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Erosion damage in diamond coatings byhigh velocity sand impactsD. W. Wheeler a & R. J. K. Wood aa School of Engineering Sciences, University of Southampton ,Highfield, Southampton SO17 1BJ, UKPublished online: 30 Nov 2007.

To cite this article: D. W. Wheeler & R. J. K. Wood (2007) Erosion damage in diamondcoatings by high velocity sand impacts, Philosophical Magazine, 87:36, 5719-5740, DOI:10.1080/14786430701713828

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Philosophical Magazine,Vol. 87, No. 36, 21 December 2007, 5719–5740

Erosion damage in diamond coatings byhigh velocity sand impacts

D. W. WHEELER and R. J. K. WOOD*

School of Engineering Sciences, University of Southampton,Highfield, Southampton SO17 1BJ, UK

(Received 10 July 2007; in final form 25 September 2007)

For a diamond-coated component, the shear stresses at the coating–substrateinterface, generated by solid particle impingement, are known to affect interfacialintegrity. If these stresses are of sufficient magnitude, coating-debonding causedby interfacial crack propagation can be initiated, which can later lead tocatastrophic failure of the coating. This paper describes a set of experimentsconducted on CVD diamond coatings at a constant particle impingement velocity(250m/s), using sieved silica sand varying in diameter from 125 to 500 mm.The objective of this work was to examine the influence of the stress field onthe integrity of the coating by varying the depth at which the maximum shearstress occurred. Detailed studies of the coating failure time with respect to thenormalized depth of maximum shear stress show that particle impacts generatinga maximum shear stress at, or close to, the coating–substrate interface resultsin rapid debonding of the coating. Coatings thick enough to contain themaximum shear stress within the coating and away from the interface exhibit thelongest life when subjected to solid particle impacts. The results are alsocompared to other erosion studies and the differences between them areexplained.

1. Introduction

The high erosion resistance of diamond coatings produced by chemical vapourdeposition (CVD) is well known and has been the subject of a number of studies [1–3].This has led to diamond being investigated as a possible coating for components,such as control valves, used in the offshore oil industry, which are vulnerable toerosion from sand particles entrained in hydrocarbon fluids. However, if diamondcoatings are to be applied in this way, it is vital to understand the damagemechanisms by which the coatings become debonded. Of equal importance is thetask of identifying the conditions under which debonding does not occur. Incommon with other coatings of a brittle character, CVD diamond can failcatastrophically in an erosive environment, often without visible indications ofdeterioration [4]. In a previous paper [5], ultrasonic scanning has shown that, underrepeated particle impacts, there is a progressive increase in the incidence of interfacialdiscontinuities. This suggested that the impact of the sand particles caused

*Corresponding author. Email: rjw3@soton.ac.uk

Philosophical Magazine

ISSN 1478–6435 print/ISSN 1478–6443 online � 2007 Taylor & Francis

http://www.tandf.co.uk/journals

DOI: 10.1080/14786430701713828

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debonding of the coating at the coating–substrate interface. However, furtherinvestigations were necessary to identify the mechanism by which this debondingoccurred.

Other erosion studies of both diamond films and free-standing diamond haveshown that the major damage features observed are complete or partial Hertzian ringcracks [1, 3, 6]. These cracks form around the perimeter of the contact zone wherethe tensile stress is at its maximum. However, this stress is largely confined to thenear-surface regions of the material and decreases rapidly with increasing depth.Furthermore, although Hertzian ring cracks are usually associated with impact fromspherical particles, they have also been observed in other studies by the presentauthors [7, 8] where the shapes of the impacting particles deviate significantly fromthat of a perfect sphere. CVD boron phosphide coatings impacted by sub-rounded355–500mm sand at a velocity of 33m/s exhibited ring cracks that were in goodagreement with those predicted by Hertz. A similar finding was observed in a studyof bulk CVD diamond [8] impacted by 200 mm diameter cubo-octahedral diamondgrit at a velocity of 268m/s, even though examination of the grit following impactrevealed that it had undergone significant fragmentation on impact.

Another aspect of Hertzian contacts is the occurrence of shear stresses thatare generated in the region beneath the contact. In a coating system, these shearstresses can cause debonding via the propagation of cracks at the coating–substrateinterface. The extent of this debonding is determined by the shear strength of theinterface and the shear stresses caused by the applied load [9]. The propagationof interfacial cracks is known to be a mixed mode event, consisting of both mode I(tensile) and mode II (shear) components [10]. However, analysis by Comninou [11]has suggested that the growth of an interface crack is more intimately connectedwith failure in shear rather than in tension. Therefore, it is important to understandthe role played by shear stresses in the delamination process.

Coating adhesion can be severely influenced by deposition parameters andprecursors as well as surface preparation and roughness. The thermal mismatchbetween the coating and substrate can cause interfacial shear stresses to beestablished prior to the superimposition of tribologically induced shear stresses.The maximum interfacial shear stress, taken from Klein [12], can be given by:

�max ¼

ffiffiffi3

2

rEs

1þ �sð Þts�

1þ �cð ÞEctc1� �c

� �1=2�"cj j ð1Þ

where Ec, �c, tc and Es, �s, ts are the elastic moduli, Poisson’s ratios and thicknessesof the coating and substrate, respectively. �"c is the strain mismatch in the coating,defined as the difference between strain in the coating and substrate strain at thedeposition temperature:

�"c ¼�L

Lo

� �c

��L

Lo

� �s

ð2Þ

where (�L/Lo)c and (�L/Lo)s represent the thermal expansion or unit elongationof the coating and substrate, respectively, at the deposition temperature [12].Applying these expressions to the coating system in the present study – a 30 mm thickdiamond coating on a 5mm thick tungsten substrate – this gives a modest interfacial

5720 D. W. Wheeler and R. J. K. Wood

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strain mismatch of 0.0002 and a maximum shear stress of 12MPa assuming adeposition temperature of 900�C. The thermal expansion for diamond was takenfrom Klein [12], while the figure for tungsten was taken from Knibbs [13]. Therefore,for the current coating system these levels are too low to disbond the coating unlessvery large defects are created at the interface, which accelerate shear drivendelamination.

The objective of the present study was to examine the effect of stress fieldsgenerated by high velocity sand erosion on the behaviour of diamond coatings.By using sieved sand of different diameters at a nominally constant velocity toimpact diamond coatings of the same thickness (30 mm), the effect of varying thedepth of maximum shear stress on coating integrity can be evaluated. The coatingthickness was not changed so as to minimize the effects of variations in residual stressand microstructure; the columnar structure of diamond coatings leads to increasinggrain size and, therefore, increasing intrinsic flaw size with thickness. The silicasand erodent was used as it is often found in erosive environments experiencedby components such as valves. Although not as regular in shape as spherical glassbeads, silica sand is arguably more representative of actual process/serviceconditions.

2. Calculation of the stress field

Table 1 lists the relevant material properties [14–17] of both the diamond coating andthe silica sand erodent used in this study. Some of these values are used in thecalculations described below.

The contact conditions in the case of a spherical particle impacting the surface ofan elastic target have been calculated using the dynamic Hertzian expressions ofTimoshenko and Goodier [18]. While it is recognized that fully elastic contactconditions may not be operative in the present study, other studies [1, 6–8] haveshown that Hertz provides a reasonable approximation in impact and erosionsituations, particle fragmentation notwithstanding.

The maximum load, Fm, is calculated using:

Fm ¼5��e3

� �3=54k

3E1

� ��2=5

R2V6=5 ð3Þ

Table 1. Table of relevant mechanical properties for CVD diamond andSiO2 [14–17].

Parameter CVD Diamond Silica (SiO2)

Elastic modulus, E (GPa) 1157 87Shear modulus, G (GPa) 540 36Poisson’s ratio, � 0.07 0.21Density, � (kg/m3) 3520 2650Hardness, H (GPa) 80 11Fracture toughness, K1c (MPa

ffiffiffiffim

p) 6.0 1.3

Behaviour of diamond coatings under high velocity sand erosion 5721

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The mean contact pressure, Pm, is:

Pm ¼1

�

5��e3

� �1=54k

3E1

� ��4=5

V 2=5 ð4Þ

where �e is the density of the impacting particle, E1 the elastic modulus of the

diamond, R the particle radius and V the particle velocity. The value of k is obtained

using the following equation:

k ¼9

161� �21� �

þ 1� �22� � E1

E2

� �� � �ð5Þ

where E1, �1, and E2, �2 are the elastic moduli and Poisson’s ratios of the target

material and erodent, respectively. The values of Fm and Pm from equations (3)

and (4) can be used to calculate the maximum contact radius, am:

am ¼

ffiffiffiffiffiffiffiffiffiFm

�Pm

rð6Þ

The duration of elastic impact, te, can be calculated using the following formula:

te ¼ 2:945��e4

1� �21E1

� �þ

1� �22E2

� �� �2=5V�1=5R ð7Þ

One of the limitations of the Hertzian approach is that it is only strictly applicable

in cases where am/R50.1, where am is the mean contact radius and R is the radius

of the spherical indenter – in this case the particle. Use of this theory can give rise

to errors, which can increase with increasing am/R ratio and are particularly marked

in materials of low Poisson’s ratio. Under the conditions employed in this study

(see section 3.0 for details), the am/R ratio was calculated to be 0.4. For this reason,

the modified expressions proposed by Yoffe [19] for am/R40.1 were used in

calculating the principal stresses �z, �� and �r, which are the axial, circumferential

and radial stresses, respectively; the definitions of the principal stress directions are

shown in figure 1 [20]. In the calculations of the principal stresses, the following

expressions were used:

�r ¼ �� ¼2Fm

�a4mð3þ 2�1Þzða

2 þ z2Þ1=2 � ð3þ 2�1Þz2

� ð1þ 2�1Þa

2=2� a2zða2 þ z2Þ�1=2�

ð8Þ

z

θ

0

r

Figure 1. Schematic diagram showing the axial (z), circumferential (�) and radial (r)directions referred to in this paper [20]. Key: 0¼ centre of contact.

5722 D. W. Wheeler and R. J. K. Wood

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�z ¼2Fm

�a4m2z2 � a2m � 2z a2m þ z2

� �1=2þ 2a2mz a2m þ z2

� ��1=2h i

ð9Þ

At the surface of the target material, the maximum tensile stress at the contact circle,

�r(max), can also be calculated, using the following expression:

�rðmaxÞ ¼1

21� 2�1ð ÞPm ð10Þ

In considering the stresses acting on the coating, it is important to remember that

the stress ratio �/Po (where Po, the maximum contact pressure¼ 3/2Pm) is dependent

on �, the Poisson’s ratio of the material concerned. The depth, z�, at which the

maximum shear stress occurs, usually quoted as z�¼ 0.48am, is for a material having

a Poisson’s ratio of 0.3. However, the Poisson’s ratio of diamond, though dependent

upon crystallographic orientation, is considerably lower than 0.3. The aggregate

value is usually quoted as 0.07 [14] and it is this figure that was used in recalculating

the values of principal stresses.Using �� from equation (8) and �z from equation (9), the shear stress, �1, was

calculated using the following expression [21]:

�1 ¼1

2�z � ��j j ð11Þ

Figure 2 shows the plot of �1/Po with depth using �¼ 0.07. It shows that the

shear stress has a maximum value below the surface:

�max ¼ 0:48Po ð12Þ

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0 0.1 0.2 0.3 0.4 0.5 0.6

τ / Po

z/ a

m

Figure 2. Graph showing the variation of normalized shear stress (�/Po) with depth atthe central axis of contact for 165mm diameter silica sand impacting on diamond at 250m/s.

Behaviour of diamond coatings under high velocity sand erosion 5723

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The depth, z�, at which this occurs, is 0.32am. The final parameter, the verticaldisplacement, w, of the coating in the centre of the impact site is given by:

w ¼3ðl� vÞFm

16G1amð2� R2=a2mÞ ð13Þ

where G is the shear modulus of the target.In calculating the magnitude and location of the maximum shear stress for a

coating system, the assumption is made that the influence of the substrate on the stressfield is negligible. In a theoretical analysis, El-Sherbiney and Halling [22] have statedthat the effect of the substrate can be ignored if CT/am40.5, where CT is the coatingthickness, i.e. it can be treated as a homogeneous material. However, for thin coatings,where CT/am50.5, finite element analysis is required to overcome the complicationspresented by the substrate. In all calculations described in this paper, the influence ofthe substrate has been found to be negligible and has, therefore, been disregarded. Thereasons for such an approach are discussed in more detail later in this paper.

3. Experimental

The diamond coatings used in the present study were deposited onto tungstensubstrates and lapped to a surface roughness (Ra) of 0.2� 0.03 mm. A lapped finishwas chosen for the test samples as planar diamond coated inserts may be usedto reduce wear rates within the internal components of choke valves ratherthan coating all the surfaces of these complex shapes. The planar inserts would belapped prior to insertion as the steady-state erosion rates of lapped coatings arelower than as-grown surfaces [5]. Also, it is easier to see the circumferential cracks onlapped coatings and, hence, measure their diameters under the microscope. The filmshad a thickness of 30 mm, while the average grain size on the growth surface wasapproximately 20 mm. Figure 3 shows a micrograph of an untested surface. Theywere tested in a high velocity air–sand erosion rig, details of which can be foundelsewhere [23]. In the tests, silica sand was used at a nominally constant velocity

10µm

Figure 3. Micrograph of the untested surface of a 30mm lapped diamond coating.

5724 D. W. Wheeler and R. J. K. Wood

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of 250m/s; the air flow rate of the rig for each of the four sand sizes was differentin order to ensure nominally identical particle velocities of the various sand sizes.The rationale behind selecting this velocity is that hydrocarbon velocities in chokevales can be as high as 300–400m/s, thus entrained particles can be accelerated toapproximately 250m/s within the choke valve trim. Also, 250m/s was chosenbecause it was the highest velocity possible with the rig for all the different sandsizes tested. The particle velocities were calibrated using high speed photographyand the scatter in particle velocities were typically between �15 and �18m/s forthe different sand sizes. The sand flux rate was 0.5 kg/m2/s, which was selected toensure that particle–particle interactions were minimized. The nominal impact anglein all tests was 90� 2�: this was chosen to coincide with the angle of maximumerosion for brittle materials. However, it should be noted that a variety of erodentimpact angles can be expected within a choke valve but similar erosion damageto that generated at 90� has been seen at angles down to 30� from experimentsconducted by the authors, see [24]. In addition, increased numbers of impacts arerequired to generate damage features at more oblique angles making these studiesdifficult and lengthy to run.

The sand was sieved into four separate size ranges: 125–180, 180–250, 250–355and 355–500 mm. The mean sand sizes, which were 165, 227, 322 and 441mm, werecalculated using measurements taken from electron micrographs of the sand priorto the erosion tests. Figure 4 shows micrographs of the four grades of sand used,

100µm

(a)

100µm

(b)

100µm

(c)

100µm

(d)

Figure 4. Micrographs of unused (a) 125–180, (b) 180–250, (c) 250–355 and (d) 355–500 mmsand.

Behaviour of diamond coatings under high velocity sand erosion 5725

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while further details of the sand can be found in table 2. Although it may appear

from figure 4 that the various grades are significantly different in shape,

measurements of large numbers of individual grains from electron micrographs

have indicated that the mean roundness factor (RF) only varies between 0.63

(125–180 mm sand) and 0.77 (355–500 mm sand). A roundness factor of 1 denotes

a perfect sphere [25].The sand was sieved to ensure that the impact conditions could be as tightly

controlled as possible. At a constant impact velocity, z�, the depth at which the

maximum shear stress, �max, occurs is dependent on the particle size. As z� is related

to the contact radius, it can be seen that larger particles will generate �max at greater

depths. For this reason, the test conditions in the present study were chosen so that

the effect of z� on the coating life could be examined. The exact details of the tests are

listed in table 3.The duration of each test was varied in order to ensure that the number of

particle impacts remained constant. The number of impacts, N, on a zone of area, A,

where A ¼ �(2am)2, was calculated using equation (14). This expression assumes

that any impact having its centre within 2am will overlap the previous one.

The number of impacts per hour for the different sand sizes is listed in table 3.

N ¼A’t

msð14Þ

where ’ is the flux rate (kg/m2/s), t is the test duration (s) and ms is the mass of a sand

particle (kg) given by:

ms ¼4�sand�R

3

3ð15Þ

Table 3. Details of the tests conducted (CT ¼ coating thickness).

Range ofsand sizes(mm)

Mean sanddiameter (mm)

Air flowrate (m3/h)

Particlevelocity (m/s)

am(mm)

CT

(mm)z�

(mm) z�/CT

N(h)

125–180 165 320 250� 15 31 30 10 0.33 4440180–250 227 350 250� 15 43 30 14 0.47 3124250–355 322 360 250� 16 61 30 20 0.67 2220355–500 441 380 250� 18 84 30 27 0.90 1556

Table 2. Characteristics of the silica sand erodent.

Sand sizerange (mm)

Mean sanddiameter (mm)

Meanroundness factor

Standarddeviation

125–180 165 0.63 0.13180–250 227 0.68 0.19250–355 322 0.74 0.11355–500 441 0.77 0.18

5726 D. W. Wheeler and R. J. K. Wood

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4. Results

The results of the tests are listed in table 4: they show that, at a velocity of 250m/s,

particle size had a considerable influence on coating life. The coating impacted by

the 355–500 mm sand, where �max is close to the interface, failed after 2min.

In contrast, the coating impacted by the 125–180mm sand, where �max was closer

to the coating surface than to the interface, failed after 18 h. Figure 5 displays

the time to failure, tF, of the coatings in graphical form. The graph indicates

an approximately exponential relationship between tF and mean particle diameter.Examination of the coatings prior to failure revealed the presence of microscopic

pin-holes, many of which had completely penetrated through to the substrate.

y = 31381e -0.0247x

R 2 = 0.9947

y = 57842e-0.0229x

R 2 = 0.9943

0.1

1

10

100

1000

10000

0 100 200 300 400 500

Mean particle diameter (µm)

Time(min ) tPH (min )

tF (min

Figure 5. Graph showing the relationship between mean particle diameter and the timerequired for pin-hole formation (tPH) and failure (tF) at a mean particle velocity of 250m/s.

Table 4. Effect of sand size on the number of impacts required for pin-hole formationand coating failure (tPH¼ time for pin-hole formation; tF¼ time to coating failure;

N¼ number of particle impacts).

Sand sizerange (mm) tPH (min) N (pin-holes) tF (min) N (failure)

125–180 462 34 000 1080 80 000180–250 120 6200 300 19 000250–355 15 560 45 1700355–500 0.5 13 2 52

Behaviour of diamond coatings under high velocity sand erosion 5727

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An example of one of these features, from the coating impacted by the 125–180 mmsand, is shown in figure 6. Similar features on the coatings eroded by other sand

sizes can be seen in figures 7–9. In all four tests, the time at which pin-holes were

first observed was after approximately one-third of the overall coating life.

This suggests that they could represent an early indication of coating failure. For

this reason, the time of pin-hole formation, tPH, has also been plotted in figure 5.A fuller description of the initiation and growth of these pin-holes can be

found elsewhere [26]. To summarize, the first stage of this process is the formation

of a circumferential crack, an example of which can be seen in figure 7.

Previous work [4] by the authors found that the paths taken by the circumferential

cracks are transgranular and do not appear to be influenced by grain boundaries.

Following the formation of a circumferential crack, further sand impacts cause

the material bounded by the crack to be ejected, resulting in a pin-hole. In the

present study, most of the observed pin-holes were fully formed, i.e. the diameter of

the central area where material has been removed was the same as that of the

10µm

Figure 7. Micrograph taken from a 30mm diamond coating tested at 250m/s using180–250 mm sand for 2 h showing a circumferential crack.

10µm

Figure 6. Micrograph from the same sample as figure 3, tested at 250m/s for 8 h using125–180 mm sand, showing a pin-hole.

5728 D. W. Wheeler and R. J. K. Wood

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circumferential crack. Therefore, in this case the terms ‘circumferential crack

diameter’ and ‘pin-hole diameter’ can be regarded as interchangeable. In the present

specimens, the mean circumferential crack/pin-hole diameters are approximately

five times greater than the mean grain size of the coatings at the growth surface. They

therefore, encompass several grains and have not resulted from the ejection of a

single grain.In other work by the present authors [27], images of the coating–substrate

interface acquired using scanning acoustic microscopy (SAM) has shown that the

circumferential cracks and pin-holes were only found on regions of the coating

that had become locally debonded at the coating-substrate interface. An example of

such an image can be seen in figure 10; the pale regions denote areas of the coating

that have become debonded: at these locations the amplitude of the reflected waves

is highest owing to the almost total reflection at these regions. The figure shows

two pin-holes situated on debonded regions. No pin-holes were found to have

formed on regions of the coating that had not become debonded. This finding

10µm

Figure 8. Micrograph taken from a 30mm diamond coating tested at 250m/s using355–500 mm sand for 1min showing a pin-hole.

10µm

Figure 9. Micrograph taken from a 30mm diamond coating tested at 250m/s using250–355 mm sand for 30min showing a pin-hole.

Behaviour of diamond coatings under high velocity sand erosion 5729

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suggested that the circumferential cracks may be formed via a mechanism of stresswave reflection and reinforcement, which is more usually found in liquid impactstudies [28, 29]. This mechanism will be considered in more detail later in this paper.

5. Discussion

5.1 Effect of stress field on coating performance

To explore further the reasons for the superior performance of the coatings wherethe z�/CT ratio is low, it is necessary to consider the impact conditions. They aresummarized in table 5. To take into account the variations in particle sizes and,therefore, impact velocities, the values have been listed in ranges for each grade ofsand used in the experiments. The two extremes of each range correspond to thelargest sand particle/lowest velocity in the range and vice versa. As an example,for 355–500 mm sand at 250� 18m/s, the range is for a 355 mm particle at 268m/sand a 500 mm particle at 232m/s.

The table shows that high forces and deflections are predicted to be generatedby the impacting particles. As an example, the tensile stresses generated by theimpacts have been calculated to be up to 6.0GPa. This is far in excess ofthe tensile strength of the diamond coating; although the tensile strength of thecoatings used in the present study is not known, other studies, for exampleFeng et al. [1] have reported a value of 1.5GPa. However, the influence of residualstress has not been considered. Raman spectroscopy of diamond coatings ontungsten has indicated that the aggregate residual stress close to the surface to beapproximately 0.9GPa and compressive in nature [30], although it is recognized

1 mm

Figure 10. Scanning acoustic microscopy (SAM) image of a 60 mm diamond coatingerosion-tested for 5 h at 268m/s showing coating delamination (white areas) and pin-holes(arrowed circular features) located on delaminated regions of the coating.

5730 D. W. Wheeler and R. J. K. Wood

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that the residual stress may change with depth owing to variations in defect levels.The presence of stresses of this magnitude, although small compared with theoverall tensile stress, will therefore increase the stress required to initiate Hertzianring cracking.

To ascertain the effect of the substrate on the behaviour of the coating, thecontact conditions for the impact of silica sand particles on tungsten were calculatedand the results compared with those in table 5. The values of elastic modulus andPoisson’s ratio for tungsten used in the calculations were 400GPa and 0.29,respectively [31]. It was found that for a 441 mm diameter sand particle impactingtungsten at 250m/s, the contact radius (85mm) was essentially no different to that ofsand upon diamond under the same conditions (83 mm). Moreover, the maximumcontact pressure, 18.5GPa, and maximum shear stress, 8.7GPa, are not significantlydifferent from the corresponding values for sand on diamond, which were 20.3 and9.5GPa, respectively. These findings, therefore, justify the approach in section 2,which stated that, in making the Hertzian calculations, the influence of the substratewas disregarded.

In considering the values given in table 5, it should be remembered that they arecalculated on the assumption that the contact is elastic and that both particle andtarget remain undeformed on impact. Sieving of sand used in the present studyrevealed reductions in mean particle sizes on impact by between 58% (125–180mmsand) and 66% (355–500 mm sand). As a result, the actual stresses generated in thecoatings may be significantly lower than predicted owing to the high incidence ofparticle fragmentation on impact.

The data in figure 5 has been re-plotted in figure 11 to show the relationshipbetween N(pin-holes) and N(failure) with the depth of maximum shear, z�,normalized to the coating thickness, CT. The graph indicates that, as z�/CT isreduced, there appears to be an exponential increase in the number of impactsrequired for both pin-hole formation and failure. This mirrors the trend seen infigure 5.

Table 5. Impact calculations for the different sand sizes at a constant velocity of 250m/s.

Sand size range (mm)

125–180 180–250 250–355 355–500

Parameter Min. Max. Min. Max. Min. Max. Min. Max.

R (mm) 62.5 90 90 125 125 177.5 177.5 250V (m/s) 265 235 265 235 266 234 268 232Fm (N) 25 46 53 88 102 177 208 347Po (GPa) 20.8 19.8 20.8 19.8 20.8 19.8 20.8 19.8Pm (GPa) 13.9 13.2 13.9 13.2 13.9 13.2 13.9 13.2am (mm) 24 33 35 46 48 65 69 92dm (mm) 48 66 70 92 96 130 138 184te (ms) 0.10 0.15 0.15 0.21 0.21 0.30 0.29 0.43�r(max) (GPa) 6.0 5.7 6.0 5.7 6.0 5.7 6.0 5.7�max (GPa) 9.8 9.3 9.8 9.3 9.8 9.3 9.8 9.3z�/CT 0.26 0.35 0.37 0.49 0.52 0.70 0.74 0.98

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It is necessary to account for this apparently exponential increase in N as z�/CT is

reduced. For each of the four impact conditions, the variation of �max as a function

of z�/CT was plotted; these are shown in figure 12. Once again, the influence of

the substrate is ignored. They show that the normalized shear stress, �/Po, at the

0

0.1

0.2

0.3

0.4

0.5

0.6

0 1 2 3 4

z / CT

τ / P

o

125-180µm

180-250µm

250-355µm

355-500µm

Figure 12. Graph showing the variation of normalized shear stress �/Po, with normalizeddepth, z/CT, for 30mm diamond coatings on tungsten erosion-tested at 250m/s. The fourcurves represent the four different diameter sand particles used in the erosion tests.

y = 7E+06e-12.892x

R2 = 0.9936

y = 4E+06e-13.729x

R2 = 0.9937

0

20000

40000

60000

80000

100000

120000

0 0.2 0.4 0.6 0.8 1

zτ /CT

NN (pin-holes)

N (failure )

Figure 11. Graph showing the effect of z�/CT on the number of impacts (N) forpin-hole formation and coating failure at a particle velocity of 250m/s and for sandranging between 165 and 441 mm. The error bar ranges are a function of the variations inparticle velocity and, therefore, contact radius.

5732 D. W. Wheeler and R. J. K. Wood

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coating–substrate interface, when z�/CT¼ 1, is 0.31 for the 125–180mm sand and

0.39 for the 180–250mm sand. They are significantly lower than the figures for the

other two sand sizes (0.45 and 0.48). The level of �/Po as a function of z�/CT is

summarized in table 6.The data listed in table 6 has been plotted in graphical form in figure 13.

It shows an approximately exponential relationship between N and �/Po at z�/CT¼ 1.

It is significant that this closely mirrors figure 11, supporting the suggestion that

the formation of pin-holes is linked to the coating-debonding process. It also

suggests that normalized shear stresses (�/Po)50.27 are not damaging to the

integrity of the coating. Therefore, given that Po¼ 20GPa, it can be inferred that the

interfacial shear strength of the coating–substrate interface, �i, is of the order of

5.4GPa.The initiation of cracking in brittle materials usually occurs from intrinsic flaws

present in the microstructure. Previous studies of the erosion behaviour of CVD

y = 3E+09e-34.747x

R2 = 0.8569

y = 4E+09e-38.114x

R

τ / P0 at z / CT=1

2 = 0.8251

0

20000

40000

60000

80000

100000

120000

0 0.1 0.2 0.3 0.50.4

Nu

mbe

r of i

mpa

cts

N(pin-holes)

N(failure)

Expon.(N(failure))

Expon.(N(pin-holes))

Figure 13. Graph showing the relationship between number of impacts and �m/Po atz/CT¼ 1 for 30mm lapped diamond coatings erosion-tested at 250m/s.

Table 6. Number of impacts for pin-hole initiation as a function of �/Po at thecoating–substrate interface at 250m/s.

Sand size range (mm) N(pin-hole) N(failure) �/Po at z�/CT¼ 1 � at z�/CT¼ 1 (GPa)

125–180 34 000 80 000 0.31 6.2180–250 6200 19 000 0.39 7.9250–355 560 1700 0.45 9.2355–500 13 52 0.48 9.7

Behaviour of diamond coatings under high velocity sand erosion 5733

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diamond have shown that the microstructure of the nucleation surface of CVDdiamond contains significant amounts (up to 5%) of grain boundary porosity [5].The size of these flaws can be as large as 5 mm. They, therefore, constitute cracknucleation sites that will assist the debonding process, if the stress is sufficiently high.

In summary, the results show that sand particle impacts generating shear stressesclose to the coating–substrate interface will result in rapid coating-debonding,leading to catastrophic failure of the coating. For particle impacts where themaximum shear stress is within the coating but away from the interface, the damageto the coating is minimal. However, although Hertz theory appears to explain thedebonding of the coatings, it is necessary to identify the cause of the circumferentialcracks and pin-holes.

5.2 Formation of circumferential cracks

The diameters of the circumferential cracks and pin-holes were measured andcompared with the contact diameter as predicted by Hertz theory. The mean contactdiameters were calculated using the mean particle radius from each sand sizerange. The results are listed in table 7: it can be seen that, although Hertz theoryappears to explain the effect of the shear stress on the coating integrity, it does notappear to explain the formation of the circumferential cracks and pin-holes.Figure 14 shows mean crack diameter plotted against mean particle size. To enableeasy comparison, the dependence of Hertzian contact diameter is also plotted.With the exception of the tests conducted using 125–180mm sand, the mean crackdiameters are significantly smaller than the Hertzian contact diameter, dm.Moreover, table 7 shows that there is no significant dependence of crack diameteron the sand size used in the different tests.

This absence of any correlation between Hertz theory and circumferentialcrack diameter requires that other mechanisms be considered. One explanationcould be that the circumferential cracks on the surface are formed by stress wavereflection and interaction at locally debonded regions of the coating. This mechanismis more usually found in liquid impact studies [28, 29]. However, the discrepancyin hardness between sand and diamond means that the contact conditions in thiscase may bear a closer resemblance to liquid impact than to Hertzian contact.

The two possible processes of stress wave reflection and reinforcement areshown in schematic form in figure 15 [32]. Bulk compression and shear waves arereflected at the rear surface to return to the front surface of the target to reinforce

Table 7. Comparison of measured crack diameters with Hertz theory at 250m/s.

Range ofsand sizes(mm)

Mean sanddiameter(mm)

Mean Hertziancontact diameter

dm (mm)

Mean crackdiameter(mm)

Standard deviation(crack diameter)

(mm)

No. ofcracks/pin-

holes

125–180 165 62 93 16 6180–250 227 86 92 10 4250–355 322 122 93 11 12355–500 441 168 106 24 13

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the Rayleigh surface wave, which generates a localized tensile stress at this surface.

This creates a ring of tensile stress and could explain the discontinuous

cracks surrounding the area of impact. These cracks are short and discrete owing

to the short duration of the impact, typically less than 1 ms [33]. Close examination of

the circumferential crack shown in figure 7 reveals it to be a ring of discontinuous

cracks rather than a single ring crack. In contrast, Hertzian ring cracks nucleate from

a favourably orientated surface flaw just outside the contact circle and then

propagates around the contact circle to form a surface ring crack [34].On the basis of the two stress wave reflection scenarios, the radii of the

circumferential cracks were predicted by Bowden and Field [28] and later extended

0 20 40 60 80

100 120 140 160 180 200

0 200 400 600

Mean Particle Diameter (µm)

Mean Crack Diameter(µm)

Mean CircumferentialCrack Diameter (µm)

Hertz Contact Diameter(µm) SW reinforcementdiameter d1 (µm)

SW reinforcementdiameter d' (µm)

Figure 14. Graph showing the relationship between mean particle diameter and themean circumferential crack diameter for 30mm diamond coatings on tungsten tested at250m/s. The Hertz contact diameter is also included for comparison. The error bars denote1 standard deviation.

CT

y1

c1c1

cR

0

(a)

0y’

c1 c1

cRc2

c2

(b)

CT

Figure 15. Two possible processes of stress wave reinforcement to generate circumferentialcracks in CVD diamond [32]. Key: 0¼ origin of impact; c1¼ compression wave; c2¼ shearwave; cR¼Rayleigh wave.

Behaviour of diamond coatings under high velocity sand erosion 5735

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by Seward et al. [29]. The ratios of the compression and shear wave velocities

are given by:

c1c2

¼2ð1� �Þ

ð1� 2�Þ

� 1=2

¼ 1:47 ð16Þ

The velocities of the three wave types in diamond used in the calculations were

c1¼ 18 235m/s, c2¼ 12 400m/s and cR¼ 11 160m/s. A Poisson’s ratio, �, of 0.07 was

used in the velocity calculations. Using this information, it is possible to predict the

radii of these two reinforcements, y1 and y0, as a function of coating thickness, CT.

The calculated radii are:

y1CT

¼ 1:52 ð17Þ

and

y1

CT¼ 2:14 ð18Þ

This gives the diameters of the circumferential cracks as:

d1 ¼ 2y1 þ�y ð19Þ

and

d1 ¼ 2y1 þ�y ð20Þ

�y is the diameter over which the high pressure phase exists and is equal to 2RV/ce(in the case of liquid impact): in the present case, R is the mean radius, V is

the impact velocity and ce is the speed of sound in the erodent, the value of which

(6079m/s) was calculated using equation (21):

ce ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiE

��

1� �

1� 2�ð Þ 1þ �ð Þ

� �sð21Þ

The values of elastic modulus (E), density (�) and Poisson’s ratio (�) for silica (SiO2)

used in calculating ce can be found in table 1.Using equations (17)–(20), the predicted stress wave reinforcement diameters for

a 30 mm coating have also been plotted in figure 14. It can be seen that reasonable

agreement exists between the measured circumferential crack diameters and the

predicted diameter d1. The slight variation in d1 is due to the variation in the term

�y, which is dependent on sand size, although the influence of �y on the stress wave

reinforcement diameters is small.Although the dominant reinforcement for materials with low Poisson’s ratios

should be y0 [29], it should be remembered that the Poisson’s ratio of diamond is

known to vary between 0.01 and 0.2 depending on the exact crystallographic

orientation; the aggregate value is 0.07 [14]. These variations in Poisson’s ratio within

the coating, together with microstructural defects could result in discrepancies

between the predicted diameters and the measured crack diameters. It should

be emphasized that the predicted stress wave reinforcement diameters do not take

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into account microstructural defects in the coating. Features such as columnar grainsand grain boundaries, as well as the presence of residual stresses, may influencewave propagation through the coating. The stress wave reinforcement diameters mayalso be altered by scattering of bulk waves at the coating–substrate interface bygrain-boundary porosity; the calculations above ignore such effects and assumea perfect interface. Nevertheless, it is evident that the stress wave reinforcementdiameters are closer to the circumferential crack diameters than the predictedHertzian contact diameter.

In proposing the stress wave reinforcement mechanism by which thecircumferential cracks are formed, it is recognized that the Hertz impact theoryhas been used to explain sub-surface failure, while at the same time it hasbeen dismissed as an explanation for the formation of the circumferential cracks.This apparent logical inconsistency can be reconciled by recalling that shear stresseshave also been attributed to being the cause of sub-surface damage in non-Hertzianimpact conditions, for instance liquid impact. In studies of liquid impact on PMMAtargets, Bowden and Brunton [35] found evidence of damage below the surface ata depth of about half the contact radius. This location is close to where the maximumshear stress occurs for elastic contact as predicted by Hertz. However, the shearstress is also likely to be augmented by the interaction of release waves from thecontact periphery to give a net tension. This has been demonstrated experimentallyin liquid impact studies of PMMA [36, 37]. It is possible that this is happening inthe sand impact of diamond; however, this needs to be investigated further.

In theoretical work, shear stress as a result of liquid impact has also beenpredicted. In a finite element model of liquid impact onto a silicon sample coatedwith a 30 mm diamond film, de Botton [38] found that the model predicted theexistence of an intensive peak of in-plane shear stresses just beneath the pointat which the load terminates. This mirrors the quasi-static analysis as described byvan der Zwaag and Field [9].

5.3 Use of erosion data to assist coating design

The results of the present tests have shown that coatings exhibiting the greatestresistance to debonding are those in which the stress field is contained within thecoating. Moreover, there appears to be a critical normalized depth of maximumshear stress (z�/CT), below which the life of the coating is limited only by the low rateof micro-chipping by the impacting sand particles. This is of great importance inthe design of coating systems exposed to erosive particles in service and shows thatcoatings less than a certain thickness offer little resistance to sand particle impacts.However, it does not automatically follow that increasing the thickness of thecoating confers enhanced erosion resistance. In certain circumstances, residualstresses present in the coating may be of sufficient magnitude to be detrimentalto both the erosion resistance and the coating adhesion. Therefore, there may be apoint beyond which any further increase in coating thickness will not procure anyextra benefit in terms of coating performance.

The findings in this study can be used to assist the design of coated componentsfor use in erosive environments. The data from this study have been used to

Behaviour of diamond coatings under high velocity sand erosion 5737

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construct a map, shown in figure 16, of velocity against sand radius showingthe regions where pin-holes are found (z�/CT� 0.3), where they have not been seen(z�/CT50.3) and where rapid failure of the coating occurs (z�/CT� 1). This map onlyapplies to diamond coatings on tungsten 30 mm in thickness. This work should beextended to cover coatings of greater thickness and on different substrates.

6. Conclusions

This study has looked at the effect of varying the depth of a maximum shear stressof 9.5GPa on the integrity of diamond coatings subjected to high velocity erosionby silica sand. This was achieved by using finely sieved sand of different diameters ata constant nominal velocity of 250m/s.

The erosion experiments indicate that sub-surface shear stresses, generated by theimpact of the sand particles, are responsible for the generation of coating-debonding.When the maximum shear stress occurs close to the coating–substrate interface, thecoating fails rapidly and catastrophically. For this reason, diamond coatings usedin erosive environments must be sufficiently thick to ensure that �max is containedwithin the coating and is away from the interface.

The results have shown an approximately exponential relationship betweenparticle size and number of impacts necessary to initiate pin-holes. As an example, areduction in the mean particle size by one-third (441 to 165 mm) increases the numberof impacts necessary to generate pin-holes by a factor of approximately 2600.

Examination of the eroded coatings revealed the presence of circumferentialcracks and pin-holes, which were observed to have formed approximately tF¼ 0.3,

y = 1E+07x –2.5149

y = 2E+08x –2.4989

1

10

100

1000

10000

10 100 1000

Sand Radius (µm)

Velocity(m/s)

Velocity forz/CT = 1

Velocity forz/CT = 0.3

Power (Velocityfor z/ CT = 0.3)

Power (Velocityfor z/ CT = 1)

No pin-holes

Rapid failure ofcoating

Pin-holes

Figure 16. Graph of particle impact velocity versus sand radius for lapped 30 mm diamondcoatings on tungsten showing the theoretical velocities required for z�/CT¼ 0.3 and z�/CT¼ 1.

5738 D. W. Wheeler and R. J. K. Wood

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where tF is the time to failure of the coating. Images acquired using scanningacoustic microscopy have shown that these features are only found on delaminatedareas of the coating. This suggests that coating delamination is a necessarypre-condition for the nucleation and growth of circumferential cracks and pin-holes.The formation of these features, therefore, appears to provide a visible indicationthat coating delamination is taking place at the interface, which may be followedby catastrophic failure of the coating.

Hertz impact theory appears to explain the debonding mechanism in diamondcoatings subjected to impact from sand particles. The results suggest that for 30 mmcoatings tested at 250m/s, when z�/CT50.3, pin-holes are not generated asthe maximum shear stress, �max, is insufficient to generate coating delamination.In these cases, the life of the coating can be considered to be limited only by the lowrate of micro-chipping. Under the conditions used in the present study, theadditional interfacial shear stress required to promote coating delamination appearsto be approximately 5.4GPa.

The mean circumferential crack/pin-hole diameters do not agree with thepredicted Hertzian contact diameters. Furthermore, the measured crack and pin-holediameters appear to be independent of particle size and morphology. Instead, it isthought that the circumferential cracks are formed via a mechanism of stress wavereflection and reinforcement at locally debonded regions of the coating. Thereasonable agreement between the measured crack diameters with stress wavereinforcement diameter appears to support this hypothesis.

The results from this study have indicated that, in order to predict the behaviourof diamond coatings under conditions of high velocity sand erosion, the modelmust incorporate elements of both dynamic Hertzian coating debonding and stresswave reinforcement crack propagation.

References

[1] Z. Feng, Y. Tzeng and J.E. Field, Thin Solid Films 212 35 (1992).[2] C.S.J. Pickles, E.J. Coad, G.H. Jilbert, et al., Mater. Res. Symp. Proc. 383 327 (1995).[3] R.H. Telling, G.H. Jilbert and J.E. Field, Proc. SPIE 3060 56 (1997).

[4] D.W. Wheeler and R.J.K. Wood, Wear 233/235 306 (1999).[5] D.W. Wheeler and R.J.K. Wood, Wear 225/229 523 (1999).[6] R.H. Telling and J.E. Field, Diamond Relat. Mater. 8 850 (1999).

[7] D.W. Wheeler and R.J.K. Wood, Surf. Coat. Technol. 200 4456 (2006).[8] D.W. Wheeler and R.J.K. Wood, Phil. Mag. Lett. 85 367 (2005).[9] S. Van der Zwaag and J.E. Field, Phil. Mag. 46 133 (1982).[10] A.G. Evans, M.D. Drory and M.S. Hu, J. Mater. Res. 3 1043 (1988).

[11] M. Comninou, Trans. ASME: J. Appl. Mech. 44 631 (1977).[12] C.A. Klein, Opt. Eng. 40 1115 (2001).[13] R.H. Knibbs, J. Phys. E 2 515 (1969).

[14] J.E. Field, The Properties of Natural and Synthetic Diamond (Academic Press, New York,

1992).[15] R.S. Sussmann, J.R. Brandon, G.A. Scarsbrook, et al., Diamond Relat. Mater. 3 303

(1994).

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[16] P.H. Shipway and I.M. Hutchings, Wear 193 105 (1996).[17] R.H. Telling and J.E. Field, Wear 233/235 666 (1999).[18] S.P. Timoshenko and J.N. Goodier, Theory of Elasticity (McGraw-Hill, New York,

1970).[19] E.H. Yoffe, Phil. Mag. 50 813 (1984).[20] B.R. Lawn, Fracture of Brittle Solids, 2nd ed. (Cambridge University Press, Cambridge,

1993).[21] K.L. Johnson, Contact Mechanics (Cambridge University Press, Cambridge, 1985).

[22] M.G.D. El-Sherbiney and J. Halling, Wear 40 325 (1976).[23] R.J.K. Wood and D.W. Wheeler, Wear 220 95 (1998).[24] D.W. Wheeler and R.J.K. Wood, Wear 250 795 (2001).

[25] S. Raadnui and B.J. Roylance, Lubr. Eng. 51 432 (1995).[26] D.W. Wheeler and R.J.K. Wood, Proceedings of the International Tribology Conference

Nagasaki (2000) (Japanese Society of Tribologists, Tokyo, 2000), pp. 1095–1099.[27] D.W. Wheeler and R.J.K. Wood, Diamond Relat. Mater. 10 459 (2001).[28] F.P. Bowden and J.E. Field, Proc. R. Soc. Lond. A 282 331 (1964).

[29] C.R. Seward, J.E. Field and E.J. Coad, J. Hard Mater. 5 49 (1994).[30] D.W. Wheeler, PhD thesis, University of Southampton 92001.[31] E. Lassner and W.D. Schubert, Tungsten (Kluwer/Plenum, New York, 1999).

[32] E.J. Coad and J.E. Field, Proc. SPIE 3060 169 (1997).[33] J.E. Field, and I.M. Hutchings, 1984. Proceedings of the Third International

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Conf. Ser. 70, 349 (1984).

[34] B.R. Lawn, J. Appl. Phys. 39 4828 (1968).[35] F.P. Bowden and J.H. Brunton, Proc. R. Soc. Lond. A 263 433 (1961).[36] T. Obara, N.K. Bourne and J.E. Field, Wear 186/187 388 (1995).[37] N.K. Bourne, T. Obara and J.E. Field, Phil. Trans. R. Soc. Lond. A 355 607 (1997).

[38] G. De Botton, Wear 219 60 (1998).

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