude leached fields).

PDCsamples A B C D E F

DiamondEDXmean

wt.% Co

2.9 0.3 2.9 0.8 2.7 0.4 3.5 0.4 3.4 0.2 3.2 0.2

WC-CoEDXmean

wt.% Co

8.2 0.2 16.7 0.2 9.8 0.2 11.2 0.2 9.6 0.1 7.7 0.1

D t

(mm)0.2 0.2 0.8 0.1 0.5 0.1 0.1 0.1 0.3 0.1 0.1 0.1

xi (mm) 3.0 0.1 3.3 0.2 2.7 0.1 2.4 0.1 2.6 0.1 2.8 0.1

Considering that diffusion time t is almost equal between samples,D t parameter permits to qualita-

tively evaluate diamond grains sizes instead of aggregates ones. Here, B and C displays values ofD t more

than two times higher than that of samples A, D, E and F. Theses results may be due to higher diamondgrains sizes in sample B and C than in the others.

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3. Experimental study

A vertical lathe-type device was used to simulate drilling conditions. Cutters brazed on sample holderswere adjusted downward on the lathe shaft. Ring-stone counter-faces were made of a manufactured mortarrock (1m in external diameter, 0.5m in internal diameter and 0.6m thick with a density of kg m3). Thismortar ensures homogeneous chemical composition (silica content of wt.%.) and mechanical properties(compressive strength of MPa and young modulus of GPa). Experiments were carried out according toreal drilling conditions (Fig. 4a): normal load ranged from 3000 to 5000N, back rake angle at 15, penetrationdepth of 2mm and mean cutting speed of 1.8m s1. Tests were conducted in atmospheric environment andno lubricant was added into the contact.

Sample holder

WC-Co

FN

FT

excavation

Wear !at area : Af

Cutting active area : Ac

Back rake angle :

PDC

(a)

Fc

Ac

FcN

FcT

(b)

Ff

Af

FfN

FfT

(c)

Figure 4: Schematics of cutter/rock interactions: (a) overall cutter disposition; (b) cutting components; (c)friction components.

In order to produce significant wear on samples, each test needed several mortar rings. Experiments wereperformed following four sequences for each mortar ring and each sequence represents three radial round-trips (i.e. an excavation length about 510m). As a consequence, one mortar ring works for a total lengthof 2040m. Seven of them were required to cover an experimental drilling process of 12 580m. At the end ofeach sequence, the height of material lost was measured to calculate cutting active area Ac and cutter wornvolume Vc.

4. Wear rate analysis

PDC drill bits are made of tens of cutters (e.g. VTD616 tools from Varel International have 48 facecutters). Operating parameters as weight and torque on bit, defined for a constant penetration speed, couldbe considered as independent of the number of bits [7]. This condition is assumed by a correct cuttersrepartition on the bit, which ensures a homogenized wear on every PDC [8]. Therefore, wear behavior anddrilling performance information based on single cutter experiments are relevant and can be extrapolated tounderstand the whole tool behavior. Afterward, Fairhurst and Lacabanne [9] assume that cutting action andsliding friction can also be considered as independent (Eq. 2) in the drilling procedure (Fig. 4b and Fig.4c). Thus, normal force FN applied onto a cutter can be expressed as the sum of friction normal force F fNand

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cutting normal force F cN . Moreover, an approximation of FfN can be expressed as the difference between

normal force applied to a cutter and initial value of the normal force, noted as F 0N:

FN = FfN + F

cN F fN + F 0N (2)

The same approach is assumed for the transverse force FT, so that (Eq. 3):

FT = FfT + F

cT F fT + F 0T (3)

Because this study is clearly a case of abrasive friction between cutter and hard rock, Archards model isan interesting choice. This model has been extensively involved in tribological studies because of its simplelinear relationship (Eq. 4) between wear volume Vc and the product of normal force by sliding distance L(Fig. 5a):

Vc = k F fNL k (FN F 0N

)L (4)

The coefficient of proportionality k is usually called wear rate and could be expressed as a function ofrock or cutter hardness, but only proportionality is considered here, and its meaning is not identified.

0.5

0.4

0.3

0.2

0.1

0.0

Wea

r vol

ume

(mm3

)

15x1061050Ffn L (N.m)

R2=98.4 %

(a)

160x10-9

120

80

40

0

Wea

r rat

e (m

m3N

m-1 )

A B C D E FPDC sample(b)

Figure 5: Wear rate evaluation: (a) Archards model applied to sample F; (b) wear rates results.

Wear rate calculus show that cutter A gives the best wear behavior with a rate value lower than 1 108mm3 N1 m1, while cutter B obtains the highest rate value over 16 108mm3 N1 m1.

5. Cutting capacity

Detournay and Defourny [10] established a linear relationship between torque on cutter (i.e. FT) andweight on cutter (i.e. FN). This equation involves three constant parameters , and which are respectivelythe intrinsic specific energy, the friction coefficient and the cutting coefficient (Eq. 5):

FT = FN +Ac(1 ) (5)Moreover, specific energy E represents the dissipated energy Em needed to cut a unitary volume of rock

VR. The energy Em equals the transverse force FT multiplied by the cutter travel distance L. The lateraldisplacement of the tool front face implies that dug volume VR equals the product of active area Ac bydistance L. As a consequence, FT and Ac measurements permit specific energy calculations (Eq. 6):

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E =EmVR

=FTAc

= FNAc

+ (1 ) (6)

The ratio between and E characterizes drilling process efficiency , which represents the cutting part inthe overall mechanical action. Eventually, a pure cutting process means that = 0 then E = E0 whereE0 is the initial value of E (Eq. 7):

=

E=E0E

(7)

For all cutters, experiments revealed that efficiency plotted as a function of distance L follows a de-creasing and nonlinear curve (Figure 6). When excavation test starts, efficiency is closed to 1 (new cutterfully efficient) and as expected, tends to 0 when the distance L becomes greater (mathematically infinite).The experimental cutting efficiency can reach values higher than 1, but these values are due to fluctuationsin rock homogeneity and transitory periods occurring before cutting process stabilization. Accordingly, anexponential law as a function of excavating distance seems adequate to empirically evaluate relative efficiencybehavior for each series of PDC samples. A constant coefficient u, expressed in meters, is introduced hereand is identified as cutting capacity (Eq. 8):

= exp

( 1u L)

(8)

1.2

1.1

1.0

0.9

0.8

0.7

0.6

Cutti

ng e

fficie

ncy

12x1031086420Distance (m)

(a)

20x103

18

16

14

12

Cutti

ng c

apac

ity (m

)

A B C D E FPDC sample(b)

Figure 6: Cutting efficiency analysis: (a) Cutting efficiency vs. distance model for sample F; (b) cuttingcapacity results.

The lowest value of cutting capacity u of 12 km was measured with B and the highest value around 20 kmwas obtained with A and F cutters.

6. Quality model

Obviously, separate analyzes of wear endurance and cutting efficiency do not clearly discriminate therelative quality of cutters. The grade assessment of PDC samples depends on its tribological behavior (i.e.friction and wear), cutting efficiency and rock cutting resistance (i.e. intrinsic specific energy). A low wearrate and a high cutting efficiency of the sample ensure a high quality cutter. In order to compare cutterperformances, a quality criterion must involve both wear rate and cutting efficiency . For that purpose, wefirst consider the grinding ratio G, which is the ratio between rock wear volume V R and cutter wear volume

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Vc. The grinding ratio is commonly used to estimate cutters resistance by abrasive wear. By combiningprevious equations, this ratio can be directly related to the parameters , , k and (Eq. 9):

G =V RVc

=AcL

k F fNL=

F cTkF fT

=F cT

k(FT F cT)=

k

(FTF 0T 1)1

=

k

(1

1)1

(9)

By introducing the experimental cutting capacity parameter u, the grinding ratio can be expressed asfollows (Eq. 10):

G =

k

[1

exp( 1u L) 1

]1=

k

[exp

(L

u

) 1]1

=

k

[L

u+

+n=2

(L

u

)n]1(10)

From here, it is interesting to define the quality factor Q, which is a dimensionless value integrating allvariations of cutting efficiencies over travel distance LT (Eq. 11). This distance should not overpass cuttingcapacity of the considered cutter (i.e. LT < u ). However, LT should be high enough to measure significantwear evolution on samples.

Q =

LT

u

k(11)

This definition of quality factor takes into account coefficients and and permits to normalize and tocompare different cutters when they meet variations in rock mechanical properties. Then, the ratio u on kexplains the compromise between cutting efficiency and wear rate in the quality formula. During experiments,rock inhomogeneities and contact variations can influence wear kinetic and affect performance appreciationof a cutter. Therefore, factor quality Q normalizes wear behavior with regard to dissipated energy duringthe cutting process. For that reason, it includes parameters previously met as , , LT, k and u (Tab. 3).

Table 3: Summary of mechanical results for sample A to F.

PDC k u QSamples (106 J m3) (109mm3 N1 m1) (km) (104)

A 0.261 0.007 24.9 0.8 9.6 0.6 19.6 0.6 169 5.4B 0.196 0.004 30.4 0.9 164.7 8.6 12.0 0.4 4 0.1C 0.218 0.005 30.0 0.8 62.0 3.7 13.4 0.4 12 0.4D 0.234 0.005 25.5 0.7 28.5 1.2 16.3 0.6 41 0.4E 0.230 0.011 28.4 1.5 16.6 1.1 14.2 0.5 55 2.0F 0.210 0.011 29.1 1.2 25.7 1.2 19.8 0.7 44 0.2

These results display the interest in confronting parameters and evaluating the quality factor. Accordingto quality factor results (Fig. 7), cutter A is clearly the best one with a Q factor about 169 104, which isconfirmed by its low wear rate and its high cutting efficiency. In contrast, the cutter B registers the worst Qfactor of only 4 104.

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10424

10524

10624

107

Quali

ty fa

ctor

A B C D E FPDC sample

Figure 7: Quality factors results.

As it has been described earlier, samples of this study contain various amount of cobalt in WC-Co partbut similar proportion has been observed in diamond. Cobalt ductile phase is directly associated to wearkinetic and the higher the cobalt proportion, the easier the abrasion of a drilling tool. In other words, mastercobalt distribution in diamond permits to handle tools wear resistance. Cutters D, E and F are made bythe same manufacturer and the leached depth is the only parameter differentiating them. Obviously, leachedsamples can not be discriminated from non-leached samples by the quality factor here. Samples E and Fare leached on less than 400 m depth which represent only 20% of diamond layer thickness. This couldexplain the low influence of the leaching process on long excavation distances and samples worn over severalmillimeters.

Also, as seen above, cutter B and C may have a higher diamond grain size than others samples. This twocutters have the highest wear rates and lowest quality factors. As expressed by F. Bellin et al. [11], PDCcutters with fine grains are more abrasion resistant than cutter with coarse grain. Nevertheless, coarse grainspermit a better impact resistance.

7. Phase analysis and quality factor

To qualify relative differences between samples diamond layer, samples have been submitted to X-raydiffraction measurements (Fig. 8). Diffractograms were acquired on a XPERT Philips MRD diffractometerwith CuK radiation source beam at 40 kV and 50mA. XRD measurements are also defined by 2 Braggangles between 10 and 160 with a step size of 0.02.

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(a)

Figure 8: Diffractograms of PDC samples B, C, D, E, F and G classified from low Q (sample B) to high Q(sample C) and calculated stick pattern of diamond, tungsten carbide and cobalt carbide.

In addition to diamond material, two other phases have been identified on diffractograms: tungstencarbide (WC), cobalt carbide (CoCx) [12] and traces of cobalt (-Co).

Cobalt has three possible crystal structures: hexagonal close packed -Co phase stable at room tempera-ture, face-centered cubic -Co phase and cubic also -Co phase [13]. Only this last phase was well identifiedon diffractograms of WC-Co cutter part (Fig. 9). Cobalt elements present in PDC part come from WC-Cosubstrate by diffusion during sintering. That explains detection of -Co phase in diamond table.

The cobalt carbide phase is formed during sintering of PDC material. Cobalt is not a catalyzer of diamondformation but only a precursor because it forms a new product with carbon. Actually, M. Akhaishi et al.[14] described the cobalt action during sintering as follows:

At first the dissolution of graphite, formed on diamond grains surfaces under high temperature, intocobalt liquid phase above eutectic until saturation;

From the saturation, diamond precipitated from the solution formed and dissolution can start againuntil saturation of pure diamond into cobalt;

Therefore, diamond structure grows and becomes denser by Oswald ripening and cobalt carbide appearsin grain boundaries.

Like diamond, cobalt carbides are metastable phase at room temperature. K. Ishida and T. Nishizawa [15]note that Co3C over a pressure of 4.5GPa becomes a stable phase which correspond to a lower pressure thansynthetic diamond sintering conditions.

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40x103

35

30

25

20

15

10

Di r

acto

gram

s Int

ensit

y (co

unts)

757065605550452 Theta

100

80

60

40

20

0

Phase Card intensity

(%)

PDC part WC-Co part

Diamond WC

CoCx

-Co

Figure 9: Cobalt allotropic phases: sample D diamond and WC-Co parts diffractograms.

XRD peak intensity (Idiamond, ICoCx or Iwc) depends on the concentration of the identified crystallizedphase. Also, diffracted X-rays by diamond grains is modified by the amount of absorbent cobalt phasessurrounding them. Indeed, cobalt element has a higher atomic number than carbon element and likewiseabsorption coefficient. Thus, X-rays penetrate deeper in leached samples than non leached ones. This explainshigher intensities measured for leached samples A, E and F.

In addition, an interesting way to display relative proportions of phases in the PDC material is to calculatethe ratio between maximum peak intensity of the studied phase on the sum of maximum peak of all presentphases (I) in the sample (Tab. 4). This operation only leads to relative results because attenuation coefficientsof phases are not taken into account [16].

Table 4: Calculus of relative proportion of cobalt carbide and tungsten carbide in PDC sample A to F.

PDC samples A B C D E FICoCx/I 3.5 0.9 7.9 0.7 8.1 0.6 11.4 0.9 0.9 0.9 0.7 0.4IWC/I / 16.4 0.9 6.8 0.7 8.3 1.1 / /

The tungsten carbide particle in diamond face may be due to pollutions in the mold use to press andsinter samples. WC phase was detected on only B, C and D and it is well-known by manufacturers that WCgrains pollution can weaken diamond grain cohesion [17]. Sample B clearly has the greatest proportion ofWC and this can explain its low Q value relatively to other samples.

8. Residual stresses and quality factor

Three-dimensional finite element analyzes have been carried out to evaluate post sintering residual stresses.The diamond/carbide interface variations of samples B, C and D (i.e. also E and F) are considered. Allsamples are supposed to be sintered at a maximum temperature of 1380 C under an isostatic pressure of5.5GPa [18]. Then, a cooling until 1000 C is taken into account maintaining pressure to pass the solidusof the carbide part. Eventually, a last cooling is assumed until 20 C at atmospheric pressure. All physicalproperties used here are theoretical and identical for all numerical simulations (Tab. 5). The numericalsimulation software Abaqus was used here with a steady state coupled temperature/displacement step and atetragonal mesh of 0.5mm size.

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Table 5: Physical properties of PDC and WC-Co [19].

Material Density Thermal Specific Thermal Youngs Poissonconductivity heat expansion coefficient modulus ratio

(kg m3) (W m1 K1) (J kg1 K1) (106K1) (GPa)PDC 3510 543 790 2.5 890 0.07

WC-Co 15000 100 230 5.2 579 0.22

Radial (r) and axial (z) normal stresses are acquired at the end of a simulation. Negatives values of stressare related to compressive stresses and positives ones to traction stresses. Residual stresses are expressed inpercentage, relatively to the maximum absolute traction value obtain in radial and axial components with theflat interface. This avoids calibrations of numerical values and considers only changes in stresses distributionand amplitude comparatively to simple flat interface (Fig. 10).

(a) (b)

Figure 10: Residual stress distributions on a cross section simulated for flat interface: (a) radial stresses; (b)axial stresses.

All designs show a cap type radial stress distribution in compression in PDC part and in traction incarbide substrate. This distribution is factually confirmed by several microsections made by electroerosion(Fig. 11a) which display a cap type crack on their diamond part. In fact, radial stresses induce compressivefield lines in the PDC material (Fig. 11b) and the addition of traction axial stresses cause cap-like crackpropagation guided by these field lines.

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(a)

Axial traction stress

Radial compressive stress

Radial compressive stress !eld line

WC-Co

PDC

(b)

Figure 11: 11 Cap type crack formation: (a) cap type cracks observed on a microsection realized by elec-troerosion; (b) illustration of radial and axial actions.

High traction residual stresses favor cracks propagation and diamond grain decohesion in materials. Sam-ples have different compressive radial stress distribution in their diamond table (Fig. 12a). A flat designhas its diamond face perimeter in radial traction. This explains the manufacturers choice in trying to avoidtraction field at the tip of a cutter by studying more complex interface designs. Interface designs are alsointeresting for minimizing axial traction residual stresses. As for radial distribution, a flat interface producesthe highest traction values (Fig. 12b). After all, sample D, E and F have the most efficient design and thiscould explain their good Q result. Moreover, sample A, which has clearly the best Q factor, is based onthe same design with a more complex junction in interface center. This may be made in order to moderatestresses contrast between the diamond table compressive axial stresses and the tungsten carbide oppositelyin traction.

(a) (b)

Figure 12: Residual stress distributions for sample A, C, D, E, F and G: (a) radial stress component vs.radial distance; (b) axial stress component vs. axial distance

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More generally, residual stresses may affect quality results of drag bits, but they should have a greaterinfluence toward resilience behavior of materials which is not studied here.

9. Conclusion

PDC cutters were submitted to wear tests and a comparison between all these cutters requires an overlapof information. The PDC cutters evaluation tends to balance ability to withstand abrasive wear and to beefficient as long as possible. Archards linear model permits an evaluation of wear rate but a long bit life couldbe related to a poor cutting performance. For this purpose, an exponential law properly associates cuttingefficiency to excavation distance and led to determine a cutting efficiency coefficient. The cutting efficiencycoefficient on wear rate ratio establishes a quality factor and associate to sample wear, aggressiveness of therock field and energy spent to cut it.

Four crucial parameters influencing cutters abrasive resistance have been highlighted in this study:

The cobalt content in diamond is one of the most influential parameters toward cutters abrasive re-sistance and resilience. The increase of cobalt content in diamond part also increases samples wearrates and resilience. However, depleting cobalt on few hundred microns does not have a great effect onquality factor when long distance tests are performed. In addition, cobalt is a precursor of diamondformation and not a catalyzer, because cobalt carbide remains after PDC sintering;

As already expressed in previous studies and here, the finest diamond grains are the more abrasiveresistant cutters;

Low quality cutters contain tungsten carbide particles in diamond part;

Residual stresses are another field of interest concerning quality. Traction residual stresses promotecracks propagation in diamonds and lower abrasion resistance by weakening grain boundary.

Acknowledgment

We thank Armines Geosciences laboratory for performing the wear experiments and the Varel EuropeCompany for providing cutters used in this study. This work is performed under the program ANR-09-MAPR-0009 of Agence Nationale de la Recherche.

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IntroductionPDC samplesExperimental studyWear rate analysisCutting capacityQuality modelPhase analysis and quality factorResidual stresses and quality factorConclusion