Simulation Studies of Solid-Particle and Liquid-Drop Erosion of NiAl Alloy Rong Liu, Kuiying Chen, Ju Chen, Jingrong Zhao, Ming Liang

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1 World Aademy of Siene, Engineering and Tehnology International Journal of Mehanial and Mehatronis Engineering Vol:9, No:5, 5 Simulation Studies of Solid-Partile and iquid-drop Erosion of NiAl Alloy Rong iu, uiying Chen, Ju Chen, Jingrong Zhao, Ming iang International Siene Index, Mehanial and Mehatronis Engineering Vol:9, No:5, 5 waset.org/publiation/84 Abstrat This artile presents modeling studies of NiAl alloy under solid-partile erosion and liquid-drop erosion. In the solid-partile erosion simulation, attention is paid to the oxide sale thikness variation on the alloy in high-temperature erosion environments. The erosion damage is assumed to be deformation wear and utting wear mehanisms, inorporating the influene of the oxide sale on the eroded surfae; thus the instantaneous oxide thikness is the result of synergeti effet of erosion and oxidation. For liquid-drop erosion, speial interest is in investigating the effets of drop veloity and drop size on the damage of the target surfae. The models of impat stress wave, mean depth of penetration, and maximum depth of erosion rate (Max DER) are employed to develop various maps for NiAl alloy, inluding target thikness vs. drop size (diameter), rate of mean depth of penetration (MDRP) vs. drop impat veloity, and damage threshold veloity (DTV) vs. drop size. eywords iquid-drop erosion, NiAl alloy, oxide sale thikness, solid-partile erosion. S I. INTRODUCTION OID-partile erosion and liquid-drop erosion both are popular wear modes that ause serious problems in many engineering systems, inluding steam and jet turbines, pipelines and valves arrying partiulate matter, and fluidized bed ombustion systems. Solid-partile erosion is aused by the impingement of small, solid partiles against a surfae, resulting in the loss of the material []. iquid-drop erosion an be desribed as the ollision at high speed of liquid droplets with a solid surfae, whih auses the removal of material from the surfae []. Although experimental investigation prevails in erosion researh, due to high apital ost and long duration of erosion tests, various simulation models have been developed, inluding physis-based and statistis-based erosion models, to predit/reveal the erosion resistane/mehanisms of materials. One of the most popular models was developed based on an ideal dutile, non-work hardening solid material eroded by rigid partiles [3]. Another model was reated for single-partile erosion of metals that assumed that material utting and material deformation ourred simultaneously but further suggested that deformation wear governed at normal impat while utting wear prevailed at aute angles [4]-[6]. Erosion of metalli materials at high temperatures is influened by oxidation. Erosion-oxidation maps are very Rong iu is with Carleton University, Ottawa, Ontario, S 5B6 Canada (phone: 63-56; fax: ; Rong.iu@arleton.a). uiying Chen is with National Researh Counil Canada, Ottawa, Ontario, A R6 Canada ( uiying.chen@nr-nr.g.a). Ju Chen, Jingrong Zhao, and Ming iang are with University of Ottawa, Ottawa, Ontario, N 6N5 Canada ( juhen@hotmail.om, zjrstaie@hotmail.om, Ming.iang@uOttawa.a). useful in high-temperature erosion study beause they are a means by whih the hange in erosion-orrosion mehanism ranging from the erosion of the substrate to the erosion of the orrosion produt is given as a funtion of an erosion and orrosion parameter [7]. Several physis-based models have been developed, whih desribe the interation between erosion and oxidation [8]-[]. Aording to the thikness of the oxide on the eroded surfae, three boundaries were defined as at the first boundary the protetion provided by the oxide sale was negligible and the substrate surfae took most of the impat energy when the oxide film was thin; at the seond boundary the oxide was able to take all the plasti deformation and therefore there was no any plasti deformation taking plae in the substrate beause the oxide sale thikness reahed the same level as the plasti deformation zone; and at the third boundary the impat from partiles was all absorbed by the oxide sale and no plasti deformation ourred in the substrate region []. The earliest model of liquid impingement erosion was established to investigate the deformation of the solid target material in the initial stage of damage [], whih proposed that at the moment of initial impingement, a stress wave generated immediately traveled bak from solid-liquid ontat into liquid and the liquid exhibited ompressible behavior. This model was improved, suggesting that high pressure ourred in liquid impingement erosion and expressed the impat pressure as a funtion of the density of the liquid, the ompressibility of the liquid and the impat veloity of liquid droplet [3], and the pressure equation was modified with the impat of spherial drop and onsideration of the elasti deformation of the liquid drop [4]. In order to predit the response of a material in liquid impingement erosion, sientists attempted to find the relationships between erosion resistane and mehanial properties of materials suh as hardness, tensile strength, frature toughness and strain energy. The measurements of erosion resistane of materials an fall into the main aspets suh as maximum rate of weight loss, mean depth of penetration, rationalized erosion rate and maximum depth of erosion rate (Max DER) [5]-[]. In this researh, the resistane of NiAl alloy, whih is a widely used alloy in erosion environments, to solid-partile erosion and liquid-drop erosion was investigated through analytially modeling. An analytial model was reated that an predit the oxide sale thikness at a given time interval for steels and alloys under high-temperature erosion at a set partile impat veloity and impinging angle, based on the four-regime lassifiation of eroded surfae [9] and the formulation of oxide growth rate [], utilizing deformation International Sholarly and Sientifi Researh & Innovation 9(5) 5 46 sholar.waset.org/37-689/84

2 World Aademy of Siene, Engineering and Tehnology International Journal of Mehanial and Mehatronis Engineering Vol:9, No:5, 5 International Siene Index, Mehanial and Mehatronis Engineering Vol:9, No:5, 5 waset.org/publiation/84 wear and utting wear mehanisms of materials in erosion [6]. The obtained results from the model were plotted to show the oxide thikness variation with erosion time of NiAl alloy under different temperatures and erosion onditions suh as partile impat veloity and partile impinging angle. For liquid impingement erosion analytial models of impat stress wave, mean depth of penetration, and Max DER were employed. The liquid impingement erosion resistane of NiAl alloy was haraterized by establishing the relationships between target thikness and drop size (diameter), between rate of mean depth of penetration (MDRP) and drop impat veloity, and between damage threshold veloity (DTV) and drop size. II. SOID-PARTICE EROSION MODEING A. Formulation of Oxidation Oxidation proess ontrols the oxide growth on a metal surfae in high-temperature environments. ang et al. [9] defined the rate of oxide sale growth in high-temperature erosion using: dx dt e, () X where e is the paraboli rate of oxide growth, whih is a funtion of the target metal omposition, the orrosive ondition and the erosive ondition; is the erosion rate of orrosion produt (oxide), whih is a funtion of the type of orrosion produt and the erosive ondition. To ompute the oxide sale growth rate, the value of e must be obtained as an initial input. With the input value of temperature T, the relationship between the paraboli onstant of oxide growth p and e is given as [] o p e avm bm, () where, for an oxide M a O b a and b are the numbers in the desription, M o is the atomi weight of oxygen, and V m is the molar volume of the target metal. Rearranging () gives: av m e. (3) p bm o B. Formulation of Erosion In high-temperature erosion, the oxide thikness on the metal target surfae is redued by erosion. To obtain the oxide thikness redution rate, the erosion mehanisms at high temperatures should be learly identified. Bitter [5] devised a method to desribe erosion based on energy onservation. It was assumed that the total erosion energy W e was onstant for two types of erosion, deformation erosion ( ) and utting erosion ( and ). In detail, the total erosion energy an be expressed as [5] We WD W, if C α α, (4) We WD W, if C α α, (5) where α is the inident partile angle impating on the target material. is the impat angle at whih the horizontal veloity equals zero when the partile leaves the surfae. The deformation erosion energy is given as [5] W D M ( V sinα ), (6) δ and the utting erosion energy is expressed as [5] MC( V sinα ) ( sinα ) C V, (7) W C V osα χ V sinα V sinα M [ V os α ( α ) ] 3/ V sin. (8) χ W C The parameters in (7) and (8) are given as [5].88 C y 4 d y, (9) / π 5 / q q, () y.8y d 4 E y q d E E q, () E where d is the density of partile; E, E, q and q are the Young s modulus and Poisson s ratio of partile and target material, respetively; δ is deformation wear fator; χ is utting wear fator; M is the total mass of impinging partiles; V is partile impat veloity; y is elasti load limit. The erosion theory given by [5] shows omplex forms in terms of expression and implementation, whih were onerned by [6] to seek a simpler analytial solution. The new solutions ould readily orrelate experimental data. The simplified erosion model for erosion loss in weight takes the following form and MV W os α sin nα M ( V sinα, if φ ε MV os α M ( V sinα κ ), if W φ ε α α, () α > α, (3) where κ is the veloity omponent normal to the surfae below whih no erosion takes plae in ertain hard materials; φ and ε are utting and deformation wear fators, respetively; n is a onstant. In order to obtain the thikness redution rate of the oxide sale, the total mass of impat partiles M in () and (3) was hanged to m/d, where m is partile mass per unit area per seond and d is the density of partile. This gives the erosion loss in thikness as International Sholarly and Sientifi Researh & Innovation 9(5) 5 46 sholar.waset.org/37-689/84

3 World Aademy of Siene, Engineering and Tehnology International Journal of Mehanial and Mehatronis Engineering Vol:9, No:5, 5 International Siene Index, Mehanial and Mehatronis Engineering Vol:9, No:5, 5 waset.org/publiation/84 and mv os α sin nα m V φd ( sinα, if εd mv os α m( V sinα, if φd εd α α, (4) α > α. (5) C. Growth Rate of Oxide Sale The above analysis proedure inludes two aspets: inrease in oxide sale thikness due to oxidation and redution of oxide sale thikness beause of erosion attak. From the above analyses, the instantaneous sale thikness hange rate an be obtained. Consider () again, ombining (3), (4) and (5), the hange rate of oxide sale thikness is expressed as and dx dt dx dt avm P bm o X avm P bm o X mv os α sin nα m( V sinα, φd εd if α α, (6) mv os α m( V sinα, φd εd if α > α. (7) To solve the above differential equations, the value of paraboli onstant of oxide growth p must be known. It an be obtained experimentally aording to the equation []: [ X ( f )], (8) P t where is the density of oxide sale; f is the stoihiometri fator that aounts for the perentage of the metal onsumed in the formation of oxide; and t is the time of exposure. Thus, one the parameters in (6) and (7) are defined, the differential equations an be solved and the variation of the oxide thikness with erosion time for a given partile impat veloity and impinging angle an be obtained. Based on the variation of the oxide thikness, the erosion behavior an be predited with respet to the four-regime of eroded surfae [9]. Regime erosion of metal may not our unless the metal is non-oxidable. If the oxide thikness dereases with erosion time, the oxide sale will be totally removed from the eroded surfae after a ertain period of time and eventually the substrate material will be subjeted to erosion. In this ase, regime oxidation-affeted erosion predominates. On the ontrary, if the oxide growth rate in erosion proess is greater than the oxide growth rate without erosion proess involved, oxidation will benefit the erosion resistane of the substrate material; then regime 3 erosion-enhaned oxidation takes plae. Finally, as the growth rate of the oxide is high enough to avoid the partiles reahing the substrate surfae, erosion an only our in the oxide sale. This erosion falls into regime 4 oxide erosion. III. IQUID-DROP EROSION MODEING A. Impat Stress Wave In the liquid impingement erosion theories given by []-[4]; it was suggested that at the moment of initial impingement, a stress wave generated immediately traveled bak from solid-liquid ontat into liquid at a ertain veloity and the liquid exhibited ompressible behavior. High pressure ourred in liquid impingement erosion due to water-hammer effet and the impat pressure an be expressed as funtions of liquid properties and drop normal impat veloity (V ). Heymann [3] deemed that in onsideration of droplet impating at 9 degree on a smooth and rigid surfae, the impat stress reahed the maximum (peak) near the ontat area, however, at the exat ontat point it remained a relatively small (bottom) value due to the release of the waves that generated the pressure distribution map. This high pressure led to the ourrene of ring raks and fratures in the area within radius r in the top surfae layer of the target, as shematially shown in Fig.. Fig. Ring raks indued in the top surfae layer of the target attaked by liquid drop The radius r is expressed as [] h r, (9) [( / ) ] / d R where h is the thikness of target, see Fig., and d R are the dilatational veloity and Rayleigh wave veloity, respetively. Considering the inherent elastiity of the material, the veloity of Rayleigh wave is generally thought to be equal to that of shear wave, and then an be alulated as [4] R G, () where G and are the shear modulus and density of target material, respetively. The ourrene of erosion damage on target surfae depends on the duration of drop inidene time and the duration of the stress wave. When the former is longer International Sholarly and Sientifi Researh & Innovation 9(5) 5 46 sholar.waset.org/37-689/84

4 World Aademy of Siene, Engineering and Tehnology International Journal of Mehanial and Mehatronis Engineering Vol:9, No:5, 5 International Siene Index, Mehanial and Mehatronis Engineering Vol:9, No:5, 5 waset.org/publiation/84 than the latter, erosion damage ours [], i.e., d h >. S Therefore, to avoid erosion damage, the minimum target thikness an be determined by ds h, () where d is the size (diameter) of liquid drop, and S are sound speeds of liquid and solid, respetively, an be alulated by [5], [6] κ, () S E, (3) where κ is the bulk modulus of liquid drop and E is the Young's modulus of solid target; and are the densities of liquid drop and solid target, respetively. From () it is evident that for a given target material the minimum thikness h for preventing erosion damage from ourring is solely proportional to the drop size for erosion damage ourring. Fig. Inoming liquid drop on solid surfae at an inident angle θ [7] Fig. 3 Mean depth of penetration of liquid drop into solid surfae B. Mean Depth of Penetration When a liquid droplet having a diameter d impats a solid surfae at an inlined angle θ with a veloity V, as illustrated in Fig. [7]; [5] desribed the rate of mean depth of penetration (MDRP), as shown in Fig. 3, by the following equations, whih is the hange rate of an average thikness of the surfae subjeted to liquid impat erosion. 3 η Ap ' V, (4) MDRP ε F 3 η Ap V, (5) MDRP. F F ε where η is the effiieny of energy transfer between the liquid and solid, ε is the energy to remove unit volume of the target material, V is the ritial veloity for normal drop impat at whih erosion ours, F and A are exposed target area and p projeted target area, respetively. Aording to Fig. [7], V V / osθ (6) The volume of eroded surfae layer ( V ) related to the energy ( ε ) absorbed by eroded material is given as ε V S F h, (7) S where S is the erosion strength parameter that an be determined by a omputational proedure based on experimental measurements. To be more general, [6] proposed an expression of erosion rate (E r ) with the inident angle, E r n ( V V osθ V ) osθ, (8) where V denotes the veloity below the ritial value of no mass loss, n [5,3] is a onstant and depends on the target material properties. When θ, V V, in this ase, it is assumed that η and F A. Substituting () into (7) p gives d F S Combining (), (3), (5) and (9) yields S ε (9) 3 κ V (3) MDRP E 4d S C. Maximum Depth of Erosion Rate Hattori [7] ompared maximum depth of erosion rate (Max DER) of different materials, orrelating Max DER with exposure time. Three time intervals an be identified in the Max DER-t map: inubation, aeleration, and maximum rate stages. The duration time of inubation depends on the impat veloity. The exponent of erosion rate is given on the basis of the volume International Sholarly and Sientifi Researh & Innovation 9(5) sholar.waset.org/37-689/84

5 World Aademy of Siene, Engineering and Tehnology International Journal of Mehanial and Mehatronis Engineering Vol:9, No:5, 5 International Siene Index, Mehanial and Mehatronis Engineering Vol:9, No:5, 5 waset.org/publiation/84 of the liquid impinging per unit time and is also ertainly proportional to impat veloity. Thus impat veloity is a key parameter to be investigated, espeially threshold veloity at the moment when erosion rate is zero or negligible. In terms of threshold veloity, [8] and [9] defined pathbreaking damage threshold veloity (DTV) as the lower impat veloity at whih damage ourred. The material s erosion resistane was widely haraterized by absolute damage threshold veloity (ADTV). Hand and Field [] proposed a linear relationship between ADTV and log of the frature toughness of target material for mm diameter water drops. They attempted to minimize the number of impats and to derease the veloity in order to get the threshold value. Evans et al. [] defined a theoretial expression for DTV given by DTV.4 IC R w d / 3, (3) where is the frature toughness of target material, C IC w is ompressive wave veloity, whih is related to material properties [4] 4 κ G 3 w, (3) where G and κ are the shear modulus and bulk modulus of solid target, respetively. The value of DTV is benefiial for ontrolling the impat veloity, prediting the exat timing of damage ourrene and avoiding the damage. IV. EROSION OF AUMINUM-NICE AOY A. Parameters in Models for NiAl Alloy The NiAl alloy investigated in this researh is CMSX-4; its hemial omposition is given in Table I. The oxidation behavior of Ni-Al alloy has been investigated by [8], showing that two alumina phases (θ-al O 3 and α-al O 3 ) are present in the oxide produt. The values of the paraboli rate onstant p were alulated from the experimental measurements of the oxide geometry at different temperatures, and also using other parameters, aording to (8); these values are reported in Table II [8]. TABE I CHEMICA COMPOSITION OF CMSX-4 AOY Ni Cr Co Al W Mo Ta Hf Re TABE II PARABOIC OXIDATION RATE CONSTANTS OF CMSX-4 AOY Temperature ( C) p (kg /m 4 h) E-9 9.4E E-8 In the differential equations (6) and (7), utting and deformation wear fators, φ and ε, were determined based on the assumptions that for the materials with high hardness more energies of utting wear and deformation wear are required to remove the target material during an erosion proess, and for high strength alloys large values of φ and ε are required. These assumptions indiate that hardness and strength may exhibit some intrinsi orrespondenes to φ and ε values. Based on suh orrelations, a parametri method was applied to obtain φ and ε for various alloys with the assistane of material properties of these alloys suh as hardness, yield strength and tensile strength. The alulated values of φ NiAl and ε NiA, along with other parameters that are required by (6) and (7) are listed in Table III. For the κ value (veloity omponent normal to the surfae below whih no erosion takes plae) in the equations, as suggested by [6]; for metals it is often the ase that κ is negleted beause the utting wear predominates and the κ value is usually very small ompared to the partile veloity. The onstant n in the equations was taken as 5, aording to the test onduted by [6]. TABE III PARAMETERS OF AUMINUM-NICE AOY FOR OXIDE THICNESS COMPUTATION Parameter Value a (M ao b, Al O 3) b (M ao b, Al O 3) 3 (molar volume of the alloy).4-5 (m 3 /mol) (Atomi weight of oxygen).6 (kg/mol) d (density of partile) 7 (kg/m 3 ) φ (utting wear fator) (N m/kg) ε (deformation wear fator) (N m/kg) The material properties of the liquid and NiAl alloy used in the liquid-drop erosion model are given in Table IV. The minimum target thikness to avoid the ourrene of damage was omputed with inreasing the drop size using (). The and S values were alulated from () and (3). TABE IV PARAMETERS OF AUMINUM-NICE AOY AND IQUID FOR EROSION MAPS κ - bulk modulus of NiAl 3 GPa E - Young s modulus of NiAl 5 GPa G - shear modulus of NiAl 94 GPa - frature toughness of NiAl IC 5 6 Pa.m / - density of NiAl kg/m 3 H - hardness of NiAl 8 HB - density of liquid 3 kg/m 3 κ - bulk modulus of liquid. GPa The MDRP of eroded NiAl surfae was omputed against the veloity of liquid droplet using (3). It is suggested that erosion strength parameter S is approximately proportional to the hardness of target surfae material [7]. Therefore for the S value of NiAl alloy, the experimental measurement on pure Al to obtain it S value in the previous researh by Hattori [7] International Sholarly and Sientifi Researh & Innovation 9(5) sholar.waset.org/37-689/84

6 World Aademy of Siene, Engineering and Tehnology International Journal of Mehanial and Mehatronis Engineering Vol:9, No:5, 5 International Siene Index, Mehanial and Mehatronis Engineering Vol:9, No:5, 5 waset.org/publiation/84 was utilized. Using () and (3) to obtain the C R and C w values for NiAl alloy with the material properties in Table IV and substituting these values together with other material properties in Table IV into (3), the DTV was omputed with varying drop size. B. Results of NiAl Alloy from Models The omputations were implemented using Matlab omputer program. The variations of the oxide sale thikness with erosion time of NiAl alloy under high-temperature erosion were omputed for different erosion onditions and the results are plotted in Figs As shown in Fig. 4, at high temperatures without partile impat, oxide growth rates are appreiable and proportional to expose time, and also the growth rate of oxide thikness is proportional to temperature. At 95, the oxide thikness inreases to. µm from original value of. µm at the time t s within 6 s. At 9, the oxide thikness reahes.9 µm, and at 85, the oxide thikness reahes.4 µm. The thikness growth rate at 95 is about 3 times higher than the rate at 85, and.5 times the rate at 9. Fig. 4 Variations of oxide sale thikness with time for NiAl alloy without partile impat Fig. 5 Variations of oxide sale thikness with time for NiAl alloy under erosion at partile impat veloity of m/s and partile impat angle of 5 degree Fig. 6 Variations of oxide sale thikness with time for NiAl alloy under erosion at partile impat veloity of 5 m/s and partile impat angle of 9 degree Fig. 7 Variations of oxide sale thikness with time for NiAl alloy under erosion at partile impat veloity of 5 m/s and partile impat angle of 45 degree The omputational results of liquid-drop erosion for NiAl alloy are plotted in Figs. 8-. It is shown that the minimum target thikness for avoiding erosion damage inreases linearly with drop size (diameter), see Fig. 8. The inrease of required target thikness with larger drop size an be explained as the bigger the droplet, the larger the ontat area is and also the heavier the impat of drop is, thus the more severe the attak of erosion is. For the MDRP of NiAl alloy, as shown in Fig. 9, the MDRP is trivial at very low drop veloities (< m/s), but it inreases steadily with drop veloity between m/s and 4 m/s, and then rises rapidly at high drop veloities. Doubtlessly, drop veloity has signifiant influene on the MDRP, whih is parametrially related to erosion resistane. In regard of the DTV, it dereases with drop size, as seen in Fig.. Within the range of drop size 5 to µm, whih is ommon in reality, the orresponding DTV is very high and above m/s. Therefore, in pratie, if the drop veloity is less than m/s, erosion damage would not our on NiAl alloy. International Sholarly and Sientifi Researh & Innovation 9(5) sholar.waset.org/37-689/84

7 World Aademy of Siene, Engineering and Tehnology International Journal of Mehanial and Mehatronis Engineering Vol:9, No:5, 5 International Siene Index, Mehanial and Mehatronis Engineering Vol:9, No:5, 5 waset.org/publiation/84 Fig. 8 Target thikness ~ drop size map of NiAl alloy Fig. 9 MDRP ~ drop impat veloity map of NiAl alloy Fig. DTV ~ drop size map of NiAl alloy V. DISCUSSION Without erosion attak, the oxide thikness on NiAl alloy surfae inreases with temperature. This is beause oxidation is promoted by temperature. However, it is observed that the growth rate of the oxide on NiAl alloy is very low due to the limited Al ontent, ompared with that on pure Al [9]. In addition, the trend of the oxide thikness growth is atually paraboli; however, beause the time interval is only 6 s and the value of paraboli onstant is small, the plotted urves exhibit a shape lose to straight line. When partiles impat the NiAl alloy surfae that has an oxide sale of µm, at a veloity of m/s and at an impinging angle of 5 degree, the thikness of the oxide is redued from initial µm to.84 µm in 6 s, as shown Fig. 5. In other words, when erosion is involved, the oxide thikness dereases with time. It an be deduted that after a ertain period of time, the oxide thikness will beome zero. In this ase, the substrate material will be eroded and oxidation will not benefit preventing erosion degradation, that is, erosion is the type of regime oxidation-affeted erosion. Furthermore, when the partile impat veloity is raised, the frequeny of partile impat on the target surfae is inreased; then the oxide removal from the surfae is expedited. As illustrated in Fig. 6, within 6 s at the partile impat veloity of 5 m/s, the oxide thikness beomes negative, that is, no oxide is on the surfae at all. Also, at the same partile impat veloity of 5 m/s, the smaller impinging angle auses larger oxide removal. This an be seen by omparing the urves in Fig. 6 with those in Fig. 7. This indiates that for dutile materials (metals), utting wear predominates in erosion, whih has been proved by previous researh [6], [3]. Moreover, from Figs. 5-7, it is observed that at the partile impat veloities of m/s and 5 m/s, the temperature almost does not affet the oxide thikness; in partiular, at the higher veloity the oxide thikness does not vary with temperature, as seen in Figs. 6 and 7. The reason for this is that the oxide growth rate of this alloy is very low, therefore at high partile impat veloities there is no enough time in the interval between impats for oxide to form. From Figs. 9 and, it is lear that in liquid-drop erosion when drop veloity is very low (< m/s) and droplet is very small (< µm), erosion damage would nearly not our on NiAl alloy. However, the inreasing rate of MDRP for this alloy is raised by drop veloity inrease, whih an be desribed by the derivative of the MDRP equation. On the other hand, the dereasing rate of DTV is redued by drop size inrease, whih an be demonstrated by the derivative of the DTV equation. This may be explained by the avitation damage mehanism, whih is ativated when a suffiient liquid volume exists at the solid/water interfae, in addition to the drop kineti energy. VI. CONCUSIONS The variation of the oxide thikness with erosion time an reveal the damage behavior of the eroded surfae. Due to the low growth rate of the oxide, the oxide thikness dereases with erosion time for NiAl alloy under high-temperature erosion, whih indiates that oxidation does not play a signifiant role in ontribution to erosion resistane of this alloy. The oxide thikness results show that the erosion damage at the smaller partile impinging angle is larger, whih onfirms that utting wear predominates the erosion of this alloy, whih is dutile. The minimum target thikness (m) for NiAl alloy to avoid erosion damage is inreased with drop diameter (m) by a fator of The higher the drop veloity, the larger the rate of mean depth of penetration is, and the greater the drop diameter, the lower damage threshold veloity is. The rate of mean depth of penetration inreases rapidly with high drop veloities. Within International Sholarly and Sientifi Researh & Innovation 9(5) sholar.waset.org/37-689/84

8 World Aademy of Siene, Engineering and Tehnology International Journal of Mehanial and Mehatronis Engineering Vol:9, No:5, 5 International Siene Index, Mehanial and Mehatronis Engineering Vol:9, No:5, 5 waset.org/publiation/84 the range of drop size 5 to µm, the damage threshold veloity for this alloy is above m/s. ACNOWEDGMENT The authors are grateful for finanial support from the Natural Siene & Engineering Researh Counil of Canada (NSERC), in-kind support form National Researh Counil Canada, and both finanial and in-kind support of ennametal Stellite In. REFERENCES [] P. J. Blau, Frition and Wear Transitions of Materials. Noyes Publiations: Park Ridge, 989. [] G. S. Springer, Erosion by iquid Impat. John Wiley & Sons In.: Washington D.C., 976. [3] I. Finnie, Erosion of surfaes by solid partiles, Wear, vol. 3, pp. 87-3, 96. [4] J. G. A. Bitter, A study of erosion phenomena, Part I, Wear, vol. 6, no., pp. 5-, 963. [5] J. G. A. Bitter, A study of erosion phenomena, Part II, Wear, vol. 6, no. 3, pp. 69-9, 963. [6] J. H. Neilson and A. Gilhrist, Erosion by a stream of solid partiles, Wear, vol., no., pp. -, 968. [7] G. Sundararajan, An analysis of the erosion-oxidation interation mehanisms, Wear, vol. 45, no., pp. 5 8, 99. [8] S. Hogmark, A. Hammersten, and S. Soderberg, On the ombined effets of orrosion and erosion, in Pro. 6th Int. Conf. on Erosion by iquid and Solid Impat, Cambridge, 983, pp [9] C. T. ang, F. S. Pettit, and N. Birks, Mehanisms in the simultaneous erosion-oxidation attak of nikel and obalt at high temperature, Metall. Trans. A, vol. 8, no., pp , 987. [] M. M. Stak and. Bray, Interpretation of wastage mehanisms of materials exposed to elevated temperature erosion-orrosion using erosion-orrosion maps and omputer graphis, Wear, vol , no., pp , 995. [] D. M. Rishel, F. S. Pettit, and N. 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Yao, Analytial modeling of solid-partile erosion of Stellite alloys in ombination with experimental investigation, Wear, vol. 39, no. -, pp. 6-3, 4. Rong iu was born in China on August 5, 96. She reeived a Bahelor degree of mehanial engineering from Northeastern University, Shenyang, iaoning, China, in 983; a Master degree of mehanial engineering from Northeastern University, Shenyang, iaoning, China, in 99; a Master degree of materials engineering from University of Wollongong, Wollongong, New South Wales, Australia, in 995; a Ph.D. degree of mehanial engineering from Deakin University, Geelong, Vitoria, Australia, in 998. She was a Mehanial Engineer of Shenyang Aluminum Magnesium Engineering and Researh Institute, China, during 983 to 987 and 99 to 994. She was a Postdotoral Fellow of the Department of Chemial and Materials Engineering, University of Alberta, Canada, during 998 to. She was an Assistant Professor of the Department of Mehanial and Aerospae Engineering, Carleton University, Canada, during to 5. She was an Assoiate Professor of the Department of Mehanial and Aerospae Engineering, Carleton University, Canada, during 5 to. She was a Professor of the Department of Mehanial and Aerospae Engineering, Carleton University, Canada, from until now. Published book hapter: Chapter 4 High-Temperature Wear/Corrosion Resistant Stellite Alloys and Tribaloy Alloys, in CRC Handbook on Aerospae and Aeronautial Materials, CRC Press, Taylor & Franis, July. Published artile: Analytial modeling of solid-partile erosion of Stellite alloys in ombination with experimental investigation, Wear, vol. 39, no. -, pp. 6-3, 4. Published artile: A frature toughness model for brittle oating on dutile substrate under indentation loading, Engineering Frature Mehanis, vol. 8, pp. 7-8,. Her researh interests inlude frature mehanis of high-temperature materials; erosion and orrosion of superalloys; surfae oatings; finite element analysis. Professor iu is a member of the Amerian Soiety for Metals (ASM) and a member of the Professional Engineers of Ontario (PEO), Canada. Professor iu was awarded by Carleton University Researh Works in 9. International Sholarly and Sientifi Researh & Innovation 9(5) sholar.waset.org/37-689/84