- Email: [email protected]
Computer simulation of erosion-corrosion interactions at elevated temperatures
WEAR ELSEVIER
Wear
Computer
181-183
(1995)
516-523
simulation of erosion-corrosion elevated temperatures M.M. Stack, Q. Song-Roehrle,
Corrosion and Protection
Centre, UMIST, P.O. Box
interactions
at
F.H. Stott, G.C. Wood
88, Sackville Street, Manchester M60 IQD, UK
Received 25 May 1994; accepted 16 September 1994
Abstract Although there have been some attempts to model erosion by solid particles at elevated temperatures, there have been few efforts to develop a model which can generate images of the surface morphologies in the various erosion-corrosion regimes. Many classifications of erosion-corrosion regimes have been identified and there is evidence that there are at least three such regimes. The physical significance of the surface in such regimes may be difficult to visualize, particularly when the situation is neither “erosion-dominated” (erosion of the substrate) nor “corrosion-dominated” (erosion plays a minor role compared with corrosion). The object of this research has been to develop a physical model to simulate the transitions between erosion+rrosion regimes at elevated temperatures. Properties of the particle (shape, size, velocity, hardness, flux), the target (corrosion resistance, hardness, impact angle) and the environment (gas composition and temperature) are considered in the model. The results are then used to construct a computer-generated image of the eroding surface. This paper describes the physical basis of the model and shows how the transitions between the regimes can be achieved by variation of the erosion and corrosion parameters. Typical results are shown and compared with existing erosion-corrosion data. The future development of the research is outlined in terms of the application to other environments in which erosion
Computer simulation; Erosion;
Corrosion; Particle impact
1. Introduction
Although much progress has been made in the understanding of erosion-corrosion of materials by solid particles at elevated temperatures in recent years, there are still areas which are not well understood. Erosion-corrosion is a major problem in many energy conversion processes such as oil and gas conversion and coal combustion technologies. A synergy is observed between erosion and corrosion. This essentially means that, in some conditions, corrosion can enhance the erosion of the materials. However, in other cases, the formation of a corrosion product(such as a protective oxide) can inhibit erosion. Improved understanding of erosion
0043-1648/95/$09.50 0 1995 Elsevier Science S.A. All rights reserved SSDl 0043-1648(94)07028-8
temperature was observed; the erosion-corrosion rate increased with temperature up to a critical temperature and subsequently decreased with further increases in temperature. This peak in the erosion+zorrosion rate shifted to higher temperatures with increasing alloy Cr content [2] and higher wastage rates with increased particle velocity [1,2]. One of the most interesting and important results from such studies was that it revealed that ranking materials in order of “erosion-corrosion resistance” in one environment may be erroneous because the relative erosion-corrosion resistance of materials could reverse if the conditions were changed significantly [4]. Another significant finding on the effect of alloy corrosion resistance was that good steady-state alloy corrosion resistance did not necessarily guarantee good alloy erosion-corrosion resistance, a common misunderstanding which is made about resistance of materials to erosion-corrosion. In some of the earlier studies on the effect of erosion-corrosion of mild steel it was found that, within a certain temperature range, the degradation was less than that for stainless steel,
MM. Stack et al. / Wear 181483
the more corrosion resistant alloy [2]. Other findings were that the relationship between erosion-corrosion rate and velocity depended on the erosion-corrosion regime, with wide differences in the velocity dependence encountered in the various erosion-corrosion regimes 1561. There have been many interesting attempts to model erosion
517
(1995) 516-523
phology of the material undergoing erosion-corrosion for a given set of conditions, using mathematical models and computer simulation techniques. The simulation is used to test various hypotheses of the mechanisms of erosion-corrosion in the different erosion-corrosion regimes. The mathematical models are used to generate three-dimensional erosion-corrosion maps where the effects of three variables on the erosion-corrosion rate (defined by weight change) are presented.
2. Theoretical basis of the model The basis of the model is described as follows. A particle is initialized and the horizontal position of the particle X is chosen randomly within a “flux width” region; (area under erosion). The vertical position of the particle Y is chosen according to the input data and the stage at which the simulation occurs. The coordinates of the particle landing on the metal are calculated according to the impact angle and the surface morphology. The particle movement is determined by the impact angle, and the impact energy by particle velocity V and mass m (Fig. 1). The metal deformation is determined by the hardness H of metal and the indentation volume A (in two-dimensional simulation, area is used instead of volume, and the mass is varied accordingly), i.e. mV2i2 =hY
(1)
The particle mass is calculated as the product of the sphere area and the density in the two-dimensional simulation: m = rR2D,
(2)
where R is the particle radius and D, the particle density. Since oxide scale forms on top of the metal during erosion-corrosion, the particle impact energy is transformed into deformation of the metal and the oxide. Hence, Eq. (1) can be written as: m V2/2 = H,,,A, + H,,A,,
Fig. 1. Schematic diagram particle on a surface.
(3)
showing
the trajectory
of an eroding
518
M.M. Stack et al. / Wear 181-183
where H,, Ho, are the hardness of the metal and the oxide respectively and A, and A, are the chipping areas for metal and oxide respectively. This means that if there is no oxide on the surface, the indentation volume is constant; on the other hand, if the oxide scale is thick enough to absorb the particle impact energy, the erosion of the base metal does not occur. (This equation assumes no interaction between oxide and metal vertically or laterally.) The erosion model used to generate the experimental results is established by analysing the contact force from metal to particle. Other forces such as friction force and those due to particle collisions are ignored. The contact force is assumed to initiate from the middle point of the contact area and cross the particle centre, as shown in Fig. 2. The contact force accelerates the particle along its assumed vector direction. Generally, this assumed contact force decelerates the particle movement. Furthermore, it is assumed that the indentation does not cause any time delay. Within a given time interval, the particle movement can be traced according to its initial velocity. The indentation area can then be calculated. A velocity V, caused by the contact force, can be derived from Eq. (3) by replacing V as V. The vector sum of 1/l and the initial velocity Vo determines the direction and mode of particle movement for the next instant, i.e. velocity V, as shown in Fig. 3. Fig. 4 shows the analysis of a particle striking a surface. After each impact, the resultant velocities are calculated for the particles. The particle shape assumed is spherical thus enabling frictional and rotational effects to be ignored, without affecting the results significantly. (However, it should be pointed out that for realistic simulation of erosion with angular particles such effects cannot be ignored.) The number of particles impacting the surface (assuming that particles hit uniformly) is given by
(1995) 516-523
Velocity Caused By Contact Force -\” Erod;t
___v--
Vo Initial Velocity Velocity Assumption Fig. 3. Schematic diagram showing the velocity relationship the particle and the target.
\\
7 Assumed Contact ! Force
/’ ,’
\\ Force Analysis
’
\ -__
between
.
\\
Fig. 4. Schematic impact.
Impact Angie
\\\
N=
L
of A Single Impact
diagram
showing
the force
analysis
of a single
W 4/3?rR3D,
where W is the total mass of particles. *
Area
Point
Force
Assumption
Fig. 2. Schematic diagram particle and the metal.
showing
the contact
force between
the
impact interval(s) = T, x 3600/N
(5)
where T, is the exposure time in hours. For the model, it is assumed that no two particles impact the surface simultaneously, owing to the limitations of the computer memory. However, for simulation of more realistic erosion situations, simultaneous impact by large number of particles must be assumed. In this case, the time interval per unit area under erosion would be calculated, as has been carried out in the work of Sundararajan [ll]. The model for film growth is given by
M.M. Stack et al. / Wear 181483
x= (Ky
(6)
where X is the oxide thickness, t the time and k a constant which is related to temperature as follows:
519
(1995) 516-523
Table 1 The input screen which can be modified
during the erosion-corrosion
simulation Input
File Load Input Data File Save Input Data As
(7) Model
X= (Xz,+K At)‘”
(8)
where X0 is the thickness before impact, and At the impact interval. Eq. (5) assumes parabolic oxide growth. (However, it should be pointed out that this may be a simplistic assumption. In the case when the scale is continually thinning, the growth law may be paralinear. In addition, when the oxides formed are very thin, i.e. co.1 pm, the rate law may be linear, i.e. X=Kt. The latter rate law applies to transient oxidation (the initial oxidation process before the steady-state oxide is formed).) The overall weight change is calculated assuming weight gain for oxygen uptake by metal, and weight loss for metal consumed during oxidation. Table 1 shows the data input menu on which individual data can be input and different models can be selected. These data include properties of the particle, the target and the corrosion environment. Hence, various models can be tested using the simulation process in order to validate the theory of the mechanism of erosioncorrosion.
Chipping Oxide Film Growth Particle Shape Size in Radius
Metal Density (Dm) Hardness (Hm) Oxide Film Growth Style PB Ratio (PB) Density (Dox) Hardness (Hox) Initial Thickness (Tox) Coefficient (K) Activation Energy (Q) Environment Temperature (T) Partial Pressure (PP) Testing Time (Tt) Variable X axis Symbol Varying To By Increment
2.1. Effect of temperature and velocity on the erosion of alloys at elevated temperatire
The model was used to simulate the erosion of a material which formed a layer of oxide (for example iron oxide) on the surface at elevated temperatures. As shown above, the growth rate of the oxide was assumed to be parabolic, and the particle shape was chosen to be spherical. The particle hardness was significantly greater than that of the oxide and the metal. (Clearly the resistance of the oxide to erosion damage depends on the ratio of particle to target hardness [17].) Erosion resistance is thought to become independent of particle hardness when the hardness of the particle is a factor of 1.5 that of the target). Typical results on the effect of velocity and temperature are shown Figs. 5-7. These parameters were chosen because they separately show the transitions through the erosion-corrosion regimes in different directions, i.e. from “erosion-dominated” to “corrosion-dominated” behaviour and vice versa. For example, the effect of velocity is to increase the erosion of the material, and that of temperature to increase the corrosion rate. Figs. 5-7 are sample results on the effects of such variables on the erosion-corrosion of the surface; however, a whole succession of images may be generated
(s)
Velocity (V) Density (Dp) Hardness (Hp) Impact Angle (A) Total Height (H)
as in ()
Display Style Particle Radius Metal Height Flux Width Pause Time Output
File What to Output Save Output Data
As
for the effects of different process parameters using the model and the associated computer graphics. The effect of temperature was tested (Fig. 5) at impact angles of 50” and at a velocity of 10 m s-’ for a fixed number of impacts (88 impacts). The light area on the surface indicates oxide formation, and the dark area, the metal substrate. The simulation results demonstrate that, at temperatures of 500 “C, there was little evidence of oxide on the surface (Fig. 5(a)). This indicates that corrosion was almost negligible compared with erosion and the metal wastage was dominated by the erosion process. This was the so-called “erosiondominated” regime. As the temperature was increased to 700 “C (Fig. 5(b)), there was evidence that the extent of oxidation during the erosion process had increased.
520
MM. Stack et al. I Wear 181-183
(1995) 516-523
(a)
(b)
(b) Fig. 6. Effect of velocity on the erosionxorrosion process at an impact angle of 50” and at temperatures of 700 “C: (a) 5 m s-‘; (b) 15 m s-‘.
ic) Fig. 5. Effect of temperature on the erosion-corrosion process at an impact angle of 50” and at velocities of 10 m SK’: (a) 500 “C; (b) 700 “c; (c) 900 “C.
However, it was shown that the oxide did not form a complete layer over the surface. The contact radius which the particles made on the surface included both oxide and metal. Hence, there was evidence of a transition to “erosion-corrosion-dominated” behaviour. However, because the basis of the model did not include the corrosion-enhanced erosion process, there was no indication of a transition to a regime of significantly higher wastage rates than at room temperatures, as had been observed from laboratory erosion-corrosion results [l-3]. At 900 “C (Fig. S(c)), oxide thickening
was evident and the layer now provided a barrier to the eroding particles, thus marking the transition to “corrosion-dominated” erosion+orrosion behaviour, where erosion assumes less importance than corrosion in the overall degradation mechanism of the material. It has been pointed out that there is justification now for the existence of up to four erosion+zorrosion regimes, “erosion-dominated”, “corrosion-dominated” and two transitional regimes intermediate between these processes, where corrosion enhances erosion and corrosion inhibits erosion [6]. The above model describes at least two of these regimes relatively well. Velocity effects were simulated by varying the velocity between 5 m SK’ and 15 m s-l (Figs. 5(b) and 6), at temperatures of 700 “C. The results showed that the transitions through the erosion-corrosion regimes occurred as the impact energy increased. At the lower velocities of 5 m s-l (Fig. 6(a)) the predominant erosion process was chipping of the oxide scale, thus indicating “corrosion-dominated” behaviour. As the velocity was increased to 10 m s-’ (Fig. 5(b)) the oxide thickness decreased, and the layer did not fully cover the surface. This marked the transition to so-called “erosioncorrosion-dominated” behaviour. At the highest velocity
MM. Stack et al. I Wear 181483
521
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model to date describes some if not all of the phenomena of erosion-corrosion behaviour encountered in practice.
2.2. The use of computer graphics to describe erosion-corrosion erosion-corrosion
Fig. 7. Erosion-corrosion maps showing (a) variation of weight change (mg cm-‘) with impact angle and temperatures for velocities of 5 m s-‘, 10 m s-’ and 15 m s-‘, and (b) variation of weight change with impact angle and velocity for temperatures of 500 “C, 700 “C and 900 “C.
of 15 m s-l (Fig. 6(b)) the erosion damage was significantly greater than at lower velocities, and the oxide layer on the surface was very thin. Above such velocities, transition to “erosion-dominated” behaviour would occur, because above such values, corrosion would be insignificant in influencing the damage mechanism compared with erosion of the underlying metal substrate. Fig. 7 shows the results from the series of simulations of erosion at various temperatures, velocities and impact angles. Clearly, the erosion-corrosion rate (weight loss) decreases as a function of temperature, and at low temperatures is relatively independent of temperature, Fig. 7(a). These results are interesting because they suggest that the model has validity at both low and high temperatures; however, the intermediate regime, that in which corrosion enhances the erosion of the material is not accurately described by the physical model outlined above, because all the experimental results indicate that the erosionxorrosion rate increases with temperature in this regime [l-3]. The increase in erosion-corrosion rate with velocity is consistent with results reported for the effects of velocity in such environments [2,3,5]. Hence, there is evidence that the
regimes identified on maps
The development of erosiorxorrosion maps, where the change in erosion-corrosion mechanism is described in terms of erosion and corrosion variables, is undoubtedly a powerful long term approach towards developing approaches on minimizing erosion-corrosion damage. Maps have been developed by various investigators [10,12], and the transitions through the erosion-corrosion regimes have been shown on such maps. However, there are various areas which have not been addressed in the development of such maps. Erosion-corrosion processes typically involve the interaction of many parameters. In aqueous erosion-corrosion environments, variables have been combined in dimensionless groups (such as Reynold’s number) such that the damage mechanism can be described in terms of a range of variables. The construction of erosioncorrosion maps which incorporate combinations of erosion and corrosion parameters may only apply to a limited range of practical erosion-corrosion environments. However, such multi-variable maps would be invaluable to engineers and designers involved in minimizing damage due to erosiorxorrosion. At present, research is being carried out by the authors to test the validity of this approach. The work outlined above has addressed the development of three-dimensional maps where the change in erosion-corrosion rate (given by weight change) is presented as a function of impact angle, velocity, and temperature. The combination of parameters in which the overall weight change is minimized can be identified from such maps, as long as the maps provide some indication of the erosionxorrosion rate. Wear maps which have been recently developed for wear of tool steels incorporate contours of wear rates, and the location of minimum wear is identified as a “safety zone”[l8]. Recent attempts at the development of erosion-corrosion maps have incorporated this useful concept [12]. The development of a model using computer simulation to demonstrate the physical significance of the regimes encountered on such maps is useful because it is a relatively simple method of identifying the predominant erosion process on the material surface. Such an approach can be combined with the erosion-corrosion map to give overall snapshots of the erosion-corrosion mechanisms of the material.
522
M.M. Stack et al. I Wear 181483
3. Discussion
Simulation is an experimental technique which enables various hypotheses to be tested. At present, the theories of the mechanism of damage in the “erosiondominated” and high temperature “corrosion-dominated” regime, outlined above, are consistent with the observations from experimental results. The formation of a “critical oxide thickness” [19] results in a reduction in the erosion-corrosion rate at elevated temperatures (Fig. 7). Implicit in the model is that oxides can absorb more deformation than metal because of the higher hardness, as shown in Fig. 7, hence leading to reduction of metal erosion at elevated temperatures. However, the formation of oxide at such temperatures can cause extensive corrosion of the surface particularly if the oxide growth rates are high. Hence, weight change measurements are not always the most accurate method of calculation of the damage due to erosion-corrosion. The metal wastage in some cases can be a more meaningful measurement. This measurement may be obtained easily by the simulation, and will show different trends to weight change, particularly in the “corrosiondominated” regime. Hence, the simple model outlined above describes this regime reasonably well. The model, however, does not describe the regime in which the erosion-corrosion rate increases significantly with increasing temperature. This is the so-called “erosion+orrosion-dominated” regime. There is no general consensus as to why such rapid increases in wastage rate with temperature are observed in this regime, and it is generally agreed that this is the least understood of the various erosion-corrosion regimes. The oxides on the surface are generally too thin to be detected using conventional microscopy techniques such as SEM, and therefore the mechanism of damage is unclear. It has been shown that the wastage rate, in this regime, can increase by up to one order of magnitude from temperatures of 25 “C to 300 “C, but that the hardness of the underlying alloy may decrease by less than 30% (i.e. for conventional steels), suggesting that loss of oxide in addition to metal must contribute to the overall wastage rate [2]. However, there is very little evidence for this theory. Currently, two theories of the mechanism of damage in this regime which are being evaluated are as follows: (i) Poor oxide cohesion leads to a reduction in erosion resistance, compared with that of a thick cohesive layer. If the oxide formed during erosion does not develop into a cohesive layer, it may suggest that the scale is significantly less erosion resistant than the underlying metal. This would account for the rapid increase in wastage rates with increasing temperature observed for this regime. However, if this is the case, it means that a factor which defines
(1995) 516-523
oxide cohesion in addition to oxide hardness needs to be incorporated in the model. (ii) Formation of oxide in the “erosion-corrosion-dominated” regime may weaken the resistance of the underlying metal to erosion, causing subsurface cracks, and leading to enhanced erosion of the surface at elevated temperatures. There is some evidence from research in aqueous erosioncorrosion environments that the high erosioncorrosion rates in the analogous regime (in which a protective film forms over the surface) cannot be justified wholly in terms of loss of corrosion product [20]. (Unlike the high temperature gaseous situation, electrochemical techniques can be used to measure the increase in corrosion rate, defined by the current, in this regime. The current can be integrated over time and compared with the mass loss measurements). Such theories are being evaluated by modifying the model outlined above and using simulation. One of the interesting results to emerge from this work is the development of a model which incorporates a particle to hardness ratio, which has often been neglected in solid particle erosion modelling work. In practical erosion*orrosion situations, particles are not necessarily harder than the target, and are not always inert. At high temperatures, in many erosion-corrosion systems, particles such as ash (with high sulphur content) may deposit on the surface, and lead to corrosion rather than erosion damage. One of the models outlined above considers that particles should cause little damage, if the particle hardness approaches that of the target. Future work will simulate the situation where particle deposits may cause enhanced corrosion on the surface rather than enhanced erosion. The maps which have been developed using the model can show the effects of more than two variables and provide a means of locating the minimum and the maximum erosion-corrosion rate of the material. By defining an axis which relates to properties of the alloy (i.e. % Cr content is indicative of alloy oxidation resistance) [21], the maps can be used for materials selection purposes, and this work is being carried out at present. Hence, maps can be quite a powerful tool either in the process of optimization of process parameters in order to minimize damage due to erosion-corrosion, or in the selection of an appropriate material for exposure to a particular erosion4orrosion environment. The additional use of computer graphics to define the degradation mechanism on the surface is a useful method of assessing the erosion-corrosion mechanism on the surface, and a means of establishing the criteria which may result in a reduction of the damage of the material. Such computer generated surfaces can, in turn, explain the physicalsignificance of the erosion
M.M. Stack et al. / Wear 181-183
4. Conclusions
6)
A physical model has been developed to model erosion-corrosion by solid particles at elevated temperatures. (ii) Properties of the particle, target and the environment can be varied in the simulation tests. (iii) The model has been used to generate computer images of the eroding surface at elevated temperatures. (iv) The model has also been used to construct threedimensional maps where the change in erosion-corrosion rate (defined by weight change) is given as a function of three variables, temperature, velocity and impact angle.
References V.K. Sethi and R.G. Corey, Proc. 7th Int. ConjI on Erosion by Liquid and Solid Impact, University of Cambridge, 1987, paper 73. [21 A.J. Ninham, I.M. Hutchings and J.A. Little, Pmt. Conj: on Corrosion ‘89, NACE, Houston, TX, 1989, paper 544. [31 F.H. Stott, M.M. Stack and G.C. Wood, Proc. Conj: on Corrosion-Erosion-Wear of Materials at Elevated Temperatures, NACE, Houston, TX, 1990, paper 12, pp. 1-16. t41 M.M. Stack, F.H. Stott and G.C. Wood, Proc. Conf: Materials for Combined Cycle Power Plant, Institute of Materials, UK, 1991, pp. 253-261
it1
t51
523
(1995) 516-523 M.M.
Stack,
F.H.
Stott
and
G.C.
Wood,
J. de Physique IV,
(1993) 687-694. and F.H. Stott, Wear, in press. PI M.M. Stack, J. Chacon-Nava [71 Yung Y Liu and K. Natesan, Proc. ht. Nat. Conf. on Metallurgical Coatings, San Diego, CA, 1988. PI D.M. Rishel, F.S. Pettit and N. Birks, Proc. Conf: Corrosion-Erosion-Wear of Materials at Elevated Temperatures, NACE, Houston, TX, 1990, paper 16, pp. l-23. V. Nagarajan and LG. Wright, Oxid. Met., 35 [91 A.J. Markworth, (1991) 1. G. Sundararajan, Proc. Con$ Corrosion-Erosion-Wear of MaWI terials at Elevated Temperatures, NACE, Houston, TX, 1990, paper 11, l-33. G. Sundararajan, Wear, 149 (1991) 129-153. Pll M.M. Stack, Proc. 1st. Znt. Symp. on Pmcess Industry Piping, WI 14-18 December 1993, NACE, Houston, TX, 37 (1-13). and J.R. Nicholls, Corros. Sci., 35 (5-8) (1993) P31 D.J. Stephenson 1015-1026. P41 I.M. Hutchings, Proc. 5th Int. Con& Erosion by Liquid and Solid Impact, 36-1, University of Cambridge, 1979, paper 36. P51 I. Finnie, Proc. Cons? U.S. Congress on App. Mech., 1958, p. 527. M.M. Stack, F.H. Stott and G.C. Wood, J. Phys. D: Appl. Phys, WI 25 (1992) A170-A176. of Coal Conu71 I.M. Hutchings, Proc. Con$ on ErosionCorrosion version System Materials, NACE, Houston, 393, Berkeley, 1979. S.C. Lim, Y.B. Liu, S.H. Lee and K.H.W. Seah, Wear, 162-164 WI (part B) (1992) 971-974. [I91 V.K. Sethi and I.G. Wright, Proc. Symp. on Corrosion and Metals and Particle Erosion at High Temperatures, Mineral Materials Society, 1989, pp. 245-263. 1201 Z. Yue, P. Zhou and J. Shi, Proc. Confi Wear of Materials, 763-8, April 1987. M.M. Stack, Q. Song Roehrle and F.H. Stott, Ttib. Int., in PI preparation.
Wear
Computer
181-183
(1995)
516-523
simulation of erosion-corrosion elevated temperatures M.M. Stack, Q. Song-Roehrle,
Corrosion and Protection
Centre, UMIST, P.O. Box
interactions
at
F.H. Stott, G.C. Wood
88, Sackville Street, Manchester M60 IQD, UK
Received 25 May 1994; accepted 16 September 1994
Abstract Although there have been some attempts to model erosion by solid particles at elevated temperatures, there have been few efforts to develop a model which can generate images of the surface morphologies in the various erosion-corrosion regimes. Many classifications of erosion-corrosion regimes have been identified and there is evidence that there are at least three such regimes. The physical significance of the surface in such regimes may be difficult to visualize, particularly when the situation is neither “erosion-dominated” (erosion of the substrate) nor “corrosion-dominated” (erosion plays a minor role compared with corrosion). The object of this research has been to develop a physical model to simulate the transitions between erosion+rrosion regimes at elevated temperatures. Properties of the particle (shape, size, velocity, hardness, flux), the target (corrosion resistance, hardness, impact angle) and the environment (gas composition and temperature) are considered in the model. The results are then used to construct a computer-generated image of the eroding surface. This paper describes the physical basis of the model and shows how the transitions between the regimes can be achieved by variation of the erosion and corrosion parameters. Typical results are shown and compared with existing erosion-corrosion data. The future development of the research is outlined in terms of the application to other environments in which erosion
Computer simulation; Erosion;
Corrosion; Particle impact
1. Introduction
Although much progress has been made in the understanding of erosion-corrosion of materials by solid particles at elevated temperatures in recent years, there are still areas which are not well understood. Erosion-corrosion is a major problem in many energy conversion processes such as oil and gas conversion and coal combustion technologies. A synergy is observed between erosion and corrosion. This essentially means that, in some conditions, corrosion can enhance the erosion of the materials. However, in other cases, the formation of a corrosion product(such as a protective oxide) can inhibit erosion. Improved understanding of erosion
0043-1648/95/$09.50 0 1995 Elsevier Science S.A. All rights reserved SSDl 0043-1648(94)07028-8
temperature was observed; the erosion-corrosion rate increased with temperature up to a critical temperature and subsequently decreased with further increases in temperature. This peak in the erosion+zorrosion rate shifted to higher temperatures with increasing alloy Cr content [2] and higher wastage rates with increased particle velocity [1,2]. One of the most interesting and important results from such studies was that it revealed that ranking materials in order of “erosion-corrosion resistance” in one environment may be erroneous because the relative erosion-corrosion resistance of materials could reverse if the conditions were changed significantly [4]. Another significant finding on the effect of alloy corrosion resistance was that good steady-state alloy corrosion resistance did not necessarily guarantee good alloy erosion-corrosion resistance, a common misunderstanding which is made about resistance of materials to erosion-corrosion. In some of the earlier studies on the effect of erosion-corrosion of mild steel it was found that, within a certain temperature range, the degradation was less than that for stainless steel,
MM. Stack et al. / Wear 181483
the more corrosion resistant alloy [2]. Other findings were that the relationship between erosion-corrosion rate and velocity depended on the erosion-corrosion regime, with wide differences in the velocity dependence encountered in the various erosion-corrosion regimes 1561. There have been many interesting attempts to model erosion
517
(1995) 516-523
phology of the material undergoing erosion-corrosion for a given set of conditions, using mathematical models and computer simulation techniques. The simulation is used to test various hypotheses of the mechanisms of erosion-corrosion in the different erosion-corrosion regimes. The mathematical models are used to generate three-dimensional erosion-corrosion maps where the effects of three variables on the erosion-corrosion rate (defined by weight change) are presented.
2. Theoretical basis of the model The basis of the model is described as follows. A particle is initialized and the horizontal position of the particle X is chosen randomly within a “flux width” region; (area under erosion). The vertical position of the particle Y is chosen according to the input data and the stage at which the simulation occurs. The coordinates of the particle landing on the metal are calculated according to the impact angle and the surface morphology. The particle movement is determined by the impact angle, and the impact energy by particle velocity V and mass m (Fig. 1). The metal deformation is determined by the hardness H of metal and the indentation volume A (in two-dimensional simulation, area is used instead of volume, and the mass is varied accordingly), i.e. mV2i2 =hY
(1)
The particle mass is calculated as the product of the sphere area and the density in the two-dimensional simulation: m = rR2D,
(2)
where R is the particle radius and D, the particle density. Since oxide scale forms on top of the metal during erosion-corrosion, the particle impact energy is transformed into deformation of the metal and the oxide. Hence, Eq. (1) can be written as: m V2/2 = H,,,A, + H,,A,,
Fig. 1. Schematic diagram particle on a surface.
(3)
showing
the trajectory
of an eroding
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M.M. Stack et al. / Wear 181-183
where H,, Ho, are the hardness of the metal and the oxide respectively and A, and A, are the chipping areas for metal and oxide respectively. This means that if there is no oxide on the surface, the indentation volume is constant; on the other hand, if the oxide scale is thick enough to absorb the particle impact energy, the erosion of the base metal does not occur. (This equation assumes no interaction between oxide and metal vertically or laterally.) The erosion model used to generate the experimental results is established by analysing the contact force from metal to particle. Other forces such as friction force and those due to particle collisions are ignored. The contact force is assumed to initiate from the middle point of the contact area and cross the particle centre, as shown in Fig. 2. The contact force accelerates the particle along its assumed vector direction. Generally, this assumed contact force decelerates the particle movement. Furthermore, it is assumed that the indentation does not cause any time delay. Within a given time interval, the particle movement can be traced according to its initial velocity. The indentation area can then be calculated. A velocity V, caused by the contact force, can be derived from Eq. (3) by replacing V as V. The vector sum of 1/l and the initial velocity Vo determines the direction and mode of particle movement for the next instant, i.e. velocity V, as shown in Fig. 3. Fig. 4 shows the analysis of a particle striking a surface. After each impact, the resultant velocities are calculated for the particles. The particle shape assumed is spherical thus enabling frictional and rotational effects to be ignored, without affecting the results significantly. (However, it should be pointed out that for realistic simulation of erosion with angular particles such effects cannot be ignored.) The number of particles impacting the surface (assuming that particles hit uniformly) is given by
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Velocity Caused By Contact Force -\” Erod;t
___v--
Vo Initial Velocity Velocity Assumption Fig. 3. Schematic diagram showing the velocity relationship the particle and the target.
\\
7 Assumed Contact ! Force
/’ ,’
\\ Force Analysis
’
\ -__
between
.
\\
Fig. 4. Schematic impact.
Impact Angie
\\\
N=
L
of A Single Impact
diagram
showing
the force
analysis
of a single
W 4/3?rR3D,
where W is the total mass of particles. *
Area
Point
Force
Assumption
Fig. 2. Schematic diagram particle and the metal.
showing
the contact
force between
the
impact interval(s) = T, x 3600/N
(5)
where T, is the exposure time in hours. For the model, it is assumed that no two particles impact the surface simultaneously, owing to the limitations of the computer memory. However, for simulation of more realistic erosion situations, simultaneous impact by large number of particles must be assumed. In this case, the time interval per unit area under erosion would be calculated, as has been carried out in the work of Sundararajan [ll]. The model for film growth is given by
M.M. Stack et al. / Wear 181483
x= (Ky
(6)
where X is the oxide thickness, t the time and k a constant which is related to temperature as follows:
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Table 1 The input screen which can be modified
during the erosion-corrosion
simulation Input
File Load Input Data File Save Input Data As
(7) Model
X= (Xz,+K At)‘”
(8)
where X0 is the thickness before impact, and At the impact interval. Eq. (5) assumes parabolic oxide growth. (However, it should be pointed out that this may be a simplistic assumption. In the case when the scale is continually thinning, the growth law may be paralinear. In addition, when the oxides formed are very thin, i.e. co.1 pm, the rate law may be linear, i.e. X=Kt. The latter rate law applies to transient oxidation (the initial oxidation process before the steady-state oxide is formed).) The overall weight change is calculated assuming weight gain for oxygen uptake by metal, and weight loss for metal consumed during oxidation. Table 1 shows the data input menu on which individual data can be input and different models can be selected. These data include properties of the particle, the target and the corrosion environment. Hence, various models can be tested using the simulation process in order to validate the theory of the mechanism of erosioncorrosion.
Chipping Oxide Film Growth Particle Shape Size in Radius
Metal Density (Dm) Hardness (Hm) Oxide Film Growth Style PB Ratio (PB) Density (Dox) Hardness (Hox) Initial Thickness (Tox) Coefficient (K) Activation Energy (Q) Environment Temperature (T) Partial Pressure (PP) Testing Time (Tt) Variable X axis Symbol Varying To By Increment
2.1. Effect of temperature and velocity on the erosion of alloys at elevated temperatire
The model was used to simulate the erosion of a material which formed a layer of oxide (for example iron oxide) on the surface at elevated temperatures. As shown above, the growth rate of the oxide was assumed to be parabolic, and the particle shape was chosen to be spherical. The particle hardness was significantly greater than that of the oxide and the metal. (Clearly the resistance of the oxide to erosion damage depends on the ratio of particle to target hardness [17].) Erosion resistance is thought to become independent of particle hardness when the hardness of the particle is a factor of 1.5 that of the target). Typical results on the effect of velocity and temperature are shown Figs. 5-7. These parameters were chosen because they separately show the transitions through the erosion-corrosion regimes in different directions, i.e. from “erosion-dominated” to “corrosion-dominated” behaviour and vice versa. For example, the effect of velocity is to increase the erosion of the material, and that of temperature to increase the corrosion rate. Figs. 5-7 are sample results on the effects of such variables on the erosion-corrosion of the surface; however, a whole succession of images may be generated
(s)
Velocity (V) Density (Dp) Hardness (Hp) Impact Angle (A) Total Height (H)
as in ()
Display Style Particle Radius Metal Height Flux Width Pause Time Output
File What to Output Save Output Data
As
for the effects of different process parameters using the model and the associated computer graphics. The effect of temperature was tested (Fig. 5) at impact angles of 50” and at a velocity of 10 m s-’ for a fixed number of impacts (88 impacts). The light area on the surface indicates oxide formation, and the dark area, the metal substrate. The simulation results demonstrate that, at temperatures of 500 “C, there was little evidence of oxide on the surface (Fig. 5(a)). This indicates that corrosion was almost negligible compared with erosion and the metal wastage was dominated by the erosion process. This was the so-called “erosiondominated” regime. As the temperature was increased to 700 “C (Fig. 5(b)), there was evidence that the extent of oxidation during the erosion process had increased.
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(a)
(b)
(b) Fig. 6. Effect of velocity on the erosionxorrosion process at an impact angle of 50” and at temperatures of 700 “C: (a) 5 m s-‘; (b) 15 m s-‘.
ic) Fig. 5. Effect of temperature on the erosion-corrosion process at an impact angle of 50” and at velocities of 10 m SK’: (a) 500 “C; (b) 700 “c; (c) 900 “C.
However, it was shown that the oxide did not form a complete layer over the surface. The contact radius which the particles made on the surface included both oxide and metal. Hence, there was evidence of a transition to “erosion-corrosion-dominated” behaviour. However, because the basis of the model did not include the corrosion-enhanced erosion process, there was no indication of a transition to a regime of significantly higher wastage rates than at room temperatures, as had been observed from laboratory erosion-corrosion results [l-3]. At 900 “C (Fig. S(c)), oxide thickening
was evident and the layer now provided a barrier to the eroding particles, thus marking the transition to “corrosion-dominated” erosion+orrosion behaviour, where erosion assumes less importance than corrosion in the overall degradation mechanism of the material. It has been pointed out that there is justification now for the existence of up to four erosion+zorrosion regimes, “erosion-dominated”, “corrosion-dominated” and two transitional regimes intermediate between these processes, where corrosion enhances erosion and corrosion inhibits erosion [6]. The above model describes at least two of these regimes relatively well. Velocity effects were simulated by varying the velocity between 5 m SK’ and 15 m s-l (Figs. 5(b) and 6), at temperatures of 700 “C. The results showed that the transitions through the erosion-corrosion regimes occurred as the impact energy increased. At the lower velocities of 5 m s-l (Fig. 6(a)) the predominant erosion process was chipping of the oxide scale, thus indicating “corrosion-dominated” behaviour. As the velocity was increased to 10 m s-’ (Fig. 5(b)) the oxide thickness decreased, and the layer did not fully cover the surface. This marked the transition to so-called “erosioncorrosion-dominated” behaviour. At the highest velocity
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model to date describes some if not all of the phenomena of erosion-corrosion behaviour encountered in practice.
2.2. The use of computer graphics to describe erosion-corrosion erosion-corrosion
Fig. 7. Erosion-corrosion maps showing (a) variation of weight change (mg cm-‘) with impact angle and temperatures for velocities of 5 m s-‘, 10 m s-’ and 15 m s-‘, and (b) variation of weight change with impact angle and velocity for temperatures of 500 “C, 700 “C and 900 “C.
of 15 m s-l (Fig. 6(b)) the erosion damage was significantly greater than at lower velocities, and the oxide layer on the surface was very thin. Above such velocities, transition to “erosion-dominated” behaviour would occur, because above such values, corrosion would be insignificant in influencing the damage mechanism compared with erosion of the underlying metal substrate. Fig. 7 shows the results from the series of simulations of erosion at various temperatures, velocities and impact angles. Clearly, the erosion-corrosion rate (weight loss) decreases as a function of temperature, and at low temperatures is relatively independent of temperature, Fig. 7(a). These results are interesting because they suggest that the model has validity at both low and high temperatures; however, the intermediate regime, that in which corrosion enhances the erosion of the material is not accurately described by the physical model outlined above, because all the experimental results indicate that the erosionxorrosion rate increases with temperature in this regime [l-3]. The increase in erosion-corrosion rate with velocity is consistent with results reported for the effects of velocity in such environments [2,3,5]. Hence, there is evidence that the
regimes identified on maps
The development of erosiorxorrosion maps, where the change in erosion-corrosion mechanism is described in terms of erosion and corrosion variables, is undoubtedly a powerful long term approach towards developing approaches on minimizing erosion-corrosion damage. Maps have been developed by various investigators [10,12], and the transitions through the erosion-corrosion regimes have been shown on such maps. However, there are various areas which have not been addressed in the development of such maps. Erosion-corrosion processes typically involve the interaction of many parameters. In aqueous erosion-corrosion environments, variables have been combined in dimensionless groups (such as Reynold’s number) such that the damage mechanism can be described in terms of a range of variables. The construction of erosioncorrosion maps which incorporate combinations of erosion and corrosion parameters may only apply to a limited range of practical erosion-corrosion environments. However, such multi-variable maps would be invaluable to engineers and designers involved in minimizing damage due to erosiorxorrosion. At present, research is being carried out by the authors to test the validity of this approach. The work outlined above has addressed the development of three-dimensional maps where the change in erosion-corrosion rate (given by weight change) is presented as a function of impact angle, velocity, and temperature. The combination of parameters in which the overall weight change is minimized can be identified from such maps, as long as the maps provide some indication of the erosionxorrosion rate. Wear maps which have been recently developed for wear of tool steels incorporate contours of wear rates, and the location of minimum wear is identified as a “safety zone”[l8]. Recent attempts at the development of erosion-corrosion maps have incorporated this useful concept [12]. The development of a model using computer simulation to demonstrate the physical significance of the regimes encountered on such maps is useful because it is a relatively simple method of identifying the predominant erosion process on the material surface. Such an approach can be combined with the erosion-corrosion map to give overall snapshots of the erosion-corrosion mechanisms of the material.
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3. Discussion
Simulation is an experimental technique which enables various hypotheses to be tested. At present, the theories of the mechanism of damage in the “erosiondominated” and high temperature “corrosion-dominated” regime, outlined above, are consistent with the observations from experimental results. The formation of a “critical oxide thickness” [19] results in a reduction in the erosion-corrosion rate at elevated temperatures (Fig. 7). Implicit in the model is that oxides can absorb more deformation than metal because of the higher hardness, as shown in Fig. 7, hence leading to reduction of metal erosion at elevated temperatures. However, the formation of oxide at such temperatures can cause extensive corrosion of the surface particularly if the oxide growth rates are high. Hence, weight change measurements are not always the most accurate method of calculation of the damage due to erosion-corrosion. The metal wastage in some cases can be a more meaningful measurement. This measurement may be obtained easily by the simulation, and will show different trends to weight change, particularly in the “corrosiondominated” regime. Hence, the simple model outlined above describes this regime reasonably well. The model, however, does not describe the regime in which the erosion-corrosion rate increases significantly with increasing temperature. This is the so-called “erosion+orrosion-dominated” regime. There is no general consensus as to why such rapid increases in wastage rate with temperature are observed in this regime, and it is generally agreed that this is the least understood of the various erosion-corrosion regimes. The oxides on the surface are generally too thin to be detected using conventional microscopy techniques such as SEM, and therefore the mechanism of damage is unclear. It has been shown that the wastage rate, in this regime, can increase by up to one order of magnitude from temperatures of 25 “C to 300 “C, but that the hardness of the underlying alloy may decrease by less than 30% (i.e. for conventional steels), suggesting that loss of oxide in addition to metal must contribute to the overall wastage rate [2]. However, there is very little evidence for this theory. Currently, two theories of the mechanism of damage in this regime which are being evaluated are as follows: (i) Poor oxide cohesion leads to a reduction in erosion resistance, compared with that of a thick cohesive layer. If the oxide formed during erosion does not develop into a cohesive layer, it may suggest that the scale is significantly less erosion resistant than the underlying metal. This would account for the rapid increase in wastage rates with increasing temperature observed for this regime. However, if this is the case, it means that a factor which defines
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oxide cohesion in addition to oxide hardness needs to be incorporated in the model. (ii) Formation of oxide in the “erosion-corrosion-dominated” regime may weaken the resistance of the underlying metal to erosion, causing subsurface cracks, and leading to enhanced erosion of the surface at elevated temperatures. There is some evidence from research in aqueous erosioncorrosion environments that the high erosioncorrosion rates in the analogous regime (in which a protective film forms over the surface) cannot be justified wholly in terms of loss of corrosion product [20]. (Unlike the high temperature gaseous situation, electrochemical techniques can be used to measure the increase in corrosion rate, defined by the current, in this regime. The current can be integrated over time and compared with the mass loss measurements). Such theories are being evaluated by modifying the model outlined above and using simulation. One of the interesting results to emerge from this work is the development of a model which incorporates a particle to hardness ratio, which has often been neglected in solid particle erosion modelling work. In practical erosion*orrosion situations, particles are not necessarily harder than the target, and are not always inert. At high temperatures, in many erosion-corrosion systems, particles such as ash (with high sulphur content) may deposit on the surface, and lead to corrosion rather than erosion damage. One of the models outlined above considers that particles should cause little damage, if the particle hardness approaches that of the target. Future work will simulate the situation where particle deposits may cause enhanced corrosion on the surface rather than enhanced erosion. The maps which have been developed using the model can show the effects of more than two variables and provide a means of locating the minimum and the maximum erosion-corrosion rate of the material. By defining an axis which relates to properties of the alloy (i.e. % Cr content is indicative of alloy oxidation resistance) [21], the maps can be used for materials selection purposes, and this work is being carried out at present. Hence, maps can be quite a powerful tool either in the process of optimization of process parameters in order to minimize damage due to erosion-corrosion, or in the selection of an appropriate material for exposure to a particular erosion4orrosion environment. The additional use of computer graphics to define the degradation mechanism on the surface is a useful method of assessing the erosion-corrosion mechanism on the surface, and a means of establishing the criteria which may result in a reduction of the damage of the material. Such computer generated surfaces can, in turn, explain the physicalsignificance of the erosion
M.M. Stack et al. / Wear 181-183
4. Conclusions
6)
A physical model has been developed to model erosion-corrosion by solid particles at elevated temperatures. (ii) Properties of the particle, target and the environment can be varied in the simulation tests. (iii) The model has been used to generate computer images of the eroding surface at elevated temperatures. (iv) The model has also been used to construct threedimensional maps where the change in erosion-corrosion rate (defined by weight change) is given as a function of three variables, temperature, velocity and impact angle.
References V.K. Sethi and R.G. Corey, Proc. 7th Int. ConjI on Erosion by Liquid and Solid Impact, University of Cambridge, 1987, paper 73. [21 A.J. Ninham, I.M. Hutchings and J.A. Little, Pmt. Conj: on Corrosion ‘89, NACE, Houston, TX, 1989, paper 544. [31 F.H. Stott, M.M. Stack and G.C. Wood, Proc. Conj: on Corrosion-Erosion-Wear of Materials at Elevated Temperatures, NACE, Houston, TX, 1990, paper 12, pp. 1-16. t41 M.M. Stack, F.H. Stott and G.C. Wood, Proc. Conf: Materials for Combined Cycle Power Plant, Institute of Materials, UK, 1991, pp. 253-261
it1
t51
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(1995) 516-523 M.M.
Stack,
F.H.
Stott
and
G.C.
Wood,
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(1993) 687-694. and F.H. Stott, Wear, in press. PI M.M. Stack, J. Chacon-Nava [71 Yung Y Liu and K. Natesan, Proc. ht. Nat. Conf. on Metallurgical Coatings, San Diego, CA, 1988. PI D.M. Rishel, F.S. Pettit and N. Birks, Proc. Conf: Corrosion-Erosion-Wear of Materials at Elevated Temperatures, NACE, Houston, TX, 1990, paper 16, pp. l-23. V. Nagarajan and LG. Wright, Oxid. Met., 35 [91 A.J. Markworth, (1991) 1. G. Sundararajan, Proc. Con$ Corrosion-Erosion-Wear of MaWI terials at Elevated Temperatures, NACE, Houston, TX, 1990, paper 11, l-33. G. Sundararajan, Wear, 149 (1991) 129-153. Pll M.M. Stack, Proc. 1st. Znt. Symp. on Pmcess Industry Piping, WI 14-18 December 1993, NACE, Houston, TX, 37 (1-13). and J.R. Nicholls, Corros. Sci., 35 (5-8) (1993) P31 D.J. Stephenson 1015-1026. P41 I.M. Hutchings, Proc. 5th Int. Con& Erosion by Liquid and Solid Impact, 36-1, University of Cambridge, 1979, paper 36. P51 I. Finnie, Proc. Cons? U.S. Congress on App. Mech., 1958, p. 527. M.M. Stack, F.H. Stott and G.C. Wood, J. Phys. D: Appl. Phys, WI 25 (1992) A170-A176. of Coal Conu71 I.M. Hutchings, Proc. Con$ on ErosionCorrosion version System Materials, NACE, Houston, 393, Berkeley, 1979. S.C. Lim, Y.B. Liu, S.H. Lee and K.H.W. Seah, Wear, 162-164 WI (part B) (1992) 971-974. [I91 V.K. Sethi and I.G. Wright, Proc. Symp. on Corrosion and Metals and Particle Erosion at High Temperatures, Mineral Materials Society, 1989, pp. 245-263. 1201 Z. Yue, P. Zhou and J. Shi, Proc. Confi Wear of Materials, 763-8, April 1987. M.M. Stack, Q. Song Roehrle and F.H. Stott, Ttib. Int., in PI preparation.