Analytical modeling of solid-particle erosion of Stellite alloysin combination with experimental investigation

S. Nsoesie a, R. Liu a,n, K.Y. Chen b, M.X. Yao c

a Department of Mechanical and Aerospace Engineering, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, Canada K1S 5B6b Institute for Aerospace Research, National Research Council of Canada, 1200 Montreal Road, Ottawa, Ontario, Canada K1A 0R6c Kennametal Stellite Inc., P.O. Box 5300, Belleville, Ontario, Canada K8N 5C4

a r t i c l e i n f o

Article history:Received 24 June 2013Received in revised form19 November 2013Accepted 24 November 2013Available online 1 December 2013

Keywords:Stellite alloySolid-particle erosionModelingErosion rateParticle impact velocityParticle impinging angle

a b s t r a c t

This article presents the analytical modeling of erosion behavior of Stellite alloys under solid-particleimpact. The erosion rates of five selected Stellite alloys, which are currently or potentially applied in anenvironment condition involving erosion, are investigated experimentally at two particle impactvelocities of 84 and 98 ms�1, and at two impingement angles of 301 and 901. The Sheldon–Kanhere(S–K) model that utilizes the indentation hardness theory to derive a particle penetration equation ismodified to fit the experimental data of Stellite alloys. The most significant improvement of this modifiedmodel is to include the effect of particle impingement angle. This introduces two parameters in themodel, which are determined by fitting the experimental data of the five Stellite alloys. With thismodified model, for Stellite alloys that have similar chemical compositions to the alloys studied in thisresearch, the erosion rates at the particle impact velocity of 84 m s�1 or 98 m s�1 can be predicted forany particle impingement angles less than 301. The limitations of this model are discussed.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

Erosive wear, as one of wear degradations, is the multitudinousphenomena characterized by a progressive deterioration of mate-rials. There are a couple of parameters that influence the erosionrate of materials. The extent to which each parameter contributesto the erosion rate would depend on the environmental conditionstogether with the type of material under investigation. The mainimpact parameters are impact angle, particle velocity, particle size,shape and properties of both the abrasive particles and the targetmaterial under consideration [1]. Due to high cost and longduration involved in erosion testing, physics-based and statistics-based erosion models have been developed to predict/reveal theerosion resistance/mechanisms of materials. These models couldalso be used to predict the life of metals in erosive environments.A number of studies have proposed a variety of correlativeequations between impact parameters and erosion damage causedby solid particle impact.

Finnie [2] developed the first erosion model for ductile materi-als where he considered erosion as a micro-machining process. Hismodel was based on an ideal ductile, non-work hardening solidtarget material eroded by rigid particles. Finnie [3] furtherexpanded his original model and proposed an erosion formulation

derived from analyzing the motion equations of a single particleimpacting a ductile surface. Although the calculations of theequations agreed with experimental data for low impact angles(between 151 and 301), it however contradicted experimentalresults for impact angles greater than 601 and even predicts zeroerosion rate at near 901 impact angles. Tilly [4] studied ductilematerial erosion, and proposed a removal mechanism involving ascrapping and extrusion of materials to form ridges that werevulnerable when attacked by particles moving at a high velocity.Tilly [5] further developed a two-stage model of the erosionprocess for ductile materials. Bitter [6,7] proposed a model forsingle-particle erosion of metals with an assumption that bothtypes of erosion mechanisms (cutting and deformation) occurredsimultaneously but further noted that “deformation wear” wouldbe the dominant wear mechanism at normal incidence while“cutting wear” would be dominant at shallow angles. The erosiontheory given by Bitter [6,7] showed complex forms in terms ofexpression and implementation, which were concerned by Neilsonand Gilchrist [8] to seek a simpler analytical solution. Hutchingsand Winter [9] investigated the work hardening and annealingeffects on the erosion mechanism of ductile materials. In theirstudies, they used a large steel sphere attacking on an aluminumsurface to investigate single particle erosion, and postulated thatthe material removal mechanism was the shearing of the surfacelayer of the ductile metal target in the direction of motion of theprojectile and an overhanging lip was formed and removedduring the erosion process. Hutchings [10] developed a model

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/wear

Wear

0043-1648/$ - see front matter & 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.wear.2013.11.026

n Corresponding author. Tel.: þ1 613 5202600x8397; fax: þ1 613 5205715.E-mail address: Rong.Liu@carleton.ca (R. Liu).

Wear 309 (2014) 226–232

of multiple-particle erosion of metals using spherical particlesimpacting at normal angle and represented their results as massloss per unit mass of impinging particles. He postulated that themechanism of material removal was the formation and detach-ment of platelets of the material, and assumed that only after acritical strain was attained in the material would this detachmentoccur. Sundararajan and Shewmon [11] proposed a model formultiple-particle erosion of metals using the same criterion of acritical strain needed for material removal; their findings agreedbetter with experimental erosion data compared to Hutching'smodel [10]. Sheldon and Kanhere (S–K) developed an erosionmodel to study large single particle impact on 6061-TO aluminumsurface [12]. In this model, a particle penetration equation wasderived using the indentation hardness theory; the erosion ratewas formulated including particle diameter, density and impactvelocity, as well as target surface hardness.

Stellite alloys are a family of cobalt-based alloys containing alarge amount of chromium, Cr (20–30 wt%), also tungsten, W (4–18 wt%) or molybdenum, Mo (up to 28 wt%) and a small amount(o3 wt%) of carbon, C [13]. These alloys are generally strength-ened by the precipitation of various carbides in the cobalt solidsolution matrix, which provides a unique combination of mechan-ical and tribological properties such as high hardness and strength,superior adhesive and abrasive wear resistance and excellent solidparticle and cavitation erosion resistance. They also display excel-lent corrosion and oxidation resistance due to the high Cr content.These superior properties to other alloys make Stellite alloyswidely employed in various applications, typically in gas turbineengines, oil production and refining, and mechanical manufactur-ing that involve metal to metal wear, fretting, hot corrosion,particle erosion plus others. Although some experimental studiesin erosion behavior of Stellite alloys have been reported [14,15],the reported data are very limited, which has retarded theapplication of these alloys in erosive environments. Since model-ing can reduce the high cost and long duration involved in erosiontesting, material researchers have been resorting to this approachin the erosion study. However, among the erosion models nonecan be used to effectively predict the erosion damage or loss ofStellite alloys. To this end, the present research attempted to createan erosion model for Stellite alloys. The S–K model [12], originallydeveloped for 6061-TO aluminum, was modified by fitting theexperimental data of five selected Stellite alloys under solid-particle erosion, and further improved by taking into account theparticle impinging angle, which was neglected in the S–K model.Using this model, the erosion resistance of a Stellite alloy whichhas a similar chemical composition to one of the alloys studied inthis research at the particle impact velocity of 84 ms�1 or 98 ms�1

can be predicted for different particle impingement angles. How-ever, this model has limitations; therefore, it is more suitable forcomparative study of erosion resistance between Stellite alloys.

2. Formulation of erosion model

In studying the hardness of metals by means of indenting a testsurface with a sphere, Meyer (1908) found that the diameter of therecovered indentation, d, for a given hard sphere is related to theapplied load, F, by the relation

F ¼ pdn; ð1Þ

where p is the load for unit diameter and n is the loga-rithmic index. The S–K model was derived from the energybalance consideration involving Meyers's relation on velocity-indentation. The associated kinetic energy (KE) for a normallyimpacting spherical particle with velocity, V, diameter, D, and mass

density, ρp, is given by [12]

KE¼ 12

34π

D2

� �3" #

ρpV2: ð2Þ

The work doneW, by the indenting sphere in a direction, x, normalto the surface from the time of surface contact until penetrationstops at a depth, q, is [12]

W ¼Z q

0Fdx ð3Þ

replacing F in Eq. (3) with Meyer's relation, the following can beobtained:

W ¼Z q

0pdndx: ð4Þ

Based on these relations, Sheldon and Kanhere [12] wentfurther and proposed that the material removal per particle orper gram of particles of the same size would be proportional to thecube of the penetration depth, q

w� q3 ¼D3V3ρ3=2p

H3=2v

ð5Þ

where w is the volume of material removed per gram of particles,i.e., erosion rate (m3/g); D is the particle diameter (m); V is theimpact velocity (m/s); ρp is the particle density (kg/m3); and Hv isthe Vickers hardness of the target material (Pa).

3. Solid-particle erosion test

To testify the validity of Eq. (5) for Stellite alloys, the solid-particleerosion test was conducted on five selected Stellite alloys, which arecommonly or potentially used for erosion resistance in various fields.The chemical compositions of these alloys are listed in Table 1. Thefirst three alloys contain high carbon content, thus a large volumefraction of carbides, as shown in Fig. 1. Alloy C also contains very hightungsten content, which results in a large amount of (W,Co)6Ccarbide in addition to Cr7C3 carbide. The last two alloys contain verylow carbon content, but high molybdenum, which induces a largeamount of intermetallic compounds Co3Mo and CoMo6 in themicrostructures, as shown in Fig. 1. Alloy D also has precipitatedCr23C6 due to higher carbon content, compared to alloy E.

The hardness of these alloys was measured on a MicrohardnessTester Unit, Model SMT-X7 Dual Indenter, under an indentationload of 2 kg. Ten tests were made on each alloy and the averagehardness values are reported in Table 2, with the measurementerror within 4.23%. The density data of the alloys were provided bythe alloy supplier and are also reported in Table 2.

The erosion tests of the Stellite alloys were conducted on an S.S.WHITE Airbrasive Micro-Blasting Jet Machine, Model 6500 ErosionChamber, according to the ASTM G76-02 Standard Test Method forConducting Erosion Tests by Solid Particle Impingement Using GasJets [16]. The specimen holder contains a screw which allows the

Table 1Chemical compositions (wt%, Co in balance) of Stellite alloys.

Alloy Element

Cr W Mo C Fe Ni Si Mn Others

Alloy A 30 4.5 1.5 1.6 3 3 2 2Alloy B 30 4 1.5 1 3 2.5 0.7 1.4Alloy C 22 32 0 1.5 0 0 0 0Alloy D 24.2 0 11.8 0.35 1 3.8 0.45 0.52 2.07NbAlloy E 27 0 11 0.25 3 2.75 1 1

S. Nsoesie et al. / Wear 309 (2014) 226–232 227

specimen to be adjusted and rotated at various angles so as tocorrespond to the different impingement angles in the test. Twotypical impingement angles of 301 and 901, which representdifferent erosion mechanisms, were selected for each alloy. Theduration time (10 min) of each test was selected so as the erosionlosses of the alloy specimens can be identified and compared. Eachspecimenwas machined to a rectangular block with the dimensionof 76�25�3 mm3. The sand (erodent particles) used for this testis angular in shape and commercial AccuBRADE-50 blend #3 alphaalumina powder with an average particle size of 50 mm andhas the density of 3890 kg/m3. The erosion test unit containing

erodent particles (sand) was placed on a scale throughout the testprocess; the mass of this unit was recorded before and afterrunning each test. Thus the amount of sand used in each test couldbe quantified by taking the difference between these two values.

According to the ASTMG76-02 Standard, the distance between thenozzle head and the tested specimen surface for hard materials wasset to be 5 mm, because at this shorter distance, reasonable damagecould be identified on the specimen surface. In the test the voltagecontroller was adjusted to a value between 4 and 6 V, which couldachieve a particle flow rate in the range of 84–98 ms�1.

4. Erosion model for Stellite alloys

4.1. Erosion rates

Four tests were performed on each alloy at each test condition(particle velocity and impingement angle). The averages of mass

Cr7C3 carbide

(W,Co)6C

Cr7C3 carbide

Cr7C3 carbide

Cr7C3 with intermetallic Co3Mo and CoMo6

Cr7C3 with intermetallic Co3Mo and CoMo6

Precipitated Cr23C6

Fig. 1. SEM microstructures: (a) alloy A; (b) alloy B; (c) alloy C; (d) alloy D; and (e) alloy E.

Table 2Vickers hardness and density data of Stellite alloys.

Alloy Alloy A Alloy B Alloy C Alloy D Alloy E

Vickers hardness (GPa) 4.36 3.78 6.16 3.95 3.70Density (kg/m³) 8387 9720 8387 8400 8420

S. Nsoesie et al. / Wear 309 (2014) 226–232228

loss for each alloy were calculated from the four test results.The erosion rate is expressed as the ratio of the mass loss of thetarget material to the mass of the erodent particle used as follows:

Erosion rate; ER μg=g� �¼ specimen mass loss ðμgÞ

mass of sand used ðgÞ : ð6Þ

As a statistics analysis measurement, the values of standarddeviation, s, of the erosion rates, were computed for errorestimation. The average erosion rates in mg/g at impact velocitiesof 84 and 98 ms�1 for the five alloys, together with the experi-mental errors (3s), are reported in Table 3. The erosion rates inm3/g that were computed from the S-K model using Eq. (5) arepresented in Table 4. In order to fit the experimental erosion ratesto the S-K model, the weight losses of the experimental data wereconverted to the volume losses; the erosion rates per gram oferodent particle in m3/g are presented in Table 5.

4.2. Model modification

It is shown that the experimental erosion rates are in the orderof 10–11 m3/g while the predicted erosion rates from the S–Kmodel are in the order of 10�17 m3/g. This is due to the fact thatthe S–K model was developed originally based on the experi-mental data of aluminum which is much softer and less erosion-resistant than Stellite alloys. Aluminum and Stellite alloys fall intotwo different categories of materials with respect to mechanicalproperties. Aluminum is more ductile than Stellite alloys. There-fore, before proceeding further, the predicted erosion rates shouldbe multiplied by a factor of 106 to correct for the difference inorder. Thus, the appropriate erosion model equation to be used forStellite alloys is

w¼ CD3V3ρ3=2p

H3=2v

: ð7Þ

where C is a constant known as the order correction factor with avalue of 106. To perceive a visual comparison between the S–Kmodel results and the experimental data, both of the erosion ratesare plotted together in Fig. 2.

From the comparison, it is observed that the predicted values oferosion rate from the S–K model do not best fit the experimentalerosion rates in that all the predicted values are higher than theexperimental measurements. The main reason for this differencemay be the fact that the S–K model does not account for the

particle impingement angle. Therefore modification of this modelto better suit these alloys is necessary.

The modification for the S–K model is to include the particleimpingement angle, α. The modified model contains a new erosionrate function, w1, of five variables, i.e., w1 (D, V, ρp, HV , and α).Checking each variable in w1 and considering the actual physics ormechanisms occurring during the erosion process, it is customaryto assume that a change in the particle impact angle wouldmost likely affect the normal and tangential components of theparticle impact velocity on the target material. This tends to affectthe erosion mechanism occurring at each particle impact angle.

Table 3Experimental erosion rates, ER (mg/g), with the errors (3s).

Alloy ER at 84 ms�1

and 301ER at 84 ms�1

and 901ER at 98 ms�1

and 301ER at 98 ms�1

and 901

Alloy A 1997110 119782 3257189 2197107Alloy B 246790 2077103 3487107 2977176Alloy C 2667116 173796 3647128 2497107Alloy D 2927122 2407155 423796 270782Alloy E 333790 213781 3777134 223795

Table 4S–K model erosion rates, ER (m3/g�10�17).

Alloy Volume lossat 84 ms�1

Volume lossat 98 ms�1

Alloy A 6.25 9.93Alloy B 3.72 5.90Alloy C 7.48 11.9Alloy D 7.23 11.5Alloy E 8.00 12.7

Table 5Experimental erosion rates, ER (m³/g�10�11).

Alloy ER at 84 ms�1

and 301ER at 84 ms�1

and 901ER at 98 ms�1

and 301ER at 98 ms�1

and 901

Alloy A 2.38 1.43 3.88 2.62Alloy B 2.54 2.14 3.58 3.06Alloy C 3.18 2.07 4.34 2.98Alloy D 3.49 2.86 5.04 3.21Alloy E 3.96 2.54 4.48 2.65

Fig. 2. Comparison of erosion rate results of Stellite alloys: (a) at particle impactvelocity of 84 ms�1 and (b) at particle impact velocity of 98 ms�1.

S. Nsoesie et al. / Wear 309 (2014) 226–232 229

Therefore, the modified particle impact velocity will be expressedas a function of particle impact angle and the “originally set”impact velocity from now forth, i.e., V1 is a function of twovariables, V1(V, α), expressed as

V1 ¼ VK ; ð8Þwhere V1 is the modified particle impact velocity (m/s); V is theoriginally set particle impact velocity (m/s); and K is a dimension-less function of α, K(α), and is defined as the angle correctionfactor. After working through fitting algorithms of the experi-mental data and comparing these results to the values of wobtained from Eq. (7) for each alloy, the proposed form of K forthese Stellite alloys was found to take the following form:

K ¼ XB; ð9Þand

X ¼ A sinα

2

� �� �13; ð10Þ

where A is a constant referred to as the shifting coefficient; and Bis another constant called the shifting exponent. It should be notedthat both the shifting coefficient and shifting exponent are targetmaterial-dependent. The compacted form of the modified model isgiven as

w1 ¼C1D

3ðVKÞ3ρ3=2p

H3=2v

: ð11Þ

Substituting Eqs. (9) and (10) into Eq. (11) yields the followingexpression:

w1 ¼C1D

3ðVðAð sin ðα=2ÞÞ1=3ÞBÞ3ρ3=2p

H3=2v

: ð12Þ

4.3. Determination of constants

To determine the two constants, A and B, in Eq. (12) for each ofthe five Stellite alloys under study, an iteration process was taken.Taking C¼1�106, D¼50�10�6 m, ρp and Hv values for the alloyconcerned, α¼301 or 901 and V¼84 m/s or 98 m/s, inserting thesevalues into Eq. (12) and making trials on the values of A and B,towards the corresponding experimental erosion rates in Table 5for w1, the values of A and B were determined such that the w1

values from Eq. (12) reached the experimental erosion rates withan error less than 5%. The fitted A and B values for each alloy aresummarized in Tables 6 and 7. It is found that although the valuesof A and B vary from alloy to alloy they are close to each otherwithin the Stellite alloys. Also, it is noticed that the values of A andB vary insignificantly with the particle impact velocity.

Since the A and B values for each alloy do not vary significantlywith the particle impact velocity, with the values of A and Bobtained for each alloy, for a given particle impact velocity, theerosion rate of the alloys in Table 1 at any impinging angle can bepredicted. Also, it is found that the difference in the A and B values

between the alloys is very small so that for any Stellite alloy thathas a chemical composition similar to that of one of the five alloysin Table 1 the erosion rate can be estimated using the modified S–K model.

5. Discussion on results

5.1. Limitation of the modified S–K model

Using the modified S–K model, for the five Stellite alloys inTable 1, at the particle impact velocities of 84 and 98 ms�1,respectively, the erosion rates at various particle impingementangles between 101 and 901 were predicted; the results areillustrated in Fig. 3. It is shown that for the two particle impactvelocities, the erosion rates of all the alloys decreased with theimpingement angle.

However, according to the experimental findings of previousstudies [17], these alloys should behave differently at particleimpingement angles smaller and larger than the “critical impinge-ment angle” that may be around 301. As depicted Fig. 4, formetallic materials (metals), at small impingement angles, erosionrate increases with the increase in impingement angle until theangle reaches the “critical impingement angle” and thereafter theerosion rate decreases with impingement angle.

The deviation of the predicted erosion rates from the experi-mental observation is caused by the fact that the modified S–Kmodel was obtained by fitting the experimental data of erosion at301 and 901 impingement angles using a statistics method and thephysical behavior of the materials under erosion with respect tothe “critical impingement angle” is not concerned. Therefore, thismodel has a deficiency in predicting the erosion rate of Stellitealloys at particle impingement angles less than 301. In otherwords, the erosion behavior of these alloys changes significantlyat the impingement angles around 301. Further research has beenplanned to conduct an erosion test on Stellite alloys at the particleimpingement angles around or less than 301 and thus continue toimprove the S–K model.

5.2. Effects of hardness on erosion rate

In Eq. (12) the only material property parameter of targetsurface is hardness. If all the other parameters are kept unchanged,the erosion rate is inversely proportional to the hardness of targetsurface. Of course, the parameters A and B are material property orfeature related, because they vary among Stellite alloys. Thereforeit cannot be simply concluded that the harder the target surface,the less the erosion loss. The hardness of Stellite alloys mainlycomes from various carbides, but for low-carbon Stellite alloys, forexample, alloy D and alloy E, the large amounts of intermetalliccompounds are also the main contribution to hardness. In general,the hardness of Stellite alloys increases with their carbon content,

Table 6Fitted constants and predicted erosion rates from the modified model for particleimpact velocity of 84 ms�1.

Alloy Coefficient A Exponent B ER value(m3/g�10�11)for 301 angle

ER value(m3/g�10�11)for 901 angle

Alloy A 3.56 �0.413 2.26 1.49Alloy B 3.5 �0.15 2.58 2.22Alloy C 3.235 �0.3917 3.19 2.15Alloy D 3.452 �0.2893 3.64 2.72Alloy E 2.95 �0.3833 3.86 2.63

Table 7Fitted constants and predicted erosion rates from the modified model for particleimpact velocity of 98 ms�1.

Alloy Coefficient A Exponent B ER value(m3/g�10�11)for 301 angle

ER Value(m3/g�10�11)for 901 angle

Alloy A 3.5 �0.391 3.87 2.61Alloy B 3.45 �0.204 3.64 2.96Alloy C 3.75 �0.3867 4.32 2.93Alloy D 3.23 �0.3917 4.91 3.31Alloy E 3.67 �0.4277 4.26 2.77

S. Nsoesie et al. / Wear 309 (2014) 226–232230

but other elements, such as tungsten and molybdenum, also playan important role in determining the hardness of Stellite alloys. Asshown in Tables 1 and 2, the hardness of Stellite alloys generallyincreases with their carbon content, but it is abnormal for alloy C.This alloy has much higher hardness though it contains less carbonthan alloy A. The carbides in alloy A and alloy B are Cr-rich Cr7C3

carbide, as shown in Fig. 1. However, due to the very high tungstencontent, in addition to Cr-rich carbide, there is a large volumefraction of (W,Co)6C carbide in alloy C, which enhances thehardness. Although alloy D and alloy E contain very low carboncontent, they have comparable hardness to alloy B which ismedium-carbon Stellite alloy. This is attributed to the largeamounts of intermetallic compounds Co3Mo and CoMo6. To betterinvestigate the influence of hardness on the erosion resistance forStellite alloys, the S–K model predicted and experimental erosionrates, along with the alloy hardness values, are summarized inTables 8 and 9. It is seen that generally the erosion resistance ofStellite alloys increases with the hardness, but the type andamount of carbides and intermetallic compounds also influencesignificantly the erosion rate.

Two main material damage/removal mechanisms involved insolid-particle erosion wear have been suggested [6,7], which arethe cutting and extensive/repeated deformation of the targetmaterial. At the inclined angle (301) impact, the cutting of thetarget surface by particles is accompanied with shearing of thesub-surface layer; therefore both hardness and ductility of thesurface material are the key factors characterizing the erosionbehavior of the surface. Hardness dominates the resistance of thesurface to cutting, while ductility controls the plastic deformationof the sub-surface. On the contrary, at the normal angle (901)impact, the particles exert compressive loads on the target surface;therefore, the overall surface is subjected to compressive stresses,but local areas of the surface could be under tension due to thenon-uniform particle impact on the surface, leading to local plasticdeformation of the surface.

As demonstrated by the erosion rate results in Tables 8 and 9, at301 impact, alloy A has the highest hardness among the alloysexcept alloy C and it exhibits the best resistance. Alloy C, although,is the hardest, the large amounts of (W,Co)6C carbide are morebrittle than Cr7C3 carbide [18]; under the continuous particleimpact, these carbides were vulnerable, adding to the erosion loss.Furthermore, the intermetallic compound strengthened alloys,alloy D and alloy E, have comparable hardness to the Cr-richcarbide strengthen alloy, alloy B, but the former exhibited muchlower erosion resistance. This is also due to the brittleness of theintermetallic compounds Co3Mo and CoMo6. However, at 901

Fig. 3. Predicted erosion rates at various particle impingement angles using themodified S–K model: (a) at 84 ms�1 particle impact velocity and (b) at 98 ms�1

particle impact velocity.

Fig. 4. Schematic diagram showing the influence of the particle impact angle onerosion rate of materials [14].

Table 8Hardness and erosion rates (m3/g�10�11) at particle impact velocity of 84 ms�1.

Alloy Vickershardness(GPa)

S–K modelER valuefor 301angle

ExperimentalER value for301 angle

S–K modelER valuefor 901angle

ExperimentalER value for901 angle

Alloy A 4.36 2.26 2.38 1.49 1.43Alloy B 3.78 2.58 2.54 2.22 2.14Alloy C 6.16 3.19 3.18 2.15 2.07Alloy D 3.95 3.64 3.49 2.72 2.86Alloy E 3.70 3.86 3.96 2.63 2.54

Table 9Hardness and erosion rates (m3/g�10�11) at particle impact velocity of 98 ms�1.

Alloy Vickershardness(GPa)

S–K modelER valuefor 301angle

ExperimentalER value for301 angle

S–K modelER valuefor 901angle

ExperimentalER value for901 angle

Alloy A 4.36 3.87 3.88 2.61 2.62Alloy B 3.78 3.64 3.58 2.96 3.06Alloy C 6.16 4.32 4.34 2.93 2.98Alloy D 3.95 4.91 5.04 3.31 3.21Alloy E 3.70 4.26 4.48 2.77 2.65

S. Nsoesie et al. / Wear 309 (2014) 226–232 231

impact, the hardness of Stellite alloys played more predominantrole in resisting plastic deformation and thus controlled theerosion damage; of course, the brittleness also has influence, asobserved on alloy C.

Expedited particle impact increased the erosion losses of thealloys, as shown in Table 3. Moreover, alloy D and alloy E allcontain a large volume fraction of intermetallic compounds ofCo3Mo and CoMo6, which are mixed with Cr7C3 carbide in theeutectic. These intermetallic compounds, on one hand, enhancedthe hardness of the alloys; on the other hand, were brittle andvulnerable under repeated particle impact. Since alloy D hasslightly higher molybdenum and carbon contents than alloy E, itis more brittle due to the larger volume fractions of intermetalliccompounds and carbide. When the velocity of the hard particleswas increased, the impact of the particles on the target surfacebecame more severe, which would cause more spallation of theintermetallic compounds from the target surface. This is why theerosion loss of alloy D was higher than that of alloy E at 98 m/sparticle impact velocity.

6. Conclusions

The S–K erosion model was modified and employed to predictthe erosion rate of Stellite alloys under solid-particle erosion. Themain contribution of this modification was to include the particleimpingement angle, thus improved the S–K model with morereasonable prediction of erosion rate.

Using this modified S–K model, for any of the Stellite alloysstudied in this research, the erosion rate at the particle impactvelocities of 84 and 98 ms�1 can be predicted for different particleimpinging angles. Also, with this model, for any Stellite alloys thathave a similar chemical composition to one of the alloys studied inthis research, the erosion rate can be estimated.

However, due to the physical characteristics of metallic materi-als under erosion, that is, a “critical impingement angle” (around301) exists that alters the trend of the erosion rate with the particleimpingement angle, while the modified model was derived fromfitting experimental data using a statistics tool, this model haslimitations in predicting the erosion rate of Stellite alloys at theparticle impingement angles less than 301. In addition, since theerosion test was performed at the two particle impact velocitiesonly, this model is more suitable for the comparative study oferosion resistance between Stellite alloys.

To further improve the S–K model, future work is necessary.Firstly, the erosion test on Stellite alloy needs to be extended at the

particle impingement angles less than 301. Secondly, a wide rangeof particle impact velocity should be tested. Finally, this model wascreated based on the test data at room temperature; therefore it islimited to the environment condition.

Acknowledgments

The authors are grateful for the financial and testing equipmentsupport from MATICS, National Research Council Canada, andKennametal Stellite Inc.

References

[1] I.M. Hutchings, Mechanical and metallurgical aspects of the erosion of metals,in: A.V. Levy (Ed.), Proceedings of the Conference on Corrosion/Erosion of CoalConversion System Materials, NACE, Houston, 1979, pp. 393–428.

[2] I. Finnie, Some reflections on the past and future of erosion, Wear 186–187 (1)(1995) 1–10.

[3] I. Finnie, The mechanism of erosion in ductile materials, in: R.M. Hagth-ormthwaite (Ed.), Proceedings of the Third US National Congress of AppliedMechanics, ASME, New York, 1958, pp. 70–82.

[4] G.P. Tilly, Sand erosion of metals and plastics: a brief review, Wear 14 (4)(1969) 241–248.

[5] G.P. Tilly, A two stage mechanism of ductile erosion, Wear 23 (1) (1973) 87–96.[6] J.G.A. Bitter, A study of erosion phenomena, Part I, Wear 6 (1) (1963) 5–12.[7] J.G.A. Bitter, A study of erosion phenomena, Part II, Wear 6 (3) (1963) 169–190.[8] J.H. Neilson, A. Gilchrist, Erosion by a stream of solid particles, Wear 11 (2)

(1968) 111–122.[9] I.M. Hutchings, R.E. Winter, Particle erosion of ductile metals: a mechanism of

material removal, Wear 27 (1) (1974) 121–128.[10] I.M. Hutchings, A model for the erosion of metals by spherical particles at

normal incidence, Wear 70 (3) (1981) 269–281.[11] G. Sundararajan, P.G. Shewmon, A new model for the erosion of metals at

normal Incidence, Wear 84 (2) (1983) 237–258.[12] G.L. Sheldon, A. Kanhere, An investigation of impingement erosion using sing

particles, Wear 21 (1) (1972) 195–209.[13] J.R. Davis, Nickel, Cobalt, and Their AlloysASM International, Materials Park

(2000) 362–406.[14] C.J. Heathcock, A. Ball, B.E. Protheroe, Cavitation erosion of cobalt-based

Stellite alloys, cemented carbides and surface-treated low alloy steels, Wear74 (1) (1981) 11–26.

[15] W.L. Silence, Effect of structure on wear resistance of Co-, Fe-, and Ni-base, in:K.C. Ludema, S.K. Rhee (Eds.), Proceedings of the International Conference onWear of Materials, ASME, New York, 1987, pp. 77–85.

[16] ASTM G76-02 Standard Test Method for Conducting Erosion Tests by SolidParticle Impingement Using Gas Jets, ASTM International, USA, 2007.

[17] S. Kamran, K. Chen, P. Patnaik, S. Yun, Y. Han, Current Status of ModelingErosion and Erosion–Corrosion for Alloys and Protective Coatings, NRCProtected A, vol. II, LTR-SMPL-2010-0223 Report, National Research CouncilCanada, Ottawa, 2011.

[18] S. Kapoor, R. Liu, X.J. Wu, M.X. Yao, Temperature-dependence of hardness andwear resistance of Stellite alloys, in: Proceedings of the 2012 InternationalConference on Aerospace, Mechanical, Automotive and Materials Engineering(ICAMAME 2012), Paris, France, 2012, pp. 964–973.

S. Nsoesie et al. / Wear 309 (2014) 226–232232