- Email: [email protected]
Hot-gas corrosion and creep deformation of vessels operating under pressure
Corrosion Science, Vol. 40, No. 213, pp. 439446, 1998 0\, 1998 Else&r Science Ltd. All rights reserved.
Pergamon
Printed in Great Britain. 001&938X/98 %19.00+0.00
PII: SOOlO-938X(97)00150-9
HOT-GAS CORROSION AND CREEP DEFORMATION VESSELS OPERATING UNDER PRESSURE V. ROSENBAND Faculty
of Aerospace
Engineering,
Technion-Israel
OF
and A. GANY Institute
of Technology,
Haifa 32000, Israel
analysis of vessel failure under the joint action of gaseous chemical corrosion and creep is carried out for vessels operating under high-temperature and high-pressure conditions. The analysis takes into account possible changes in oxidation rate due to breakdown of the oxide layer under the action of mechanical stresses at the metal-oxide interface. The service life time of the vessel is estimated by specifying the reduction in wall thickness during vessel operation due to both corrosion and “quasi-viscous” creep. 0 1998 Elsevier Science Ltd. All rights reserved Abstract-An
Keywords:
metal oxidation,
gas corrosion,
creep.
INTRODUCTION In service, materials are very often exposed simultaneously to thermal, mechanical and corrosive loads. It is only relatively recently that attention has been given to the possible interactions of these types of loadings.‘,2 This interest has been stimulated by a number of factors. Higher service temperatures in modern high-temperature plants facilitate interactions of metals with the environment, thereby increasing the risk of premature failure of components. High safety demands on materials make necessary a more accurate knowledge of interactions which affect the life time in service. There is now a trend towards maximum economy in the use of materials which requires component design to be based on a study of all the stresses, including mechanical and chemical interactions. Estimation of corrosion and creep resistance of metal vessels operating under highpressure and high-temperature conditions (e.g. various chemical devices, steam generators, pipelines, etc.) is essential for their design and usage. In this paper, an estimate of the service life time of the vessel has been made by specifying the reduction in wall thickness during vessel operation due to both corrosion and “quasi-viscous” creep. CALCULATION Corrosion
RESULTS AND DISCUSSION
consideration
Consider a titanium cylindrical vessel of internal radius r,, and external radius R,. The vessel is kept under constant temperature T,, and internal pressure PO in an oxidizing atmosphere (air), so that the external surface of the vessel undergoes gaseous corrosion.
Manuscript
received 22 May 1997; in amended
form 18 September 439
1997
440
V. Rosenhand and A. Gan!
It is well known that titanium tubings are very susceptible to intensive high-temperature oxidation in air and are even sometimes subject to ignition as a result of hot work operations.’ A uniform single-phase oxide layer, with preferable migration of oxygen ions inwards, is assumed to develop on the external surface. Its thickness s(t) increases with time as: dij d, = K,,f’(ci)exp(~E;R;r,,).
(1)
where cj = d,, at I = 0. Here, K,, is the pre-exponent and E is the activation energy for the appropriate to non-protective linear oxidation law. As usual, ,f’(S) = (/Lo“),” where II = 0 corresponds oxidation and n = 1 to protective parabolic oxidation. It would be expected that metals that oxidize by anionic diffusion on convex surfaces and that have a high PillingBedworth ratio will exhibit highly stressed oxides and thick layers of oxides can be grown without spalling.5 If the oxide is highly adherent. then the initial outer oxide will be pushed further away from the metal as new oxide forms beneath it. These layers will eventually develop tensile stresses due to their enforced expansion. Whether or not this oxide layer is protective depends appreciably on the mechanical stresses at the metaloxide interface due in part to the difference in volume of the metal and the resulting oxide.” As oxidation proceeds. the metal wall thickness decreases, and. at some instant, the maximum tangential stress on the internal vessel surface reaches a limiting value, equal to the metal yield stress. (T,,,.The time for occurrence of metal plastic deformation due to corrosion thinning of the wall is taken as the service life time of the vessel. The value of equivalent stress on the internal vessel surface ger, = r~,~- 0,. where cr(,,, O? are the components of a stress tensor. is:’
(2) where R = R,,-ii is the instantaneous radius of the metal--oxide interface. The contact pressure, PC. appears at this interface due to the difference in the volumes of metal and its oxide. For a metal-oxide composite cylindrical specimen:h.x
whereIL. A,. A,. ,LL E,,, and _/& arc volume thermal expansion coefficients. Poisson’s ratios and Young’s moduli respectively of the metal and the oxide. The Pilling--Bedworth ratio x is the ratio of the volume of the oxide to the volume of metal from which it is formed. Since the volume of a metal is usually less than that of the oxide formed from this metal, the newly formed oxide pushes the already existing layer generating the tensile stress in it. The values of those tensile stresses increase as thickness of scale increases. which can result in breaking of this layer. leading to a non-protective oxidation regime. The equivalent stress at the metal-oxide interface is
Hot-gas corrosion and creep deformation of vessels operating under pressure
2P,R; =----+ Oeq R;-R2
2P,R;r;
441
(4)
R2(Ri - ri)’
where the first term describes the growth stress appearing during the oxidation process, and the second one the stress under internal loading action. If the equivalent stress at the metal-oxide interface exceeds the oxide yield stress ooXthen failure occurs for brittle oxide scale,9 which results in non-protective oxidation, otherwise protective oxidation is where the oxide scale gives protection to corrosion. It is considered that the stresses generated during oxidation cannot be relieved by plastic deformation of the oxide scale. The plastic-deformation process may be by simple slip or it could involve a high-temperature creep process. However, it is known’ that titanium oxide has insufficient slip systems to deform coherently and therefore it would be expected to behave in a brittle manner. The temperature of macroscopic plasticity of rutile is above 600”C.‘” Diffusional creep (Herring-Nabarro creep) occurs only at temperatures above half the melting point of the oxide, equal to 1870°C for rutile. Therefore the creep would seem to be an unlikely mechanism for relieving surface-oxide stresses during low-temperature oxidation.‘,” In addition, experiments carried out with various oxides revealed that under tensile loading no appreciable plastic deformation occurred.5,‘2 Consequently, it is considered that in the case being considered the scale fracture is the only mode of relief of scale growth stresses. A similar approach was done on analysis of the fracture of the scale exhibiting negligible creep relaxation during hard anodizing of aluminium,13 which, like titanium, also proceeds by preferential diffusion of oxygen through the scale. It was shown that the effect of curvature is to increase the maximum shear stresses in oxide scale for a convex surface. However, in contrast to our analysis, in Manning’s analysis of energy storage in a scale exhibiting negligible creep relaxation it is considered that all energy stored in the oxide is used only in scale failure, but does not impact on the metal deformation. This approach could hold for the case of metal wires, being considered in Manning’s paper, but is questionable for our case of thin-walled tubes. Figure 1 presents the dependence of o-eqon 6 for a titanium vessel with r. = 0.594m, R. = 0.600m (flo = Ro/ro = 1.Ol) operating under internal pressures PO = 0.5 MPa and 1.OMPa at various temperatures. In consideration of their temperature dependence, all parameters necessary for the calculation were taken from.‘4,‘5 When PO = 1 MPa, (T,~is always more than cr,, and non-protective oxidation takes place. At PO = 0.5 MPa, nonprotective oxidation occurs for temperatures above 500°C. For lower temperatures, at first oeq < g,, and protective oxidation takes place. With thickening of the oxide layer, g’eqincreases and, at 6 = 6*, it becomes equal to rroX.When attaining such conditions, breakage of the oxide layer and development of a new protective oxide underlayer are expected. Simultaneously, an abrupt change in oxidation rate occurs. The dependence of 6 on time for oxidation of titanium in air at 500°C is presented in Fig. 2. Such modes of oxidation kinetic curves were observed experimentally.4 The dotted curve demonstrates the change in the oxide layer thickness without considering mechanical stresses. When evaluating vessel service life-time, the known kinetic constants Kc,p for a protective parabolic law and K,, for non-protective linear law for oxidation of titanium was used:lh Kop = 2.52 exp ( -25,500/T)g2/cm4
set
442
I
100
I
___----
____--
90
___r--
_---. ____-____---I I
1
80
t
!
r-----v 50
I I
&,,,T=400"C
I
10
0
Fig
I.
The dependence
of stress at the metal
titanium
vessel.
(
30
20
oxide Interl’ax
1P,,= 0.5MPa;
(-
on the oxide -) P,, =
layer thickness.
l’or a
I .OMPa.
K,,, = 4.7 x IO’ exp ( ~~24,500; ‘Og, cm' set In the case of protective parabolic oxidation. the service life-time of the vessel is estimated as the sum of the times for consecutive breaking of the oxide layers until a metal layer of thickness h is consumed:
(5) Here. poxis the oxide density. : is the amount 01‘ oxide which is generated from a unit mass of oxygen and /I is the thickness of metal which has to be oxidized in order to reach the condition. gCi, = G,,, at the internal surface of the vessel. For non-protective linear oxidation: (6) It is easy to show, from eqn (2) that lr = R,,-r,,( 1 +I/‘,, Fig. 3 presents
the dependencies
u,,,)’ ’
t*( K,) for the foregoing
(7) titanium
vessel at P,, = 0.5 MPa.
Hot-gas
corrosion
0
and creep deformation
200
of vessels operating
600
400
t, Fig. 2.
Calculated time dependence titanium vessel at 500°C. (----)
600
443
under pressure
1000
h
of the oxide layer thickness on the external surface Breakaway oxidation; (- - -) protective oxidation.
of a
Creep considerations
In the above analysis, the decrease in vessel strength due to deformation under hightemperature creep loading of the metal, resulting in a decreasing wall thickness, was not considered. At low temperatures, loading above the yield stress but below the maximum tensile strength usually results in a limited amount of deformation which does not increase, even after long periods, because the hardening processes within the metal counteracts the applied stress. At high temperatures, however, thermally activated softening processes cause further, time-dependent deformation, resulting in the familiar time-strain (creep) curve. This creep deformation progresses with time as a result of “quasi-viscous” flow. The secondary or steady-state creep, in which the strain rate remains constant, to a first approximation, is most pronounced. The simultaneous effect of creep and corrosion on the vessel service life-time can be estimated on the basis of the secondary creep model.17 The experimental data for the high-temperature creep of titanium are in good agreement with the power law for thermally activated creep: E = Bo” exp (- Q/RT,J,
(8)
where E is the rate of secondary creep, Q is the activation energy for creep, 0 is the stress and m is a constant. For titanium, B = 5 x 106; Q/R = 30,000 K and m = 4.4, yielding E in h-’ when 0 is expressed in MPa.‘8x19 The influence of corrosion on the rate of steady-state creep in the second creep stage
444
V. Rosenband
and A. Gany
50
40
30
)I . * CI
20
f
10
0
-10
100
200
300
400
500
600
Temperature,*C Fig.
:
i-he dependence
(
or the ~tt;ut~um ~c~sc’i set\ tw
) Corrosion
ottI!.
C- -I combined
ct,rrwon
I~l&ttme
on temperature.
p,, -7 0.5 MPa
and creep of the vessel wall.
can be expressed through the decrease in the vessel wall cross section due to corrosion. It is well known”’ that, for steady creep of the thin-walled hollow cylinder vessel stressed component of a creep-strain rate, by an constant internal pressure. P,,. the tangential & = l4,.‘1’, is equal to:
where II = d,..dt denotes the radial velocity in the radial distance. I’. Creep of a metal due to mechanical loading at higher temperatures can result in rupture of the scale layer. Titanium undergoes creep even at normal atmospheric temperatures,” and at high temperatures the rate of titanium creep is much above the rate of titanium oxide creep. At T = 820 C and c = 32 MPa. for instance. the rate of titanium steady-state creep is creep in rutile is only 1.91 x IWJ I/h. of 4. I3 I ‘h,“’ whereas the rate of steady-state Therefore. it can be predicted that creep of oxide scale will not be able to relieve the stress during metal creep, resulting in rupture of the scale layer. This process r-e-exposes the base metal surface and corrosion attack is intensitied. Because of this, it is suggested that the strength of the corrosion product layer during creep can be neglected and non-
Hot-gas
corrosion
and creep deformation
of vessels operating
under pressure
445
protective linear oxidation of the outer surface of a vessel takes place. For incompressible material R_r
~
(&I-r&ll r
-K,,exp(-E/RT,)t.
(10)
eqns (9) and (10) imply that the rate of wall thickness reduction is defined by the two thermal activated processes of corrosion and creep. As presented in Fig. 4, the increase in internal radius due to the simultaneous action of creep and corrosion was calculated for the foregoing titanium vessel by numerical integration of eqn (9) with allowance for eqn (10) at various service temperatures, T,,. It is seen that, as r increases, the rate of the process sharply increases, resulting in asymptotic convergence to infinity (vessel failure) at a certain time, t*. Figure 3 presents the dependence of the service life-time, t*, on T,,. It can be seen that the combined effect of creep and corrosion results in a much shorter t* value than would occur due to corrosion only. Thereby, in the case being considered, high-temperature creep is of primary importance in failure of the vessel. CONCLUSIONS The service life time of the vessel operating in the oxidizing atmosphere under high temperature and pressure was considered. It was shown that service life time is determined
1.60
-
1.45
To-500%
To-400°C
0 S
1.30
To-300%
1.15
-
1.00
0
4
8
12
16
20
In t, hr Fig. 4.
Time dependence
of the vessel relative internal radius, and creep, PC,= 0.5 MPa.
r/r,,, under joint action of corrosion
446
V. Rosenband
and A. Gany
by reducing in thickness of the vessel wall thanks to combined action of metal hot-gas corrosion and creep deformation. Analysis of mechanical stresses in the metal-oxide surface, as the consequence in difference of volumes of a metal and an oxide formed from this metal, revealed the possibility of the oxide layer destruction resulting in transition from protective to non-protective oxidation. Results of calculations carried out for the titanium vessel identified that high-temperature creep deformation of metal is of primary importance in failure of the vessel. .~~,kno,ll~,dyc~nlrrlr The research was supported the Ministry
of Immigrant
Absorption.
by the (;iladl
Fund of the Center for Absorption
m Science of
State of Israel.
REFERENCES
6. Rosenband. 7. Kachanov.
V.. Gany. A. and Timnat. L.M..
8. Rosenband. 0. Hearn.
Y.M.
O\-it/. ,Mviul\.
IYY5. 43, 141.
Furlticrt~lc,trtcll,c of I/W T~KWI~ u/ f’lcr\tic I/I
Mowing.
Mir.
1974.
V. and Gany. A. C1owo.\ SC,;.. I YY5. 37. I YY I.
E.J.. in Mrc~/w~ric~.c o/ ,Lltr/cvic//.\. Vol.
I.
Pergamon
10. Groves. c‘.W. P,o~wt/ir~,y.v of r/w Briti\/~ C‘wtn~r/~~Sor.wil
Prea.
I Y70.
1977 15, IO?.
I I. Stringer. J. C‘owo\. Sci.. 1970. 10, 5 I? 12. Douglass. D.L. o.\-it/. ,vlcri/l\. 196’). 1. I77 13. Manning.
M.I.
C’orro\. SC,/.. 19X1. 21. 301
14. Smithella. C.J. (ed.). ,I-I~/trl\ Rcfcvwzcv RooX. 5th rdn. Buttsr\+orth\. 1.S. Samsono\.
16. Kofstad. 17. Nada.
G.V.
P.. Anderson.
P.B. and Krudtna.
IY. Cuff. F.B. and Grant.
Book Company.
Ncn York,
P/T).\.. 1954. 3. XS N.J. n,,
20. Kachanov.
L M.. 0.vnoc.i 7iwii
21. McQuillan.
A.D.
W.M.
1076.
1973.
0. J. .I Lc.r\ C‘ow~o/r .21v/tr/.c. 1961. N3, X9.
A.. 7%wr1. of F/OII, mu/ Fwc~/~~w of Soliclc. Vol. 7. McGraw-Hill
18. Dorn. J.E. J. Mw/I.
2’7. Hirthe.
London.
(ed.). T/w O.\-i& Hn~~t//w~k. IEI Plenum. UCM York.
and McQuillan.
and Brittain.
/rwr .1yv, IYj2. 20, Ii4 Po/:w/w\ti. M.K..
Morkwa.
I Y?’
7‘i/~n~/rrrv. ButccrMot-th Scientltic Pubhcation.
J.O. .I. ,d/rr. ~‘~w~~. .%a
1963. 46, II
I.
lY56.
1063.
Pergamon
Printed in Great Britain. 001&938X/98 %19.00+0.00
PII: SOOlO-938X(97)00150-9
HOT-GAS CORROSION AND CREEP DEFORMATION VESSELS OPERATING UNDER PRESSURE V. ROSENBAND Faculty
of Aerospace
Engineering,
Technion-Israel
OF
and A. GANY Institute
of Technology,
Haifa 32000, Israel
analysis of vessel failure under the joint action of gaseous chemical corrosion and creep is carried out for vessels operating under high-temperature and high-pressure conditions. The analysis takes into account possible changes in oxidation rate due to breakdown of the oxide layer under the action of mechanical stresses at the metal-oxide interface. The service life time of the vessel is estimated by specifying the reduction in wall thickness during vessel operation due to both corrosion and “quasi-viscous” creep. 0 1998 Elsevier Science Ltd. All rights reserved Abstract-An
Keywords:
metal oxidation,
gas corrosion,
creep.
INTRODUCTION In service, materials are very often exposed simultaneously to thermal, mechanical and corrosive loads. It is only relatively recently that attention has been given to the possible interactions of these types of loadings.‘,2 This interest has been stimulated by a number of factors. Higher service temperatures in modern high-temperature plants facilitate interactions of metals with the environment, thereby increasing the risk of premature failure of components. High safety demands on materials make necessary a more accurate knowledge of interactions which affect the life time in service. There is now a trend towards maximum economy in the use of materials which requires component design to be based on a study of all the stresses, including mechanical and chemical interactions. Estimation of corrosion and creep resistance of metal vessels operating under highpressure and high-temperature conditions (e.g. various chemical devices, steam generators, pipelines, etc.) is essential for their design and usage. In this paper, an estimate of the service life time of the vessel has been made by specifying the reduction in wall thickness during vessel operation due to both corrosion and “quasi-viscous” creep. CALCULATION Corrosion
RESULTS AND DISCUSSION
consideration
Consider a titanium cylindrical vessel of internal radius r,, and external radius R,. The vessel is kept under constant temperature T,, and internal pressure PO in an oxidizing atmosphere (air), so that the external surface of the vessel undergoes gaseous corrosion.
Manuscript
received 22 May 1997; in amended
form 18 September 439
1997
440
V. Rosenhand and A. Gan!
It is well known that titanium tubings are very susceptible to intensive high-temperature oxidation in air and are even sometimes subject to ignition as a result of hot work operations.’ A uniform single-phase oxide layer, with preferable migration of oxygen ions inwards, is assumed to develop on the external surface. Its thickness s(t) increases with time as: dij d, = K,,f’(ci)exp(~E;R;r,,).
(1)
where cj = d,, at I = 0. Here, K,, is the pre-exponent and E is the activation energy for the appropriate to non-protective linear oxidation law. As usual, ,f’(S) = (/Lo“),” where II = 0 corresponds oxidation and n = 1 to protective parabolic oxidation. It would be expected that metals that oxidize by anionic diffusion on convex surfaces and that have a high PillingBedworth ratio will exhibit highly stressed oxides and thick layers of oxides can be grown without spalling.5 If the oxide is highly adherent. then the initial outer oxide will be pushed further away from the metal as new oxide forms beneath it. These layers will eventually develop tensile stresses due to their enforced expansion. Whether or not this oxide layer is protective depends appreciably on the mechanical stresses at the metaloxide interface due in part to the difference in volume of the metal and the resulting oxide.” As oxidation proceeds. the metal wall thickness decreases, and. at some instant, the maximum tangential stress on the internal vessel surface reaches a limiting value, equal to the metal yield stress. (T,,,.The time for occurrence of metal plastic deformation due to corrosion thinning of the wall is taken as the service life time of the vessel. The value of equivalent stress on the internal vessel surface ger, = r~,~- 0,. where cr(,,, O? are the components of a stress tensor. is:’
(2) where R = R,,-ii is the instantaneous radius of the metal--oxide interface. The contact pressure, PC. appears at this interface due to the difference in the volumes of metal and its oxide. For a metal-oxide composite cylindrical specimen:h.x
whereIL. A,. A,. ,LL E,,, and _/& arc volume thermal expansion coefficients. Poisson’s ratios and Young’s moduli respectively of the metal and the oxide. The Pilling--Bedworth ratio x is the ratio of the volume of the oxide to the volume of metal from which it is formed. Since the volume of a metal is usually less than that of the oxide formed from this metal, the newly formed oxide pushes the already existing layer generating the tensile stress in it. The values of those tensile stresses increase as thickness of scale increases. which can result in breaking of this layer. leading to a non-protective oxidation regime. The equivalent stress at the metal-oxide interface is
Hot-gas corrosion and creep deformation of vessels operating under pressure
2P,R; =----+ Oeq R;-R2
2P,R;r;
441
(4)
R2(Ri - ri)’
where the first term describes the growth stress appearing during the oxidation process, and the second one the stress under internal loading action. If the equivalent stress at the metal-oxide interface exceeds the oxide yield stress ooXthen failure occurs for brittle oxide scale,9 which results in non-protective oxidation, otherwise protective oxidation is where the oxide scale gives protection to corrosion. It is considered that the stresses generated during oxidation cannot be relieved by plastic deformation of the oxide scale. The plastic-deformation process may be by simple slip or it could involve a high-temperature creep process. However, it is known’ that titanium oxide has insufficient slip systems to deform coherently and therefore it would be expected to behave in a brittle manner. The temperature of macroscopic plasticity of rutile is above 600”C.‘” Diffusional creep (Herring-Nabarro creep) occurs only at temperatures above half the melting point of the oxide, equal to 1870°C for rutile. Therefore the creep would seem to be an unlikely mechanism for relieving surface-oxide stresses during low-temperature oxidation.‘,” In addition, experiments carried out with various oxides revealed that under tensile loading no appreciable plastic deformation occurred.5,‘2 Consequently, it is considered that in the case being considered the scale fracture is the only mode of relief of scale growth stresses. A similar approach was done on analysis of the fracture of the scale exhibiting negligible creep relaxation during hard anodizing of aluminium,13 which, like titanium, also proceeds by preferential diffusion of oxygen through the scale. It was shown that the effect of curvature is to increase the maximum shear stresses in oxide scale for a convex surface. However, in contrast to our analysis, in Manning’s analysis of energy storage in a scale exhibiting negligible creep relaxation it is considered that all energy stored in the oxide is used only in scale failure, but does not impact on the metal deformation. This approach could hold for the case of metal wires, being considered in Manning’s paper, but is questionable for our case of thin-walled tubes. Figure 1 presents the dependence of o-eqon 6 for a titanium vessel with r. = 0.594m, R. = 0.600m (flo = Ro/ro = 1.Ol) operating under internal pressures PO = 0.5 MPa and 1.OMPa at various temperatures. In consideration of their temperature dependence, all parameters necessary for the calculation were taken from.‘4,‘5 When PO = 1 MPa, (T,~is always more than cr,, and non-protective oxidation takes place. At PO = 0.5 MPa, nonprotective oxidation occurs for temperatures above 500°C. For lower temperatures, at first oeq < g,, and protective oxidation takes place. With thickening of the oxide layer, g’eqincreases and, at 6 = 6*, it becomes equal to rroX.When attaining such conditions, breakage of the oxide layer and development of a new protective oxide underlayer are expected. Simultaneously, an abrupt change in oxidation rate occurs. The dependence of 6 on time for oxidation of titanium in air at 500°C is presented in Fig. 2. Such modes of oxidation kinetic curves were observed experimentally.4 The dotted curve demonstrates the change in the oxide layer thickness without considering mechanical stresses. When evaluating vessel service life-time, the known kinetic constants Kc,p for a protective parabolic law and K,, for non-protective linear law for oxidation of titanium was used:lh Kop = 2.52 exp ( -25,500/T)g2/cm4
set
442
I
100
I
___----
____--
90
___r--
_---. ____-____---I I
1
80
t
!
r-----v 50
I I
&,,,T=400"C
I
10
0
Fig
I.
The dependence
of stress at the metal
titanium
vessel.
(
30
20
oxide Interl’ax
1P,,= 0.5MPa;
(-
on the oxide -) P,, =
layer thickness.
l’or a
I .OMPa.
K,,, = 4.7 x IO’ exp ( ~~24,500; ‘Og, cm' set In the case of protective parabolic oxidation. the service life-time of the vessel is estimated as the sum of the times for consecutive breaking of the oxide layers until a metal layer of thickness h is consumed:
(5) Here. poxis the oxide density. : is the amount 01‘ oxide which is generated from a unit mass of oxygen and /I is the thickness of metal which has to be oxidized in order to reach the condition. gCi, = G,,, at the internal surface of the vessel. For non-protective linear oxidation: (6) It is easy to show, from eqn (2) that lr = R,,-r,,( 1 +I/‘,, Fig. 3 presents
the dependencies
u,,,)’ ’
t*( K,) for the foregoing
(7) titanium
vessel at P,, = 0.5 MPa.
Hot-gas
corrosion
0
and creep deformation
200
of vessels operating
600
400
t, Fig. 2.
Calculated time dependence titanium vessel at 500°C. (----)
600
443
under pressure
1000
h
of the oxide layer thickness on the external surface Breakaway oxidation; (- - -) protective oxidation.
of a
Creep considerations
In the above analysis, the decrease in vessel strength due to deformation under hightemperature creep loading of the metal, resulting in a decreasing wall thickness, was not considered. At low temperatures, loading above the yield stress but below the maximum tensile strength usually results in a limited amount of deformation which does not increase, even after long periods, because the hardening processes within the metal counteracts the applied stress. At high temperatures, however, thermally activated softening processes cause further, time-dependent deformation, resulting in the familiar time-strain (creep) curve. This creep deformation progresses with time as a result of “quasi-viscous” flow. The secondary or steady-state creep, in which the strain rate remains constant, to a first approximation, is most pronounced. The simultaneous effect of creep and corrosion on the vessel service life-time can be estimated on the basis of the secondary creep model.17 The experimental data for the high-temperature creep of titanium are in good agreement with the power law for thermally activated creep: E = Bo” exp (- Q/RT,J,
(8)
where E is the rate of secondary creep, Q is the activation energy for creep, 0 is the stress and m is a constant. For titanium, B = 5 x 106; Q/R = 30,000 K and m = 4.4, yielding E in h-’ when 0 is expressed in MPa.‘8x19 The influence of corrosion on the rate of steady-state creep in the second creep stage
444
V. Rosenband
and A. Gany
50
40
30
)I . * CI
20
f
10
0
-10
100
200
300
400
500
600
Temperature,*C Fig.
:
i-he dependence
(
or the ~tt;ut~um ~c~sc’i set\ tw
) Corrosion
ottI!.
C- -I combined
ct,rrwon
I~l&ttme
on temperature.
p,, -7 0.5 MPa
and creep of the vessel wall.
can be expressed through the decrease in the vessel wall cross section due to corrosion. It is well known”’ that, for steady creep of the thin-walled hollow cylinder vessel stressed component of a creep-strain rate, by an constant internal pressure. P,,. the tangential & = l4,.‘1’, is equal to:
where II = d,..dt denotes the radial velocity in the radial distance. I’. Creep of a metal due to mechanical loading at higher temperatures can result in rupture of the scale layer. Titanium undergoes creep even at normal atmospheric temperatures,” and at high temperatures the rate of titanium creep is much above the rate of titanium oxide creep. At T = 820 C and c = 32 MPa. for instance. the rate of titanium steady-state creep is creep in rutile is only 1.91 x IWJ I/h. of 4. I3 I ‘h,“’ whereas the rate of steady-state Therefore. it can be predicted that creep of oxide scale will not be able to relieve the stress during metal creep, resulting in rupture of the scale layer. This process r-e-exposes the base metal surface and corrosion attack is intensitied. Because of this, it is suggested that the strength of the corrosion product layer during creep can be neglected and non-
Hot-gas
corrosion
and creep deformation
of vessels operating
under pressure
445
protective linear oxidation of the outer surface of a vessel takes place. For incompressible material R_r
~
(&I-r&ll r
-K,,exp(-E/RT,)t.
(10)
eqns (9) and (10) imply that the rate of wall thickness reduction is defined by the two thermal activated processes of corrosion and creep. As presented in Fig. 4, the increase in internal radius due to the simultaneous action of creep and corrosion was calculated for the foregoing titanium vessel by numerical integration of eqn (9) with allowance for eqn (10) at various service temperatures, T,,. It is seen that, as r increases, the rate of the process sharply increases, resulting in asymptotic convergence to infinity (vessel failure) at a certain time, t*. Figure 3 presents the dependence of the service life-time, t*, on T,,. It can be seen that the combined effect of creep and corrosion results in a much shorter t* value than would occur due to corrosion only. Thereby, in the case being considered, high-temperature creep is of primary importance in failure of the vessel. CONCLUSIONS The service life time of the vessel operating in the oxidizing atmosphere under high temperature and pressure was considered. It was shown that service life time is determined
1.60
-
1.45
To-500%
To-400°C
0 S
1.30
To-300%
1.15
-
1.00
0
4
8
12
16
20
In t, hr Fig. 4.
Time dependence
of the vessel relative internal radius, and creep, PC,= 0.5 MPa.
r/r,,, under joint action of corrosion
446
V. Rosenband
and A. Gany
by reducing in thickness of the vessel wall thanks to combined action of metal hot-gas corrosion and creep deformation. Analysis of mechanical stresses in the metal-oxide surface, as the consequence in difference of volumes of a metal and an oxide formed from this metal, revealed the possibility of the oxide layer destruction resulting in transition from protective to non-protective oxidation. Results of calculations carried out for the titanium vessel identified that high-temperature creep deformation of metal is of primary importance in failure of the vessel. .~~,kno,ll~,dyc~nlrrlr The research was supported the Ministry
of Immigrant
Absorption.
by the (;iladl
Fund of the Center for Absorption
m Science of
State of Israel.
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