A model to predict the solid particle erosion rate of metals and its assessment using heat-treated steels

Wear 248 (2001) 162–177

A model to predict the solid particle erosion rate of metals and itsassessment using heat-treated steels

D.J. O’Flynn1, M.S. Bingley∗, M.S.A. Bradley, A.J. Burnett2

The Wolfson Centre for Bulk Solids Handling Technology, The University of Greenwich, Woolwich, London SE18 6PF, UK

Received 14 November 2000; accepted 14 November 2000

Abstract

A new predictive model for the wear rate of metals during solid particle impact erosion is presented. The model proposes that erosionrate is related to the product of toughness (UT) and uniform strain (εU). Predictions for the variation of erosion rate with impact angle arealso made. The validity of the model was assessed using an extensive set of new experimental data generated for heat-treated steels. Twosteels were heat treated to form a total of 12 different microstructures, each having distinctly different mechanical behaviour. Erosion testswere carried out at a combination of three impact velocities and three angles of particle impingement in a rotating disc accelerator erosiontester. Fine olivine sand was used as the abrasive at one feed rate. Tensile tests were carried out on all the heat-treated steels over a range oftemperatures from room temperature to 400◦C. The model predictions were not satisfied by mechanical property measurements made atroom temperature. However, for each given erosion test condition, a good linear relationship was found between room temperature erosionrate and 1/UTεU when mechanical properties were measured at elevated temperatures. The elevated temperature chosen to give the best-fitwas between 200 and 300◦C depending on the impact velocity. It is believed that the significance of the elevated temperature propertymeasurements is that they account for localised heating occurring at the impacting particle during the high strain/strain-rate deformationtypical of erosion. Certain heat-treatments gave a poorer fit to the relationship and explanations for this are proffered. The model was alsoable to account for changes in erosion rate with impact angle. Suggestions are made for improving the model and to refine its predictivecapability. © 2001 Elsevier Science B.V. All rights reserved.

Keywords:Erosion; Martensite; Heat-treated steels

1. Introduction

The use of conventionally measured mechanical proper-ties to predict the erosion behaviour of a target material isan attractive proposition since this form of testing is sim-ple, cheap to conduct and data is readily available for manymaterials. For this reason, researchers have made manyattempts to assess the relationship between mechanicalproperties and the erosion process, with varying degrees ofsuccess. Early investigations of the erosion of metals con-centrated on the influence of indentation hardness [1–13],as it was postulated that this would determine the depth to

∗ Corresponding author. Tel.:+44-1634-883-495;fax: +44-1634-883-153.E-mail addresses:[email protected] (D.J. O’Flynn), [email protected] (M.S. Bingley), [email protected](M.S.A. Bradley), [email protected] (A.J. Burnett).

1 Present address: Dynamic suspensions Ltd, 20 Fison Way, Thetford,Norfolk, 1P24 1.

2 Present address: Svedala Bulk Materials Handling (Bristol), PO Box821, Ashton Vale Rd, Bristol, BS99 5ZB, UK.

which an impinging particle would penetrate a surface and,hence, govern the volume of material removed. There islittle evidence of a direct correlation between erosion andhardness when a wide range of metals is considered. Simi-lar results have been obtained in investigations investigatingthe effect of ductility and impact energy [1,14,15].

Despite the evidence of previous work, it is possible that arelatively simple relationship between mechanical propertiesand erosion may still be found. It seems surprising, for in-stance, that attempted correlations between erosion rate anda combination of mechanical properties have rarely been at-tempted despite more rigorously derived models indicatingthat such an approach might be necessary. For instance, inthe wear model proposed by Hutchings [16] erosion rate isdependent upon hardness,H, and the coefficient,K (whichgoverns the ‘efficiency’ of material removal). It is expectedthat K is itself material dependent and is related to one ormore mechanical properties. Thus, Hutchings’ model im-plies that erosion rate is dependent upon hardness combinedwith at least one other mechanical property. The data col-lected in the present experimental work has been applied to

0043-1648/01/$ – see front matter © 2001 Elsevier Science B.V. All rights reserved.PII: S0043-1648(00)00554-8

D.J. O’Flynn et al. / Wear 248 (2001) 162–177 163

a number of such models to provide an analysis of their ap-plicability. This work will be presented in a further paper.

In the present paper, a new model is presented whichindicates that erosion is dependent on a combination ofmechanical properties hitherto unconsidered. One furtherunique feature of the present work is that room temperatureerosion is considered to be dependent on elevated temper-ature mechanical properties. The impetus for this unusualapproach came from previous work by Bingley et al. [17]who discovered that the relative room temperature erosionresistance of three similar low carbon steels could only beexplained by their elevated temperature behaviour and theirrelative propensity to dynamic strain ageing at these temper-atures. It is considered that the measurement of propertiesat these elevated temperatures is consistent with the beliefthat significant local temperature rises occur during roomtemperature erosion due to the combined effects of highstrain and high strain rate deformation.

2. The development of an erosion model for metals

2.1. Assumptions made in the model

Most models of erosive wear involve a hardness termbecause this property is expected to control the depth ofpenetration of an impacting particle and, consequently, thevolume of material swept out. In contrast, the present modelassumes an energy approach in determining material re-moval rates. Here the kinetic energy of the impacting parti-cle is assumed to be translated into strain energy required toproduce deformation and fracture of the target material. It is,therefore, considered that the volume of material removedas wear debris is dependent primarily on the toughness ofthe material. Toughness,UT, is defined as the deformationenergy (per unit volume of material) required to producefracture, and in a tensile test is given by the area under thetrue-stress–true-strain curve. The true-strain to failure wastaken to be ln(A0/Af ), whereA0 andAf were, respectively,the initial and final cross-sectional areas of the tensile speci-mens. The area under the true-stress–true-strain curve is noteasy to measure directly and a simplified approach, based oneasily measurable mechanical properties, was taken in orderto determine it. The materials were assumed to harden in atwo stage linear fashion; from yield to the ultimate tensilestrength (UTS) and from the UTS to the true fracture stress.The areas under the two stage linear true-stress–true-straincurves could then be calculated simply from such plots (asillustrated in Fig. 1). It is very important to note that cal-culating the energy to failure (toughness) by this methodtakes into account the rather large strains expected to benecessary for material removal during erosive wear.

Other models that have considered the influence of duc-tility on erosive wear have tended to use simple tensileelongations as a measure of this property rather than the

Fig. 1. Measurement of toughness assuming a 2-stage linear hardeningmodel.

greater strains inherent in reduction of area measurements.Furthermore, models that have incorporated strength haveused yield strength or UTS rather than true fracture strength(which takes into account high strain work hardening) as ameasure of strength. The calculation of toughness used hereincorporates both of these factors and is consistent with thebelief that metal removal during erosion requires substantialamounts of deformation to occur. It would be interesting tosee if other models exhibited improved correlations if eitherof these approaches was taken.

The mechanisms of material removal (as illustrated inFig. 2) are generally considered to be different at low andhigh impact angles [2,8,18–23]. Nevertheless, it is sug-gested here that as both involve deformation and fractureprocesses, that toughness is equally relevant in considera-tions of each. It is considered to be primarily responsible fordetermining the amount of energy required to remove thehighly deformed material formed into “chips” at low impactangles or crater “lips” formed at angles close to normalincidence. For the impact of a particle of given energy, itmay be considered that if all the energy was expended in re-moving material (by plastic deformation and fracture) then

Fig. 2. Mechanisms of material removal at low and high impact angles.

164 D.J. O’Flynn et al. / Wear 248 (2001) 162–177

the volume of material removed would be inversely propor-tional to the toughness of the material. However, to furthercomplicate matters, it is unlikely that all of the energy ofthe particle will be used in producing these highly deformed“chips” and “lips”. A certain portion of the volume sweptout at low angles of incidence will simply be deformed anddisplaced in a ploughing action. For impacts at normal inci-dence in particular, a significant amount of kinetic energy isalso expended in deforming the sub-surface directly belowthe impact crater. Here the levels of deformation are muchlower than in the highly deformed crater lips. Detailed ex-amination of hardness indentations has certainly indicatedthis. Tabor [24] indicated that the average strain below aspherical hardness indenter was around 0.1. In comparison,experiments by Dugdale [25] indicated that the materialwithin raised lips produced by pyramidal indenters had shearstrains of between 1 and 2. Further portions of energy willbe unavailable for metal removal during erosion at all impactangles as some kinetic energy is retained by the particle afterimpact [26].

It seems likely that the mechanical properties of the tar-get material will strongly effect the efficiency of materialremoval. It is believed by the authors that it is the uniformstrain that controls this efficiency, i.e. the proportion of ma-terial actually removed as highly deformed wear debris. Uni-form strain to ‘necking’ in a tensile test,εU, is defined as theplastic strain required for the onset of localised deformation(‘necking’) in a test specimen. In the case of ductile metals,this ‘necking’ generally begins at maximum load duringtensile deformation. Interestingly, uniform strain is alsoequivalent to the work hardening exponent,n, in the Hollo-man relationship [27] and is, therefore, a measure of workhardening capacity. There are a number of reasons why uni-form strain might be considered as a suitable indicator of theefficiency of metal removal, and these will now be outlined.

In the case of particles impacting a surface at low anglesof incidence, the main material removal mechanism is gen-erally considered to be chip formation or cutting. Low angleerosion may perhaps be compared to abrasion. In the caseof abrasive wear, Hutchings [16] describes three types ofmaterial removal mechanism; cutting, wedge formation andploughing. Only cutting and wedge formation lead to metalremoval. It is suggested that there is a critical ‘attack angle’,θc, below which the ploughing mechanism occurs. As attackangle is increased above this critical angle, a transition fromploughing to cutting occurs. It is here proposed that a critical‘attack angle’ for cutting also exists for erosive wear at lowangles, with the formation of ‘chips’ only occurring at an-gles greater than this critical angle. It must be noted that thiscritical angle is not the impact angle of the impinging parti-cle, but rather the effective angle made by the leading face ofthe particle with the target surface. Cutting will only occur ifthe orientation of the particle at impact leads to an effectiveangle greater than the critical angle for cutting. As in thecase of abrasive wear, it is expected that the critical angle forcutting will be dependent on the mechanical properties of

the eroding surface. Hutchings [16] considered that the duc-tility and work hardening characteristics were particularlyimportant. High ductility or work hardening rate is expectedto give rise to high critical angles leading to low abrasionwear rates. The proposed choice of uniform strain as a fac-tor affecting the critical angle can, thus, be justified since itis a measure of both ductility and work hardening capacity.

Erosion at or close to normal incidence can be thought ofas an indentation process, leading to the formation of crater‘lips’ of highly deformed material which are subsequentlyremoved as platelets after impact by a number of succes-sive particles. The process of lip formation is similar to the‘piling up’ described by Tabor [24] around an indenter inan hardness test. If a metal has a high capacity for workhardening, (such as a ductile annealed metal), deformationtends to spread to the bulk material, leading to ‘sinking in’.By contrast, ‘piling up’ or lip formation occurs in metalswith a low capacity for work hardening (such as metalsthat are already highly deformed and are, therefore, lessductile), where deformation will be more localised close tothe indenter. Therefore, in terms of erosive wear, a ductilemetal with a high capacity for work hardening (a high workhardening exponent,n) will tend to ‘sink in’ when impactedby a hard particle, such that a ‘lip’ around the impact craterwill not be formed. Any reduction in the tendency for ‘lips’to form in turn reduces the number and volume of plateletsthat are formed, and thereby lowers the rate at which ero-sion platelet removal occurs. Less ductile metals with a lowcapacity for work hardening, (lown), on the other hand aremore likely to form crater ‘lips’ when impacted by hardparticles thereby giving rise to enhanced erosion rates.

It is argued above that erosion behaviour is influenced bythe tensile uniform strain value of the target material. Fromthese arguments it would be expected that erosion rate bean inverse function of uniform strain. However, we have nobasis for understanding the exact mathematical relationship.In the following derivation of a predictive model for erosionwear it is assumed for simplicity that erosion rate and uni-form strain have an inverse linear relationship. Later, it willbe shown that assessment of the model using experimentaldata indicates that this appears to be a reasonable assump-tion, and that no other relationship gives a consistent im-provement in the correlation between experiment and theory.

2.2. Derivation of the predictive model

The initial assumptions are that of a perfectly rigid parti-cle indenting a perfectly plastic surface with a constant in-dentation pressure. The kinetic energy of a particle of mass,m, impacting the target surface at an impact velocity,V, isgiven by the expression:

KE = mV2

2(1)

Therefore, the volume of material deformed and removed,if all the energy of the particle goes into removing material


is given by Eq. (2).

Volume= mV2

2UT(2)

whereUT is the toughness of the target material.At very low particle impact angles, when cutting is the

only mechanism operating,UT is equal to the energy per unitvolume required to remove the highly deformed volume ofmaterial swept out by the particle in the form of a chip. Atnormal incidence,UT is equal to the energy per unit volumerequired to remove the highly deformed material that hasbeen formed into ‘lips’. However, the above expression forthe volume removed needs to be modified since not all of thedeformed crater volume is removed and not all the particle’senergy is expended in the removal of material. The efficiencyof material removal needs to be considered.

At very low angles of impact, part of the swept out de-formed volume is simply displaced by a ploughing actionand, thus, the volume removedVR may, according to themodel, be given by the expression (appropriate for lowangles ofθ ):

VR = amV2

εUUT(3)

whereεU is the uniform strain to necking in a tensile testand ‘a’ a constant for the cutting mechanism. Therefore,a/εU is a term indicating the efficiency of metal removal bycutting, with εU being the material dependent part of thatterm (i.e.εU is the material dependency of the efficiency ofmaterial removal).

At normal incidence, all of the energy of the impactingparticle does not go into lip formation, since part of theenergy goes into sub-surface deformation below the impactcrater. The volume of material removed by the mechanismof lip formation at normal incidence is, therefore, given bythe expression:

VR = bmV2

εUUT(4)

whereb is a constant for the lip or platelet formation mech-anism of metal removal, and, therefore,b/εU gives the effi-ciency of metal removal by lip formation. Here,εU indicatesthe material dependency of the tendency to form lips.

Therefore, we can conclude that erosion rate can be givenby the following expressions. For very low particle impactangles, erosion is by cutting:

EC = aV2

εUUT(5)

and for impact at normal incidence erosion is by lip forma-tion:

EL = bV2

εUUT(6)

More generally, at a given angleθ :

Eθ = cV2

εUUT(7)

wherec lies somewhere betweena andb and is a functionof impact angle,θ .

The above model is sufficient in itself for an examinationof the dependency of erosion rate on mechanical properties,but it would be more useful if the relationship betweencand impact angle was better understood. Therefore, it isworthwhile considering howc might be related toθ .

Assuming that cutting occurs due to the velocity compo-nent of the impinging particle parallel to the eroding surface,then the erosion rate due to the cutting mechanism at anygiven angleθ is given by:

EθC = a(V cosθ)2f (θ)

εUUT(8)

Heref (θ) is a term to account for the angular dependenceof the cutting mechanism. It is considered that the efficiencyof the cutting mechanism will be reduced by the energy‘wasted’ in producing widespread deformation beneath theimpacting particle. Consequently, proportionally less energywill be available for localised shear strain leading to chipformation and material removal. This might be consideredakin to a surface grinding process in which a large volume ofmaterial is deformed relative to the depth of cut. In erosion,the energy dissipated in the sub-surface deformation processmight be expected to depend on the kinetic energy perpen-dicular to the surface, i.e. proportional toV 2 sin2 θ . This en-ergy is lost to the cutting process, and it follows that for agiven tangential kinetic energy the cutting process is less ef-ficient for a higher impact angle. Thus,f (θ) = 1−sin2 θ ; andan expression giving the angular dependence ofEθ C results:

EθC = aV2

εUUTcos2 θ(1 − sin2 θ) = aV2

εUUTcos4 θ (9)

However, a proportion of the kinetic energy perpendicularto the target surface results in material removal through up-ward flow and lip formation. This is of course particularlysignificant for angles close to the normal. Assuming, there-fore, that lip formation is a consequence of the velocitycomponent normal to the eroding surface, then at any givenangleθ , the erosion rate due to this mechanism is given by:

EθL = b(V sinθ)2

εUUT(10)

Assume, in a manner similar to the treatment by Bit-ter [18,19], that at an angleθ , the total erosion rate,Eθ is simply equal to the sum of these two components(i.e. Eθ = EθC + EθL). It is then possible to write an ex-pression for erosion rate that incorporates impact angle,θ :

Eθ = V 2

εUUT[a cos4 θ + b sin2 θ ] (11)


Table 1Chemical compositions (wt.%)

Steel C S P Mn Si Ni Cr Cu Mo A1

EN 42 0.72 0.023 0.010 0.69 0.21 0.02 0.02 – 0.001 0.008EN 24 0.43 0.05 0.034 0.65 0.23 1.31 1.30 0.21 0.291 0.053

Therefore,c in Eq. (7) can be determined from the equation:

c = a cos4 θ + b sin2 θ (12)

It can be readily appreciated thatc ∼ a at very low anglesandc = b at normal incidence.

3. Experimental details

A thorough examination of the models predictions re-quired extensive measurement of erosion and mechanicalproperties. Steels were chosen for the test programme be-cause of their ability to be heat-treated into a variety ofconditions with a wide range of mechanical properties. Twosteels were selected; a eutectoid 0.8% C steel (EN42) anda 0.4% C low alloy steel (EN24). Their chemical composi-tions are detailed in Table 1. The 12 heat treated conditionsand resultant hardnesses are summarised in Table 2.

The erosion tester selected for the test programme was a‘rotating disc accelerator’ type erosion tester, designed andconstructed by Burnett [28,29]. The tester allows a rangeof impact angles between 5 and 90◦ and velocities up to35 m s−1. For each steel a matrix of test conditions com-prising impact angles, 8, 30 and 90◦ and velocities of 15,25 and 35 m s−1 were used. The abrasive in each case wasfine olivine sand and a particle concentration equivalent toa particle density of 4 kg m−3 was selected for all tests. Thesteady state erosion rate for each material (defined as thevolume of material removed by a unit mass of striking abra-sive, in units of mm3 kg−1) was taken to be the erosion rate

Table 2The heat treatments used to produce the desired microstructures for the test programme

No Microstructure Steel Rockwell C-scalehardness (Rc)

Heat treatmentprocess

1 Pearlite EN42 16 850◦C/1 h, rapidly cooled to 690◦C. Isothermally transformed at 690◦C, air cooled.2 Spherodised EN42 16 850◦C/1 h, rapidly cooled to 570◦C. Isothermally transformed at 570◦C, air cooled.

Tempered at 700◦C/24 h, air cooled.3 Pearlite EN24 25 850◦C/1 h, rapidly cooled to 620◦C. Isothermally transformed at 620◦C, air cooled.4 Upper bainite EN24 35 850◦C/1 h, rapidly cooled to 400◦C. Isothermally transformed at 400◦C, air cooled.5 Lower bainite EN24 45 850◦C/1 h, rapidly cooled to 320◦C. Isothermally transformed at 320◦C, air cooled.6 Martensite EN24 55 850◦C/1 h, oil quenched.7 450◦C tempered martensite EN24 45 850◦C/1 h, oil quenched. Tempered at 450◦C/1/2 h, air cooled.8 550◦C tempered martensite EN24 40 850◦C/1 h, oil quenched. Tempered at 550◦C/1 h, air cooled.9 650◦C tempered martensite EN24 35 850◦C/1 h, oil quenched. Tempered at 650◦C/1 h, air cooled.

10 700◦C tempered martensite EN24 24 850◦C/1 h, oil quenched. Tempered at 700◦C/24 h, air cooled.11 Bainite–martensite

mixture (50:50)EN24 46 850◦C/1 h, rapidly cooled to 400◦C. Isothermally transformed at

400◦C/3.30 min, water quenched.12 Pearlite–martensite

mixture (50:50)EN24 28 850◦C/1 h, rapidly cooled to 620◦C. Isothermally transformed at

620◦C/45 min, water quenched.

determined after each target had been struck by 600 g ofabrasive. This, from experience, was deemed sufficient forsteady state erosion conditions to exist.

All tensile tests were conducted using conventional testequipment, with the addition of a calibrated tube furnacefor tests conducted at elevated temperatures. Microhardnesstests were performed on the as-received (bulk) material andin the sub-surface zone of sectioned and polished erodedspecimens.

4. Comparison of the theory with experimental testresults

An extensive set of erosion and mechanical propertydata was collected. A summary of the erosion test resultscan be found in Table 3. Tables 4 and 5 provide details ofthe mechanical properties considered most relevant to thework described in this paper. The yield strength, true UTS,true fracture stress, uniform strain and toughness are givenat room temperature, 200 and 300◦C. In general, the datashows the expected trends. Yield stress, for instance, gener-ally increases with increasing temperature. The trends withtemperature in UTS and particularly true fracture stress areless obvious and even occasionally appear anomalous. Thisis because the stress at fracture depends on a complicated in-teraction between flow stress, work hardening rate and duc-tility. For instance, whereas flow stress and work hardeningrate might be expected to decrease with increasing tempera-ture, a large compensatory increase in ductility might result


Table 3Steady state erosion rates determined for all erosion test conditions

Microstructure Steady state erosion rates (mm3 kg−1)

15 m s−1 impact 25 m s−1 impact 35 m s−1 impact

8◦ 30◦ 90◦ 8◦ 30◦ 90◦ 8◦ 30◦ 90◦

EN 42 pearlite 3.234 1.535 0.335 5.377 3.603 2.048 13.508 8.335 5.029Spherodised 1.759 0.924 0.426 4.877 3.389 1.899 22.012 11.056 5.283EN 24 pearlite 1.447 0.400 0.307 2.428 2.322 1.425 6.284 7.596 5.235Upper bainite 2.138 1.293 0.335 4.291 3.812 2.785 12.124 7.143 4.320Lower bainite 3.234 1.400 0.649 19.059 9.549 4.008 20.082 12.046 7.531Martensite 1.759 1.592 1.325 4.453 2.538 2.048 11.639 9.509 6.543450◦C tempered martensite 2.919 1.942 0.914 11.142 7.311 3.940 20.891 13.072 8.318550◦C tempered martensite 4.277 2.153 0.607 15.994 6.732 4.125 30.354 22.883 11.923650◦C tempered martensite 1.251 1.100 0.467 6.826 6.121 2.707 10.767 10.497 4.514700◦C tempered martensite 1.481 1.242 0.698 8.719 4.943 2.261 40.058 22.613 10.483Bainite–martensite mixture (50:50) 5.944 3.395 1.632 21.952 11.586 6.400 17.315 15.663 10.942Pearlite–martensite mixture (50:50) 4.398 3.277 3.348 12.790 7.683 3.742 19.883 10.798 6.161

Table 4Room temperature tensile properties

Microstructure Yield stress(MN m−2)

True UTS(MN m−2)

True fracturestress (MN m−2)

True fracturestraina

True uniformstrain

Toughness(MN m−2)

EN42 steelsPearlite 300 738 1035 0.317 0.147 228Spherodised 302 606 947 0.803 0.129 584

EN24 steelsPearlite 579 924 1442 0.956 0.094 1093Upper bainite 959 1282 1383 0.231 0.055 296Lower bainite 1298 1610 1891 0.639 0.062 1100

Martensite450◦C tempered martensite 1253 1406 1582 0.511 0.035 759550◦C tempered martensite 1088 1269 1925 0.944 0.062 1482650◦C tempered martensite 904 1075 1432 0.791 0.083 971700◦C tempered martensite 714 848 1693 1.172 0.108 1439Bainite–martensite (50:50 mixture)Pearlite-martensite (50:50 mixture) 555 908 1410 0.925 0.088 1036

a Based on reduction in area.

Table 5Elevated temperature tensile properties

Microstructure Yield stress(MN m−2)

True UTS(MN m−2)

True fracturestress (MN m−2)

True fracturestraina

True uniformstrain

Toughness(MN m−2)

200◦C 300◦C 200◦C 300◦C 200◦C 300◦C 200◦C 300◦C 200◦C 300◦C 200◦C 300◦C

EN42 steelsPearlite 260 140 686 823 875 877 0.466 0.212 0.128 0.121 343 837Spherodised 270 250 540 593 952 1116 0.900 1.015 0.121 0.121 632 817

EN24 steelsPearlite 524 409 828 848 1630 1769 1.022 1.075 0.099 0.095 1202 1343Upper bainite 884 979 1124 1171 1752 1721 0.600 0.628 0.055 0.053 840 888Lower bainite 1248 1273 1569 1620 2067 2143 0.644 0.814 0.041 0.077 1154 1501Martensite 1498 1737 2829 1.042 0.062 2339450◦C tempered martensite 1048 1198 1328 1393 1981 2276 0.710 0.875 0.043 0.056 1156 1578550◦C tempered martensite 1048 994 1120 1248 1833 1840 0.875 0.739 0.047 0.058 1275 1117650◦C tempered martensite 674 744 888 1000 1484 1836 1.109 1.001 0.069 0.088 1289 1374700◦C tempered martensite 484 464 770 812 1154 1933 0.733 1.180 0.097 0.120 674 1534Bainite–martensite (50:50 mixture) 1523 1348 1887 1555 2575 2485 0.416 0.963 0.039 0.049 909 1919Pearlite–martensite (50:50 mixture) 549 524 911 1015 1230 1565 0.476 0.711 0.077 0.113 484 860

a Based on reduction in area.


Fig. 3. A typical plot of erosion rate against /µTεU using room temperature mechanical property test data.

in higher levels of stress before fracture intervenes. The exactvariation of these parameters with temperature is obviouslysensitive to microstructure. It is the true fracture stress andstrain that are of particular significance in the present workas they largely determine the level of toughness.

To simplify the assessment of the models predictionssmaller subsets of this data were first examined. The modelpredicts an empirical relationship between erosion rate and1/UTεU for a given set of erosion conditions. Plots were,therefore, made of erosion rate against 1/UTεU. No suchrelationship was found to exist for room temperature me-chanical properties (an example is given in Fig. 3). Theunusual step was then taken of examining the same rela-tionship between room temperature erosion and elevatedtemperature mechanical properties. This approach was sug-gested by previous work carried out by Bingley et al. [17],referred to earlier, which found that elevated temperatureproperties satisfactorily explained the erosion behaviour ofthe low carbon steels under investigation. The empirical re-lationships examined under each set of erosion conditionsare given in Fig. 4. It can be seen that apart from a cou-ple of “rogue” data points on each graph the linear relation-ship between erosion rate and 1/UTεU is generally obeyed.The best fit line indicated ignores these rogue data points.It should be noted that the appropriate elevated temperaturechosen to give the best fit between theory and experimentvaries with impact velocity. This will be discussed furtherlater.

The ability of the model to predict the angular dependenceof erosion rate was then considered and Eq. (7) was assessed.At each impact angle investigated, onec value was chosento give the best fit between the experimental and predicted(Eq. (7)) erosion rates. It was assumed for convenience thatc was constant for a given impact angle and did not vary

with velocity. If UT is expressed in units of kN mm−2 andV in m s−1, thenEθ is in mm3 kg−1 andc can be calculatedaccordingly. The best-fitc values were found to be 10.05×10−4, 6.87 × 10−4 and 3.72 × 10−4 for 8, 30 and 90◦,respectively. If it is assumed thatc = a at 8◦ impact andc = b at 90◦, then Eq. (12) gives a predicted value forc of6.58× 10−4 at 30◦ impact. This is almost coincident withthe experimentally obtained best-fit value of 6.87 × 10−4.This agreement gives confidence in the predictive capabilityof the model. However, it is realised that the model will haveto be proven over a wider range of impact angles beforeconfidence can be fully justified. It will be noted that Eq. (11)does not predict a peak in the erosion rateEθ with impactangle θ as is commonly observed. However, the presentexperimental results do not display such a peak either, orat least suggest that the peak occurs at angles of less than8◦. This may be because erosion testing in the present workwas carried out using a centrifugal accelerator type tester.Evidence has been gathered [30] that such a tester inducesparticle rotation, which increases the efficiency of cutting atlow angles.

The full set of experimental data was then used to plotexperimental erosion rate against predicted (Fig. 5(a)) us-ing the c values indicated above. The agreement betweenexperiment and theory shows significant scatter but is gen-erally encouraging for the validity of the model. A large im-provement to the observed correlation may be achieved ifthe rogue data points evident in the empirical relationships(referred to above) are removed (see Fig. 5(b)).

An estimation of the erosion efficiencies is also of interest.If erosion efficiency,η, is defined as the fraction of theimpacting particles kinetic energy used in the removal ofmaterial, then use of Eq. (7) will lead us to an expressionfor η:


Fig. 4. Erosion rate against 1/UTεU using elevated temperature mechanical property test data for the following erosion test conditions: (a) 15 m s−1 at8◦ impact angle, mechanical properties measured at 200◦C; (b) 15 m s−1 at 30◦ impact angle, mechanical properties measured at 200◦C; (c) 15 m s−1 at90◦ impact angle, mechanical properties measured at 200◦C; (d) 25 m s−1 at 8◦ impact angle, mechanical properties measured at 200◦C; (e) 25 m s−1 at30◦ impact angle, mechanical properties measured at 200◦C; (f) 25 m s−1 at 90◦ impact angle, mechanical properties measured at 200◦C; (g) 35 m s−1

at 8◦ impact angle, mechanical properties measured at 300◦C; (h) 35 m s−1 at 30◦ impact angle, mechanical properties measured at 300◦C; (i) 35 m s−1

at 90◦ impact angle, mechanical properties measured at 300◦C.“Rogue” Results are given by open data points.


Fig. 4 (Continued).


Fig. 4 (Continued).


Fig. 5. Experimental erosion ratev, predicted erosion rate (cV2/UTεU). Fig. 5 (a) shows complete set of experimental data. Fig. 5 (b) is shown afterremoval of “rogue” data points. Values ofc varies with impact angle in the following manner:c = 10.05× 10−4 at 8◦ impact angle,c = 6.87× 10−4 at30◦ impact angle,c = 3.72× 10−4 at 90◦ impact angle.

η = 2c

εU(13)

This gives erosion efficiencies of between 1.7 and 4.1% (de-pending on the value ofεU) for erosion at 8◦ and 35 m s−1.The erosion efficiency is significantly lower, between 0.6and 1.5%, for similar erosion conditions at 90◦, with inter-mediate values at 30◦. This compares with estimated erosionefficiencies of between 1 and 8% at 90◦ impact for materialswith a similar hardness to those in the present work, as indi-cated by Sundararajan [31]. However, Sundararajan definederosion efficiency differently as the ratio of worn volume tocrater volume.

One undoubted limitation of the present work is thatc hasonly been obtained empirically as the result of curve-fitting.It is supposed thatc itself is independent of material proper-ties and that the only mechanical property controlling wearefficiency isεU as is indicated by Eq. (13). However, the

present model offers no theoretical justification or under-standing of the factors that determinec. It is expected thoughthat c will be dependent on the characteristics of the im-pacting particles and the effect these characteristics have onthe plastic flow of the target material. Thus,c will undoubt-edly be influenced by particle size, shape and the interfacialfriction between particle and target material.

Although in the above analysis, as presented in Fig. 5(a)and (b),c was assumed to be constant for a given impactangle, closer inspection of the data indicated that this was notstrictly true. It was noted that for a given angle,c increasedslightly as velocity increased. This sensitivity to velocitywas reduced if the predicted erosion rate was assumed to beproportional toVn, wheren > 2, rather thanV2. Plots oflog experimental erosion ratev log impact velocity showedthe power exponentn to be approximately 2.4, althoughthere was the indication that it might be greater at higherangles. Accuracy of analysis was hindered by erosion only


Fig. 6. Experimental erosion ratev, predicted erosion rate (cV2.4/UTεU). ‘Rogue’ data points have been removed. Values ofc varies with impact anglein the following manner:c = 25.97× 10−5 at 8◦ impact angle,c = 17.32× 10−5 at 30◦ impact angle,c = 9.37× 10−5 at 90◦ impact angle.

being carried out at three impact velocities. However, thefigure of 2.4 was consistent with the work of others (e.g.[32]). Replotting experimentalv predicted erosion rates withV2.4 replacingV2 gives a still better fit between theory andexperiment (Fig. 6). Here thec values at 8, 30 and 90◦ are,respectively, 25.97× 10−5, 17.32× 10−5 and 9.37× 10−5.Unfortunately, it is difficult to reconcile such a relationshipwith the energy balance that the model is premised on.

5. Discussion

The results presented here indicate that generally erosionrate increases as 1/UTεU increases. That is to say that ero-sion resistance increases as the product of tensile toughnessand uniform strain (measured at elevated temperatures)increases, as suggested by the proposed model. A certainamount of scatter is observable showing that the model is farfrom perfect. However, it is thought that much of this scattercan be explained satisfactorily without detracting from thevalidity of the model. Certain materials were found to showconsistently poorer obedience to the clearly apparent trendthan others. These ‘rogue’ materials were EN24 700◦Ctempered martensite, EN24 upper bainite and the EN42materials. An explanation can be proffered in each case.

EN24 700◦C tempered martensite is one of the softest ofthe EN24 microstructures used in the test programme, andalso has the highestεU value measured in tensile tests. Hard-ness measurements taken in the sub-surface region belowthe worn surface demonstrated that of the EN24 materials,700◦C tempered martensite had the greatest proportionateincrease in hardness during erosive wear (see Table 6). Iftensile tests could be made of material in this hardened zone

it would be expected to have a considerably lowerεU valuethan that measured within the bulk material. All materialswould of course be expected to display this characteristic.However, although all materials hardened during erosion (tovarying degrees), those that hardened the most would beexpected to haveεU values most affected by the changein mechanical properties of the surface material. It mightbe expected, therefore, that EN24 700◦C tempered marten-site, which has a high capacity for work hardening, wouldbe most affected. This is demonstrated by the fact that thismaterial consistently deviates from the general trend havingerosion rates much greater than expected for the calculatedproduct of toughness and uniform strain values.

This finding highlights the possibility that measuring themechanical properties of the work hardened sub-surfaceregion rather than bulk mechanical properties may givebetter correlation with erosion rate in any erosive wearmodel. This of course is readily acknowledged. Previouswork has demonstrated that erosion rate correlates betterwith sub-surface hardness than bulk hardness. To take intoaccount surface hardening during erosion, it is suggestedthat the relevant mechanical properties (uniform strain andtoughness), should be determined for the erosion hardenedsurface material (perhaps at appropriate elevated tempe-ratures), thereby increasing the accuracy of the model. Un-fortunately an erosion test would be required to determinethe degree of erosion hardening before this could be car-ried out, therefore, contradicting the purpose of a predictivemodel. The availability of practical means of determiningthese surface properties must also be questioned.

Upper bainite and the two EN42 materials, were alsofound to lie away from the general trend, albeit to vary-ing extents. Each showed erosion rates much lower than


Table 6Microhardness measurements and the equivalent flow stresses in the eroded sub-surface zones

Microstructure Vickers-microhardnessmeasurementsa

Equivalent flowstresses (MN m−2)

Tensile fracturestress (MN m−2)

Bulk 8◦ 30◦ 90◦ Bulk 8◦ 30◦ 90◦ Room temperature 300◦C

EN 42 steelsPearlite 260 350 375 400 858 1155 1238 1320 1035 877Spherodised 250 300 335 390 825 990 1106 1287 947 1116

EN 24 steelsPearlite 295 340 380 400 974 1122 1254 1320 1442 1769Upper bainite 425 440 440 460 1403 1452 1452 1518 1383 1721Lower bainite 415 540 540 550 1370 1782 1782 1815 1891 2143Martensite 685 740 740 750 2260 2442 2442 2475 2829450◦C tempered martensite 415 495 495 510 1370 1634 1634 1683 1582 2276550◦C tempered martensite 395 400 420 500 1304 1320 1386 1650 1925 1840650◦C tempered martensite 360 400 420 435 1188 1320 1386 1435 1432 1836700◦C tempered martensite 275 335 368 410 908 1106 1214 1353 1693 1933Bainite–martensite (50:50 mixture) 600 700 725 745 1980 2310 2392 2458 2485Pearlite–martensite (50:50 mixture) 300 395 465 475 990 1304 1535 1568 1410 1565

a Subsurface measurements after 35 m s−1 impact, Maximum hardness in subsurface zone at different impact angles is given.

expected, given their measured toughness and uniform strainvalues. It is possible that the toughness values calculatedfrom tensile test results may be much lower than expected,due to premature failure of the test specimen during neck-ing. These materials all contain high volume fractions ofcarbides which act as stress concentrators, allowing the nu-cleation of voids during the fracture process. The void nu-cleating effect of the carbide particles is exacerbated by theeffect of necking during tensile tests when a tri-axial stressstate operates within the neck region. Such a stress state isnot present during erosion. That being the case, the carbideparticles may play a less significant role in material frac-ture and removal during erosion itself. Therefore, the role oftoughness in determining erosion properties cannot be dis-counted but it has to be questioned whether the tensile test isthe most appropriate test to measure a toughness value ap-propriate to erosion. The stress system set up during erosiondue to an impacting particle is certainly far more complexthan that in a simple tensile test, probably being a combina-tion of compression and shear. It is possible that determin-ing the toughness of the target material using a test moreapplicable to the erosion process could make improvementsto the model. Alternatives include the use of the compres-sion or upset test to determine failure properties under com-pressive loading, or a rolling test to determine the strainto the onset of ‘edge cracking’. Material failure in thesetests is perhaps more closely related to that occurring duringerosion.

Although the predictions of erosion performance fromthe proposed model correlate quite well to the measuredvalues from erosion testing, these ‘rogue’ materials con-tribute significantly to the scatter observed. ComparingFig. 5(a) and (b) clearly shows that if the ‘rogue’ materialsare removed from the analysis a much clearer relationshipcan be observed.

Clearly, the choice of heat-treated steels to assess the va-lidity of the model was an unfortunate one. In retrospect itwould have been better to have chosen simple single phasealloys without the complex, inhomogeneous microstructuresdisplayed by heat-treated steels. Steels were chosen partlybecause of the desire to prove the applicability of the modelto industrially relevant materials.

The most radical feature of the present work is undoubt-edly the use of elevated temperature properties to assessroom temperature erosion performance. Most models andanalyses ignore the effect of localised heating resulting fromthe high strain rate deformations typical of the erosion pro-cess. However, temperature rises associated with erosionhave been reported [14,33–38]. Earlier it was shown thatthe combination of mechanical properties proposed in themodel correlated better with erosion test results when thesemechanical properties were determined at elevated temper-atures. It is, therefore, considered that elevated temperaturetensile tests measure the mechanical properties of the steelunder conditions closer to those experienced during erosion.Tensile tests were conducted at room temperature, 200, 300and 400◦C. It was found that the best correlation’s occurredbetween mechanical properties measured at 200◦C and ero-sion data generated at 15 and 25 m s−1 impact velocities,and when 300◦C properties were compared with erosiondata for an impact velocity of 35 m s−1. Therefore, it can beconcluded that the relevant temperature for tensile testing isimpact velocity dependent, suggesting that the local temper-ature rise during impact varies in a similar fashion. This isto be expected, and is in broad agreement with Hutchings[23], and Doyle and Ball [35].

It is pertinent to ask whether the erosion process canreasonably generate temperatures of 200–300◦C. A simpleenergy balance gives a very crude assessment of the possi-ble temperature rises. Assume that a portion of an impacting


particles kinetic energy is transferred to strain energy inthe highly deformed chips or lips that are produced dur-ing erosion. The approximate rise in temperature,1T, inthese highly deformed zones can be calculated, if adiabaticconditions are assumed, from the expression:

UT = ρCH1T (14)

whereρ is the density of the target material andCH is its spe-cific heat capacity. Assume that for steel,ρ = 7800 kg m−3

andCH = 480 J kg−1 K−1, and taking a typical value ofUTas 1000× 106 N m−2 gives 1T = 267◦C. This indicatesthat the temperature in the deformed zone is around 290◦C,satisfactorily close to 300◦C, the temperature assumed inthe present work for erosion at 35 m s−1. At lower impactvelocities a lower temperature rise might be expected ifadiabatic conditions no longer prevail and heat flow awayfrom the deformed zone becomes significant. It is interest-ing to note that temperatures of 200 and 300◦C correspondwell to those suggested by Bingley et al. [17]. Dynamicstrain ageing at these temperatures offered an explanationfor the erosion performance of the low carbon steels exam-ined in their work. A rise of 200–300◦C is also typical ofthat experienced by the bulk of machine chips during latheturning under similar conditions of high strain/strain ratedeformation to those experienced during erosion.

Nevertheless, it should be understood that the appropriatetemperatures at which the tensile testing is carried out maynot actually be the same as the temperatures generated at theeroding surface. The tensile test can only hope to measuremechanical properties relevant to the erosive process, butcannot be expected to simulate the high strain rate conditionspertaining to erosion. However, it might be the case that thetemperature and strain rate combination of the tensile testresults in comparable mechanical behaviour to that of theinduced temperature and strain rate conditions of the erosiontest. It cannot be denied though that there is a question markregarding the use of low strain-rate, elevated temperaturetests to simulate the mechanical response under the highstrain rate conditions found in erosion. This is especially sowhen it is considered that at high strain-rates the thermalprocesses which usually cause a reduction in flow stress withincreasing temperature might not operate.

The mechanisms of material removal at low and highangles are usually considered to be radically different. Itis, therefore, perhaps surprising that the same two materialparameters (toughness and uniform strain/work hardeningexponent) have been found in the present work to controlthe erosion rate under all conditions. With this in mind itis interesting to draw an analogy between metal removalduring erosion and that during grinding, and consider amodel developed by Shaw [39] to explain some of the pecu-liarities of the grinding process. Shaw contrasted grindingwith conventional metal cutting and considered that themain difference between them was the rake angle of thecutting action. Grinding takes place with large (negative)rake angles whilst in conventional cutting the rake angle is

approximately zero. In this sense, the cutting by impactingparticles during erosion might be expected to be similar togrinding. Shaw’s model likened grinding, and the defor-mation an abrasive particle produces in the workpiece, tothat of a Brinell ball hardness indenter. In both processesthere is considerable resistance to upward flow of material.Thus, he proposed that the mechanism of chip formation ingrinding is akin to that of lip formation in a Brinell hard-ness test and one would, therefore, expect that the materialproperties controlling each process would be the same.

If we interpret this in terms of the erosion process, it maybe inferred that the mechanisms of metal removal at low andhigh impact angles are not distinctly different, as is generallyassumed, but involve essentially the same process in eachcase. Necessary to material removal at both low and highimpact angles is the upward flow of material around the im-pacting particle and both processes are, therefore, governedby the same material properties. Of course the efficiency ofupward flow is different at low and high angle impacts, andthis is reflected in the different values of the proportional-ity constantsa andb in the model developed in the presentpaper. Upward flow might be expected to be easier at lowangles because the lateral trajectory of the particle aids theupward movement of material at its leading edge. This isreflected in the proportionality constanta (for the cuttingmechanism) being higher thanb (that for lip formation).

The proportionality constantc (as well asa andb) is as-sumed to be a constant for all ductile metals undergoing ero-sion due to impact by the type of particles used in the presentwork, and by the mechanisms outlined in this paper. That isto say, it is presumed to be independent of material proper-ties. The assumption is that the only mechanical propertiesinfluencing erosion are toughness and uniform strain. A cer-tain amount of scatter would obviously result if this was aninvalid assumption. The magnitude of the constantc will ofcourse also depend on how, and in what tests, the mechani-cal properties (toughness and uniform strain) are measured.If a test other than a tensile test is used, for example anupset test, then a different toughness value will result and,hence, a change in the proportionality constantc will be ne-cessitated. This will of course be of little consequence to thepredictions of the model if the relative changes in toughnessandc are the same for all materials.

Finally, it is illustrative to compare the model developedin this paper with one developed by Sundararajan [40–42].Sundararajan’s model, like the present one, is based on anenergy balance and assumes that erosion occurs due to thelocalisation of plastic flow to form lips. However, his modelassumes that localisation will not occur until a critical strainis reached in the sub-surface zone whereby the work hard-ening rate dσ/dε = 0. The present, much simpler, modelassumes by contrast that upward flow around the impactingparticle will occur without the need for prior work harden-ing of the sub-surface material. There is a reasonable bodyof evidence for such an assumption. Shaw and de Salvo [43]have shown that upward flow will occur for all except blunt


indenters (where the semi-angle of the conical indenter wasgreater than∼80◦). Dugdale [25] indicated likewise, andshowed that the displaced material was heavily strained.In an impact erosion scenario it seems plausible that suchheavily strained material would be easily removed fromthe surface under either the initial or subsequent impacts.A further difference between the two models is that theone presented in this paper is explicit in its assumption thatmaterial removal during erosion occurs due to fracture afterlarge deformations. Thus, the toughness of the material isseen to be the dominant factor controlling erosion rate. Bycontrast, Sundararajan assumes that fracture immediatelyfollows localisation of plastic flow at a critical strain depen-dent on material properties. Thus, it is not explicit in themodel that large plastic strains are essential for removal ofmaterial during erosion, although it is true that calculatedvalues of the critical strain are often large.

There is further evidence that erosion is controlled by adeformation and fracture process, rather than the alternativemechanism proposed by Sundararajan. Microhardness,HV,measurements were taken beneath the wear surface on sec-tioned specimens and a hardness profile of the sub-surfacezone constructed. Table 6 indicates the bulk hardness and themaximum sub-surface hardness (immediately beneath thewear surface) for specimens eroded at 35 m s−1 and impactangles of 8, 30 and 90◦, respectively. Significant work hard-ening is evident at all impact angles but tends to increasewith impact angle. It is a matter of speculation whether thisis a true trend or not. It may merely be a reflection of thegreater difficulty in locating the true maximum hardness inthe subsurface zones created by 8◦ impacts. These zonesare much shallower than those formed by 90◦ impacts andconsequently have a steeper hardness profile. Also shownin Table 6 are the maximum equivalent flow stresses of thework hardened material in the sub-surface zones assumingthat flow stress is equal to 3.3HV. The final columns indi-cate the fracture stresses of the materials (see also Tables 4and 5) obtained from tensile tests at room temperature and300◦C (appropriate for erosion at 35 m s−1). It may beobserved that in most cases the maximum flow stress inthe sub-surface zone of specimens impacted at 90◦ is onlymarginally less than the measured fracture stress. It can beeasily imagined that a subsequent impact would be sufficientto cause further work hardening sufficient for fracture totake place. The sub-surface hardnesses and flow stresses at8 and 30◦ are less than those at 90◦. Nevertheless, it seemsprobable that the higher shear strains experienced during im-pact at these shallower angles would allow the greater workhardening necessary for the fracture stress to be attained.

The measured hardness and calculated flow stress mea-surements also offer an explanation for the behaviour oftwo of the ‘rogue’ materials and their deviation from thepredictions of the model. The EN42 pearlite is seen to havea much higher maximum equivalent flow stress than thefracture stress indicated by tensile tests. Consequently, thetoughness of the material during erosion is likely to be much

higher than would be suggested by tensile measurements.This may in turn explain why its erosion resistance is muchhigher than would be predicted from a model based ontensile toughness. This does not detract from the essence ofthe model which simply proposes that erosion is controlledby toughness. It merely implies that for certain materialsthe tensile test is not the best test from which to gain an es-timate of toughness under erosion conditions. EN24 700◦Ctempered martensite, on the other hand, is seen in Table 6to have a maximum equivalent flow stress significantlylower than its fracture stress measured in a tensile test. Itstoughness during erosion is for some reason much less thanthat measured in a tensile test. This may explain why it hasan erosion rate much higher than predicted.

It may be concluded from this analysis that an erosionmodel based on toughness is entirely plausible. Furthermore,as mentioned previously, the experimental data collected inthe present work has been applied to a number of previouslydeveloped erosion models, two by Hutchings [16,37,44] andthe strain localisation model of Sundararajan [40–42]. Eachof these models was found to be deficient in predicting theobserved erosion rates. This work will be reported on in afuture paper.

As the model stands its practical use may be somewhatlimited. Vagaries in the results obtained on heat treatedsteels have cast doubt on the wider applicability of the modelto all ductile metals. It was suggested earlier that some ofthese anomalies could perhaps be removed by measuring theproperties of sub-surface hardened material (rather than bulkproperties) and measuring toughness in a test in which thestress state was closer to that of the actual erosion process.The model is also a deliberately simple one in contrast to themathematical rigour displayed by others, notably Sundarara-jans [40–42]. Nevertheless, despite its limitations, the modelis important in a number of respects. In contrast to mostprevious models it proposes that it is toughness rather thanhardness that is the most influential property with regard toerosion. Whilst toughness is believed to have an influentialrole in the abrasive wear of polymers (the Ratner–Lancastercorrelation) its possible role in metal erosion/abrasion hasbeen neglected. Sundararajan [42] indicated that there wasno evidence of a correlation between erosion rate and a pa-rameter similar to toughness, the mechanical energy density.This is defined as the product(σY + σUTS)εF/2. However,there are significant differences between the mechanicalenergy density and toughness as measured in the presentwork. It is first of all unclear whether theεF used to calcu-late mechanical energy density is the true strain to fracturebased on reduction in area. Furthermore, the level of stressassumed fails to take into account high-strain work harden-ing, which as calculations of toughness in the present workshow is significant. It can be seen in Table 4 that the truefracture stress is often significantly higher than the UTS.

The role of elevated temperature mechanical properties indetermining room temperature erosion behaviour is specula-tive and has never been considered before. The implication


of the present work is that the major effect of high strain-ratedeformation during the erosion process is the localised heat-ing that occurs at particle impact. This in turn influencesthe mechanical properties governing the material deforma-tion and removal processes. One effect of measuring theproperties of steels at elevated temperatures is a tendencyto narrow the range of these properties. Thus, martensite,which has extremely low toughness and ductility at roomtemperature, has much higher values at temperatures as lowas 300◦C. This might partly explain the general observa-tion that heat treatment of steels, despite producing a widerange of room temperature properties, has less effect thanmight be expected on erosion behaviour. Finally the rogueresults attained in the present work, and the explanationsproffered for them if correct, serve to illustrate once againthe incredibly complex nature of material behaviour duringerosion.

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Documents

A model to predict the solid particle erosion rate of metals and its assessment using heat-treated steels