# Erosion-Oxidation Response of Boiler Grade Steels: A Mathematical Investigation

Authors: S. K. Das; Shubha Hegde; P. K. Dey; S. P. Mehrotra
Journal: Research Letters in Materials Science
 (2008)

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## Abstract

A ductile erosion model embodying the mechanisms of erosion involving cutting wear and repeated plastic deformation has been developed to predict erosion rates of boiler grade steels. The issue of erosion-oxidation interaction has also been addressed to further predict the mass loss resulted from this composite mechanism. A deterministic formalism for the kinetics of oxide-scale growth and a probabilistic approach to characterize the material loss are employed to describe simultaneous actions of high-temperature oxidation and mechanical erosion. The model predictions are in good agreement with the published data.


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## Body

## 1. Introduction

Erosion
is a process by which material is removed from the layers of a surface impacted
by a stream of abrasive particles. The magnitude of the wear is quantified by
the volume or mass of the material that is removed by the action of the
impacting particles.
In coal-fired boilers, ash particles collide with the
surface of the boiler steel components (air preheater, economizer, and
super-heater tubes) resulting in considerable erosion of metallic materials.
Such erosion, together with the processes of blocking, fouling, and corrosion,
shortens the service life of the boiler components. The resulting penalty is
not only the cost of replacing the components but also the cost of stoppage of
power production. It is desirable, therefore, to be able to predict the rate of
erosion of the boiler components in order to systematically plan the
maintenance and/or replacement schedules of these components to avoid forced
outages [1–5].High-temperature
erosion, which involves the conjoint action of high-temperature oxidation and
damage due to solid particle impact, is a complex process. Material damage
occurs through the interaction of both oxidation and erosion, with metal
recession rates often enhanced as a result of the synergetic effect of these
two processes. In this paper, mathematical investigations have been carried out
on the basis of a ductile erosion model to characterize and quantify the wear behavior
and mechanism of various boiler grade steels. The erosion-oxidation synergetic
impact is also modeled to characterize the material damage in a high-temperature-oxidizing
environment based on a composite deterministic-probabilistic modeling
framework.


## 2. Mathematical Simulation

There are three important phenomena by which metal is
removed by the impacting particles at elevated temperature:(i)
removal
of material due to cutting wear,(ii)
removal of material due to repeated plastic deformation,(iii)
effect of temperature on tensile properties of the material. The first two phenomena are
applicable to erosion at room temperature.


### 2.1. Mechanism of Cutting Wear

An ash particle,
that strikes the surface at an acute angle and at a velocity greater than the
critical velocity needed for the penetration of the material’s surface, removes
some material in a process similar to the cutting action of a machine tool
(micromachining action). At the impact location, the particle loses a fraction
of its kinetic energy to the target material in the form of heat and energy for
deformation of the surface. When the shear strain exceeds the elastic strain
limit of the target material,
the particle penetrates the surface of the
material and ploughs along the surface, removing material.In the case of cutting wear, the
material's resistance to deformation needs to be overcome by the impacting
particles to penetrate the surface of the material. The differential equation of
motion for the depth of penetration is given as [1–3] (1)mpd2Ldt2=−πdp2Lcσy, where L is the depth of
penetration, mp is the mass of the particle, dp is the diameter of the particle, t is the time, σy is the yield stress of the target material, and c is a particle shape factor.
For sphere particles, shape factor is equal to 3.The erosion rate due to cutting
wearεc, defined as the ratio of the mass of the material eroded (m), from the
target surface to mass of the impacting particle (mp), is
given by the following equation [1–3]: (2)εc=mmp=kcρmρp3/2dp3v3sin3β33σy3/2(πρp(dp3/6))=k1ρmρp1/2v3sin3βσy3/2, where V and β are the impacting velocity and angle of the particle,
respectively. ρm and ρp are the densities of the
target material, and the particle Kc and K1 are constants [1–3].


### 2.2. Mechanism of Plastic Deformation Wear

During particle
impact, the loss of material from an eroding surface may occur as a consequence
of a composite sequential mechanism similar to a combined process of
extrusion-forging mechanism. The extruded platelets from shallow craters made
by the impacting particle are further forged into a strained condition. Because
of the high-strain rates, adiabatic shear heating occurs in the surface region
immediate to the impact site. The kinetic energy of the impacting particles is
sufficient to generate considerably greater force being imparted to the metal
than is required to create platelets on the surface and as a consequence, a
work hardened zone formed, and steady state erosion begins.Particle kinetic
energy, responsible for extrusion-forging process during plastic deformation,
is given as [1–3] (3)E1=12πdp36ρp⁢V2sin⁡2β=π12ρpdp3⁢V2sin⁡2β, where dp and ρp are the particle diameter and
density, respectively, and V and β are the
particle incident velocity and angle, respectively. The final expression for
the erosion rate, due to plastic deformation, εp, is [1–3] (4)εp=mmp=Kpρmρp3/2dp3⁢V3sin⁡3βHV3/2(ρpπdp3⁢/6)=K2ρmρp1/2⁢V3sin⁡3βHV3/2, where K2 is a constant [1–3].


### 2.3. Overall Erosion Rate

It is difficult to predict
accurately the proportions contributed by each of the two mechanisms to the
overall material loss. However, the overall erosion rate, combining the cutting
and plastic deformation wear mechanisms, may be then given by the following
equation [1–3]: (5)ε=K3ρmρp1/2⁢V3sin⁡3βσy3/2, where K3 is a constant
pertaining to erosion modelling of ductile metal surfaces impacted by fly ash.


### 2.4. Model for Erosion-Oxidation Interaction

Material removal from
a brittle oxide surface on a ductile substrate at high temperature is due to a
composite mechanism, involving fracture, chipping, oxide spallation at the
metal-oxide interface, cutting wear, and plastic deformation of metal
substrate. Following the general oxidation law, the thickness of the oxide
layer``δ" formed during time ``θ" is given as [6, 7](6)δ=Kθn, where K and n are mechanism
dependent kinetic parameters. K generally being related to temperature, through Arrhenius relationship: (7)K=Ae(−Q/RT), where A is an experimentally determined Arrhenius constant
(preexponential factor), Q is the
activation energy, R is the universal
gas constant, and T is the absolute
temperature.Erosion can be
described as a stochastic phenomenon. In the spatial domain, individual erosion
events take place in a random manner. It is assumed that the instantaneous
number of events on the entire surface can increase deterministically as a
linear function of time.  The average
oxide-scale thickness,〈δ〉, under the influence of erosion, is given by the
following dimensionless equation [6, 7]: (8)〈δ〉=nK(Fπσ2)nγ(n,Fπσ2θ), where Fπσ2θ          represents dimensionless time, F is the average dimensional flux of impinging erodent, and σ is the radius of erosion footprint. ``γ" is the incomplete gamma function and is
given by [6, 7] (9)γ(ξ,x)=∫0xuξ−1⁢exp⁡(−u)du. The following mass loss equation
is derived from the above equation to quantify the erosion under the influence
of oxidation: (10)ΔM(θ)=(1−fm)ρ0〈δ〉−fmFπσ2ρ0∫0θ〈δ〉dθ, where ΔM(θ), fm, and ρ0 are total erosion loss, mass fraction of oxide associated
with the steel/alloy, and densities of individual oxides (NiO, Fe2O3,
and Cr2O3), respectively.


## 2.1. Mechanism of Cutting Wear

An ash particle,
that strikes the surface at an acute angle and at a velocity greater than the
critical velocity needed for the penetration of the material’s surface, removes
some material in a process similar to the cutting action of a machine tool
(micromachining action). At the impact location, the particle loses a fraction
of its kinetic energy to the target material in the form of heat and energy for
deformation of the surface. When the shear strain exceeds the elastic strain
limit of the target material,
the particle penetrates the surface of the
material and ploughs along the surface, removing material.In the case of cutting wear, the
material's resistance to deformation needs to be overcome by the impacting
particles to penetrate the surface of the material. The differential equation of
motion for the depth of penetration is given as [1–3] (1)mpd2Ldt2=−πdp2Lcσy, where L is the depth of
penetration, mp is the mass of the particle, dp is the diameter of the particle, t is the time, σy is the yield stress of the target material, and c is a particle shape factor.
For sphere particles, shape factor is equal to 3.The erosion rate due to cutting
wearεc, defined as the ratio of the mass of the material eroded (m), from the
target surface to mass of the impacting particle (mp), is
given by the following equation [1–3]: (2)εc=mmp=kcρmρp3/2dp3v3sin3β33σy3/2(πρp(dp3/6))=k1ρmρp1/2v3sin3βσy3/2, where V and β are the impacting velocity and angle of the particle,
respectively. ρm and ρp are the densities of the
target material, and the particle Kc and K1 are constants [1–3].


## 2.2. Mechanism of Plastic Deformation Wear

During particle
impact, the loss of material from an eroding surface may occur as a consequence
of a composite sequential mechanism similar to a combined process of
extrusion-forging mechanism. The extruded platelets from shallow craters made
by the impacting particle are further forged into a strained condition. Because
of the high-strain rates, adiabatic shear heating occurs in the surface region
immediate to the impact site. The kinetic energy of the impacting particles is
sufficient to generate considerably greater force being imparted to the metal
than is required to create platelets on the surface and as a consequence, a
work hardened zone formed, and steady state erosion begins.Particle kinetic
energy, responsible for extrusion-forging process during plastic deformation,
is given as [1–3] (3)E1=12πdp36ρp⁢V2sin⁡2β=π12ρpdp3⁢V2sin⁡2β, where dp and ρp are the particle diameter and
density, respectively, and V and β are the
particle incident velocity and angle, respectively. The final expression for
the erosion rate, due to plastic deformation, εp, is [1–3] (4)εp=mmp=Kpρmρp3/2dp3⁢V3sin⁡3βHV3/2(ρpπdp3⁢/6)=K2ρmρp1/2⁢V3sin⁡3βHV3/2, where K2 is a constant [1–3].


## 2.3. Overall Erosion Rate

It is difficult to predict
accurately the proportions contributed by each of the two mechanisms to the
overall material loss. However, the overall erosion rate, combining the cutting
and plastic deformation wear mechanisms, may be then given by the following
equation [1–3]: (5)ε=K3ρmρp1/2⁢V3sin⁡3βσy3/2, where K3 is a constant
pertaining to erosion modelling of ductile metal surfaces impacted by fly ash.


## 2.4. Model for Erosion-Oxidation Interaction

Material removal from
a brittle oxide surface on a ductile substrate at high temperature is due to a
composite mechanism, involving fracture, chipping, oxide spallation at the
metal-oxide interface, cutting wear, and plastic deformation of metal
substrate. Following the general oxidation law, the thickness of the oxide
layer``δ" formed during time ``θ" is given as [6, 7](6)δ=Kθn, where K and n are mechanism
dependent kinetic parameters. K generally being related to temperature, through Arrhenius relationship: (7)K=Ae(−Q/RT), where A is an experimentally determined Arrhenius constant
(preexponential factor), Q is the
activation energy, R is the universal
gas constant, and T is the absolute
temperature.Erosion can be
described as a stochastic phenomenon. In the spatial domain, individual erosion
events take place in a random manner. It is assumed that the instantaneous
number of events on the entire surface can increase deterministically as a
linear function of time.  The average
oxide-scale thickness,〈δ〉, under the influence of erosion, is given by the
following dimensionless equation [6, 7]: (8)〈δ〉=nK(Fπσ2)nγ(n,Fπσ2θ), where Fπσ2θ          represents dimensionless time, F is the average dimensional flux of impinging erodent, and σ is the radius of erosion footprint. ``γ" is the incomplete gamma function and is
given by [6, 7] (9)γ(ξ,x)=∫0xuξ−1⁢exp⁡(−u)du. The following mass loss equation
is derived from the above equation to quantify the erosion under the influence
of oxidation: (10)ΔM(θ)=(1−fm)ρ0〈δ〉−fmFπσ2ρ0∫0θ〈δ〉dθ, where ΔM(θ), fm, and ρ0 are total erosion loss, mass fraction of oxide associated
with the steel/alloy, and densities of individual oxides (NiO, Fe2O3,
and Cr2O3), respectively.


## 3. Results

The erosion rates have been
computed as function of ash particle impingement velocity, impingement angle,
percentage silica in the ash sample, average density of ash particles, density
of the steel component, yield stress of the steel component, and temperature of
the steel component. The computations have been carried out for three boiler grade steels, namely, carbon steel, 1.25
Cr-1Mo-V steel, and alloy steel 800.Some typical results of model predictions are discussed here. Figure1 depicts the erosion rate (mg/kg of erodent) as a function of impact velocity
for a given impingement angle of 30° and at room temperature for
1.25Cr-1Mo-V steel. The simulated result is validated with the published
literature [1, 2] and is found to be in good agreement.  Figure 2 shows the erosion rate as a function
of impingement angle for carbon steel at different temperatures of the
substrate, that is, 303, 573, and 873 K, respectively. The prediction of
temperature dependent erosion is also validated with the published data [1, 2].
It is observed that for low values of impingement angle, the erosion rate
increases with an increase in the impingement angle, and the maximum erosion rate
occurs with impingement angle between 20°–40°. Thereafter,
the erosion rate decreases. This has also been validated with the published
data. The erosion rate with variation of impact velocity for the three steels
is shown in Figure 3, while Figure 4 shows the change in erosion behavior with
change in the temperature of the substrate. It is observed that 1.25 Cr-1Mo-V
steel shows least erosion rate (or maximum erosion resistance), whereas the
alloy steel 800 has the maximum erosion rate (or least erosion resistance). Figure 5 shows the erosion behavior with respect to
silica content of 55% and 70% in the ash. It is seen that an increase of 15%
silica in the ash results in 2–3 times enhancement in the erosion rate. A mass loss graph is shown in Figure 6 depicting
dimensionless mass change as a function of dimensionless time. Erosion losses
of three different oxides, namely, chromium, iron, and nickel oxides for alloy
steel 800 are shown under solid particles impact. The quantitative mass loss
prediction is verified with the published data [6, 7].Figure 1
Variation of erosion rate with impingement velocity for 1.25 Cr-1Mo-V Steel (impingement angle = 30° and at room temperature).Figure 2
Variation of erosion rate with impingement angle for Carbon steel (room temperature, and elevated temperatures 573 K and 873 K).Figure 3
Variation of erosion rate with impingement velocity for different grades of steel (room temperature and impingement angle = 30°).Figure 4
Variation of erosion rate with temperature for different grades of steel (impingement velocity = 20 m/s and impingement angle = 30°).Figure 5
Effect of silica content on the erosion rate for carbon steel (impingement velocity = 30 m/s, impingement angle = 30°).Figure 6
Variation of dimensionless mass change with dimensionless time for alloy 800 steel for different oxides.


## 4. Conclusion

A mathematical model has been developed to
predict the erosion rate for fly ash particles impingement on typical boiler
grade steels. Stochastic approach is employed to model erosion-oxidation interaction
phenomena. The following conclusions are drawn:(i)
erosion
rate increases monotonically with an increase in impact velocity for a given
impingement angle and temperature of the substrate;(ii)
erosion
rate is maximum for impact angles in the range of 20°–40° for
a given velocity and temperature;(iii)
the
erosion rate is significantly enhanced with an increase in silica content of
the ash;(vi)
erosion
rate of nickel oxide is faster with regard to iron and chromium oxides, which
is attributed to the relatively faster growth of nickel oxide with respect to
other oxides.



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*Source: 542161-2008-04-30.xml*