- Email: [email protected]
Transition from power-law to viscous creep behaviour of p-91 type heat-resistant steel
ELSEVIER
Transition
Materials Science and Engineering A234+236 (1997) 962-965
from power-law to viscous creep behaviour type heat-resistant steel
of P-91
LuboS Kloc *, VAclav SkleniEka Institute of Physics of Materials,
Academy
of Sciences
of the Czech Republic,
.&kooa
22, CZ-61662
Brno,
Czech Republic
Received 18 February 1997; received in revised form 14 March 1997
Abstract Short-term creeptestswere performed on a 9% Cr (P-91 type) steelat temperaturesfrom 873 to 923 K and at stresses below 100MPa by means of the helicoid spring specimens technique. The steady state creep rates correspond to viscous behaviour under the above conditions,characterizedby the apparentstressexponentcloseto 1. Sincethe stressexponent at higher stresses is about 10, the changein the deformation mechanismat lower stresses is evident. The deformation mechanisms map resultingfrom the presenteddata showsthat the serviceloading conditionsrespondto the viscouscreep.Extrapolation from power-lawcreepregime to low stresses can causeseriousunderestimationof predicted deformation rates. The primary stagecan be describedby the Li’s equation.Preliminary annealingat 873 K for 1.8x lo7 s reducesthe primary strain, but it hasno effect on the steady statecreep rate. 0 1997ElsevierScienceS.A. Keywords:
Viscous creep; Power-law creep; Heat-resistant steel; Extrapolation
1. Introduction Current knowledge of the creep mechanisms is based mainly on short-term laboratory experiments in powerlaw creep regime with creep rates higher than 10~ lo s ~ I. How ever, service loading of real high temperature components may lead to the rates lower than lo- ‘* s ~ I, which are typical for viscous creep. It is generally accepted that the creep mechanism can change at very
difficulties with specimen preparation. The newly developed technology of the specimen preparation by machining from tube enables an application of the technique to heat-resistant structural materials.
2. Experimental material and procedures The experiments were conducted using a P-91 type
low creep rates. Unfortunately, experimental data de-
heat resistant steel produced by Vikovice Steel
scribing viscous creep regime in structural materials are lacking, because their limited microstructural stability does not enable to run experiments at very high temperatures, where the viscous creep can also be observed at higher strain rates. The need for reliable data on the creep behaviour of heat-resistant steels at very low creep rates is evident. At present, the technique of helicoid spring specimens [l-3] is the only one which enables detection of the creep rates lower than lo- ‘* s-l. The technique has been used for experiments on model materials such as pure metals or simple solid solutions because of
(Vitkovice, Czech Republic). A tube from trial melt was supplied in a ‘ready to use’ condition. Chemical composition of the material was (in wt.%): 8.5 Cr, 0.88 MO, 0.43 Si, 0.4 Mn, 0.23 V, 0.1 Ni, 0.1 Nb, 0.1 C, 0.045 N, 0.018 Al, 0.015 P, 0.006 S. Helicoid spring specimens were machined from the tube. Most specimens were used for testing without any prior treatment, but some specimens were annealed at 873 K for 1.8 x 10’ s (6OO”C, 5000 h). The creep tests were conducted in the protective atmosphere of a purified argon. Optical measurements of individual coil spacings were performed periodically and the creep strains were derived. Since the stress and strain in helicoid spring are essentially shear ones, they were transformed to the equivalent tensile quantities using a known relations 0 = fi and
*Corresponding author. Tel.: 41218657; e-mail: [email protected]
+ 42 5 7268441; fax: +42
5
0921-5093/97/$17.00 0 1997 El sevier Science S.A. All rights reserved. PIISO921-5093(97)00364-X
L. Kloc,
V. Skleni?ka
/ Materials
Science
and Engineering
E = y/J?, where g is tensile stress, r is shear stress, E is tensile strain and y is shear strain.
A234-236
(1997)
962-965
963
&lo-' P-91
6.10-'
3. Experimental 3.1.
results w
Creep curves
Examples of creep curves measured in present experiments are shown in Fig. 1. The creep curves are characterized by pronounced primary stage, after which steady state commenced. Since the technique is based on self-loaded specimens, no initial strain at loading is included. The creep curves can be fitted by the equation derived by Li [4]: r=(,i~ln(l+~(l
-exp(
(1)
-$))+i,,,
where E is the strain, ki is the initial strain rate, i, is the steady state strain rate, t, is the primary stage relaxation period and t is the time. Steady state creep rates are about three orders of magnitude lower then initial ones. Duration of primary stage, characterized by the t, parameter, is stress independent. Preliminary long-term annealing reduces the primary strain and the primary stage duration by about 40%, but it has no effect on the steady state creep rate (Fig. 2). 3.2. Steady state creep rates
4.1o-4
2.10-'
0 0
2.106
4.106 t
Fig. 2. The effect creep curve.
of preliminary
6.106
Is1
annealing
for
5000 h at 873 K on
tion energy on applied stress (Fig. 4). The apparent activation energy Qa is defined as c-4
where R is the universal gas constant and T is the temperature. Almost constant value for viscous creep increases drastically at transition stress and then is decreasing with increasing stress for the power-law creep mechanism.
Steady state creep rates are proportional to applied stress up to about 100 MPa at 873 K, as can be seen from the Fig. 3. At higher stresses, viscous creep is replaced by the power-law creep having a stress exponent of about 10. The data points for power-law creep regime were measured and published earlier [5]. The transition from viscous to power law creep can be also clearly illustrated by the dependence of apparent activa-
P-91 0 q A -
923 K 898 K 873 K
4.10-4
3.10-' .7 MPa -6 w
10-l'
2,10-*
lo-‘3
t
,
,
1
10
100
1.10-4
1000
CT [MPal 0 0
3.106
9.106
6.106
t ISI Fig.
1. Typical
creep curves
at low stresses.
T=
898 K.
Fig. 3. Stress dependence of the steady state creep rate in both power-law and viscous regimes. The data points for power-law regime are taken from [S]. Data obtained by the helicoid spring specimen technique are marked by open symbols.
L. Kloc,
964
V. SklenZka
/Materials
Science
and Engineering
A234-236
(1997)
962-965
4.3. A map of creep mechanisms 750
P-91
When the material may deform by several different mechanisms, it is convenient to present these mechanisms in the form of a deformation mechanism map [14]. The creep deformation mechanisms map (Fig. 5) was derived from the results in the coordinates temperature vs. stress. The potential service loading conditions for the steel under consideration, i.e. temperatures 850-875 K and stresses 50-100 MPa are fully involved in the viscous creep regime, though it is not very distant from the transition to power-law creep. Therefore, viscous creep should be taken into consideration, mainly for the applications where the dimension stability is critical.
600 a 5
450
2 0"
300
I
1
,
I
,
I
I
10
,
I
,
,
100
1000
U hAPa Fig. 4. Dependence of the apparent activation energy stress. The curve is derived from fitted lines in Fig. 3.
on applied
5. Conclusions
4. Discussion 4.1. Transition from viscous to power-law creep The lines in the Fig. 3 are plotted under assumption, that both power-law and viscous mechanisms are independent and act in parallel. i,=i,+i,=ao+ba”
(3)
where i, is the steady state creep rate, i, is the rate of viscous mechanism, i, is the rate of power-law mechanism and a, b and n are temperature dependent parameters. It can be seenthat the assumption provides good representation of experimental data.
The creep behaviour of a 9% chromium steel (P-91 type) was investigated at temperatures from 873 to 923 K and at stressesbelow 100 MPa using the helicoid spring specimens technique. A detailed analysis of creep data showed that the viscous creep regime is inherent to the creep test conditions used. Mutual comparison of the creep results obtained by the helicoid spring specimen technique with the results of standard uniaxial tensile creep tests on the steel investigated has shown very good coherency of both creep test techniques. The transition from power-law creep with the stress exponent of about 10 to the viscous creep was found at stressesaround 100 MPa at 873 K. Any extrapolation from the power-law creep regime to stressesbelow 100 MPa may lead to serious underestimation of the creep rate predicted.
4.2. The mechanismof the viscous creep Two different mechanisms have been proposed for viscous creep. The first is Nabarro-Herring [6,7] and/or Coble [8] diffusional creep. The second is HarperDorn dislocation creep [9]. The main difference between both mechanismsconsists in grain size dependence. Since the material of only one grain size was used, the results do not provide any basis for the creep mechanism identification. The measured value of apparent activation energy for viscous creep regime is comparable or even lower than activation enthalpy of grain boundary diffusion [lo-121. On the other hand, the dislocation Harper-Dorn creep mechanism should be controlled by the pipe diffusion under the applied conditions [13]. The low value of apparent activation energy then provides no additional information about the possible mechanism.
100
7
50
% b
20
10
820
850
900
950
980
T [KI Fig. 5. Creep on Fig. 3.
deformation
mechanism
map derived
from
the results
L. Kloc,
V. SkleniCka
/ Materials
Science
Acknowledgements Financial support for this work was provided in part by the Grant Agency of the Academy of Sciences of the Czech Republic under Contract No. A2041702, and in part by the Ministry of Education of the Czech-Republic under Contract No. OC 501.20
References [l] B. Burton, G.W. Greenwood, Metal. Sci. J. 4 (1970) [2] J. Fiala, J. Cadek, Metall. Mater. 20 (1982) 277.
215.
and Engineering
A234-236
(1997)
962-965
965
[3] J. Novotng, J. Fiala, J. cadek, Metall. Mater. 23 (1985) 329. [4] J.C.M. Li, Acta Metall. 11 (1963) 1269. [5] V. SkleniEka, K. Kucharova, A. Dlouhy, J. KrejEi, in: D. Coutsouradis et al. (Eds.), Materials for Advanced Power Engineering, Part I, Liege, 1994, p. 435. [6] F.R.N. Nabarro, Report of Conference on Strength of Solids, Phys. Sot., London, 1948, p. 75. [7] C. Herring, J. Appl. Phys. 21 (1950) 437. [8] R.L. Coble, J. Appl. Phys. 34 (1963) 1679. [9] J.G. Harper, J.E. Dorn, Acta Metall. 5 (1957) 654. [lo] A.M. Huntz, P. Guiraldenq, M. Aucouturier, P. Lacombe, Mem. Sci. Rev. Metall. 66 (1969) 86. [ll] F. Chaix, A.M. Huntz, Mem. Sci. Rev. Metall. 71 (1974) 115. [12] J. Cermak, J. RbiiEkova, A. Pokorna, Ser. Mater. 35 (1996) 411. [13] A.H. Chokshi, Ser. Metall. 19 (1985) 529. [14] M.F. Ashby, Acta Metall. 20 (1972) 887.
Transition
Materials Science and Engineering A234+236 (1997) 962-965
from power-law to viscous creep behaviour type heat-resistant steel
of P-91
LuboS Kloc *, VAclav SkleniEka Institute of Physics of Materials,
Academy
of Sciences
of the Czech Republic,
.&kooa
22, CZ-61662
Brno,
Czech Republic
Received 18 February 1997; received in revised form 14 March 1997
Abstract Short-term creeptestswere performed on a 9% Cr (P-91 type) steelat temperaturesfrom 873 to 923 K and at stresses below 100MPa by means of the helicoid spring specimens technique. The steady state creep rates correspond to viscous behaviour under the above conditions,characterizedby the apparentstressexponentcloseto 1. Sincethe stressexponent at higher stresses is about 10, the changein the deformation mechanismat lower stresses is evident. The deformation mechanisms map resultingfrom the presenteddata showsthat the serviceloading conditionsrespondto the viscouscreep.Extrapolation from power-lawcreepregime to low stresses can causeseriousunderestimationof predicted deformation rates. The primary stagecan be describedby the Li’s equation.Preliminary annealingat 873 K for 1.8x lo7 s reducesthe primary strain, but it hasno effect on the steady statecreep rate. 0 1997ElsevierScienceS.A. Keywords:
Viscous creep; Power-law creep; Heat-resistant steel; Extrapolation
1. Introduction Current knowledge of the creep mechanisms is based mainly on short-term laboratory experiments in powerlaw creep regime with creep rates higher than 10~ lo s ~ I. How ever, service loading of real high temperature components may lead to the rates lower than lo- ‘* s ~ I, which are typical for viscous creep. It is generally accepted that the creep mechanism can change at very
difficulties with specimen preparation. The newly developed technology of the specimen preparation by machining from tube enables an application of the technique to heat-resistant structural materials.
2. Experimental material and procedures The experiments were conducted using a P-91 type
low creep rates. Unfortunately, experimental data de-
heat resistant steel produced by Vikovice Steel
scribing viscous creep regime in structural materials are lacking, because their limited microstructural stability does not enable to run experiments at very high temperatures, where the viscous creep can also be observed at higher strain rates. The need for reliable data on the creep behaviour of heat-resistant steels at very low creep rates is evident. At present, the technique of helicoid spring specimens [l-3] is the only one which enables detection of the creep rates lower than lo- ‘* s-l. The technique has been used for experiments on model materials such as pure metals or simple solid solutions because of
(Vitkovice, Czech Republic). A tube from trial melt was supplied in a ‘ready to use’ condition. Chemical composition of the material was (in wt.%): 8.5 Cr, 0.88 MO, 0.43 Si, 0.4 Mn, 0.23 V, 0.1 Ni, 0.1 Nb, 0.1 C, 0.045 N, 0.018 Al, 0.015 P, 0.006 S. Helicoid spring specimens were machined from the tube. Most specimens were used for testing without any prior treatment, but some specimens were annealed at 873 K for 1.8 x 10’ s (6OO”C, 5000 h). The creep tests were conducted in the protective atmosphere of a purified argon. Optical measurements of individual coil spacings were performed periodically and the creep strains were derived. Since the stress and strain in helicoid spring are essentially shear ones, they were transformed to the equivalent tensile quantities using a known relations 0 = fi and
*Corresponding author. Tel.: 41218657; e-mail: [email protected]
+ 42 5 7268441; fax: +42
5
0921-5093/97/$17.00 0 1997 El sevier Science S.A. All rights reserved. PIISO921-5093(97)00364-X
L. Kloc,
V. Skleni?ka
/ Materials
Science
and Engineering
E = y/J?, where g is tensile stress, r is shear stress, E is tensile strain and y is shear strain.
A234-236
(1997)
962-965
963
&lo-' P-91
6.10-'
3. Experimental 3.1.
results w
Creep curves
Examples of creep curves measured in present experiments are shown in Fig. 1. The creep curves are characterized by pronounced primary stage, after which steady state commenced. Since the technique is based on self-loaded specimens, no initial strain at loading is included. The creep curves can be fitted by the equation derived by Li [4]: r=(,i~ln(l+~(l
-exp(
(1)
-$))+i,,,
where E is the strain, ki is the initial strain rate, i, is the steady state strain rate, t, is the primary stage relaxation period and t is the time. Steady state creep rates are about three orders of magnitude lower then initial ones. Duration of primary stage, characterized by the t, parameter, is stress independent. Preliminary long-term annealing reduces the primary strain and the primary stage duration by about 40%, but it has no effect on the steady state creep rate (Fig. 2). 3.2. Steady state creep rates
4.1o-4
2.10-'
0 0
2.106
4.106 t
Fig. 2. The effect creep curve.
of preliminary
6.106
Is1
annealing
for
5000 h at 873 K on
tion energy on applied stress (Fig. 4). The apparent activation energy Qa is defined as c-4
where R is the universal gas constant and T is the temperature. Almost constant value for viscous creep increases drastically at transition stress and then is decreasing with increasing stress for the power-law creep mechanism.
Steady state creep rates are proportional to applied stress up to about 100 MPa at 873 K, as can be seen from the Fig. 3. At higher stresses, viscous creep is replaced by the power-law creep having a stress exponent of about 10. The data points for power-law creep regime were measured and published earlier [5]. The transition from viscous to power law creep can be also clearly illustrated by the dependence of apparent activa-
P-91 0 q A -
923 K 898 K 873 K
4.10-4
3.10-' .7 MPa -6 w
10-l'
2,10-*
lo-‘3
t
,
,
1
10
100
1.10-4
1000
CT [MPal 0 0
3.106
9.106
6.106
t ISI Fig.
1. Typical
creep curves
at low stresses.
T=
898 K.
Fig. 3. Stress dependence of the steady state creep rate in both power-law and viscous regimes. The data points for power-law regime are taken from [S]. Data obtained by the helicoid spring specimen technique are marked by open symbols.
L. Kloc,
964
V. SklenZka
/Materials
Science
and Engineering
A234-236
(1997)
962-965
4.3. A map of creep mechanisms 750
P-91
When the material may deform by several different mechanisms, it is convenient to present these mechanisms in the form of a deformation mechanism map [14]. The creep deformation mechanisms map (Fig. 5) was derived from the results in the coordinates temperature vs. stress. The potential service loading conditions for the steel under consideration, i.e. temperatures 850-875 K and stresses 50-100 MPa are fully involved in the viscous creep regime, though it is not very distant from the transition to power-law creep. Therefore, viscous creep should be taken into consideration, mainly for the applications where the dimension stability is critical.
600 a 5
450
2 0"
300
I
1
,
I
,
I
I
10
,
I
,
,
100
1000
U hAPa Fig. 4. Dependence of the apparent activation energy stress. The curve is derived from fitted lines in Fig. 3.
on applied
5. Conclusions
4. Discussion 4.1. Transition from viscous to power-law creep The lines in the Fig. 3 are plotted under assumption, that both power-law and viscous mechanisms are independent and act in parallel. i,=i,+i,=ao+ba”
(3)
where i, is the steady state creep rate, i, is the rate of viscous mechanism, i, is the rate of power-law mechanism and a, b and n are temperature dependent parameters. It can be seenthat the assumption provides good representation of experimental data.
The creep behaviour of a 9% chromium steel (P-91 type) was investigated at temperatures from 873 to 923 K and at stressesbelow 100 MPa using the helicoid spring specimens technique. A detailed analysis of creep data showed that the viscous creep regime is inherent to the creep test conditions used. Mutual comparison of the creep results obtained by the helicoid spring specimen technique with the results of standard uniaxial tensile creep tests on the steel investigated has shown very good coherency of both creep test techniques. The transition from power-law creep with the stress exponent of about 10 to the viscous creep was found at stressesaround 100 MPa at 873 K. Any extrapolation from the power-law creep regime to stressesbelow 100 MPa may lead to serious underestimation of the creep rate predicted.
4.2. The mechanismof the viscous creep Two different mechanisms have been proposed for viscous creep. The first is Nabarro-Herring [6,7] and/or Coble [8] diffusional creep. The second is HarperDorn dislocation creep [9]. The main difference between both mechanismsconsists in grain size dependence. Since the material of only one grain size was used, the results do not provide any basis for the creep mechanism identification. The measured value of apparent activation energy for viscous creep regime is comparable or even lower than activation enthalpy of grain boundary diffusion [lo-121. On the other hand, the dislocation Harper-Dorn creep mechanism should be controlled by the pipe diffusion under the applied conditions [13]. The low value of apparent activation energy then provides no additional information about the possible mechanism.
100
7
50
% b
20
10
820
850
900
950
980
T [KI Fig. 5. Creep on Fig. 3.
deformation
mechanism
map derived
from
the results
L. Kloc,
V. SkleniCka
/ Materials
Science
Acknowledgements Financial support for this work was provided in part by the Grant Agency of the Academy of Sciences of the Czech Republic under Contract No. A2041702, and in part by the Ministry of Education of the Czech-Republic under Contract No. OC 501.20
References [l] B. Burton, G.W. Greenwood, Metal. Sci. J. 4 (1970) [2] J. Fiala, J. Cadek, Metall. Mater. 20 (1982) 277.
215.
and Engineering
A234-236
(1997)
962-965
965
[3] J. Novotng, J. Fiala, J. cadek, Metall. Mater. 23 (1985) 329. [4] J.C.M. Li, Acta Metall. 11 (1963) 1269. [5] V. SkleniEka, K. Kucharova, A. Dlouhy, J. KrejEi, in: D. Coutsouradis et al. (Eds.), Materials for Advanced Power Engineering, Part I, Liege, 1994, p. 435. [6] F.R.N. Nabarro, Report of Conference on Strength of Solids, Phys. Sot., London, 1948, p. 75. [7] C. Herring, J. Appl. Phys. 21 (1950) 437. [8] R.L. Coble, J. Appl. Phys. 34 (1963) 1679. [9] J.G. Harper, J.E. Dorn, Acta Metall. 5 (1957) 654. [lo] A.M. Huntz, P. Guiraldenq, M. Aucouturier, P. Lacombe, Mem. Sci. Rev. Metall. 66 (1969) 86. [ll] F. Chaix, A.M. Huntz, Mem. Sci. Rev. Metall. 71 (1974) 115. [12] J. Cermak, J. RbiiEkova, A. Pokorna, Ser. Mater. 35 (1996) 411. [13] A.H. Chokshi, Ser. Metall. 19 (1985) 529. [14] M.F. Ashby, Acta Metall. 20 (1972) 887.