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Environmental Damage at High Temperature
25 Environmental Damage at High Temperature Most engineering materials may be subject to damage when they are exposed to corrosive environments. Since both chemical reaction and diffusion are ac celerated as temperature increases, the environmental damage of the materials at high temperature is expected to be more significant than that at ambient temperature. Oxidation of materials is the most common environmental damage. Most heat resistant alloys oxidize in air or other oxidizing atmosphere, leading to damage as described in Chapter 21. Some components of the gas turbine are exposed to a special atmosphere. The salt N a S 0 produced during combus tion of the fuel deposits on the surface of the components to form a molten salt film. The protective oxide scale, for example NiO or C r 0 scale on the sur face of the superalloys, can be dissolved into the molten salt film. Thus oxi dation of the alloys is accelerated due to loss of the protective oxide scale. This type of oxidation is referred to as hot corrosion. Some components of the petrochemical plants, for example ethylene dissociation tubes, may be subject to so-called carburization damage. The hydrocarbons that are the raw materi als of the petrochemical process decompose at high temperature and the re sultant elemental carbon penetrates into the alloy to form a carburized layer. The carburization results in expansion of the carburized layer and the addition al tensile stress produced in the non-carburized region of the tube leads to de crease in the creep fracture life. In nuclear power plants, some components are subject to irradiation of the energetic particles. T h e irradiation leads to in crease of vacancies in the metals and, consequently, to increase of diffusivity of the metals. Since creep rate and creep damage evolution (cavity growth) depend on diffusivity of the metals, the irradiation would decrease creep life of the components. 2
4
2
3
In this Chapter we introduce briefly the fundamentals of oxidation, hot corrosion and carburization.
25.1
Oxidation
When a metal is exposed to air or other oxidizing atmosphere, oxygen in the atmosphere reacts with the metal to form an oxide film If the surface film is compact and perfectly adherent the surface film does not affect the strength of the material significantly. Contrarily if the film is porous and easy to spall off 330
25
Environmental Damage at High Temperature
331
the surface, the surface layer loses the loading capacity, leading to damage as described in Chapter 21.
25. 1. 1 Thermodynamics of Oxidation T h e oxidation reaction of a metal Μ is expressed as ;tM+0 =]VL0 (25.1) The standard free energy change of the reaction (or standard free energy of formation of the oxide) AG must be negative in order for the reaction to pro ceed from the left to the right. A plot of AG versus absolute temperature Γ approximates a straight line. A number of such plots for various oxidation re actions in standard state (Pa, = 1 ) , as shown in Fig. 2 5 . 1 , show the relative thermodynamic stability of the oxides. T h e lower on the diagram, the more negative the standard free energy of formation and the more stable the oxide. When the reaction is in equilibrium, the free energy change equals to zero, i. e. 2
2
0
0
0
AG = AG + RT\nK = 0 (25.2) where K is the equilibrium constant of the reaction, R is the gas constant, and Τ is absolute temperature. Because activities of pure solids are defined as unity at all temperatures and pressures, Eq. (25. 2) becomes AG = - PTlnKp = Ρ Ώ η Ρ (25. 3) where PQ_ is the partial pressure of oxygen in the reaction system in equilibri um, or dissociation pressure of the oxide. T h e dissociation pressure of an ox ide at any temperature can be found from the nomogram scales shown in Fig. 2 5 . 1 . Consider oxidation of copper (or dissociation of copper oxide) at 900°C. Extending a line from point Ο on the left scale through the free energy line at 900°C for copper to the scale at the right marked Pq, shows that the dissociation pressure of C u 0 is about 1 0 atmospheres. Any oxygen partial pressure above this value will oxidize pure copper and any below it will reduce copper oxide to pure copper at 900°C. Similar prediction can be made for the atmospheres resulting from mixtures of H / H O and C O / C 0 in Fig 2 5 . 1 . p
p
0
( ) >
- 8
2
2
25. 1. 2
z
2
Kinetics of Oxidation
Oxidation of any metals is composed of two sequential processes · the diffusion of metal ions (or oxygen ions) through the oxide film and the oxidation reac tion at the interface (metal/oxide interface or oxide/atmosphere interface). T h e oxidation rate is controlled by the slower process. T h u s many metals and alloys follow either the parabolic or the linear rate law depending on the con trolling process. T h e weight gain at any time during oxidation is proportional to the oxide film thickness and is commonly measured continuously with time to obtain the kinetic law. Figure 25. 2 shows schematically the two kinetic laws. Note that the weight gain measurements are valid only for the case that the oxide does not evaporate or spall off the surface during oxidation.
332
High Temperature Deformation and Fracture of Materials FVHa
0
IO
-8
7
IO"
Iff*
10''
1
IO"
1
a
25. 1 Relation between free energy and temperature for oxidation of m e t a l s ' .
25.1. 2.1
Parabolic Rate Law
When the oxide layer is compact and perfectly adherent the oxidation rate is
25
Environmental Damage at High Temperature
333
<
25.2
Schematic illustration of kinetic laws for metal oxidation.
controlled by diffusion of ions through the oxide layer. For steady state diffu sion the concentrations of the reactant ion at the oxide/metal and oxide/gas interfaces may be assumed to be constant. F i c k ' s first law states that the steady state flux of reacting ions is proportional to Ac/x, where Ac is the difference in the concentrations across the oxide thickness x. T h u s the flux of ions is proportional to the rate of scale thickening, so that; (25.4) where β is a proportionality constant. Integration of Eq. (25. 4) yields (25. 5) where k = BDAc is known as the parabolic rate constant. T h e weight gain AW is proportional to the thickness and therefore can be substituted for χ in Eq. (25. 5 ) . T h u s a plot of (AW) versus time will be linear if the parabolic rate law is obeyed. An example is shown in Fig. 25. 3. Since the parabolic rate constant k = BDAc is proportional to diffusion coefficient of the ions in the oxide layer, the temperature dependence of k fol lows the usual Arrhenius relationship v
2
p
v
(25. 6) where k is a constant, Q is the activation energy for oxidation, and R is the gas constant. T h u s the activation energy can be determined by plotting the logarithm of k versus the reciprocal of temperature, 1 / T as shown in Fig. 25. 3 ( c ) . 0
p
2 5 . 1 . 2. 2
Linear Rate Law
When the oxidation rate is controlled by the reaction at the metal/oxide or ox ide/ gas interfaces the oxide film thickness is proportional to time. T h e linear law is observed in two cases: T h e oxide film is porous and non-protective and oxygen easily passes
334
High Temperature Deformation and Fracture of Materials
1/7710-Ί<.-' (c) 2
25. 3 Oxidation kinetics of pure iron. ( a ) A W versus f, (b)(AW)
( c ) the logarithm of k versus the reciprocal of temperature, 1 / T p
versus r and C 3 ]
.
through the film and arrives at the metal/oxide interface. And the oxidizing power of the atmosphere is relatively low, such as with low oxygen pressure in partial vacuum, in air diluted with inert gas, or in the mixture of CO and C 0 . Strongly oxidizing conditions generally form thick protective scales which result in the parabolic rate law. Kinetics can change during oxidation of a metal. In early stage of oxida tion the film thickness may be sufficiently low to allow linear kinetics. As the 2
25
Environmental Damage at High Temperature
335
film thickens a transition to parabolic kinetics is often observed. Conversely, microcracking and porosity may develop as the film thickens, reducing the protectiveness of the oxide. The parabolic law then fails and the kinetics ap proaches linearity at some time after the start of oxidation.
25.1.3
Oxidation of Alloys
Most engineering alloys for high temperature service belong to the Fe-Ni-Cr system and chromium is added to increase the oxidation resistance of the al loys. Fig. 25. 4 shows the effects of increasing Cr content on the oxidation rate and on the oxide morphology for Fe-Cr alloys oxidized at 1000°C. The oxida tion rate decreases rapidly and the amount of chromium oxides increases as chromium is increased to 2 0 % . In the alloys containing less than 1 6 % chromi um Fe-Cr oxides are formed and in the alloys with chromium more than 20 % a single chromium oxide is formed. T h e chromium content necessary for the formation of single C r 0 decreases with decreasing temperature and for this reason, martensite stainless steels ( 1 3 % C r ) and austenite stainless steels ( 1 8 % C r ) are acceptable in many applications at 500 — 700°C. Nickel is itself an oxidation resistant metal. Nickel in conjunction with chromium improves significantly high temperature oxidation resistance of the stainless steels. Silicon forms compact and adherent oxide films either alone or in conjunc tion with chromium However, its presence degrades creep resistance thereby silicon is added at 2 to 3 % levels to many superalloys and stainless steels. Aluminum forms protective oxide film at relatively low temperatures and increases oxidation resistance of Ni-based and Fe-based alloys. Aluminum also forms / - N i A l phase that increase significantly creep resistance of Ni-based superalloys. However, aluminum oxide does not form fast enough to repair mechanical damage during oxidation. In brief, chromium is the most important alloying element for oxidation resistance. Chromium not only increases oxidation resistance but also im proves the strength of the alloys through solid solution strengthening. Silicon and aluminum are also favorable for oxidation resistance, but they degrade the mechanical properties of the alloys and addition of these in engineering alloys is limited to a few percent. In a given environmental condition (temperature and atmosphere) selec tive oxidation takes place in multi-component alloys depending on the thermo dynamics and the kinetics of the oxidation reactions of the alloying elements. From thermodynamics point of view, the more negative the formation energy of a metal oxide, the more favorable the oxidation of the metal. From kinetics point of view, however, the rate of a chemical reaction depends on the concen trations of the reactants and the higher the content of a metal in an alloy, the more favorable the oxidation of the metal. Which metal oxidizes preferentially in an alloy depends on the coupling effect of the thermodynamics and the ki netics. For example, in the Fe-Cr alloy system C r 0 has a more negative for2
3
3
2
3
336
High Temperature Deformation and Fracture of Materials
mation energy, but the iron oxides are formed preferentially in the alloys con taining relatively low chromium content. T h e amounts of chromium oxides in crease with the increase of chromium content until single C r 0 forms, as shown in Fig. 25. 4. 2
25.1.4
3
Internal Oxidation
Under appropriate conditions oxygen in the atmosphere may dissolve in alloys, diffuse inward and cause precipitation of the oxide particles. A typical mor phology of internal oxidation is shown in Fig. 25. 5. Internal oxidations either occur alone or together with external oxidation
25
Environmental Damage at High Temperature
337
25. 5 Typical morphology of internal oxidation ^ . 1
depending on alloys and environments. Internal oxidation of an alloy includes following processes. 1) Oxygen in the atmosphere dissolves into the surface layer of the alloy, i. e. yO
-
z
[ 0 ]
M
(25. 7)
where [ 0 ] M represents elemental oxygen dissolved into the alloy. If the equi librium constant of the reaction is K j , then [ 0 ] = K. · Pb? (25. 8) 2) T h e oxygen dissolved into the alloy reacts with solute Β (oxidizing metal) to form oxide particles. [B] + u[0] -*BO„ (25.9) 3) Oxygen diffuses inward and the above two processes proceed continu ously leading to inward growth of the internal oxidation layer. T h e conditions under which internal oxidation in an alloy can occur are (1) oxygen has certain solubility in the alloy and ( 2 ) diffusion of oxygen in the alloy is faster than that of solute B. Otherwise external oxidation occurs. Generally, the diffusion rate is lower than the chemical reaction rate and the diffusion of solute Β and/or oxygen controls the internal oxidation. T h u s internal oxidation often follows parabolic rate law, i. e. x = kt (25.10) where χ is the thickness of the internal oxidation layer and k is the rate con stant. For the case that the diffusion of solute Β is so slow that it can be ig nored, the rate constant k is proportional to the diffusion coefficient of oxygen D , the kinetics in this case becomes M
M
M
2
0
338
High Temperature Deformation and Fracture of Materials
S)
where No is atomic fraction of oxygen in the surface layer of the alloy and N is atomic fraction of solute Β in the alloy. For the case that both oxygen and solute Β diffuse, the kinetic equation is given by m
B
χ = 2/(D i)
1 / 2
(25.12)
0
where γ is a dimensionless parameter that is a complex function of concentra tions and diffusivities of oxygen and solute B. This parameter can be ex pressed in two limited cases. When No* D > No" D , i. e. the diffusion of oxygen predominates, 0
.
'
TvriS)
B
,
l/z
I ^ W ) V2xrJV
(25.13)
B
N D m
Substituting Eq. ( 2 5 . 1 3 ) into Eq. ( 2 5 . 1 2 ) gives Eq. ( 2 5 . 1 1 ) . When S > N i f D , i. e. the diffusion of solute Β predominates,
B
B
0
2vN where θ= D /D . Substituting eq. ( 2 5 . 1 4 ) into eq. ( 2 5 . 1 2 ) gives _ ( π # ν ) " Ni? ν N ' Equation ( 2 5 . 1 5 ) shows that the rate of internal oxidation depends on the concentrations and diffusivities of oxygen and solute B. B
Q
B
2
x
W
B
25.2
Hot Corrosion
The alloys employed in the hot section of gas turbine engines are frequently subject to a corrosion induced by liquid N a S 0 film deposited on the surface of the alloys. T h e N a S 0 film results from the salt injected into the engines and sulfur from the combustion of the fuel. A typical example of the corrosion is shown in Fig. 25. 6 where the results of the oxidation experiments of a Nibase superalloy BT900 in air at 1000°C with and without a coating of N a S 0 film are given - - . T h e oxidation rate of the alloy is greatly accelerated by the coating of N a S 0 f i l m . This mode of attack is called hot corrosion - - . 2
2
4
4
2
4
1 6 1
1
2
68
1
4
Metallographic observations of hot corroded alloys often showed sulfides of Ni and C r , so the mechanism was initially called sulfidation. However later studies showed that the main products of hot corrosion were the same as that of oxidation of the uncoated alloys in the same atmosphere. It is well known now that the nature of hot corrosion is an accelerated oxidation. In dry air a compact and protective NiO scale is formed on the superalloy B-1900, but a dispersion of fine NiO particles are observed in the salt film This observa tion indicates that the protective oxide scale on the surface of the material dis solves at the oxide/salt interface but reprecipitates as non-protective particles within the salt film, and oxidation greatly accelerates due to loss of the pro tective scale. [6_11]
25
Environmental Damage at High Temperature
339
r/h 25. 6 Comparison of the oxidation behavior of the superalloy B-1900 with and without a coating of NaiSCUilrn™ .
25. 2. 1 Basic Fluxing Mechanism High temperature (type I) hot corrosion is observed in the temperature range about 825-950°C when the condensed salt film becomes liquid (melting point of pure N a S 0 is 884°C). T h e base-acid character of liquid N a S 0 c a n be described by the equilibrium SOT = S 0 + O " (25.16) where O can be considered as the basic component and S 0 the acidic compo nent. Since the solubility of oxygen in the molten salt is very low the oxygen necessary for fast oxidation of metallic substrate is acquired from the salt by reaction 2
4
2
4
2
3
2 -
3
S0
3
= SO +-|-0 z
(25.17)
2
Combining reactions (25. 16) and (25. 17) gives SOT = S 0 + Cf~ + y 0 2
2
(25.18)
T h e metallic substrate oxidizes, for example Ni-f--|-0
2
= NiO
(25.19)
This reaction consumes oxygen in the salt. As a result, reaction (25. 18) pro ceeds and the activity of oxide ion in the salt increases. When the activity of the oxide ion increases to a certain value, the metal oxide dissolves into the salt film through the following reaction
340
High Temperature Deformation and Fracture of Materials 2
NiO + O - = N i O t (25.20) This type of dissolution of protective oxides is called basic fluxing mechanism. Rapp and Goto proposed "negative solubility gradient" as a general cri terion for continuing hot corrosion attack. Figure 25. 7 shows a schematic drawing of this fluxing mechanism. At the oxide/salt interface, the solubility of metal oxides (or activity of the oxide ion) is locally high and the metal ox ides dissolve into the salt through reaction (25. 20). Then NiOf diffuses to ward the oxide/gas interface and precipitates as oxide particles because of lo cally low solubility of the oxides at the salt/gas interface. [12]
-
Gas phase 0 ,S0 ,SO,
Metal
2
2
Locally low MO solubility Locally high (acidic or basic) solubility for MO 25. 7 Schematic illustration of reprecipitation of porous oxides supported by a negative solubility gradient in the molten salt film
25. 2. 2
[ , 2 ]
.
Acidic Fluxing
Heat resistant alloys normally contain the alloying elements tungsten, molyb denum and vanadium. The oxides of these elements have the tendency to com bine with oxide ions in the molten salt to form tungstate, molybdate and vana date ions. 2
2
M0O3+ 0 " = M o 0 -
Ψ0 +σ=ψσ<3
(25.21)
25
Environmental Damage at High Temperature
341
V O + O -=2VQr These reactions consume the oxide ions in the salt leading to increase in acidity of the salt. As a consequence, the acidic fluxing of the protective oxide takes place, for example NiO= N i + Ο " (25.22) Al203=2Ai3++3Cr (25.23) The products of the reactions, N i , A l , M o O T , W O i " and VO3" , diffuse toward the salt/gas interface. T h e oxides W 0 , M o 0 and V 0 exhibit high vapor pressures, thereby leading to evaporation from the salt/gas interface. T h e resulting gradient in acidic solute concentration across the salt film is ide al to promote the acidic fluxing and reprecipitation of oxides NiO and/or A1 0 . When the partial pressure of S 0 in the gas phase is relatively high, fol lowing reaction takes place SO + S 0 = S z O t (25.24) T h e pyrosulfate ^ 0?~ reacts with the metal oxide by M O + SzCT = M S 0 + SOT (25. 25) This is another type of acidic fluxing mechanism. Chromium is an effective alloying element to combat hot corrosioa The reason is that the basic dissolution of C r 0 depends on oxygen pressure, 2
2
s
2 +
2 +
2
3 +
3
2
3
2
5
3
3
2
3
4
2
C r 0 + 20*- + - | θ 2
3
3
2
= 2CrOT
(25. 26)
Because hexavalent Cr is formed from trivalent Cr in the basic dissolution ac cording to reaction (25. 26) , the basic solubility of C r 0 depends on the local value of oxygen partial pressure. Since any thin salt film supporting hot corro sion will be more reducing (low value of Pq,) at the oxide/salt interface than that at the salt/gas interface, the chromate solute will necessarily experience a positive gradient and therefore not be subject to reprecipitation in the film. Finally we need to consider the role of metal sulfidation in hot corrosioa Geobel and P e t t i t observed both the formation of NiS beneath the NiO scale and the precipitation of non-protective NiO particles within the salt film. They interpreted this phenomenon in terms of the reactions: 4Ni-r-SOr = S N i O + N i S - r - O (25.27) 2
3
[6]
2
2
2NiO + 0 ^ + y 0
+
2
= 2Na +2Ni02"
(25. 28)
According to reaction (25. 27) the formation of NiS causes a local increase in the basicity of the salt film since O is a reaction product. This local increase in melt basicity would affect the dissolution of the NiO scale (reaction ( 2 4 . 2 8 ) ) by forming the basic solute Ni0 ~ which reprecipitates in the salt film as non-protective NiO particles. This indicates that sulfidation affects the salt film chemistry and contributes to basic fluxing mechanism. 2 -
2
342
25.3
High Temperature Deformation and Fracture of Materials
Carburization
Carburization is observed in industrial processes where Fe-Cr-Ni alloys are ap plied in a carbonaceous atmosphere at high temperature. Carbon is trans ferred from the atmosphere into the metal matrix, diffuses inward and causes precipitation of the carbides. Carburization is a corrosion problem mainly for cracking tubes in ethylene production, but also for components of other pet rochemical plants, for example reformer tubes in steam reforming of natural gas. The dissociation of hydrocarbons is conducted by passing naphtha-steam mixture through the cracking tubes at a temperature between 900-1100°C. During operation at high temperature, carbon penetrates in to the inner wall of the tubes and precipitates in the form of carbides M ^ Q and M 7 C 3 . Precipi tation of carbides strongly affects the properties of the materials leading to significant reduction of the service life of the dissociation tubes. Many qualitative studies have been made on the carburization process and its effects on the properties of the materials - " ' . Some numerical studies on the reaction-diffusion process and the material damage evolution during carbu rization are also made in recent decades - " - . In this section we introduce briefly these numerical studies. 1
1
17
13
22
16 1
1
25. 3. 1 Thermodynamics of Carburization The state-of-art materials are cast heat-resistant steels HK40 (25Cr-20Ni) and H P (25Cr-35Ni). Because of high Cr content, the solubility of carbon in the austenite matrix of the steels is very low and therefore carbides M Q and M7C3 precipitate during carburization. Precipitation of carbides reduces Cr content and consequently increases the carbon solubility in the matrix. There fore, it is a coupled reaction-diffusion process. 23
At a lower carbon concentration the carbide M Q is formed at first. T h e precipitated M ^ Q is later converted to M y Q and, when carbon concentration increases, M r Q precipitates directly. In order to determine the concentration of carbon in the matrix and the concentration of carbides, following reactions are considered. For carbide M ^ Q (CrieFeyCs - ) 23
17
1
(25.29)
16Cr + 7Fe + 6C = Cr Fe Q T h e equilibrium constant K of the reaction is then 16
7
pl
(25. 30) where / > ? F e and y are the activity coefficients of C r , Fe and C in the austen ite matrix, respectively, and N ,N and N are the atomic fractions of C r , Fe and C in the matrix, respectively. T h e solubility of M Q ; in the matrix is obtained from eq. (25. 30) as &
c
Ct
Fe
c
23
25
Environmental Damage at High Temperature
~ Kg · NI/> · jv ^ is the solubility parameter of M ^ Q , and it is given by N c i
where K
S1
7
K p l
6
/ c
N£ • N g • Ni. = * *^ *^ For the carbide M7C3CCr3.5Fe3.5C3[17]) the formation reaction is 7 C r + 7 F e + 6 C = 2Cr3.5Fe3.5C3 The solubility of M7C3 is then K s i
=
N
where K
ffi
a
=
w
(
2
343
5
(25
·
3
1
)
3 2 )
·
(25.33)
3/3
(25
Kg · Nh · Νψ is the solubility parameter of Μ 0 ) and it is given by
3 4 )
·
7
K
=
K
Λ
f c
(25
3 5 )
* Nh' . Nfc' • NI = * ' ' ' ' · The equilibrium constants K i and K^ can be determined from the Gibbs free energy of formation of the carbides using the following relation AG = — K T l n K p (25.36) T h u s , if we know the values of AG and the activity coefficients of Cr, Fe and C in the matrix, then the solubility of the carbides M^Ce and M7C3 can be de termined by eqs. (25. 31) and (25. 34). p
0
0
25.3. 2
Kinetics of Carburization
Carburization is an internal corrosion phenomenon and the kinetics of carburi zation is expected to follow the parabolic rate law in the same way as internal oxidation described in section 25. 1. 4. Figure 25. 8 shows the experimental re sults of pack carburization tests of HK40 and H P steels at 1000°C . T h e weight gain follows a parabolic rate law and the following expression is ap plied. [20]
2
W = Kt (25. 37) where W is weight gain of the specimen and k is a constant. T h e parabolic rate law indicates that the carburization of HK40 steel is controlled by the dif fusion of carbon. c
25. 3. 3
Numerical Simulation of Carburization
T h e model that calculates the reaction diffusion of carbon in a high Cr-Ni steel is based on F i c k ' s second law of diffusioa T h e calculation is divided into two parts: (1) a finite difference calculation for the diffusion of carbon, using fi nite space and time increments; and ( 2 ) calculation for the formation of car bides. If diffusion coefficient D is assumed to be independent of carbon content and the diffusion is considered in one dimension in space ( χ ) , the F i c k ' s sec ond law is given by
+
+
§7 = ° ( 0 & 0 Κ ^ -
ί )
( 2 5
·
3 8 )
344
High Temperature Deformation and Fracture of Materials
0.012
-
0.010 /
1273K HK40
0.008
/
0.006
0.004 1 10
1
I
1 20
. 30
40 Time/h
50
1 , 60
1
. 70
80
0.0060
0.0050 -
0.0055 h
ifc
1273K HP
0.0040
0.0035 1 20
1 30
1 40
1 50
1 60
Time/h 25. 8 weight gain as a function of carburization time at 1000t) for HK40 ( a ) and HP ( b ) steel™ .
where Z = 0 for a plane, Z = l for a cylinder, and Z=2 for a sphere. For the boundary condition, the diffusion flux of carbon through the surface of the specimen follows F i c k ' s first law of diffusion ]=-Όψ
(25.39) dx
where J is the diffusion flux of carbon. It is evident that the diffusion flux of carbon through the surface of the specimen is equal to the amount of carbon penetrating into the specimen per surface area (weight gain per surface area W) in a unit time. In the present case, W is obtained by a series of pack carbu rization tests of HK40 steel at 1000°C for the plane specimens as shown in Fig. 25. 8 ( a ) . The overall carburization is a reaction-diffusion process of carbon. The
25
Environmental Damage at High Temperature
345
carbon in the steel consists of two p a r t s the carbon in the matrix of the steel and that in the carbides. Only the carbon in the matrix can diffuse further. At any point in the steel considered by the finite difference method, the carbides M C and/or M C precipitate when the total amount of carbon is higher than Nc] ( M C ) and/or N c ( M C ) . Certain amounts of chromium and iron are also removed from the matrix, so Nci and/or N c change with the carbide pre cipitation or with time. During the carburization process, the carbide M C precipitates first with increasing the concentration of carbon in the steel. When the concentration at a point reaches N ( M 7 C 3 ) , the transformation of carbide M C into M C takes place. T h e carbide M Q precipitates directly after all of the M Q changes to M C . Therefore, there exist three precipita tion zones in the steel: zone of M C ; zone of coexisting M C and M Q ; and zone of M C . :
23
6
7
2 3
3
6
2
7
3
2
2 3
6
cl
23
6
7
3
7
23
7
3
23
7
6
23
6
7
3
Using the model of reaction-diffusion in high Cr-Ni austenitic steels dur ing carburization process stated above, the diffusion of carbon and the precipi tation of carbides during carburization of HK40 steel at 1000°C are numerical ly simulated by means of finite difference computation techniques. Figures 25. 9 show the calculated total content of carbon (solid lines) as a function of the penetration depth for a plane specimen after carburization at 1000°C for 75h. T h e profile of the carbon content exhibits a zone with abrupt decrease in the concentration of carbon where M C and M Cj coexist. T h e measured car bon concentrations are also plotted in the figure (data points). It is found that there is a reasonable agreement between the two results. 23
6
7
3.0 Γ
ΟΟ
MA
"- r J
0
0.2
0.4
0.6
I
L
08
1.0
1.2
1.4
1.6
Distance from surface/mm 25. 9 The calculated (solid lines) and the measured (data points) to tal content of carbon as a function of the penetration depth for a plane ,9]
specimen after carburization at 1000t! for 7 5 h f .
25.3.4
Carburization Damage
As mentioned above, the carburization strongly affects the properties of the
346
High Temperature Deformation and Fracture of Materials
materials. The carburization deteriorates the ductility and toughness of the materials, especially the low temperature properties. T h e effects of the car burization on the high temperature properties are less serious; the tensile and creep strengths are improved and the ductility does not decrease markedly . The most important effect of the carburization is the change of stress field within the materials. The expansion of the carburized zone leads to additional tensile stress within the uncarburized zone. The thermal expansion coefficient decreases due to carburization, giving rise to additional thermal stress when the tubes are heated up and/or cooled d o w a These additional stresses accel erate the creep damage evolution and consequently reduce the service life of the materials. [ 2 3 ]
We have developed a finite element program to calculate numerically the stress field and the creep damage evolution during carburization. The expan sion due to carburization is similar to thermal expansion and we can analyze carburization stress by means of determining thermal tress. To do this, we define the so-called carburization expansion coefficient αν as the normal strain caused by increase in carbon concentration by 1%. The volume expansion co efficient is then a = 3ai , as in thermal expansion. The value of αν is obtained from correlation between density and carbon concentration of the material. Experimental result of the relation is shown in Fig. 25. 1 0 . vc
c
[22]
1.0 1.5 2.0 Carbon centent,wt% 25. 10 Correlation between density and carbon concentration of the m a t e r i a l ^ .
A finite element model has been developed in which carbon concentration and temperature distributions on the cross section of the tubes are incorporat ed. The evolution of the stress field during high temperature service is calcu lated numerically. As examples of the calculation for HK40 steel, the stress distributions along the radial direction after service at 1000°C for 10,000 and 15,000 hours are shown respectively in Fig. 25. l l . Creep damage evolution at a point is calculated using the life fraction rule [ z o ]
25
Environmental Damage at High Temperature
347
50
ο h a
-50
ss
-100
h
9?>
-150
lOOOOh 15000h
-200 _L
-250 4
10
6
Distance from inner wall d/mm 25. 11 Stress distributions in HK40 steel along radial direction after service at lOOOt) for 10,000 and 15,000 hours™.
D = Υ)
(25. 40)
where t/is a time increment of the finite element model, ijyis the creep rupture life of the material at the mean stress and temperature within the time incre ment. It is assumed that when the damage parameter D at a point reaches uni ty, a creep crack is formed at the point. Using this method we can predict the creep crack growth process in the tube wall.
References 1 2
Jones D A. Principles and Prevention of Corrosion. Macmillan Pub. Com. N e w York, 1992 Gaskell D R. Introduction to Metallurgical Thermodynamics, 2 ed. , McGraw-Hill Book Company, 1983
3
Li Meiquan. High temperature corrosion of metals. Metallurgical Industry Press. Beijing, 2001 Wright I G. Metals Handbook, Vol. 1 3 Corrosion. 9™ ed. , A S M , Metals Park, O H , 1987 Liu Ruiyan. Study on corrosion behaviors of metallic materials in molten LiCl-LijO. Thesis for the Doctorate, Dalian University of Technology, 2004 Goebel J A , Pettit FS. Na2SU4-induced accelerated oxidation (hot corrosion) of Nickel. Met al. Trans. 1970, 1 ( 7 ) , 1 9 4 3 - 1 9 5 5
4 5 6 7 8 9
n d
:
Bornstein N S , Derescente MA. The role of sodium in accelerated oxidation phenomenon termed sulfidation. Met. Trans. , 1970, 2 ( 1 0 ) : 1856—1863 Goebel J A , Pettit F S , Goward GW. Mechanisms for hot corrosion of Nickel-based alloys. Metal. Trans. 1973, 4 ( 2 ) : 2 6 1 - 2 7 8
Rapp R A , Zhang YS. Hot corrosion of materials: fundamental studies. JOM. 1994, 1 2 47-55 10 Rapp R A , Zhang YS. Hot corrosion of materials- fundamental aspects. Molten Salt Forum V o l s , 1998, ( 5 - 6 ) : 2 5 - 3 8 . :
348 11 12 13
High Temperature Deformation and Fracture of Materials Rapp RA. Hot corrosion of matrials; A fluxing mechanism?. Corros. Sci. 2003, 4 4 ( 2 ) : 209—221 Rapp RA and Goto Κ S. Hot corrosion of metals by molten salts. I n Braunstein J and SelmanR. Molten Salts I, Electrohem Soc. Pennington NJ, 1981, 159—163 Rahmel A , Grabke Η J and Steinkusch W. Carburization - introductory survey. Corrosion and Mater. 1998, 4 9 ( 4 ) 221—225 Ramanarayanan Τ A , Petkovic R A , Mumford J D and Ozekcin A. Carburization of high chromium alloys. Corrosion and Mater. 1998, 4 9 ( 4 ) : 226—230 Mitchell D R G, Young D J and Kleemann W. Carburization of heat-resistant steels. Corro sion and Mater. 1998, 4 9 ( 4 ) : 231—236 Klower J and Heubner U. Carburization of nickel-base alloys and its effects on the mechani cal properties. Corrosion and Mater. 1998, 4 9 ( 4 ) : 237—245 Christ H-J. Experimental carburization and computer-based description of the carburization behavior of the austenitic stainless steel AISI 304L. Corrosion and Mater. 1998, 4 9 ( 4 ) : 258-265 :
:
14 15 16 17
18 19 20
21
22 23
Forseth S and Kostad P. Carburization of Fe-Ni-Cr steels in CH4-H2 mixtures at 850Corrosion and Mater. 1998, 4 9 ( 4 ) : 266—271 Meili Zhu, Qiang Xu, Junshan Zhang. Numerical simulation of Reaction-diffusion during carburization of HK40 steel. J. Mater. Sci. Tech. , 2003, 19 ( 4 ) : 327—330
1000r.
Zhu Mei-li, Yin You, Wang Tao, Liu Shutian and Zhang Junshan. Numerical simulation on stress and creep damage fraction in ethylene cracking tube. J. Dalian University of Technol ogy, 2001, 4 1 ( 2 ) : 192—196 Li Haiying, Qu xianyong, Zhu Meili and Zhang Junsha. Numerical simulation on creep dam age in HK40 and HP steel under carburization. Mechical Engineering Materials, 2005, 29 (11): 1 7 - 2 0 Yon You. Numerical simulation on the stress field and creep damage in ethylene cracking tube. Thesis, Dalian University of Technology, 2000 Tan Jialong. Thesis, Dalian University of Technology, 1985
4
2
3
In this Chapter we introduce briefly the fundamentals of oxidation, hot corrosion and carburization.
25.1
Oxidation
When a metal is exposed to air or other oxidizing atmosphere, oxygen in the atmosphere reacts with the metal to form an oxide film If the surface film is compact and perfectly adherent the surface film does not affect the strength of the material significantly. Contrarily if the film is porous and easy to spall off 330
25
Environmental Damage at High Temperature
331
the surface, the surface layer loses the loading capacity, leading to damage as described in Chapter 21.
25. 1. 1 Thermodynamics of Oxidation T h e oxidation reaction of a metal Μ is expressed as ;tM+0 =]VL0 (25.1) The standard free energy change of the reaction (or standard free energy of formation of the oxide) AG must be negative in order for the reaction to pro ceed from the left to the right. A plot of AG versus absolute temperature Γ approximates a straight line. A number of such plots for various oxidation re actions in standard state (Pa, = 1 ) , as shown in Fig. 2 5 . 1 , show the relative thermodynamic stability of the oxides. T h e lower on the diagram, the more negative the standard free energy of formation and the more stable the oxide. When the reaction is in equilibrium, the free energy change equals to zero, i. e. 2
2
0
0
0
AG = AG + RT\nK = 0 (25.2) where K is the equilibrium constant of the reaction, R is the gas constant, and Τ is absolute temperature. Because activities of pure solids are defined as unity at all temperatures and pressures, Eq. (25. 2) becomes AG = - PTlnKp = Ρ Ώ η Ρ (25. 3) where PQ_ is the partial pressure of oxygen in the reaction system in equilibri um, or dissociation pressure of the oxide. T h e dissociation pressure of an ox ide at any temperature can be found from the nomogram scales shown in Fig. 2 5 . 1 . Consider oxidation of copper (or dissociation of copper oxide) at 900°C. Extending a line from point Ο on the left scale through the free energy line at 900°C for copper to the scale at the right marked Pq, shows that the dissociation pressure of C u 0 is about 1 0 atmospheres. Any oxygen partial pressure above this value will oxidize pure copper and any below it will reduce copper oxide to pure copper at 900°C. Similar prediction can be made for the atmospheres resulting from mixtures of H / H O and C O / C 0 in Fig 2 5 . 1 . p
p
0
( ) >
- 8
2
2
25. 1. 2
z
2
Kinetics of Oxidation
Oxidation of any metals is composed of two sequential processes · the diffusion of metal ions (or oxygen ions) through the oxide film and the oxidation reac tion at the interface (metal/oxide interface or oxide/atmosphere interface). T h e oxidation rate is controlled by the slower process. T h u s many metals and alloys follow either the parabolic or the linear rate law depending on the con trolling process. T h e weight gain at any time during oxidation is proportional to the oxide film thickness and is commonly measured continuously with time to obtain the kinetic law. Figure 25. 2 shows schematically the two kinetic laws. Note that the weight gain measurements are valid only for the case that the oxide does not evaporate or spall off the surface during oxidation.
332
High Temperature Deformation and Fracture of Materials FVHa
0
IO
-8
7
IO"
Iff*
10''
1
IO"
1
a
25. 1 Relation between free energy and temperature for oxidation of m e t a l s ' .
25.1. 2.1
Parabolic Rate Law
When the oxide layer is compact and perfectly adherent the oxidation rate is
25
Environmental Damage at High Temperature
333
<
25.2
Schematic illustration of kinetic laws for metal oxidation.
controlled by diffusion of ions through the oxide layer. For steady state diffu sion the concentrations of the reactant ion at the oxide/metal and oxide/gas interfaces may be assumed to be constant. F i c k ' s first law states that the steady state flux of reacting ions is proportional to Ac/x, where Ac is the difference in the concentrations across the oxide thickness x. T h u s the flux of ions is proportional to the rate of scale thickening, so that; (25.4) where β is a proportionality constant. Integration of Eq. (25. 4) yields (25. 5) where k = BDAc is known as the parabolic rate constant. T h e weight gain AW is proportional to the thickness and therefore can be substituted for χ in Eq. (25. 5 ) . T h u s a plot of (AW) versus time will be linear if the parabolic rate law is obeyed. An example is shown in Fig. 25. 3. Since the parabolic rate constant k = BDAc is proportional to diffusion coefficient of the ions in the oxide layer, the temperature dependence of k fol lows the usual Arrhenius relationship v
2
p
v
(25. 6) where k is a constant, Q is the activation energy for oxidation, and R is the gas constant. T h u s the activation energy can be determined by plotting the logarithm of k versus the reciprocal of temperature, 1 / T as shown in Fig. 25. 3 ( c ) . 0
p
2 5 . 1 . 2. 2
Linear Rate Law
When the oxidation rate is controlled by the reaction at the metal/oxide or ox ide/ gas interfaces the oxide film thickness is proportional to time. T h e linear law is observed in two cases: T h e oxide film is porous and non-protective and oxygen easily passes
334
High Temperature Deformation and Fracture of Materials
1/7710-Ί<.-' (c) 2
25. 3 Oxidation kinetics of pure iron. ( a ) A W versus f, (b)(AW)
( c ) the logarithm of k versus the reciprocal of temperature, 1 / T p
versus r and C 3 ]
.
through the film and arrives at the metal/oxide interface. And the oxidizing power of the atmosphere is relatively low, such as with low oxygen pressure in partial vacuum, in air diluted with inert gas, or in the mixture of CO and C 0 . Strongly oxidizing conditions generally form thick protective scales which result in the parabolic rate law. Kinetics can change during oxidation of a metal. In early stage of oxida tion the film thickness may be sufficiently low to allow linear kinetics. As the 2
25
Environmental Damage at High Temperature
335
film thickens a transition to parabolic kinetics is often observed. Conversely, microcracking and porosity may develop as the film thickens, reducing the protectiveness of the oxide. The parabolic law then fails and the kinetics ap proaches linearity at some time after the start of oxidation.
25.1.3
Oxidation of Alloys
Most engineering alloys for high temperature service belong to the Fe-Ni-Cr system and chromium is added to increase the oxidation resistance of the al loys. Fig. 25. 4 shows the effects of increasing Cr content on the oxidation rate and on the oxide morphology for Fe-Cr alloys oxidized at 1000°C. The oxida tion rate decreases rapidly and the amount of chromium oxides increases as chromium is increased to 2 0 % . In the alloys containing less than 1 6 % chromi um Fe-Cr oxides are formed and in the alloys with chromium more than 20 % a single chromium oxide is formed. T h e chromium content necessary for the formation of single C r 0 decreases with decreasing temperature and for this reason, martensite stainless steels ( 1 3 % C r ) and austenite stainless steels ( 1 8 % C r ) are acceptable in many applications at 500 — 700°C. Nickel is itself an oxidation resistant metal. Nickel in conjunction with chromium improves significantly high temperature oxidation resistance of the stainless steels. Silicon forms compact and adherent oxide films either alone or in conjunc tion with chromium However, its presence degrades creep resistance thereby silicon is added at 2 to 3 % levels to many superalloys and stainless steels. Aluminum forms protective oxide film at relatively low temperatures and increases oxidation resistance of Ni-based and Fe-based alloys. Aluminum also forms / - N i A l phase that increase significantly creep resistance of Ni-based superalloys. However, aluminum oxide does not form fast enough to repair mechanical damage during oxidation. In brief, chromium is the most important alloying element for oxidation resistance. Chromium not only increases oxidation resistance but also im proves the strength of the alloys through solid solution strengthening. Silicon and aluminum are also favorable for oxidation resistance, but they degrade the mechanical properties of the alloys and addition of these in engineering alloys is limited to a few percent. In a given environmental condition (temperature and atmosphere) selec tive oxidation takes place in multi-component alloys depending on the thermo dynamics and the kinetics of the oxidation reactions of the alloying elements. From thermodynamics point of view, the more negative the formation energy of a metal oxide, the more favorable the oxidation of the metal. From kinetics point of view, however, the rate of a chemical reaction depends on the concen trations of the reactants and the higher the content of a metal in an alloy, the more favorable the oxidation of the metal. Which metal oxidizes preferentially in an alloy depends on the coupling effect of the thermodynamics and the ki netics. For example, in the Fe-Cr alloy system C r 0 has a more negative for2
3
3
2
3
336
High Temperature Deformation and Fracture of Materials
mation energy, but the iron oxides are formed preferentially in the alloys con taining relatively low chromium content. T h e amounts of chromium oxides in crease with the increase of chromium content until single C r 0 forms, as shown in Fig. 25. 4. 2
25.1.4
3
Internal Oxidation
Under appropriate conditions oxygen in the atmosphere may dissolve in alloys, diffuse inward and cause precipitation of the oxide particles. A typical mor phology of internal oxidation is shown in Fig. 25. 5. Internal oxidations either occur alone or together with external oxidation
25
Environmental Damage at High Temperature
337
25. 5 Typical morphology of internal oxidation ^ . 1
depending on alloys and environments. Internal oxidation of an alloy includes following processes. 1) Oxygen in the atmosphere dissolves into the surface layer of the alloy, i. e. yO
-
z
[ 0 ]
M
(25. 7)
where [ 0 ] M represents elemental oxygen dissolved into the alloy. If the equi librium constant of the reaction is K j , then [ 0 ] = K. · Pb? (25. 8) 2) T h e oxygen dissolved into the alloy reacts with solute Β (oxidizing metal) to form oxide particles. [B] + u[0] -*BO„ (25.9) 3) Oxygen diffuses inward and the above two processes proceed continu ously leading to inward growth of the internal oxidation layer. T h e conditions under which internal oxidation in an alloy can occur are (1) oxygen has certain solubility in the alloy and ( 2 ) diffusion of oxygen in the alloy is faster than that of solute B. Otherwise external oxidation occurs. Generally, the diffusion rate is lower than the chemical reaction rate and the diffusion of solute Β and/or oxygen controls the internal oxidation. T h u s internal oxidation often follows parabolic rate law, i. e. x = kt (25.10) where χ is the thickness of the internal oxidation layer and k is the rate con stant. For the case that the diffusion of solute Β is so slow that it can be ig nored, the rate constant k is proportional to the diffusion coefficient of oxygen D , the kinetics in this case becomes M
M
M
2
0
338
High Temperature Deformation and Fracture of Materials
S)
where No is atomic fraction of oxygen in the surface layer of the alloy and N is atomic fraction of solute Β in the alloy. For the case that both oxygen and solute Β diffuse, the kinetic equation is given by m
B
χ = 2/(D i)
1 / 2
(25.12)
0
where γ is a dimensionless parameter that is a complex function of concentra tions and diffusivities of oxygen and solute B. This parameter can be ex pressed in two limited cases. When No* D > No" D , i. e. the diffusion of oxygen predominates, 0
.
'
TvriS)
B
,
l/z
I ^ W ) V2xrJV
(25.13)
B
N D m
Substituting Eq. ( 2 5 . 1 3 ) into Eq. ( 2 5 . 1 2 ) gives Eq. ( 2 5 . 1 1 ) . When S > N i f D , i. e. the diffusion of solute Β predominates,
B
B
0
2vN where θ= D /D . Substituting eq. ( 2 5 . 1 4 ) into eq. ( 2 5 . 1 2 ) gives _ ( π # ν ) " Ni? ν N ' Equation ( 2 5 . 1 5 ) shows that the rate of internal oxidation depends on the concentrations and diffusivities of oxygen and solute B. B
Q
B
2
x
W
B
25.2
Hot Corrosion
The alloys employed in the hot section of gas turbine engines are frequently subject to a corrosion induced by liquid N a S 0 film deposited on the surface of the alloys. T h e N a S 0 film results from the salt injected into the engines and sulfur from the combustion of the fuel. A typical example of the corrosion is shown in Fig. 25. 6 where the results of the oxidation experiments of a Nibase superalloy BT900 in air at 1000°C with and without a coating of N a S 0 film are given - - . T h e oxidation rate of the alloy is greatly accelerated by the coating of N a S 0 f i l m . This mode of attack is called hot corrosion - - . 2
2
4
4
2
4
1 6 1
1
2
68
1
4
Metallographic observations of hot corroded alloys often showed sulfides of Ni and C r , so the mechanism was initially called sulfidation. However later studies showed that the main products of hot corrosion were the same as that of oxidation of the uncoated alloys in the same atmosphere. It is well known now that the nature of hot corrosion is an accelerated oxidation. In dry air a compact and protective NiO scale is formed on the superalloy B-1900, but a dispersion of fine NiO particles are observed in the salt film This observa tion indicates that the protective oxide scale on the surface of the material dis solves at the oxide/salt interface but reprecipitates as non-protective particles within the salt film, and oxidation greatly accelerates due to loss of the pro tective scale. [6_11]
25
Environmental Damage at High Temperature
339
r/h 25. 6 Comparison of the oxidation behavior of the superalloy B-1900 with and without a coating of NaiSCUilrn™ .
25. 2. 1 Basic Fluxing Mechanism High temperature (type I) hot corrosion is observed in the temperature range about 825-950°C when the condensed salt film becomes liquid (melting point of pure N a S 0 is 884°C). T h e base-acid character of liquid N a S 0 c a n be described by the equilibrium SOT = S 0 + O " (25.16) where O can be considered as the basic component and S 0 the acidic compo nent. Since the solubility of oxygen in the molten salt is very low the oxygen necessary for fast oxidation of metallic substrate is acquired from the salt by reaction 2
4
2
4
2
3
2 -
3
S0
3
= SO +-|-0 z
(25.17)
2
Combining reactions (25. 16) and (25. 17) gives SOT = S 0 + Cf~ + y 0 2
2
(25.18)
T h e metallic substrate oxidizes, for example Ni-f--|-0
2
= NiO
(25.19)
This reaction consumes oxygen in the salt. As a result, reaction (25. 18) pro ceeds and the activity of oxide ion in the salt increases. When the activity of the oxide ion increases to a certain value, the metal oxide dissolves into the salt film through the following reaction
340
High Temperature Deformation and Fracture of Materials 2
NiO + O - = N i O t (25.20) This type of dissolution of protective oxides is called basic fluxing mechanism. Rapp and Goto proposed "negative solubility gradient" as a general cri terion for continuing hot corrosion attack. Figure 25. 7 shows a schematic drawing of this fluxing mechanism. At the oxide/salt interface, the solubility of metal oxides (or activity of the oxide ion) is locally high and the metal ox ides dissolve into the salt through reaction (25. 20). Then NiOf diffuses to ward the oxide/gas interface and precipitates as oxide particles because of lo cally low solubility of the oxides at the salt/gas interface. [12]
-
Gas phase 0 ,S0 ,SO,
Metal
2
2
Locally low MO solubility Locally high (acidic or basic) solubility for MO 25. 7 Schematic illustration of reprecipitation of porous oxides supported by a negative solubility gradient in the molten salt film
25. 2. 2
[ , 2 ]
.
Acidic Fluxing
Heat resistant alloys normally contain the alloying elements tungsten, molyb denum and vanadium. The oxides of these elements have the tendency to com bine with oxide ions in the molten salt to form tungstate, molybdate and vana date ions. 2
2
M0O3+ 0 " = M o 0 -
Ψ0 +σ=ψσ<3
(25.21)
25
Environmental Damage at High Temperature
341
V O + O -=2VQr These reactions consume the oxide ions in the salt leading to increase in acidity of the salt. As a consequence, the acidic fluxing of the protective oxide takes place, for example NiO= N i + Ο " (25.22) Al203=2Ai3++3Cr (25.23) The products of the reactions, N i , A l , M o O T , W O i " and VO3" , diffuse toward the salt/gas interface. T h e oxides W 0 , M o 0 and V 0 exhibit high vapor pressures, thereby leading to evaporation from the salt/gas interface. T h e resulting gradient in acidic solute concentration across the salt film is ide al to promote the acidic fluxing and reprecipitation of oxides NiO and/or A1 0 . When the partial pressure of S 0 in the gas phase is relatively high, fol lowing reaction takes place SO + S 0 = S z O t (25.24) T h e pyrosulfate ^ 0?~ reacts with the metal oxide by M O + SzCT = M S 0 + SOT (25. 25) This is another type of acidic fluxing mechanism. Chromium is an effective alloying element to combat hot corrosioa The reason is that the basic dissolution of C r 0 depends on oxygen pressure, 2
2
s
2 +
2 +
2
3 +
3
2
3
2
5
3
3
2
3
4
2
C r 0 + 20*- + - | θ 2
3
3
2
= 2CrOT
(25. 26)
Because hexavalent Cr is formed from trivalent Cr in the basic dissolution ac cording to reaction (25. 26) , the basic solubility of C r 0 depends on the local value of oxygen partial pressure. Since any thin salt film supporting hot corro sion will be more reducing (low value of Pq,) at the oxide/salt interface than that at the salt/gas interface, the chromate solute will necessarily experience a positive gradient and therefore not be subject to reprecipitation in the film. Finally we need to consider the role of metal sulfidation in hot corrosioa Geobel and P e t t i t observed both the formation of NiS beneath the NiO scale and the precipitation of non-protective NiO particles within the salt film. They interpreted this phenomenon in terms of the reactions: 4Ni-r-SOr = S N i O + N i S - r - O (25.27) 2
3
[6]
2
2
2NiO + 0 ^ + y 0
+
2
= 2Na +2Ni02"
(25. 28)
According to reaction (25. 27) the formation of NiS causes a local increase in the basicity of the salt film since O is a reaction product. This local increase in melt basicity would affect the dissolution of the NiO scale (reaction ( 2 4 . 2 8 ) ) by forming the basic solute Ni0 ~ which reprecipitates in the salt film as non-protective NiO particles. This indicates that sulfidation affects the salt film chemistry and contributes to basic fluxing mechanism. 2 -
2
342
25.3
High Temperature Deformation and Fracture of Materials
Carburization
Carburization is observed in industrial processes where Fe-Cr-Ni alloys are ap plied in a carbonaceous atmosphere at high temperature. Carbon is trans ferred from the atmosphere into the metal matrix, diffuses inward and causes precipitation of the carbides. Carburization is a corrosion problem mainly for cracking tubes in ethylene production, but also for components of other pet rochemical plants, for example reformer tubes in steam reforming of natural gas. The dissociation of hydrocarbons is conducted by passing naphtha-steam mixture through the cracking tubes at a temperature between 900-1100°C. During operation at high temperature, carbon penetrates in to the inner wall of the tubes and precipitates in the form of carbides M ^ Q and M 7 C 3 . Precipi tation of carbides strongly affects the properties of the materials leading to significant reduction of the service life of the dissociation tubes. Many qualitative studies have been made on the carburization process and its effects on the properties of the materials - " ' . Some numerical studies on the reaction-diffusion process and the material damage evolution during carbu rization are also made in recent decades - " - . In this section we introduce briefly these numerical studies. 1
1
17
13
22
16 1
1
25. 3. 1 Thermodynamics of Carburization The state-of-art materials are cast heat-resistant steels HK40 (25Cr-20Ni) and H P (25Cr-35Ni). Because of high Cr content, the solubility of carbon in the austenite matrix of the steels is very low and therefore carbides M Q and M7C3 precipitate during carburization. Precipitation of carbides reduces Cr content and consequently increases the carbon solubility in the matrix. There fore, it is a coupled reaction-diffusion process. 23
At a lower carbon concentration the carbide M Q is formed at first. T h e precipitated M ^ Q is later converted to M y Q and, when carbon concentration increases, M r Q precipitates directly. In order to determine the concentration of carbon in the matrix and the concentration of carbides, following reactions are considered. For carbide M ^ Q (CrieFeyCs - ) 23
17
1
(25.29)
16Cr + 7Fe + 6C = Cr Fe Q T h e equilibrium constant K of the reaction is then 16
7
pl
(25. 30) where / > ? F e and y are the activity coefficients of C r , Fe and C in the austen ite matrix, respectively, and N ,N and N are the atomic fractions of C r , Fe and C in the matrix, respectively. T h e solubility of M Q ; in the matrix is obtained from eq. (25. 30) as &
c
Ct
Fe
c
23
25
Environmental Damage at High Temperature
~ Kg · NI/> · jv ^ is the solubility parameter of M ^ Q , and it is given by N c i
where K
S1
7
K p l
6
/ c
N£ • N g • Ni. = * *^ *^ For the carbide M7C3CCr3.5Fe3.5C3[17]) the formation reaction is 7 C r + 7 F e + 6 C = 2Cr3.5Fe3.5C3 The solubility of M7C3 is then K s i
=
N
where K
ffi
a
=
w
(
2
343
5
(25
·
3
1
)
3 2 )
·
(25.33)
3/3
(25
Kg · Nh · Νψ is the solubility parameter of Μ 0 ) and it is given by
3 4 )
·
7
K
=
K
Λ
f c
(25
3 5 )
* Nh' . Nfc' • NI = * ' ' ' ' · The equilibrium constants K i and K^ can be determined from the Gibbs free energy of formation of the carbides using the following relation AG = — K T l n K p (25.36) T h u s , if we know the values of AG and the activity coefficients of Cr, Fe and C in the matrix, then the solubility of the carbides M^Ce and M7C3 can be de termined by eqs. (25. 31) and (25. 34). p
0
0
25.3. 2
Kinetics of Carburization
Carburization is an internal corrosion phenomenon and the kinetics of carburi zation is expected to follow the parabolic rate law in the same way as internal oxidation described in section 25. 1. 4. Figure 25. 8 shows the experimental re sults of pack carburization tests of HK40 and H P steels at 1000°C . T h e weight gain follows a parabolic rate law and the following expression is ap plied. [20]
2
W = Kt (25. 37) where W is weight gain of the specimen and k is a constant. T h e parabolic rate law indicates that the carburization of HK40 steel is controlled by the dif fusion of carbon. c
25. 3. 3
Numerical Simulation of Carburization
T h e model that calculates the reaction diffusion of carbon in a high Cr-Ni steel is based on F i c k ' s second law of diffusioa T h e calculation is divided into two parts: (1) a finite difference calculation for the diffusion of carbon, using fi nite space and time increments; and ( 2 ) calculation for the formation of car bides. If diffusion coefficient D is assumed to be independent of carbon content and the diffusion is considered in one dimension in space ( χ ) , the F i c k ' s sec ond law is given by
+
+
§7 = ° ( 0 & 0 Κ ^ -
ί )
( 2 5
·
3 8 )
344
High Temperature Deformation and Fracture of Materials
0.012
-
0.010 /
1273K HK40
0.008
/
0.006
0.004 1 10
1
I
1 20
. 30
40 Time/h
50
1 , 60
1
. 70
80
0.0060
0.0050 -
0.0055 h
ifc
1273K HP
0.0040
0.0035 1 20
1 30
1 40
1 50
1 60
Time/h 25. 8 weight gain as a function of carburization time at 1000t) for HK40 ( a ) and HP ( b ) steel™ .
where Z = 0 for a plane, Z = l for a cylinder, and Z=2 for a sphere. For the boundary condition, the diffusion flux of carbon through the surface of the specimen follows F i c k ' s first law of diffusion ]=-Όψ
(25.39) dx
where J is the diffusion flux of carbon. It is evident that the diffusion flux of carbon through the surface of the specimen is equal to the amount of carbon penetrating into the specimen per surface area (weight gain per surface area W) in a unit time. In the present case, W is obtained by a series of pack carbu rization tests of HK40 steel at 1000°C for the plane specimens as shown in Fig. 25. 8 ( a ) . The overall carburization is a reaction-diffusion process of carbon. The
25
Environmental Damage at High Temperature
345
carbon in the steel consists of two p a r t s the carbon in the matrix of the steel and that in the carbides. Only the carbon in the matrix can diffuse further. At any point in the steel considered by the finite difference method, the carbides M C and/or M C precipitate when the total amount of carbon is higher than Nc] ( M C ) and/or N c ( M C ) . Certain amounts of chromium and iron are also removed from the matrix, so Nci and/or N c change with the carbide pre cipitation or with time. During the carburization process, the carbide M C precipitates first with increasing the concentration of carbon in the steel. When the concentration at a point reaches N ( M 7 C 3 ) , the transformation of carbide M C into M C takes place. T h e carbide M Q precipitates directly after all of the M Q changes to M C . Therefore, there exist three precipita tion zones in the steel: zone of M C ; zone of coexisting M C and M Q ; and zone of M C . :
23
6
7
2 3
3
6
2
7
3
2
2 3
6
cl
23
6
7
3
7
23
7
3
23
7
6
23
6
7
3
Using the model of reaction-diffusion in high Cr-Ni austenitic steels dur ing carburization process stated above, the diffusion of carbon and the precipi tation of carbides during carburization of HK40 steel at 1000°C are numerical ly simulated by means of finite difference computation techniques. Figures 25. 9 show the calculated total content of carbon (solid lines) as a function of the penetration depth for a plane specimen after carburization at 1000°C for 75h. T h e profile of the carbon content exhibits a zone with abrupt decrease in the concentration of carbon where M C and M Cj coexist. T h e measured car bon concentrations are also plotted in the figure (data points). It is found that there is a reasonable agreement between the two results. 23
6
7
3.0 Γ
ΟΟ
MA
"- r J
0
0.2
0.4
0.6
I
L
08
1.0
1.2
1.4
1.6
Distance from surface/mm 25. 9 The calculated (solid lines) and the measured (data points) to tal content of carbon as a function of the penetration depth for a plane ,9]
specimen after carburization at 1000t! for 7 5 h f .
25.3.4
Carburization Damage
As mentioned above, the carburization strongly affects the properties of the
346
High Temperature Deformation and Fracture of Materials
materials. The carburization deteriorates the ductility and toughness of the materials, especially the low temperature properties. T h e effects of the car burization on the high temperature properties are less serious; the tensile and creep strengths are improved and the ductility does not decrease markedly . The most important effect of the carburization is the change of stress field within the materials. The expansion of the carburized zone leads to additional tensile stress within the uncarburized zone. The thermal expansion coefficient decreases due to carburization, giving rise to additional thermal stress when the tubes are heated up and/or cooled d o w a These additional stresses accel erate the creep damage evolution and consequently reduce the service life of the materials. [ 2 3 ]
We have developed a finite element program to calculate numerically the stress field and the creep damage evolution during carburization. The expan sion due to carburization is similar to thermal expansion and we can analyze carburization stress by means of determining thermal tress. To do this, we define the so-called carburization expansion coefficient αν as the normal strain caused by increase in carbon concentration by 1%. The volume expansion co efficient is then a = 3ai , as in thermal expansion. The value of αν is obtained from correlation between density and carbon concentration of the material. Experimental result of the relation is shown in Fig. 25. 1 0 . vc
c
[22]
1.0 1.5 2.0 Carbon centent,wt% 25. 10 Correlation between density and carbon concentration of the m a t e r i a l ^ .
A finite element model has been developed in which carbon concentration and temperature distributions on the cross section of the tubes are incorporat ed. The evolution of the stress field during high temperature service is calcu lated numerically. As examples of the calculation for HK40 steel, the stress distributions along the radial direction after service at 1000°C for 10,000 and 15,000 hours are shown respectively in Fig. 25. l l . Creep damage evolution at a point is calculated using the life fraction rule [ z o ]
25
Environmental Damage at High Temperature
347
50
ο h a
-50
ss
-100
h
9?>
-150
lOOOOh 15000h
-200 _L
-250 4
10
6
Distance from inner wall d/mm 25. 11 Stress distributions in HK40 steel along radial direction after service at lOOOt) for 10,000 and 15,000 hours™.
D = Υ)
(25. 40)
where t/is a time increment of the finite element model, ijyis the creep rupture life of the material at the mean stress and temperature within the time incre ment. It is assumed that when the damage parameter D at a point reaches uni ty, a creep crack is formed at the point. Using this method we can predict the creep crack growth process in the tube wall.
References 1 2
Jones D A. Principles and Prevention of Corrosion. Macmillan Pub. Com. N e w York, 1992 Gaskell D R. Introduction to Metallurgical Thermodynamics, 2 ed. , McGraw-Hill Book Company, 1983
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Li Meiquan. High temperature corrosion of metals. Metallurgical Industry Press. Beijing, 2001 Wright I G. Metals Handbook, Vol. 1 3 Corrosion. 9™ ed. , A S M , Metals Park, O H , 1987 Liu Ruiyan. Study on corrosion behaviors of metallic materials in molten LiCl-LijO. Thesis for the Doctorate, Dalian University of Technology, 2004 Goebel J A , Pettit FS. Na2SU4-induced accelerated oxidation (hot corrosion) of Nickel. Met al. Trans. 1970, 1 ( 7 ) , 1 9 4 3 - 1 9 5 5
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Bornstein N S , Derescente MA. The role of sodium in accelerated oxidation phenomenon termed sulfidation. Met. Trans. , 1970, 2 ( 1 0 ) : 1856—1863 Goebel J A , Pettit F S , Goward GW. Mechanisms for hot corrosion of Nickel-based alloys. Metal. Trans. 1973, 4 ( 2 ) : 2 6 1 - 2 7 8
Rapp R A , Zhang YS. Hot corrosion of materials: fundamental studies. JOM. 1994, 1 2 47-55 10 Rapp R A , Zhang YS. Hot corrosion of materials- fundamental aspects. Molten Salt Forum V o l s , 1998, ( 5 - 6 ) : 2 5 - 3 8 . :
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High Temperature Deformation and Fracture of Materials Rapp RA. Hot corrosion of matrials; A fluxing mechanism?. Corros. Sci. 2003, 4 4 ( 2 ) : 209—221 Rapp RA and Goto Κ S. Hot corrosion of metals by molten salts. I n Braunstein J and SelmanR. Molten Salts I, Electrohem Soc. Pennington NJ, 1981, 159—163 Rahmel A , Grabke Η J and Steinkusch W. Carburization - introductory survey. Corrosion and Mater. 1998, 4 9 ( 4 ) 221—225 Ramanarayanan Τ A , Petkovic R A , Mumford J D and Ozekcin A. Carburization of high chromium alloys. Corrosion and Mater. 1998, 4 9 ( 4 ) : 226—230 Mitchell D R G, Young D J and Kleemann W. Carburization of heat-resistant steels. Corro sion and Mater. 1998, 4 9 ( 4 ) : 231—236 Klower J and Heubner U. Carburization of nickel-base alloys and its effects on the mechani cal properties. Corrosion and Mater. 1998, 4 9 ( 4 ) : 237—245 Christ H-J. Experimental carburization and computer-based description of the carburization behavior of the austenitic stainless steel AISI 304L. Corrosion and Mater. 1998, 4 9 ( 4 ) : 258-265 :
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Forseth S and Kostad P. Carburization of Fe-Ni-Cr steels in CH4-H2 mixtures at 850Corrosion and Mater. 1998, 4 9 ( 4 ) : 266—271 Meili Zhu, Qiang Xu, Junshan Zhang. Numerical simulation of Reaction-diffusion during carburization of HK40 steel. J. Mater. Sci. Tech. , 2003, 19 ( 4 ) : 327—330
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Zhu Mei-li, Yin You, Wang Tao, Liu Shutian and Zhang Junshan. Numerical simulation on stress and creep damage fraction in ethylene cracking tube. J. Dalian University of Technol ogy, 2001, 4 1 ( 2 ) : 192—196 Li Haiying, Qu xianyong, Zhu Meili and Zhang Junsha. Numerical simulation on creep dam age in HK40 and HP steel under carburization. Mechical Engineering Materials, 2005, 29 (11): 1 7 - 2 0 Yon You. Numerical simulation on the stress field and creep damage in ethylene cracking tube. Thesis, Dalian University of Technology, 2000 Tan Jialong. Thesis, Dalian University of Technology, 1985