WeaT, 145 (1991)
251
251-282
An analysis of the erosion-oxidation interaction mechanisms G. Sundararajan Deface
Metallurgical
Research Laboratory, Kanchanbagh, Hydmabad 500258 (India)
(Received November 28, 1989; revised July 18, 1990; accepted October 8, 1990)
Abstract Materials exposed to a jet of erosive hard particles travelling at high velocities and to elevated temperatures beyond one-third of their melting point, undergo erosion as well as oxidation. Thus, it is necessary to understand the nature of the interaction between erosion and oxidation. Over the last few years, experimental data on elevated temperature erosion in an oxidizing atmosphere, particularly for steels, have become available. However, a comprehensive theoretical analysis of the erosion-oxidation (E-O) interaction is yet to be carried out. In the present paper a theoretical framework for interpreting the nature of the E-O interaction is presented. The possible erosion mechanisms involving E-O interactions are considered and their relative dominance as affected by test variables such as particle size and shape, oxidation rate, particle flux rate etc., are brought out in the form of E-O maps. A new model for the oxidation controlled erosion mechanism is also presented. Finally, a comparison is made between the predictions of the model and the experimental data available in the literature.
1. Introduction
The solid particle erosion behaviour of various metals and alloys at elevated temperatures varies depending on whether the tests are conducted below or above about 0.35 T,, where T,,, is the melting point of the eroding material. At test temperatures below about 0.35 T, or at higher temperatures with an inert atmosphere, the erosion behaviour of ductile materials appears deformation controlled as at room temperature. The only difference is that due allowance should be made for the alteration of the mechanical behaviour of the eroding material as caused by recovery and recrystallization at elevated temperatures. Much of the erosion data in this regime indicates very clearly that the velocity and impact angle dependence of the erosion rate at elevated temperatures is similar to that obtained at room temperature [l-7]. Recently, Trilok Singh and Sundarar&tn [7] have demonstrated that the mechanism of erosion under such conditions is identical to that obtained at room temperature. Beyond a test temperature of about 0.35 T,,, the oxidation of the eroding material becomes important and thus the nature of the interaction between erosion and oxidation becomes relevant and should be necessarily incorporated in the erosion model. The most comprehensive set of erosion data in the 0043-1648/91/$3.50
0 Elsevier Sequoia/Printed in The Netherlands
erosion-oxidation (E-O) regime is that due to Levy and coworkers [8-141. These investigators have characterized the erosion behaviour of a number of steels in the E-O regime (temperature range: 600-1000 “C) and, in particular, the effect of various erosion variables on the mechanism of material removal. The modelling of the erosion behaviour of materials in the E-O regime has just begun as evidenced by the work of Wright et al. [ 151 and Kang et al. [16]. The objective of the present paper is to develop a suitable theoretical model for the erosion behaviour of materials in the E-O regime and, in particular, to build upon the earlier work of Wright et at. [ 151 and Kang et al. [ 161. The paper has been divided into sections as follows. In the next section (Section Z), the salient features characteristic of erosion behaviour in the E-O regime will be briefly reviewed. The conceptual aspects of the proposed model will be considered in Section 3, while the possible E-O mechanisms will be discussed in Section 4. The regimes of relevance of the various erosion mechanisms in the E-O regime as affected by the test related variables such as particle flux rate, the particle size, and shape and the sample oxidation rate will be illustrated in Section 5 by means of E-O maps. In Section 6, a new model for the oxidation controlled erosion mechanism will be proposed. Finally, in Section 7, the predictions of the present theoretical work will be compared with the available erosion data pertinent to the E-O regime.
2. Literature review The salient features characteristic of erosion behaviour of metallic materials in the E-O regime are reviewed briefly. (1) In the case of erosion of steels at elevated temperatures, if the test temperature, the eroding material or the impact velocity is such that a significant oxide scale forms, the velocity dependence of the erosion rate characterized by the constant n (erosion rate or metal thickness loss is roughIy V”, where V is the impact velocity) is closer to or less than unity rather than the usual values in the range 2-3 ob~ed during room tempe~t~e erosion tests [8-121. The relevant data compiled in Table 1 provide support for this statement. An unusually low velocity exponent is also accompanied by a change over to a brittle erosion behaviour even in the case of ductile metals and alloys (Table 2). (2) If significant oxide scale does not form during the high temperature erosion, the velocity exponent lies in the range 2-3 as at room temperature (see Table 1) and the erosion behaviour is also ductile in nature (see Table 2). (3) The use of rounded alumina as the erodent instead of SIC causes a thicker oxide scale to form. This in turn causes a change over from a high value of n to n < 1 and also a transition from ductile to brittle erosion behaviour [9 1. This observation is mainly related to the fact that the angular
253 TABLE 1 The velocity dependence of erosion rate at elevated temperatures Steels
1. SCr-1Mo
2. 3.5Ni 3. 5Cr-O.5Mo 4. SCr-O.5Mo-1Si 5. 18Cr-12Ni-2.25Si 6. 2OCr-2.5Al-1Si 7. 8. 9. 10. 11. 12.
2.25Cr-lMc+1.4Si 2.25Cr-1Mo 5Cr-1Mo 3Cr-1.5Si 304 ss Inconel 600
Erodent?
Silica Sic Alumina Alumina Alumina Alumina Alumina Alumina Silica Alumina Alumina Alumina Silica Alumina Alumina Alumina Alumina Silica
Quartz
Size
T
Ref.
(“C)
Velocity range (m s-l)
nb
(pm) 130 130 90 130 90 130 90 90 130 90 130 90 130 90 130 130 90 120 450
850 850 850 850 650 850 850 850 850 850 850 850 850 850 850 850 850 300-650 370-580
30-70 20-100 30-70 20-100 30-70 30-70 30-70 30-70 30-70 30-70 30-70 30-70 30-70 30-70 35-70 35-70 30-70 40-120 120-250
2.0 1.9 0.82 0.62 0.55 0.74 0.70 1.10 1.70 0.66 0.98 1.00 2.03 1.60 1.10 1.00 0.82 2.8 >2
12 9 12 9 12 12 10 12 12 12 12 12 12 10 8 8 10 5 2
‘Sic, angular; silica, angulax; alumina, rounded. bE = erosion rate a V”; V is the impact velocity.
SIC is much more efficient in eroding the material or its oxide than the rounded ahunina. (4) In the case of the nickel-, iron- and cobalt-based alloys a comparison of the erosion behaviour at elevated temperatures in an inert atmosphere (no oxidation) and in an oxidizing atmosphere (E-O regime) indicates that the erosion rate is always higher in the E-O regime and also that the difference between the erosion rates (E and E-O conditions) increases with increasing hardness of the eroding material [ 15 1. In fact, in the E-O regime the erosion rate increases with increasing hardness of the alloy [ 151. (5) The magnitude of the erosion rate in the E-O regime is strongly dependent on the morphology of the oxide scale but nearly independent of its composition [S-14]. A segmented scale has the best erosion resistance while a consolidated scale has poor erosion resistance. A continuous consolidated scale gets removed by periodic spahing while the segmented scales get removed by cracking and chipping. The scale morphology is determined by test temperature, impact velocity, alloy composition and erodent size and shape [8-141. (6) Under erosion conditions the oxide scale grows more rapidly than under static or dynamic oxidation conditions [ 141. (7) Additions of silicon and chromium to the steels in the E-O regime is quite effective in reducting the erosion rate [ 8, lo]. Silicon changes the
‘54
TABLE 2 Erosion behaviour at elevated temperatures Material
Erodent
Temperature (“C)
Erosion behaviouP
Ref.
SCr-1Mo SCr-1Mo Nickel, iron and cobalt alloys Chromium steels (> 15% Cr) Chromium steels (< 15% Cr) 304 ss Steels 304 ss 304 SS, 316 SS, 410 SS 2024 Al 410 ss Ti-6Al-W Inconel 600 Tantalum
Sic Alumina Alumina Alumina Alumina Silica Silica Flyash Sic QUart7. Quartz Quartz
650-850 650-850 760 850 850 300, 650 300 650 30-500 20-250 20-250 20-250 370-580 20-250
Ductile Brittleb Brittle’ Ductile Brittle Ductile Ductile Ductile Ductile Ductile Ductile Ductile Ductile Ductile
9 9 15 8 8 5 5 4 7 3 3 3 2 3
Quartz Quartz
“Ductile if E (30”) > E (90”) and brittle if E (90”) > E (30”). ‘For V>30 m s-i. ‘Ductile when eroded in inert atmosphere.
scale morphology from a consolidated one to a segmented one and thus is effective. Addition of chromium reduces the growth rate of the oxide scale and hence is beneficial. (8) When the oxide scale is very thin and adherent, the erosion involves the deformation of both the scale and the base material underneath [9, 10, 15 1. In such cases the oxide scale buckles, becomes segmented and gets pushed down into the craters resulting in a composite oxide-metal layer in the near surface regions. (9) Controlled single impact experiments on pre-oxidized nickel-based superalloys in the temperature range 300-l 123 K, carried out by Stephenson et al. [ 17) using salt or carbon particles (300 ,um size) have given support for the concept of the critical scale thickness beyond which the scale behaves in a brittle fashion. At 700 “C, a scale 0.1 pm thick exhibited ductile response (i.e. scale deformed without cracking under Impact) while the response became brittle beyond a scale thickness of about 1 pm. In the brittle regime, the oxide scale got completely removed over a circular area proportional to the impact area. The above critical scale thickness beyond which the scale becomes brittle showed a dramatic increase beyond about 800 “C. 3. Preliminary
aspects
Before developing the models pertinent to the E-O regime, it is appropriate that we first consider the various important concepts which will provide the theoretical basis for the subsequent modelhng.
255
3.1. Steady state oxide scale thichmess (Zd If one makes the assumption that the oxide scale which forms on the eroding material during erosion is adherent and sufficiently ductile to withstand repeated impacts without developing cracks, a steady state oxide scale thickness (Z,,) can be defined as demonstrated by Kang et al. [ 161. Assume that the oxidation of the eroding metal/alloy follows the parabolic kinetics given by eqn. (1) Am2 = K,,Ot
(1)
where Am in eqn. (1) is the weight gain experienced by the metal per unit area due to intake of oxygen to form oxide scale, KPo is the parabolic rate constant and t is the time of exposure. The parabolic rate constant is usually expressed in the form [ 18 ]
KPo=A,exp( - Q/R T)
(2)
where A0 is the Arrhenius constant, Q is the activation energy for oxidation, R is the gas constant and T is the absolute temperature. The modelling of the E-O interaction requires knowledge of the rate of growth of the oxide scale thickness (Z) with time rather than the weight gain given by eqn. (1). However, as noted by Lim and Ashby [ 191, once the composition of the oxide formed is known, eqn. (1) can be transformed to give z2 = 2K$
(3)
KP = 0.5C2KPo
(4)
where C is a constant for a given oxide composition (in units of m3 kg-‘).
KP in eqn. (4) is usually referred to as the scaling constant. A value appropriate to erosion conditions should be chosen for KP since Levy et al. [ 141 have clearly demonstrated that the oxide scales grow more rapidly under erosion conditions as compared to static conditions. From eqn. (3), the rate of increase of oxide scale thickness with time is given as dZ/dt = KPIZ
(5)
Let E, be de6ned as the erosion rate of the oxide scale and F be the particle flux rate given by the ratio of particle feed rate cf> to the eroded area. Then, the rate of decrease of the oxide scale thickness due to its erosion is obtained as dZ/dt = - EJVp,,
(6)
where p. is the density of the oxide. Finally, a balance between the oxide growth by oxidation (eqn. (5)) and its removal by erosion (eqn. (6)) can be envisaged leading to a constant, steady state oxide thickness (Z,) given by Z, =KppoIE,F
(7)
Thus, the steady state oxide thickness increases with increasing temperature (through K,), decreasing oxide erosion rate and decreasing particle flux rate. An important assumption underlying eqn. (7) is that E, represents the erosion rate of the pure oxide. For this assumption to be valid, Z,, should be sufficiently large when compared to the damage zone formed on the oxide scale by the impacting erodent particle. This aspect will be considered in greater detail in the next section. 3.2. Time between impacts (tb) and time of impact &,J Unlike in the case of room temperature erosion, the time interval between two successive impacts at the same location (t,,) in the eroding material is an important parameter since it determines the extent to which the oxide grows in between impacts. The estimation of tb is dependent on whether the erodent particle is spherical or angular (say conical). Assume the erodent particle of density pP, mass mP and radius r to be spherical. Under such conditions, as shown in Appendix B, the time between successive impacts (t,,) at the same location is obtained as tb (sph.) = 0.82r41’2H’/2/crFV
(8)
In eqn. (8), H is the hardness of the eroding material, V is the impact velocity and (Y is a constant of the order of unity. A similar exercise can be carried out for a cone shaped particle with a hemispherical top (see inset of Fig. 1) to give (see Appendix B for details) tb ( con.) = 4rpP”3H2’3/3CuFV4’3
(9)
It should be noted that both eqns. (8) and (9) have been obtained after making certain simplifying assumptions. For example, it has been assumed that the rebounding particles do not interfere with the incident particles. This should be a reasonable assumption, especially at low particle flux rates wherein E-O effects become important. Equations (8) and (9) involve other assumptions which are shown to be realistic in Section 6.4. Thus, eqns. (8) and (9) should provide a realistic estimate of the time between impacts. It is also important to consider the contact duration between the particle and the eroding material during each impact event. This duration, usually called the time of impact (th), is given by eqn. (10) below in the case of a spherical particle of radius r impacting the eroding material of hardness H [20, 211 ti, (sph.) = 1.28r~,/H”~
(10)
Thus for the spherical particle, the ratio of time between impacts (eqn. (8)) to time of impact (eqn. (10)) is obtained as t&,,
(sph.) = 0.64HlcuVF
In the case of conical particles, ti,
1221 ti, (con.)=2.8rp,“3/H1’3V1/3
(II) is given to a good approximation by
(12)
257
Thus the ratio t&,, tb/th
is obtained as (eqns. (9) and (12))
(con.) = 0.48HluVF
(13)
In eqns. (8~( 13), H is defined as the hardness of the eroding material. For cases where the oxide scale on the eroding material is thin, H should represent the hardness of the underlying metal. If, on the other hand, the oxide scale is thick, H should be equated to the hardness of the oxide. The calculated values of the ratio tb/timin the case of spherical (fuII lines) and conical particles (dotted lines) are illustrated in Fig. 1 as a function of hardness (H> of the eroding material and for four values of the product VF. From Fig. 1 it is clear that the time between impacts (tb) is several orders of magnitude higher than the time of impact. As a result, the modehing of E-O interaction can be performed without any loss of accuracy by considering t,, alone. 3.3. Oxide scale growth between impacts Under parabolic oxidation conditions, the growth of oxide scale thickness (2) is described by eqn. (3). Thus, the extent to which the oxide grows between successive impacts (2,) is given as 2,2 = 2Kpt,
(14)
HARDNESS(GPa) Fig. 1. The effect of the hardness of the eroding material and the productVF on the ratio of the time between impact to the time of impact. Full lines and dotted lines correspond to spherical and conical particles respectively.
258
Substitution of eqns. (8) and (9) for t, in eqn. (14) gives the following expressions for 2, in the case of spherical and conical particles 2, (sph.) = 1.26(K,r/c~VF)~‘~(p,H)~‘~
(15)
2, (con.) = 1.63(K,r/~1’z(~‘~6H1~3/V2~3)
(16)
Equations (15) and (16) assume that the growth of the oxide scale is controlled by the metal or oxygen ion diffusion through the scale. Thus, it is assumed that the oxide scale does not get cracked as it grows, thereby providing an easy path for the oxygen diffusion to the metal-oxide interface. The validity of this assumption is discussed in Section 6.4. As wiIl be shown subsequently, the magnitude of 2, in comparison with the steady state oxide thickness (2,) has an important bearing on the nature of E-O interaction. Therefore, the variation of 2, and 2, with impact velocity (V) is illustrated in Fig. 2 for two temperatures (873 and 1073 K) and two flux rates (0.1 and 10 kg mP2 s). The magnitude of 2, is indicated for both spherical and conical particles. The values of the various parameters required for calculating Z,, (eqn. (7)) and 2, (eqns. (15) and (16)) are given in Table 3. The justification for choosing these values for the various parameters is detailed in Section 5.3 of this paper. It is clear from Fig. 2 that Z,, decreases much more strongly with impact velocity (because of the strong velocity dependence of E,) than 2,. Thus, a transition velocity beyond which Z,,
oooi-
0
I
I
20
I
I
I
LO IMPACT
60
VELOCITY
80
I
I
100
(m/s)
F’ig. 2. The variation of 2, and 2, with impact velocity at two test temperatures (873 and 1073 K) and two flux rates (0.1 and 10).
259
TABLE 3 The values of the various model parameters Constant/Variable
Symbol Values
Units
const.ant.¶ Hardness of oxide H0 Hardness of metal 2 Parabolic rate constanta Arrhenius constant Ao activation energy Q Erosion rate of oxide ‘% erosion rate constant &0 reference velocity V0 velocity exponent n Density of oxide PO Density of particle PP Erodent radius r Conversion factor for transforming K,” to Kp Cc Particle flux rate F Particle shape Critical oxide thickness & constant variable Variables Impact velocity Test temperature
V T
3.0 2.0 (0.5) 106 (104,106) 210 10-B (10-6,10-r) 10 3 5400 3200 lOO(10) 1.3 x 10-4 1.0 (0.1,lO.O) Spherical or conical
GPa GPa kga mm4 s-’ kga mm4 s-r kJ mol-’ kg kg-’ kg kg-’ m s-l kg mm3 kg me3 cun m3 kg-’ kg mm2 s-’
1, 10 f(T.l
WJ pm
5-100 600-900
m s-r “C
aKp=scaling constmt=0.5C2Ao exp(-QIRm. “E, = erosion rate of oxide =E,(V/V,,)“. cC=4MF,L3M~~,; M is the molecular weight; he is the density of iron (7860 kg mm3).
transition velocity shifts to higher values beyond 100 m s- ’ for both F values of 0.1 and 10 kg mm2 s-‘. 3.4. Defmd zone size in oxide and metal Experiments have consistently shown that the depth to which the plastic deformation extends in a material (L) when impacted by a particle is of the order of the indentation diameter [7, 23-251. Thus, L=PW
(17)
where W is the indentation (or crater) diameter and p is a constant of the order of unity. The magnitude of W depends on whether the erodent is spherical or angular (actually, conical with a half angle 0). It has been shown elsewhere [ 26 ] that in the case of spherical particles (radius r; density 4) the appropriate expression for W (and hence L) is given as L (sph.) = 2.56@r~/~V’~/H’/~
(18)
In eqn. (18), V is the impact velocity of the particle and H is the hardness of the deforming material.
260
A similar exercise can be carried out in the case of conical particles as shown in Appendix C. The result, valid for a conical particle with a half angle of about 30”, is obtained as L(con.) = 2.Oprp~~‘~V~‘~/H”~
(19)
Equations (18) and (19) are valid irrespective of whether it is the metal or the oxide scale that is deforming under impact. The only point that should be noted is that H in eqns. (18) and (19) will correspond to the hardness of the oxide (H,,) if a thick oxide is present on top of the eroding material. In contrast, if the oxide scale present during erosion is very thin (or not at aII there), H in eqns. (18) and (19) should be equated to the hardness of the eroding base material (H,,,). The effect of the hardness of the eroding material (H> on the thickness of the plastically deformed zone normalized by the particle radius (L/Y) is illustrated in Fig. 3 for both spherical and conical particles. The full lines and the dotted lines correspond to eqns. (18) and (19) respectively. At the elevated temperatures pertinent to the E-O interaction, the hardness of the metal (H,) is expected to be much lower than that of oxide (H,). Therefore, on the basis of Fig. 3 it can be concluded that the size of the deformed zone wiII be smaller in the oxide than in the case of a metallic material.
HARDNESS (GPa) F‘ig. 3. The variation of the plastic zone size normalized by the particle size as a function of hardnessat two impact velocities. The full and dotted Hnesrepresent the behaviour of spherical and conical particles respectively.
261
3.5. Critical oxide thickness (ZJ An important physical concept relevant to the modelling of the E-O interaction is that the oxide scales usually exhibit a ductile-brittle transition as a function of both thickness and temperature. This aspect is illustrated in Fig. 4. This concept has been verified specifically under impact conditions by Stephenson et al. [ 171 Bs noted earlier in Section 2. Saunders and Nichollos [27] have also noted a similar ductile-brittle transition (as in Fig. 4) in the case of chromia and alumina coatings. The important points to be noted with reference to Fig. 4 are: (1) At all temperatures, beyond a critical thickness (Z,), the scale becomes brittle and thus can be removed easily by spalling or by cracking and chipping due to particle impacts. (2) The above value of Z, changes discontinuously over a narrow temperature range, usually in the range 700-800 “C. (3) Below or above this temperature range Z, is independent of temperature.
4. E-O mechanisms On the basis of the literature review carried out in Section 2 and the physical concepts developed in Section 3, four types of E-O mechanisms can be envisaged: (1) metal erosion, (2) oxide erosion, (3) oxidation affected erosion and (4) oxidation controlled erosion. The essential features of these E-O mechanisms are illustrated in Figs. 5 and 6. The metal erosion becomes important either when there is no oxide scale present (due to inert atmosphere or too low a test temperature) or when the oxide scale is very thin, ductile and adherent (Fig. 5(b)). For the oxide scale (thickness 2) to be considered thin, a necessary condition is that L(metal) z+ Z, where L is the depth of the plastic zone in the eroding
;a TEMPERATURE
("Cl
Fig. 4. The variation of the critical oxide thickness (Z,) with temperature (a typical behaviour).
v
l
EROOENT
* OXIDE SCALE ADHERENT, DUCTILEAND THIN
No OXIDE SCALE
@>
(4
l
l
THICK.ADHERENT OXIDE ClAMAGE ZONE CONFINEDTO OXIDE SCALI
Fig. 5. Schematic representation of metal erosion mechanism (a) (b) and oxide erosion mechanisms (c).
material (L given by eqns. (18) or (19) with H=H,). If the above condition is satisfied, as shown in Fig. 5(b), the oxide scale deforms along with the bulk material below without getting cracked as was demonstrated by Stephenson et al. [ 171 by means of controlled single particle impacts. Under such conditions, there is no interaction between erosion and oxidation and the erosion rate exhibits ductile behaviour. Further, the erosion rate is largely unaffected by any variation in the particle flux rate Q. The oxide erosion represents the other extreme and is obtained if a sufficiently thick, adherent scale forms on the eroding material (see Fig. 5(c)). For this mechanism to operate, the damaged/deformed zone underneath the impacting erodent particle should be confined fully within the oxide scale or equivalently Z>L (2 is the oxide scale thickness and L is the depth of the deformed zone in the oxide). The erosion response of the material with a thick oxide scale is equivalent to that of a pure oxide. Thus, a brittle erosion response (maximum erosion at normal impact angle), a strong velocity dependence of the erosion rate, an erosion rate proportional to the normal component of the impact velocity and a negligible effect of particle flux rate on the erosion rate can be expected. The third E-O mechanism, oxidation affected erosion, was originally proposed by Kang et al. [ 161. Figure 6(a) illustrates in a schematic fashion the salient aspects of this erosion mechanism. This mechanism should become dominant when the oxide scale is sufficiently thick and prone to cracking under impact conditions but not thick enough to undergo large scale spalling. In such an event, the cracked oxide scale underneath the eroding particle tends to get pushed down into a much softer base material and in the process, the softer base metal gets squeezed out into the top surface through the cracks in the oxide scale (Fig. 6(a)). Over a period of time, the repetition
263 OXIOATION AFFECTED EROSION
OXIOATION CONTROLLED EROSION ICONTINUOUS
1
,,ETAt
1
j
METAL
]
1
METAL
lb1 OXIDATION CONTROLLED EROSION,ISPALLINGl
Fig. 6. Schematic representation of oxidation affected erosion (a), oxidation controlled erosion by continuous mode @) and oxidation controlled erosion by spalling (c).
of such a process during each impact causes a composite layer comprising the bulk metal and broken pieces of oxide scale to ultimately form (Fig. 6(a)). Thereafter, the erosion can be merely modelled as that of the metal-oxide composite. An interesting aspect of the “oxidation affected” erosion model is that the volume fraction of the oxide in the composite layer is a function of the erosion variables such as temperature, impact velocity and particle flux rate. As a result, the erosion rate of the composite can vary from a ductile to a fully brittle response depending on the volume fraction of the oxide in the composite layer. Further, unlike in the case of metal or oxide erosion, oxidation affected erosion rate will strongly depend on the test temperature and particle flux rate. The llnal erosion mechanism in the E-O regime is the oxidation controlled erosion mechanism. If the oxide scale that forms during erosion is brittle and non-adherent, the above mechanism becomes important. Within the parameters of this mode1 two possibilities can be envisaged depending on whether the brittle scale gets removed during each impact (Fig. 6(b)) or when it reaches a critical thickness (Fig. 6(c)). In the former case, whatever scale forms in between two impacts at the same location is removed completely in the subsequent impact. Thus, material removal (in the form of oxide scale)
264
is continuous. When the material is removed by such an erosion mechanism (called oxidation controlled erosion (continuous)), the plastic deformation of the underlying base metal plays a secondary role. In the second case, the oxide scale does not get removed during each impact but is only removed when it reaches a critical thickness (2,). Thus, the scale removal is discontinuous and occurs by spalling. When erosion occurs largely by this mechanism (called oxidation controlled erosion (spalling)), the important parameters are the critical oxide thickness and its variation with temperature (Fig. 4), the particle flux rate, and the test temperature (through K,).
5. E-O
mechanism
maps
5.1. The valid@ conditions E-O mechanism maps can now be constructed on the basis of the concepts developed in the last two sections. In fact, we are now in a position to develop the validity conditions for each of the four erosion mechanisms discussed in the last section. For example, the pure oxide erosion will be dominant when Z,, < 2, and Z,,> L,. The first condition ensures that the oxide scale remains intact while the second condition allows for the deformed zone caused by repeated impacts to be confined to within the scale. Similarly, for metal erosion to be the relevant mechanism the conditions to be satisfied are 2, < 2, and Z,, < 0. lL,. The second condition, as demonstrated by Leebouvier et al. [28] by means of a theoretical model, ensures that the harder oxide scale is sufficiently thin when compared to the plastically deformed zone size (La in the eroding material, that it behaves as if it is a part of the base material. If neither the condition Z,, > L, nor the condition 2, < 0. lL, is satisfied (an intermediate case) and further if 2, Z,. This condition implies that the oxide scale will never attain the steady state thickness since it becomes brittle (and thus gets removed by erosion) prior to attaining such a thickness. However, whether the oxide scale gets removed during each impact (continuous mode) or after a certain number of impacts at the same site (spalling mode) depends on the relative magnitudes of 2, (critical oxide thickness) and 2, (thickness to which the oxide grows between impacts). If 2, >&, the oxide scale gets removed during each impact and thus the relevant erosion mechanism is “oxidation controlled erosion (continuous)“. If contrast, if&
265
Apart from the validity conditions mentioned above, an additional condition for the oxidation controlled erosion mechanism to apply is that this mechanism should remove the bulk metal (after its conversion to oxide) at a faster rate than the rate at which the metal would have been removed if no oxide layer was present. As will be demonstrated later this condition is always satisfied in the E-O regime, i.e. at temperatures greater than 0.35 TIll5.2. Procedure fw the construction of maps Now that the validity conditions for each erosion mechanism are known, a flow chart to identify the dominant erosion mechanism given the input conditions (e.g. V, T, E,, F, pO, pp, I?,, H,, I$,, r, 2, and particle shape) can be easily constructed as illustrated in Fig. 7. First, the parameter Z,, is calculated using the input values and eqn. (7) and compared with the magnitude of 2, (input). If Z,,
z,,Cz, t
ZC
YES
__
NO
1
I
z,,7 -
Lo No
E,
YES z,,
Fig. 7. A flow chart
co.1 L,
illustrating the validity conditions for the various erosion mechanisms.
266
The construction of the two-dimensional E-O map using the flow chart requires first, the identification of two primary variables which can be conveniently plotted along the x and y axes of the map. Impact velocity (V) and the test temperature (7’) are the obvious choice. Though recent experiments [9] have unambiguously demonstrated the dramatic influence of the particle shape and integrity on the erosion rate in the E-O regime, the present inability to properly quantify this parameter makes it unsuitable as a primary variable. The E-O map was constructed as follows. An exhaustive set of V-T values covering the entire space of the E-O map were chosen, and for each combination of V and T the flow chart (Fig. 7) was used to identify the dominant E-O mechanism. Thus, the regimes of dominance of the various E-O mechanisms could be identified and the boundaries delineating the regimes constructed. 5.3. Choice of appropriate values fw model parameters The construction of the E-O maps requires first that the most appropriate values be chosen for the large number of erosion-related parameters listed in Table 3 (excluding the variables V and 2”). Since, the bulk of the literature data on erosion in the E-O regime pertains to steels, the values appropriate to steels were chosen for the various parameters as indicated in Table 3. A value of lo5 for A,, and 2 10 kJ mol- ’ for Q (in eqn. (2)) were chosen on the basis of the values reported by Quinn [29]. The value of C has been calculated on the basis that the scale formed is Fe203, as observed by Levy and co-workers [ 13-151 in the case of a number of ferritic steels under E-O conditions. The radius of the erodent particle was kept constant at 100 pm except when the effect of particle size on the E-O maps was investigated. The hardness of the oxide and metal (at the test temperature) were assumed as 3.0 GPa and 0.5 GPa respectively. 2, was kept within the range l-10 pm, consistent with the values reported by various investigators [ 17, 271. The erosion rate of the oxide was assumed to be proportional to V3 (where V is the impact velocity) and in the range 10e5 to lo-’ g g-’ at V= 10 m s-’ (reference velocity). A perusal of the erosion literature with regard to the particle flux and the eroded area (wherever reported) indicates that a reasonable range for F (i.e. particle flux/eroded area) lies in the range 0.1-10 kg mV2 s- ‘. Finally, coming to the two variables, the impact velocity (V) was varied continuously in the range lo-100 m s-l while the test temperature (7’) had a corresponding range of 600-900 “C. This temperature range was chosen since the oxidation effect becomes important at these temperatures in the case of iron and steels. 5.4. Analysis of E-O mechanism maps The E-O maps constructed on the basis of the flow chart given in Fig. 7 and utilizing the values listed in Table 3 for the various erosion parameters are analysed below.
267
5.4.1. The eflect of particle jSux rate (IF) In Pigs. 8(a) and 8(b), the E-O maps constructed assuming 2, = 1 pm are presented for a spherical erodent. Figure 8(a) is valid for F= 0.1 while Pig. S(b) corresponds to F= 10. Under both conditions, the dominant erosion mechanisms are metal erosion and oxidation controlled erosion (both continuous and spahing mode). Pure oxide and oxidation affected erosion mechanisms are absent mainly because 2, is too small. A comparison of Pigs. 8(a) and 8(b) brings out the effect of particle flux rate Q on the relative importance of the various erosion mechanisms. In particular, as F increases from 0.1 to 10, the regime of the metal erosion mechanism expands to both higher temperatures and lower velocities, and at the expense of the oxidation controlled erosion mechanism. 5.4.2. Th.e eflect of critical oxide thickness (2,) The effect of increasing 2, from 1 to 10 pm is seen in Pigs. 9(a) and 9(h). In comparison to Pig. 8, a narrow regime of oxidation affected erosion is now observed. In addition, the oxidation controlled erosion by spaIhng gains importance in comparison to the continuous mode. In fact, at F= 10.0 (Fig. 9(b)), the oxidation controlled erosion by continuous mode is no longer present. The spalhng mode becomes more important than the continuous mode when 2, is increased, largely because the condition for the spahing mode (i.e. 2,
60 -
o60
1
0
(4
700
TEMPERATURE
800
I00
5
600
700
TEMPERATURE
800
900
("Cl
mechanism maps for Z,= 1 km, a spherical particle and at two values of F, i.e. (a) 0.1 and (b) 10 kg me2 s. Fig. 8. The E-O
METAL
EROSIQN
ICDNlMK!4SI 0’
0 600
700
TEMPERATURE
(4
800
("0
’
600
900
@I
J
I
700
TEMPERATURE
BOO
9
00
("Cl
Fig. 9. The E-O maps for a spherical particle and 2, = 10 pm and for two values of F, i.e (a) 0.1 and (b) 10 kg me2 s.
z ’ 5
METAL
60-
EROSION
CDWnlWLED EROSIQN ISPALLWGI
01
600
I
700
TEMPERATURE
800
$
1°C)
Fig. 10. The E-O map for a spherical particle, for Z,= 100 wrn and F= 1.0.
large, it has been chosen to indicate that oxidation affected erosion and pure oxide erosion become important only then. This is not unexpected since the oxide scale thickness has to be comparable to or greater than L, (deformed zone size in the oxide) for oxidation affected and pure oxide erosion mechanisms to become important and as can be noted from Fig. 3 the value of L, lies in the range 25-100 pm for H,, = 3 GPa (r= 100 pm; spherical particle). 5.4.3. The eflect of variable 2, All the E-O maps illustrated so far have been constructed using a constant value for 2,. However, experiments have shown that 2, increases discontinuously at some temperature to a higher value [17, 271 as indicated in Fig. 4. Such a variation in 2, with temperature can be easily accommodated while constructing the E-O map by assuming the following relationship between 2, and T (test temperature). Z,=l Z&m)
pm = 1 + O.O9(T- 700)
Z,= 10 pm
T< 700 “C
(20)
700 < T < 800 “C
(21)
T> 800 “C
(22)
Figures 1 l(a) and 1 l(b) illustrate the E-O maps constructed assuming eqns. (20x22) to be valid. Figure 1 l(a) is valid for F= 0.1 while Fig. 1 l(b) pertains to F= 10. As expected, Pig. 11(a) is identical to Fig. 8(a) at T< 700 “C and to Pig. 8(b) beyond T= 800 “C. Similarly, Fig. 1 l(b) can be compared to Figs. 9(a) and 9(b) at lower and higher temperatures respectively. 5.4.4. The effect of particle shape and size and metal hardness The effects of particle shape (spherical to conical), a lo-fold decrease in particle radius (r= 100-10 pm) and a 4-fold increase in metal hardness (H,= 0.5-2 GPa, H,=constant =3 GPa) are ilhrstrated in Pigs. 12(a)-12(d) at a constant value of F= 1.0 and for Z, given by eqns. (20)-(22). The effect of changing over from a spherical to a conical particle (Figs. 12(a) and 12(b)) is to enlarge the regime of the oxidation controlled erosion by continuous mode at the expense of the spalling mode. In addition, with angular particle, the oxidation affected erosion regime also makes an appearance because of the fact that the deformed zone size is signifmantly smaller in the case of conical particles when compared to spherical particles (see Fig. 3). The effect of reduced particle size on the E-O map can be understood by comparing F’ig. 12(c) with Pig. 12(a). The regime of oxidation controlled erosion by spahing expands and new erosion mechanisms like oxidation affected erosion and pure oxide erosion become important as the particle size is reduced from 100 to 10 pm. The fact that the size of the plastic zone (L, and L,) decreases in proportion to the particle radius (Pig. 4) is largely responsible for the observed effect.
270 CRITICAL OXIDE THICKNESS lum)
CRITICAL OXIDE THICKNESS (urn) 100'
01 600
600
(a>
TEMPERATURE
('=C)
@I
1
12 /'I
5 111
1
I
100
800
TEMPERATURE
El0
1
9
(Y)
Fig. 11. The E-0 maps for spherical particles obtained assuming that 2, varies with temperature as per eqns. (20)-(22) in the text. The maps have been drawn for two values of F (a and b).
F’inally, a comparison of Figs. 12(a) and 12(d) points to the fact that the effect of a 4-fold increase in the metal hardness on the E-O map is not very significant. 5.4.5. 27~ eflect of oxidation rate The effect of the oxidation rate on the E-O map can be easily investigated by varying the magnitude of the Arrhenius constant (A,) in eqn. (2). The E-O maps for two values of A0 (lo4 and lo6 kg2 mV4 s- ‘) are presented in Figs. 13(a) and 13(b). It is obvious that the effect of increased oxidation is to diminish the metal erosion regime and to make the oxidation controlled erosion by continuous mode dominant over a large velocity and temperature regime. 5.4.6. The eflect of oxide erosion rate The changes in the E-O map caused by decreasing the oxide erosion rate by a factor of 100 can be noted by comparing Figs. 14(a) and 14(b). The regime of metal erosion is dramatically reduced as the oxide erosion rate is reduced. 5.5. conclusions A perusal of the E-O maps constructed in this section indicates that apart from impact velocity and test temperature the other important variables
271 CRITICALOXIDE THICKNESS (pm) CRITICAL OXIDE THICKNESS(urn) lad:;::..
>-
60
t s
EROSION ISPALL
CONTRMLEO
EROSION
20
1 '6k--
TEMPERATURE (VI
(al
a00 TEMPERATURE I00
@I
CRITICALOXIDE THICKNESS(Pm1
I
700
91
CRITICALOXIDE THICKNESS@ml
loo!
1
12
5
a IO
2‘ I f IT,
'or--
SPMRKAL,
FI,Q
Ii,= 2 GPa
BO-
tlElAL
‘j;
\
s
EROSION 60
x
0xlllATloN
d '
METAL EROSIO,,
40
t
CONTROLLEO LROSKM ISPALLINGI
/
0’ 600
OXlOATlON lONTROLLE0
I
700
1100
TEMPERATURE ("Cl
TEMPERATURE (“0 WI Fig.12. The effect of changingparticle shape from spherical to conical (a and b), a lo-fold decrease in particle size from 100 to 10 pm (a and c) and a four-fold increase in metal hardness (a and d) on the E-O maps. The maps assume 2, to be a function of temperature and F= 1.0.
(cl
CRITICAL OXIDE THICKNESS turn) CRITICALOXIDE THICKNESS (pm) ‘?“‘fl-T
,
600 (4
I
1
I
700
800
TEMPERATURE
V'C)
I
“6w
900
TEMPERATURE
@>
("C)
Fig. 13. The effect of changing the oxidation rate (by changing A,) by a factor of 100 on the E-O map for a spherical particle (Z,=fl7’); F=O.l).
are the particle flux rate, the parabolic rate constant, the oxide erosion rate, particle shape and size, and the critical oxide thickness. It is also obvious from the maps that of the four erosion mechanisms considered, only metal erosion and the oxidation controlled erosion mechanisms are important if realistic values pertinent to iron and steels are assumed for the various model parameters. If we consider the oxidation controlled erosion mechanisms in particular, erosion by continuous mode is favoured by low particle flux rate, low values of critical oxide thickness, large and angular particles, and high oxidation rates. Erosion by spalling mode is favoured under opposite conditions .
6. The modelling
of oxidation
controlled
erosion
In the previous section it has been demonstrated that if values appropriate to iron and steels are chosen for the various model parameters, only metal erosion and oxidation controlled erosion mechanims needs to be considered. Of these, the modelling of metal erosion has received extensive attention [ 7,25,30-341 and thus requires no further discussion. However, the modelling of oxidation controlled erosion has not yet been done and thus will be attempted in this section.
273
6.1. Oxidation controlled erosion by continuous mode Let tb be the time between impacts and CrAthe area over which the oxide layer is removed completely during impact (where cxis a constant and A is a crater or indent area). Obviously the area arAis centred around the impact point. Then, tb is simply obtained as t,,= mP IFcuI
(23)
where mp is the mass of the impacting particle. During this time t,,, the oxide scale grows to a thiclmess 2, given by 2, = ( 2KPttJ’~
(24)
Thus, the weight of oxide lost (m,) during each impact by a particle of mass m, is obtained as m0 = 4
(25)
zbh
Hence, the erosion rate is obtained as E=m,,lmP=(2aK,,lF’)1/2 (A~TQ’~P,
(26)
The parameter A/m, is dependent on whether the particle is spherical or conical. The appropriate expressions are A/m, (sph.) = 1.22V~/(N,~r)‘~
(27)
A/m, (con.) = 0.75V4B0JH,2/3~1/3r
(28)
Substitution of eqns. (27) and (28) in eqn. (26) gives E (sph.)=(1.56
LYP~/H~“~,~‘~)(~*V/F~)‘~
E (con.) = (1.22 ,p,/H,1/341’6)(K,/Fr)1/2V2/3
(29) (30)
In eqns. (29) and (30), ET,.,, represents the hardness of the base metal. The most interesting prediction of the model is the very weak velocity dependence of the erosion rate with the n value in the range 0.5-0.66 (EaV”). In addition, the model indicates that the erosion rate is influenced by the particle flux rate unlike the conventional erosion models. A strong temperature dependence for E is also predicted because KP increases exponentially with temperature. In contrast, the hardness of the base metal has only a marginal influence. 6.2. Oxidation controlled erosion by spalling Let Z, be the critical oxide thickness. The time required to achieve this thiclmess (t,) by oxidation is given as tc=zc2/2K*
(31)
As in the earlier model assume that the oxide over an area CX~gets removed by spalling once it reaches a thickness Z,. Then, the mass of the particles (M) hitting an area d over the time period t, is given as M= crFA(ZC2/2KP)
(32)
274
The mass of oxide lost (m,) is given as m, = d Z,P,
(33)
Hence the erosion rate (E) is given by E =m,lM=
2p,K,lFZ,
(34)
Thus, when the erosion is by oxide spalling, erosion rate nearly becomes independent of impact velocity and particle size. However, E strongly depends on temperature (through KP and possibly Z,), the particle flux rate and the magnitude of the critical oxide thickness. As expected, the smaller the value of Z, the greater is the erosion rate predicted by the model. However, if Z, becomes sufficiently small such that Z,
controlled erosion mechanisms to be rate controlling is that this mechanism should remove the bulk metal (in oxide form) at a faster rate than the inherent erosion rate of the bulk metal. If E, is the inherent metal erosion rate, then the above validity condition can be estimated by noting that E, equals 0.7E, (erosion rate under oxidation controlled conditions) if FezO, is the oxide. Thus, E, should be less than 0.7 times eqns. (29) or (30) for the oxidation controlled erosion by continuous mode to be considered valid. Similarly, E, should be less than 0.7 times eqn. (34) for oxidation controlled erosion by spalhng to be a valid mechanism. It can be easily shown that for reasonable values of the parameters in eqns. (29), (30) and (34), the above conditions are always satisfied as long as the impact velocity and test temperature are such that a oxidation controlled erosion regime is indicated in the E-O maps given earlier. 6.4. Assumptions of the model The oxidation controlled erosion models developed in this section present a simplified view of the actual phenomena which are much more complicated. The major assumptions underlying the model are listed and discussed below: (1) It is assumed that the rebounding particles do not interfere with the incident particles. As noted earlier, this assumption appears reasonable since at low F and V values where the E-O regime becomes important the time between impacts is orders of magnitude higher than the time of impact (see Fig. 1). (2) The model assumes that the diffusion of the metal or oxide ions through the oxide scale controls its rate of growth leading to parabolic kinetics. This assumption implies an adherent, untracked oxide scale. However, it is important to note that the present model treats the growth of the oxide scale at a very local region surrounding the impact point wherein prior impact has removed the scale. Thus, the scale needs to be adherent and
275
untracked only in this local region for the parabolic kinetics to be valid. It does not matter that the scale is heavily cracked or spalled at the macroscopic level. If, however, a non-parabolic scale growth law is found more appropriate, such a law can be incorporated in the proposed model without any difllculty. (3) The model assumes that the scale in the local region surrounding the impact point gets removed completely either during each impact (continuous mode) or after a critical number of impacts (spalling mode). The question remains as to whether such is the case or whether the oxide gets removed only partially by cracking and chipping. In the present paper the complete removal of the scale has been postulated for two reasons: (i) such an assumption simplifies the analysis and is certainly justified since the present model represents the first effort at quantifying the E-O interaction, and (ii) supporting experimental evidence for the complete removal of the oxide scale by impacting microparticles has been provided by Stephenson et al. [ 171. These investigators noted a circular area around the impact point completely free of oxides in pre-oxidized nickel-based superalloys impacted at elevated temperatures by microparticles. It should be noted however, that the partial removal of the scale can be in principle modelIed in a manner similar to that employed in the present paper. The main difference will be in eqns. (15), (16) and (31) wherein a constant term proportional to the residual oxide thickness will have to be included. (4) The model assumes that each impact event causes damage (plastic deformation or cracking) over an area CrA(where A is the impact crater area and (Yis a constant of the order of unity). This assumption is justified since both erosion and dynamic indentation experiments [23-251 have clearly shown the plastically deformed zone on the eroded/indented surface to be circular centred at the impact point and thus proportional to the crater area. In addition, single impact experiments of Stephenson et al. [ 171 have demonstrated that when the oxide scale is brittle (Z> Z,), it gets completely spalled over a circular area proportional to the impact crater area when impacted by particles. Thus, the influence area of each impact equals CYA (where (Yis a constant) irrespective of whether the oxide scale deforms or spalls. (5) The present model is strictly valid only for normal impact erosion.
7. Comparison
with the literature
data
The theoretical models developed in the last two sections indicate very clearly that for a quantitative comparison between the model and the experimental data, the values of the various material and erosion test related parameters (listed in Table 3) should be known with reasonable accuracy. Such is not the case with a number of parameters, e.g. KP, H,,,, Ho, Z,, E, and F. Thus, at the present stage, only a qualitative comparison between the model prediction and the experimental data is feasible.
276
7.1. Velocity exponent The values of the velocity exponent n (EaV”)
predicted by the various models are given in Table 4. Our E-O maps indicate that metal and oxidation controlled erosion are the two relevant mechanisms. From Table 4, it is clear that the oxidation controlled erosion mechanism is associated with a very low value of n in the range 0.5-0.66 for continuous mode and n=O (velocity independence) for spall mode. The velocity exponents reported by the various investigators who have carried out erosion experiments in the E-O regime are presented in Table 1. It is clear that when alumina is used as the erodent, the n values mostly lie in the range 0.55-l. This n value is consistent with the oxidation controlled erosion by continuous mode. In contrast, erosion experiments using silicon carbide or quartz particles or conducted at very high impact velocities (greater than 100 m s-i) result in n values greater than two, consistent with the metal erosion model. 7.2. Ductile /brittle behaviour The response of the material, either brittle or ductile, also changes with the dominant erosion mechanism as indicated in Table 4. The erosion response is ductile if metal erosion is dominant. In contrast if oxide controlled erosion is relevant, a brittle response is indicated (Le. E is maximum at normal impact angles) even for ductile materials. In the case of oxidation controlled erosion, the extent of spalling or chipping of the non-adherent oxide scale will depend largely on the normal component of the impact velocity. Thus a brittle erosion response should prevail in the above case. In Table 2, the erosion response reported by various investigators is presented. As in the case of the velocity exponent data, the use of alumina as erodent results in a brittle response consistent with the prediction of the oxidation controlled erosion models. The only exception is the data on high chromium (greater than 15% Cr) steels and this comes about because of the very thin scales formed on this alloy during erosion [S]. In contrast, the TABLE 4 The parametric dependence of the various erosion models Model
na
Natureb
Flux rate effect
1. 2. 3. 4.
2 to 3 >3 >2
Ductile Brittle Ductile or brittle
No No Yes
0.5 0.66 0
Brittle Brittle Brittle
Yes Yes Yes
Metal erosion model Oxide erosion model Oxidation affected erosion Oxidation controlled erosion Continuous mode spherical particle angular particle Spalling mode
“E = Vn, V is the impact velocity; E is the erosion rate. bBrittle if E is maximum at an impact angle of 90” and ductile if E is maximum at intermediate impact angles.
277
use of SiC erodent results in a ductile response (Table 2). The stainless steels and other alloys listed in Table 2 show a ductile response either because the tests were not conducted at sufhciently high temperatures or because their compositions were such that a thin, adherent chromium oxide or alumina scales formed during the test. A perusal of Tables 1 and 2 clearly point out the fact that a low n value (n < 1) is always associated with a brittle erosion response while a high n value (n > 2) goes with ductile response. This observation is fully consistent with our predictions for the oxidation controlled and metal erosion modeIs respectively. 7.3. The ?uzi?ure of the erod.ent One interesting conclusion that arises from the data reported in Tables 1 and 2 is that the E-O interaction is significant with alumina particles as erodent while it is not so important when Sic is used instead. This remarkable effect is mainly due to the fact that the erosion rate of either metal or ceramics (like alumina) is about an order of magnitude higher when eroded with Sic as compared to alumina [35, 361. Levy and co-workers [9, 351 have clearly demonstrated that the rounded shape of alumina as opposed to the angular shape of Sic is largely responsible for such a behaviour. Let us suppose that the oxide scale behaves like ceramics and thus gets eroded much faster when impacted Sic erodent. The effect of increased oxide erosion rate (E,) can now be analysed in terms of Pigs. 14(a) and 14(b). It is clear that an increase in E., expands the metal erosion regime at the expense of the oxidation controlled erosion regime. Thus, for a given velocity and temperature, a changeover from oxide controlled erosion to metal erosion is quite plausible when the erodent is changed from alumina to Sic. 7.4. The eflect of base metal hardness The work of Wright et al. [ 151 on a munber of high temperature alloys has clearly indicated that the E-O interaction increases with increasing hardness of the base metal (&,,). Two possible reasons for such an observation are provided below. (1) As illustrated in Fig. 3, the size of the plastically deformed zone in the base metal decreases with increasing hardness of the base metal. Thus, even for the same steady state scale thickness (Z,), the condition Z,, < 0.1 L, may not be satisfied as H,,, is increased leading to the oxidation affected erosion regime (i.e. increased E-O interaction). (2) The critical oxide thickness (2,) may not be independent of J&,, as tacitly assumed. The single impact experiments of Stephenson et al. [ 171 and the actual erosion experiments by others [8, 151 have clearly shown that when the base metal is soft (low &,) the oxide buckles and transfers the load 1argeIy to the base material. Hence, as H, increases, the tendency for oxide to spall or chip will increase. Put another way, 2, may decrease with increasing &,. If such is the case, then the increased E-O interaction with increasing base metal hardness can also be explained.
278
CRITICAL OXIDE THICKNESS (urn)
CRITICAL OXIDE THICKNESS (pm) -A---a#
a[ 600 (a>
12
di5
a 10
/iT.y, 700
800
TEMPERATURE
Fig. 14. A comparison
(Z, =f(!Z’); spherical;
("Cl
600
900
@I
TEMPERATURE
('Cl
of the E-O maps (a and b) for two values of the oxide erosion F= 1 .O).
rate
7.5. Alloying eflects The work of Levy and co-workers [S, 121 has clearly demonstrated that the addition of silicon as well as increased chromium content in steels reads to increased resistance to erosion under E-O conditions. The above effect is mainly related to the effect of silicon and chromium on the parabolic rate constant (I&‘; eqns. (1) and (2)). For example, Robertson and Manning [37] have shown that the addition of silicon to low chromium steels decreases A&” by a factor of up to lo* in the tempe~t~e range 575-650 “C and also inhibits oxide breakaway (or equivalently increases 2,). Similarly, it is well known that the addition of chromium to steel decreases KPo by a few orders of magnitude especially if the chromium level exceeds 10% [S, 381. The effect of decreasing I$, (and hence I$‘) by a factor of 100 can be visualized from Figs. 13(a) and 13(b). It is obvious that the metal erosion regime expands dramatically towards both lower velocities and higher temperatures with decreasing KP. The observations of Levy and co-workers [S, 121 of a switchover from brittle response to ductile response beyond about 15% Cr in steels and the effect of silicon addition in reducing erosion rate of steels is thus consistent with the predictions arising from the present work. 8. Conclusions (1) The methodology for the construction of E-O mechanism maps has been demonstrated by considering four possible E-O mechanisms.
(2) It has been shown that if realistic values are assumed for various parameters, metal and oxidation controlled erosion mechanisms are the only dominant mechanisms. (3) A new model for the oxidation controlled erosion mechanism predicts a very low velocity dependence of erosion rate, a brittle erosion response and a strong particle flux rate effect. (4) The available literature data, pertinent to the E-O regime, can be qualitatively rationalized on the basis of the present theoretical work.
The author wishes to express his gratitude to Dr. P. Rama Rao, Director, DMRL for his constant encouragement and for granting permission to publish this paper.
References 1 2 3 4 5 6
N. Gat and W. Tabakoff, J. Testing Evd, 8 (1980) 177. W. Tabakoff and 3. V. R. VittaI, Wear, 86 (1983) 89. N. Gat and W. Tabakoff, Wear, 50 (1978) 85. K. H. Yee, P. J. Shayler and N. CoIIings, Wear, 91 (1983) 161. Y. Sbida and H. Fujikarna,Wear, 203 (1985) 281. A. V. Levy, J. Yan and J. Patterson, in K. Ludema (ea.), Proc. Int. Co@ on Wear of Materials, American Society of Mechanical Engineers, New York, 1985, p. 708. 7 TriIok Singh and G. Sundararajan,Met&l. Truns. A, 21 (1990) 3187. 8 A. V. Levy and Yong-Fa Man, Wear, 131 (1989) 39. 9 A. V. Levy and Yong-Fa Man, Wear, 131 (1989) 53. 10 A. V. Levy and B. Q. Wang, Wear, 13X (1989) 71. 11 A. V. Levy, B. Q. Wang, Yang-Fa Man and N. Jee, Wear, 131 (1989) 85. 12 A. V. Levy and B. Q. Wang, SUM Coat. Technol., 33 (1987) 285. 13 A. V. Levy and Yong-Fa Man, Wear, 111 (1986) 173. 14 A. V. Levy, E. Shunovich and N. Jee, Wear, 120 (1986) 117. 15 1. G. Wright, V.Nagarajan and J. Stringer, Ox&i&km of Metals, 2.5(1986) 175, 16 C. T. Kang, F. S. Pettit and N. Birks, Metall. !RUBS. A, 28 (1987) 1785. 17 D. J. Stephenson, J. R. NichoIls and P. Hancock, in J. E. Field and N. S. Comey (eds.), Proc. 6th Int. Cix+f. 012Eros&n bg L&z&d and Solid Impact, Cavendish Laboratory, Cambridge, 1983, Paper 48. 18 0. Kubashewskiand B. E. Hopkins, O&dation of Met& and Alloys, Butterworths,London, 2nd ed., 1962. 19 S. C. Lim and M. F. Ashby, Acta MetaU., 35 (1987) 1. 20 I. M. Hutchings, J. Phys. D.: Appl. Phys., 10 (1977) L 179. 21 D. Tabor, The Hardness of Metals, Clarendon, Oxford, 1951. 22 C. D. Davis and S. C. Hunter, J. Mech. Phgs. Solids, 8 (1960) 236. 23 Y. Tirupataiah and G. Sundarar@n, J. Mech. P&s. Solids, in the press. 24 Trilok Sir@, S. N. Tiiari and G. Sundararajan,Wear, in the press. 25 A. Venugopal Reddy, G. Sundararajan,R. Sivakumar and P. Rama Rao, Acta Metalh, 32 (1984) 1305. 26 Y. Tirupataiah, 133.
B. Vegan
and G. Sedge,
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280 27 28 29 30 31 32 33 34 35 36 37
S. R. J. Saunders and J. R. Nicholls, Muter. SC& Engz., 5 (1989) 780. D. Leebouvier, P. Gilormini and E. Felder, Thin Solid F%ns, 17.2 (1989) 227. T. F. J. Quinn, Tribal. Int., 16 (1983) 305. I. Finnie and D. H. McFadden, Wear, 48 (1978) 181. J. G. A. Bitter, Wear, 6 (1963) 5 and 169. G. Sundararajan and P. G. Shewmon, Wear, 84 (1983) 237. I. M. Hutchings, Wear, 70 (1981) 269. G. Beckmann and J. Gotzmann, Wear, 73 (1981) 325. A. V. Levy and P. Chik, Wear, 89 (1983) 151. S. Srinivas and R. D. Scattergood, Wear, 128 (1988) 139. J. Robertson and M. I. Manning, Mater. Sci. Techml., 5 (1989) 741. 38 N. Birks and G. H. Meier, ~~tr~d~t~~ to High Temper&w-e Ck-idation ofMet&, London, 1982.
Appendix
Arnold,
A: Nomenclature
indentation or crater area Arrhenius constant defined by eqn. (2) (kg2 mV4 s-l) a constant for a given oxide composition defined by eqn. (4) (m3 kg-‘) erosion rate (kg kg- ‘) inherent erosion rate of metal (kg kg-‘) inherent erosion rate of the oxide forming the scale erosion rate of oxide at a reference velocity of 10 m s- ’ particle flux rate=fleroded area (kg mW2 s-‘) particle feed rate (kg s- ‘) hardness (Pa) hardness of metal (Pa) hardness of oxide (Pa) parabolic rate constant defined by eqn. (1) (kg2 mm4 s-‘) scaling rate constant (m2 s-l) depth of plastic deformation beneath the eroded surface mass of each erodent particle (kg) total mass of particles hitting an area CUA over the time period t, ckg) molecular weight of iron molecular weight of oxygen velocity exponent of the erosion rate activation energy for oxidation (eqn. (2)) (J mol-‘) erodent particle size (radius for spherical particles) gas constant time of exposure (s) time between impacts (s) time to achieve the critical oxide thickness of 2, (s) time of impact (s) test temperature melting point of the eroding material
281
u V W z zb
2, -G!
crater volume impact velocity (m s- ‘) crater diameter (m) oxide scale thickness (m) oxide scale growth between successive impacts at the same location (m) critical oxide thickness for spalling steady state oxide scale thickness
Greek symbols a constant defined by eqn. (8) a constant defined by eqn. (17) ; Am weight gain per unit area experienced by the metal due to intake of oxygen (kg m-‘) density of metal (kg rnm3) Pm density of the erodent particle 4 8 half angle of conical particle subscripts m metal 0 oxide particle P
Appendix
B
Spherical eroo!ent Assume a spherical erodent of radius r and mass mP. Then the number of particles impacting unit area of the eroding material every second equals F/mp where F is the particle flux rate. Also assume that each impact event causes damage (plastic deformation or cracking) over an area ~4, where A is the impact crater area and cx is a constant of the order of unity. Then, the number of particles (NJ impacting an area of CA every second is given by N= (F/m&A
A=0.257rw
(Bl) In eqn. (Bl), W is the impact crater diameter. The time between two impacts (tb) is now obtained as
t,, = 4% /r&w
032) As shown elsewhere [ 261, the dependence of the crater diameter (I%‘) on the hardness of the eroding material (u) and impact velocity (v) is given by eqn. (B3) given below w= 1.8rpp”4v1’2/H1’4
033)
28%
where T is the erodent radius. Substitution of eqn. (B3) in eqn. (BZ) and noting that mP= 4/37rr”pP one obtains the following fina expression for tb in the case of a spherical erodent t,(sph.) = 0.82rp,“2H”2/cwFV
(B41
Conical erodent Assume a conical particle with a hemispherical top (as shown in the inset of Fig. 1) of size 2r, mass rnP and half angle 6. For 8= 30”, the mass of this particle (m,) equals that of a sphere of diameter 2~. For such a conical particle t,, is given by eqn. (BZ). However, the expression for W for a conical particle (6’= 30”) is given by (see Appendix C) W=
(B5)
2rh=J3p3j~1f3
Substitution of eqn. (B5) in eqn. (B2) with %=4/3w3pP
gives
t,, (con.) = ~T-P,“~H~‘~/~@V~‘~
(B6)
Appendix C When a conical particle (inset of Fig. 1) of mass m, impacts the eroding material of hardness H with an impact velocity V, an energy balance between the incident energy of the impacting erodent and the energy consumed in forming the crater of volume U gives HU= 0.5m,V2
(Cl)
For the conical particle having a half angle of 8 = 30”, U is given by U= (7d24)(W3/tane) = 7rW3/12
(C21
Substitution of eqn. (C2) in eqn. (Cl) and solving for W one obtains w= 2rp,
1/3J,,2/3/H1/3
(C3)
Finally, an expression for the plastic zone size (L) beneath the ~pact~g erodent which equals /3W (/3 is a constant in the range 1-1.2) is obtained a% L (con.) = 2.0prpP’BV2/3/H”3
(C4)