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Measurement of hydrogen transport in a duplex stainless steel
Scripta METALLURGICA et MATERIALIA
Vol.
25, pp. 2657-2662, 1991 Printed in the U.S.A.
Pergamon Press plc All rights reserved
MEASUREMENT OF HYDROGEN TRANSPORT IN A DUPLEX STAINLESS STEEL
R B Hutchings, A Turnbull and A T May Division of Materials Metrology, National Physical Laboratory, Teddington, Middlesex, UK
(Received June 26, 1991) (Revised September 18, 1991) Introduction Duplex stainless steels offer improved resistance to stress corrosion cracking compared to 304 or 316 stainless steels, but in appropriate conditions they can be induced to fail by hydrogen embrittlement depending on the extent of hydrogen charging, mechanical testing conditions and the prior heat treatment of the alloy. Hydrogen atoms can be generated by locailsed corrosion, by cathodic charging associated with cathodic protection schemes or by galvanic interaction (for example, with a carbon steel under downhole conditions). There has been discussion in the literature concerning the transport of hydrogen atoms in duplex stainless steel (1,2) because of its implications to the failure process, charging time for experiments and the evaluation of the discharge time necessary to recover initial hydrogen-free material properties, but no detailed evaluation of hydrogen atom transport has been published. This paper describes experimental measurements to characterise hydrogen transport in a duplex stainless steel and assesses the implications for stress corrosion testing. Experimental Method Material and applied thermal treatments The material investigated was Uranus B50 duplex stainless steel supplied in a hot-rolled condition. The composition in mass% was C:0.06, Cr:21.6, Ni:6.30, Mo:2.51, Si:0.87, Cu:0.77, Mn:0.63, S:0.01, P: < 0.01. The as-received material contained about 44% austenite (3') phase embedded in the ferrite (c0 matrix and elongated in the rolling direction. Membranes of varying thickness were prepared by machining sections parallel and perpendicular to the rolling direction. These are referred to in the text as longitudinal and transverse, respectively. The direction of hydrogen flux was perpendicular to the elongated direction of the austenite phase in the longitudinal membranes, and parallel in the transverse membranes. Thermal treatment was applied as detailed in Table 1 to yield material containing varying volume fractions of the .y phase. Because of equipment limitation during much of the test programme, homogenisation at 1573 K could not be applied to all of the specimens prior to the lower temperature treatment. Hence, the microstructures of the materials thermally treated at 1473 K and less showed some retention of the 3,-phase orientation of the as-received material. TABLE 1 Volume Fraction of Austenite in Uranus B50 Duplex Stainless Steel after Heat Treatment. (Volume Fraction of As-received Material was 44%)
Heat t r e a t m e n t
(K)
temperature
Duration
(s)
Quench Medium
Volume o f a u s t e n i t e (~)
1323 1373 1473 1573
3600 3600 3600 3600
water water water oil
33 14 5 0
2657 0036-9748/91 $3.00 + .00 Copyright (c) 1991 Pergamon Press plc
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Image analysis techniques were used to evaluate the volume fraction of austenite. Discrimination of the two phases is readily possible using a scanning electron microscope with a backscatter detector which is sensitive to the chromium content of the phases. Permeation technique The electrochemical permeation technique was used to characterise hydrogen transport. An adaptation of the Devanathan-Stachurski (3) two-compartment cell (1 iitre and 0.1 litre charging and oxidation cells respectively) was used, but with the important distinction that the material used to construct the cell was PTFE with "Viton" O-rings. T h e full details of this cell as described elsewhere (4). The use of PTFE is necessary for the tests conducted at 353 K because standard laboratory glassware leaches out silicates at elevated temperatures which, on deposition on the metal surface during cathodic charging, can significantly affect the permeation transient (5). The thickness of the membranes ranged from 9.4 x 10 -5 m to 5.24 x 10 .-4 m, the range reflecting the need to ensure volume control of hydrogen transport over the range of temperature and charging conditions. The membranes were prepared initially to a lapped finish then mechanically polished progressively, finishing with 1 x 10 - 6 m diamond paste. T h e area of the specimen exposed to the environment was 4.8 × 10 - 4 m 2. The environment in both charging and oxidation cells was deaerated 0.1M NaOH prepared using triple distilled water with Aristar grade NaOH. The choice of 0.1M NaOH reflected the need to ensure constancy of the environment at the metal surface and in the solution over the period of the test and the high purity NaOH was used to avoid deposition of impurities from the solution which had been shown previously (5) to be a problem in using Analar grade reagent. The applied potential on the oxidation surface of the membrane was set to + 0.300 V with respect to the saturated calomel electrode (SCE) at 298 K. This potential was chosen to ensure that, for all charging conditions, the hydrogen atom oxidation rate was transport limited and, thus, a boundary condition of zero hydrogen concentration at the oxidation side of the membrane was satisfied. The electrode potential was monitored in-situ using double junction saturated calomel electrodes via salt-bridges containing 0 A M NaOH and constructed of PTFE tubing plugged with porous ceramic rods. Small changes in temperature can cause significant changes in the measured permeation current and hence the permeation cell was located in a thermostat bath controlled at the desired temperature. Tests were carried out at temperatures of 295.2 K, 323.2 K and 353.2 K. The cell temperature, monitored in--situ, was stable to better than + 0.3 K. Procedure Solution was added to both cell compartments after sandwiching the membrane between the ceils using a clamping arrangement. Vigorous deaeration with argon was applied to expel oxygen quickly (usually about 1200 s) and the potential in the oxidation cell set to the desired potential. Deaeration was continued but at a reduced rate. There was no specific stirring of the solution except by the bubbling of argon. Upon attaining a low stable passive current density (typically < 2 x 10 - 4 A m - 2 ) , cathodic charging was applied galvanostatically using an applied current of 10 A m -2. The time to achieve a steady--state permeation current depended on the membrane thickness and temperature but usually took several days. At steady--state the galvanostatic charging was interrupted, and the potential of the electrode in the charging cell was set to 0.0 V (SCE) to oxidise the hydrogen atoms emerging from the interior of the material. T h e transient current measured on the oxidation half-cell was allowed to decay to the level of the passive current again, and the gavanostatic charging was reapplied to yield a second rising transient. Results and Discussion The
most
effective
representation
of
permeation
transients
for
analytical
purposes
is
in
terms
of
a
Vol.
25, No.
12
HYDROGEN
TRANSPORT
2659
dimensionless plot of the normalised flux (J/JQo) as a function of the dimensionless time parameter, 7, where T is calculated from (DNt/a2). a is the membrane thickness, t is the time elapsed since the start of the permeation transient, and D N is the diffusion coefficient for hydrogen in the lattice (4). T h e normalised flux was calculated from the ratio of the current, it, at time t, to the steady state permeation current, i~, after subtracting the background values. Full details of the )aermeation currents for each test are given elsewhere (6) but values of io~a of 1.7x10 - 6 Am -1 and 7.5x10 - ° Am -1 were typical for the as-received material at temperatures of 295.2 K and 353.2 K respectively. The choice of the normalisation parameter D N is arbitrary provided it is used in a consistent manner. It is usually convenient to relate it to the lattice diffusion coefficient of the material (4). In a complex alloy and particularly a two-phase one the choice is less obvious. Nevertheless, a value of D N equivalent to the lattice diffusion coefficient of pure iron, (D N = 7.2 x 10 - 9 m2s -1 at 295.2 K, D N = 8.7 x 10 - 9 m 2 s -1 at 323.2 K and D N = 1.0 × 10 -8 m2s -1 at 353.2 K) has been used for comparative purposes but it should be stressed that this does not affect the analysis or interpretation of the data but merely affects the presentation. A first stage in analysis of permeation transients is to demonstrate that the transient reflects only transport within the bulk of the material and is not influenced by surface processes. This can be established by varying the thickness of the specimen. Examples of measured permeation transients obtained at 353.2 K for different thicknesses of longitudinal specimens of the as-received material are plotted in Fig 1. It is evident that within the scatter of the data, there is no significant effect of thickness on these normalised transients. Since partial surface control of transport would result in a relative shift in the permeation transient along the time-related axis (because there would be no simple scaling on a2), it can be concluded reliably that the permeation transients reflect volume control of the process. This has been verified also at 295.2 K which is not surprising since diffusion is much slower at ambient temperature and volume control more likely. The variability in the permeation transients at 353.2 K is about -+ 50% which is not ideal but is not untypical of tests at this elevated temperature (5). The first and subsequent permeation transients obtained using longitudinal specimens of the as-received material (thickness of about 1 x 10 - 4 m) at 295.2 K are shown in Fig 2. Several sets of data are shown representing results of repetitive transients on two individual specimens. Good agreement was obtained between first and subsequent transients on an individual specimen indicating that irreversible trapping does not significantly influence hydrogen atom transport in this alloy (the presence of irreversible trapping would be reflected in a more rapid second transient). However, there are differences evident in the permeation transients obtained using two different specimens despite the good reproducibility of first and second transients for each case. To assess the influence of the test procedure, a test was repeated on one of the specimens. Very good agreement was obtained with the previous tests (Fig 2) suggesting that the variability in results for different specimens reflected variability in the material, rather than variability in the test procedure, though further tests are desirable for confirmation. Since the volume fraction of the "y phase showed no variation between membranes, the most likely explanation for variation of the permeation transients between specimens is associated with variability in orientation of the 3' phase in the as-received alloy, which, as indicated below, can effect the permeation rate. The permeation transient derived from Fick's second law is also shown in Fig 2 and since the normalisation diffusion coefficient is based on pure iron, this figure gives an indication of the reduced diffusivity associated with the duplex alloy. It is apparent that the shapes of the measured transients and that derived from Fick's law are very similar indicating that it is acceptable to use an effective diffusion coefficient (Deft) to describe the results. The effect of thermal treatment on D e tf is represented in Fig 3 in the form of a plot of D e tf against volume fraction of the austenite phase. Included in the figure are values of D e tf obtained from transverse and longitudinal specimens from the as-received material. There is an increase of about a factor of two in diffusivity of hydrogen atoms in the transverse specimens though with some spread in the results reflecting the variability in the material. This increase of a factor of two is predicted based on transport theory for composite materials (6). Fig 3 shows that the diffusivity decreases with increasing volume fraction of the austenite. There is no detailed theory of hydrogen transport in duplex materials which accounts for the discontinuity of the embedded austenite phase and differences in diffusion coefficient and solubility. An approximate approach to diffusion in a two-phase solid, assuming continuity of both phases, indicated that the diffusion coefficient of the austenite
2660
HYDROGEN TRANSPORT
Vol.
25, No.
(about 3 × 10 -16 m2s-1 at 293 K (6)) was too low to affect the diffusivity of the composite material. Based on this conclusion, multiple-trap theory was used (6) to derive an effective diffusion coefficient for the duplex material viz.
Deff 1 + nT07/n~0~+ N l k l / P l + N2k2/P2 where D N is the lattice diffusion coefficient for w-iron, ~0 is a tortuosity factor (~0 = 0.39 when the hydrogen atom flux is perpendicular to the elongated 7 phase at 44% volume fraction), n is the number of interstitial sites for hydrogen atoms per unit volume, 0 is fraction of sites occupied, subscripts 7 and c~ refer to the austenitic and ferritic phases, and N, k and p are respectively the density of reversible trap sites and the rate constants for transfer into and out of the trap sites. The subscript 1 refers to the dominant trap site in the ferritic phase and the subscript 2 refers to the ferrite-anstenite interracial trap site. Nlkl/Pl were estimated from the fully ferritic alloy (1573K heat treatment) to be about 1.2 x 103. Substituting this value into the above equation, but using the value of D etf measured at 44% austenite (Fig 4), n~ O../n~0~ + N2k2/P2 is then estimated to be about 4.7 x 105. Using solubility data from Kuichi and McLel~anr ( ~ and from Perng and Aistetter (8) the value of .n.z0~nc~0c~ at 293K is calculated to be of the order ot 4 x 102. Hence, trapping due to the enhanced solubifity of the austenite phase can be neglected and interracial trapping must be considered to be the most likely explanation for the reduced diffusivity of the duplex steel. The effective diffusivity of the as-received material (longitudinal specimens) increases exponentially with temperature as shown by Fig 4 with an apparent activation energy of about 3.66 x 1 0 " 3 tool-land a pre-exponential factor of 4.6x10 -8 m2s-1. These data enable an estimate to be made of the rate of charging of specimens used in environment assisted cracking tests and also the rate of recovery of initial properties following prior charging. For a cylindrical specimen of radius r which is charged uniformly, the time to achieve a steady state concentration of hydrogen atoms is given approximately (9) by tss = r2'/Deff. Charging times for different radii at various temperatures are shown in Table 2. A radius of about 1.5 x 10 -3 m is typical of tensile specimens for slow strain rate testing and was used by Cohen et al (1) and by Zheng and Hardie (2). The very long periods required for charging (and equivalently in discharging) give a clear explanation for the surface nucleated cracking observed at these test temperatures and for the very prolonged periods necessary to recover hydrogen-free mechanical properties in initially thermally-charged specimens (2).
TABLE 2 Estimated Time to Achieve Steady-State in Charging of a Uranus B50 Duplex Stainless Steel
Specimen r a d i u s (m)
Temperature (K)
Def f (m2s -1 )
Charging time (s)
1.5x10 -3 3.0x10 -3
295.2
1 . S x l 0 -14
1.5x108 6.0x108
1.5×10 -3 3.0x10 -3
323.2
5.6x10 -14
4.0x107 1.6x108
1.5x10 -3 3.0x10 -3
353.2
1.8x10 -13
1.3x107 S.0xl07
12
Vol.
25, No.
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HYDROGEN T R A N S P O R T
266
Conclusions The orientation of the austenite phase relative to the direction of hydrogen atom flux influences the hydrogen atom diffusivity. The values of D etf are greater when the elongated austenite phase is orientated parallel with the direction of hydrogen flux. Variability in the permeation transients for different specimens of the same nominal orientation is considered to reflect non-uniformity in orientation of the austenite phase. The effective diffusion coefficient varies exponentially with temperature with an apparent activation energy of about 3.66 × 104 J mo1-1. The reduced diffusivity of hydrogen atoms in the duplex alloy is considered to be associated primarily with trapping at the ferrite-austenite interface. Charging and discharging times at temperatures up to 353.2 K are very long for typical slow strain rate specimens and explain the slow recovery of mechanical properties in prior-charged specimens. References 1 2 3 4 5 6 7 8 9
L. Cohen, J. Charles and (3. Smith. Proc. of Hydrogen Effects on Material Behaviour. p.363, TMS Warrendale (1990). W. Zheng and D. Hardie. Corros. Sci. 32, 23 (1991). M. Devanathan and Z. Stachurski. Proc. Roy. Soc. A270, 90 (1962). A. Turnbull, M. Saenz de Santa Maria and N. Thomas. Corros. Sci. 29, 89 (1989). A. Turnbull, R.(3. Ballinger, I.S. Hwang and R.M. Gates. Proc. of Hydrogen Effects on Material Behaviour, p.121, TMS, Warrendale (1990). A. Turnbull and R.B. Hutchings. Hydrogen diffusion and trapping in a duplex stainless steel, to be published. K. Kuichi and R.B. McLellan. Acta Metall. 31, 961 (1983). T.P.Perng and C.J. Alstetter. Acta Metall. 34, 1771 (1986). J. Crank. The Mathematics of Diffusion (2rid edn), p.79, Clarendon Press, Oxford (1975).
1.0, Permeotlon tronsient
']
Membrane thickness (/11 x 10-6)
2 3 0.~ J/J.
0 c, o
't
e
1
~oz
108 op
o~'o ® 245 496
0.4!
o '~.'® o~# o ~a o~
0.2
L~gt 102
103
I )0 &
105
106
~(DNt/Q2)
Fig.1
Effect of membrane thickness on rising permeation transients for Uranus B50 stainless steel in 0.1M NaOH at 353K. (Longitudinal membrane orientation)
2662
HYDROGEN
TRANSPORT
Vol.
o.... ,,oo t . . . . ient
•
•
12
i
•
8
;.?
•
J/J-
t Latt,ce
t
02
j
i eA
!
=`
I I
¢-~
4
i eA •
_
10-2
Fig.2
~... ""
l#
o8
06
t
25, No.
10-1
©
i
-
100 104 Z(DNt/O Z )
I
]
105
106
Rising permeation transients for Uranus B50 stainless steel in 0.1M NaOH at 295K. (longitudinal membrane orientation). Open or part-~pen points represent tests on same specimen (see text).
i0-n Membrane orientation
Temperature (K)
o Longitudinal Transverse • Longitudinal
295.2 2952 353.2 10-12
10-12
o
=
,= ~ 10-13 d
1043
8 10-14 2.8
30
3,
34
o
r
10
i
I
20 30 Austemte volume fraction (%)
Fig.3 Variation of the effective diffusion coefficient, Deft, with volume fraction of in Uranus B50 duplex stainless steel.
I 40
Fig.4 Variation of the effective diffusion coefficient, Deft, with the reciprocal of temperature for Uranus BS0 stainless steel. (Longitudinal membrane orientation)
12
Vol.
25, pp. 2657-2662, 1991 Printed in the U.S.A.
Pergamon Press plc All rights reserved
MEASUREMENT OF HYDROGEN TRANSPORT IN A DUPLEX STAINLESS STEEL
R B Hutchings, A Turnbull and A T May Division of Materials Metrology, National Physical Laboratory, Teddington, Middlesex, UK
(Received June 26, 1991) (Revised September 18, 1991) Introduction Duplex stainless steels offer improved resistance to stress corrosion cracking compared to 304 or 316 stainless steels, but in appropriate conditions they can be induced to fail by hydrogen embrittlement depending on the extent of hydrogen charging, mechanical testing conditions and the prior heat treatment of the alloy. Hydrogen atoms can be generated by locailsed corrosion, by cathodic charging associated with cathodic protection schemes or by galvanic interaction (for example, with a carbon steel under downhole conditions). There has been discussion in the literature concerning the transport of hydrogen atoms in duplex stainless steel (1,2) because of its implications to the failure process, charging time for experiments and the evaluation of the discharge time necessary to recover initial hydrogen-free material properties, but no detailed evaluation of hydrogen atom transport has been published. This paper describes experimental measurements to characterise hydrogen transport in a duplex stainless steel and assesses the implications for stress corrosion testing. Experimental Method Material and applied thermal treatments The material investigated was Uranus B50 duplex stainless steel supplied in a hot-rolled condition. The composition in mass% was C:0.06, Cr:21.6, Ni:6.30, Mo:2.51, Si:0.87, Cu:0.77, Mn:0.63, S:0.01, P: < 0.01. The as-received material contained about 44% austenite (3') phase embedded in the ferrite (c0 matrix and elongated in the rolling direction. Membranes of varying thickness were prepared by machining sections parallel and perpendicular to the rolling direction. These are referred to in the text as longitudinal and transverse, respectively. The direction of hydrogen flux was perpendicular to the elongated direction of the austenite phase in the longitudinal membranes, and parallel in the transverse membranes. Thermal treatment was applied as detailed in Table 1 to yield material containing varying volume fractions of the .y phase. Because of equipment limitation during much of the test programme, homogenisation at 1573 K could not be applied to all of the specimens prior to the lower temperature treatment. Hence, the microstructures of the materials thermally treated at 1473 K and less showed some retention of the 3,-phase orientation of the as-received material. TABLE 1 Volume Fraction of Austenite in Uranus B50 Duplex Stainless Steel after Heat Treatment. (Volume Fraction of As-received Material was 44%)
Heat t r e a t m e n t
(K)
temperature
Duration
(s)
Quench Medium
Volume o f a u s t e n i t e (~)
1323 1373 1473 1573
3600 3600 3600 3600
water water water oil
33 14 5 0
2657 0036-9748/91 $3.00 + .00 Copyright (c) 1991 Pergamon Press plc
2658
HYDROGEN T R A N S P O R T
Vol.
25, No.
12
Image analysis techniques were used to evaluate the volume fraction of austenite. Discrimination of the two phases is readily possible using a scanning electron microscope with a backscatter detector which is sensitive to the chromium content of the phases. Permeation technique The electrochemical permeation technique was used to characterise hydrogen transport. An adaptation of the Devanathan-Stachurski (3) two-compartment cell (1 iitre and 0.1 litre charging and oxidation cells respectively) was used, but with the important distinction that the material used to construct the cell was PTFE with "Viton" O-rings. T h e full details of this cell as described elsewhere (4). The use of PTFE is necessary for the tests conducted at 353 K because standard laboratory glassware leaches out silicates at elevated temperatures which, on deposition on the metal surface during cathodic charging, can significantly affect the permeation transient (5). The thickness of the membranes ranged from 9.4 x 10 -5 m to 5.24 x 10 .-4 m, the range reflecting the need to ensure volume control of hydrogen transport over the range of temperature and charging conditions. The membranes were prepared initially to a lapped finish then mechanically polished progressively, finishing with 1 x 10 - 6 m diamond paste. T h e area of the specimen exposed to the environment was 4.8 × 10 - 4 m 2. The environment in both charging and oxidation cells was deaerated 0.1M NaOH prepared using triple distilled water with Aristar grade NaOH. The choice of 0.1M NaOH reflected the need to ensure constancy of the environment at the metal surface and in the solution over the period of the test and the high purity NaOH was used to avoid deposition of impurities from the solution which had been shown previously (5) to be a problem in using Analar grade reagent. The applied potential on the oxidation surface of the membrane was set to + 0.300 V with respect to the saturated calomel electrode (SCE) at 298 K. This potential was chosen to ensure that, for all charging conditions, the hydrogen atom oxidation rate was transport limited and, thus, a boundary condition of zero hydrogen concentration at the oxidation side of the membrane was satisfied. The electrode potential was monitored in-situ using double junction saturated calomel electrodes via salt-bridges containing 0 A M NaOH and constructed of PTFE tubing plugged with porous ceramic rods. Small changes in temperature can cause significant changes in the measured permeation current and hence the permeation cell was located in a thermostat bath controlled at the desired temperature. Tests were carried out at temperatures of 295.2 K, 323.2 K and 353.2 K. The cell temperature, monitored in--situ, was stable to better than + 0.3 K. Procedure Solution was added to both cell compartments after sandwiching the membrane between the ceils using a clamping arrangement. Vigorous deaeration with argon was applied to expel oxygen quickly (usually about 1200 s) and the potential in the oxidation cell set to the desired potential. Deaeration was continued but at a reduced rate. There was no specific stirring of the solution except by the bubbling of argon. Upon attaining a low stable passive current density (typically < 2 x 10 - 4 A m - 2 ) , cathodic charging was applied galvanostatically using an applied current of 10 A m -2. The time to achieve a steady--state permeation current depended on the membrane thickness and temperature but usually took several days. At steady--state the galvanostatic charging was interrupted, and the potential of the electrode in the charging cell was set to 0.0 V (SCE) to oxidise the hydrogen atoms emerging from the interior of the material. T h e transient current measured on the oxidation half-cell was allowed to decay to the level of the passive current again, and the gavanostatic charging was reapplied to yield a second rising transient. Results and Discussion The
most
effective
representation
of
permeation
transients
for
analytical
purposes
is
in
terms
of
a
Vol.
25, No.
12
HYDROGEN
TRANSPORT
2659
dimensionless plot of the normalised flux (J/JQo) as a function of the dimensionless time parameter, 7, where T is calculated from (DNt/a2). a is the membrane thickness, t is the time elapsed since the start of the permeation transient, and D N is the diffusion coefficient for hydrogen in the lattice (4). T h e normalised flux was calculated from the ratio of the current, it, at time t, to the steady state permeation current, i~, after subtracting the background values. Full details of the )aermeation currents for each test are given elsewhere (6) but values of io~a of 1.7x10 - 6 Am -1 and 7.5x10 - ° Am -1 were typical for the as-received material at temperatures of 295.2 K and 353.2 K respectively. The choice of the normalisation parameter D N is arbitrary provided it is used in a consistent manner. It is usually convenient to relate it to the lattice diffusion coefficient of the material (4). In a complex alloy and particularly a two-phase one the choice is less obvious. Nevertheless, a value of D N equivalent to the lattice diffusion coefficient of pure iron, (D N = 7.2 x 10 - 9 m2s -1 at 295.2 K, D N = 8.7 x 10 - 9 m 2 s -1 at 323.2 K and D N = 1.0 × 10 -8 m2s -1 at 353.2 K) has been used for comparative purposes but it should be stressed that this does not affect the analysis or interpretation of the data but merely affects the presentation. A first stage in analysis of permeation transients is to demonstrate that the transient reflects only transport within the bulk of the material and is not influenced by surface processes. This can be established by varying the thickness of the specimen. Examples of measured permeation transients obtained at 353.2 K for different thicknesses of longitudinal specimens of the as-received material are plotted in Fig 1. It is evident that within the scatter of the data, there is no significant effect of thickness on these normalised transients. Since partial surface control of transport would result in a relative shift in the permeation transient along the time-related axis (because there would be no simple scaling on a2), it can be concluded reliably that the permeation transients reflect volume control of the process. This has been verified also at 295.2 K which is not surprising since diffusion is much slower at ambient temperature and volume control more likely. The variability in the permeation transients at 353.2 K is about -+ 50% which is not ideal but is not untypical of tests at this elevated temperature (5). The first and subsequent permeation transients obtained using longitudinal specimens of the as-received material (thickness of about 1 x 10 - 4 m) at 295.2 K are shown in Fig 2. Several sets of data are shown representing results of repetitive transients on two individual specimens. Good agreement was obtained between first and subsequent transients on an individual specimen indicating that irreversible trapping does not significantly influence hydrogen atom transport in this alloy (the presence of irreversible trapping would be reflected in a more rapid second transient). However, there are differences evident in the permeation transients obtained using two different specimens despite the good reproducibility of first and second transients for each case. To assess the influence of the test procedure, a test was repeated on one of the specimens. Very good agreement was obtained with the previous tests (Fig 2) suggesting that the variability in results for different specimens reflected variability in the material, rather than variability in the test procedure, though further tests are desirable for confirmation. Since the volume fraction of the "y phase showed no variation between membranes, the most likely explanation for variation of the permeation transients between specimens is associated with variability in orientation of the 3' phase in the as-received alloy, which, as indicated below, can effect the permeation rate. The permeation transient derived from Fick's second law is also shown in Fig 2 and since the normalisation diffusion coefficient is based on pure iron, this figure gives an indication of the reduced diffusivity associated with the duplex alloy. It is apparent that the shapes of the measured transients and that derived from Fick's law are very similar indicating that it is acceptable to use an effective diffusion coefficient (Deft) to describe the results. The effect of thermal treatment on D e tf is represented in Fig 3 in the form of a plot of D e tf against volume fraction of the austenite phase. Included in the figure are values of D e tf obtained from transverse and longitudinal specimens from the as-received material. There is an increase of about a factor of two in diffusivity of hydrogen atoms in the transverse specimens though with some spread in the results reflecting the variability in the material. This increase of a factor of two is predicted based on transport theory for composite materials (6). Fig 3 shows that the diffusivity decreases with increasing volume fraction of the austenite. There is no detailed theory of hydrogen transport in duplex materials which accounts for the discontinuity of the embedded austenite phase and differences in diffusion coefficient and solubility. An approximate approach to diffusion in a two-phase solid, assuming continuity of both phases, indicated that the diffusion coefficient of the austenite
2660
HYDROGEN TRANSPORT
Vol.
25, No.
(about 3 × 10 -16 m2s-1 at 293 K (6)) was too low to affect the diffusivity of the composite material. Based on this conclusion, multiple-trap theory was used (6) to derive an effective diffusion coefficient for the duplex material viz.
Deff 1 + nT07/n~0~+ N l k l / P l + N2k2/P2 where D N is the lattice diffusion coefficient for w-iron, ~0 is a tortuosity factor (~0 = 0.39 when the hydrogen atom flux is perpendicular to the elongated 7 phase at 44% volume fraction), n is the number of interstitial sites for hydrogen atoms per unit volume, 0 is fraction of sites occupied, subscripts 7 and c~ refer to the austenitic and ferritic phases, and N, k and p are respectively the density of reversible trap sites and the rate constants for transfer into and out of the trap sites. The subscript 1 refers to the dominant trap site in the ferritic phase and the subscript 2 refers to the ferrite-anstenite interracial trap site. Nlkl/Pl were estimated from the fully ferritic alloy (1573K heat treatment) to be about 1.2 x 103. Substituting this value into the above equation, but using the value of D etf measured at 44% austenite (Fig 4), n~ O../n~0~ + N2k2/P2 is then estimated to be about 4.7 x 105. Using solubility data from Kuichi and McLel~anr ( ~ and from Perng and Aistetter (8) the value of .n.z0~nc~0c~ at 293K is calculated to be of the order ot 4 x 102. Hence, trapping due to the enhanced solubifity of the austenite phase can be neglected and interracial trapping must be considered to be the most likely explanation for the reduced diffusivity of the duplex steel. The effective diffusivity of the as-received material (longitudinal specimens) increases exponentially with temperature as shown by Fig 4 with an apparent activation energy of about 3.66 x 1 0 " 3 tool-land a pre-exponential factor of 4.6x10 -8 m2s-1. These data enable an estimate to be made of the rate of charging of specimens used in environment assisted cracking tests and also the rate of recovery of initial properties following prior charging. For a cylindrical specimen of radius r which is charged uniformly, the time to achieve a steady state concentration of hydrogen atoms is given approximately (9) by tss = r2'/Deff. Charging times for different radii at various temperatures are shown in Table 2. A radius of about 1.5 x 10 -3 m is typical of tensile specimens for slow strain rate testing and was used by Cohen et al (1) and by Zheng and Hardie (2). The very long periods required for charging (and equivalently in discharging) give a clear explanation for the surface nucleated cracking observed at these test temperatures and for the very prolonged periods necessary to recover hydrogen-free mechanical properties in initially thermally-charged specimens (2).
TABLE 2 Estimated Time to Achieve Steady-State in Charging of a Uranus B50 Duplex Stainless Steel
Specimen r a d i u s (m)
Temperature (K)
Def f (m2s -1 )
Charging time (s)
1.5x10 -3 3.0x10 -3
295.2
1 . S x l 0 -14
1.5x108 6.0x108
1.5×10 -3 3.0x10 -3
323.2
5.6x10 -14
4.0x107 1.6x108
1.5x10 -3 3.0x10 -3
353.2
1.8x10 -13
1.3x107 S.0xl07
12
Vol.
25, No.
12
HYDROGEN T R A N S P O R T
266
Conclusions The orientation of the austenite phase relative to the direction of hydrogen atom flux influences the hydrogen atom diffusivity. The values of D etf are greater when the elongated austenite phase is orientated parallel with the direction of hydrogen flux. Variability in the permeation transients for different specimens of the same nominal orientation is considered to reflect non-uniformity in orientation of the austenite phase. The effective diffusion coefficient varies exponentially with temperature with an apparent activation energy of about 3.66 × 104 J mo1-1. The reduced diffusivity of hydrogen atoms in the duplex alloy is considered to be associated primarily with trapping at the ferrite-austenite interface. Charging and discharging times at temperatures up to 353.2 K are very long for typical slow strain rate specimens and explain the slow recovery of mechanical properties in prior-charged specimens. References 1 2 3 4 5 6 7 8 9
L. Cohen, J. Charles and (3. Smith. Proc. of Hydrogen Effects on Material Behaviour. p.363, TMS Warrendale (1990). W. Zheng and D. Hardie. Corros. Sci. 32, 23 (1991). M. Devanathan and Z. Stachurski. Proc. Roy. Soc. A270, 90 (1962). A. Turnbull, M. Saenz de Santa Maria and N. Thomas. Corros. Sci. 29, 89 (1989). A. Turnbull, R.(3. Ballinger, I.S. Hwang and R.M. Gates. Proc. of Hydrogen Effects on Material Behaviour, p.121, TMS, Warrendale (1990). A. Turnbull and R.B. Hutchings. Hydrogen diffusion and trapping in a duplex stainless steel, to be published. K. Kuichi and R.B. McLellan. Acta Metall. 31, 961 (1983). T.P.Perng and C.J. Alstetter. Acta Metall. 34, 1771 (1986). J. Crank. The Mathematics of Diffusion (2rid edn), p.79, Clarendon Press, Oxford (1975).
1.0, Permeotlon tronsient
']
Membrane thickness (/11 x 10-6)
2 3 0.~ J/J.
0 c, o
't
e
1
~oz
108 op
o~'o ® 245 496
0.4!
o '~.'® o~# o ~a o~
0.2
L~gt 102
103
I )0 &
105
106
~(DNt/Q2)
Fig.1
Effect of membrane thickness on rising permeation transients for Uranus B50 stainless steel in 0.1M NaOH at 353K. (Longitudinal membrane orientation)
2662
HYDROGEN
TRANSPORT
Vol.
o.... ,,oo t . . . . ient
•
•
12
i
•
8
;.?
•
J/J-
t Latt,ce
t
02
j
i eA
!
=`
I I
¢-~
4
i eA •
_
10-2
Fig.2
~... ""
l#
o8
06
t
25, No.
10-1
©
i
-
100 104 Z(DNt/O Z )
I
]
105
106
Rising permeation transients for Uranus B50 stainless steel in 0.1M NaOH at 295K. (longitudinal membrane orientation). Open or part-~pen points represent tests on same specimen (see text).
i0-n Membrane orientation
Temperature (K)
o Longitudinal Transverse • Longitudinal
295.2 2952 353.2 10-12
10-12
o
=
,= ~ 10-13 d
1043
8 10-14 2.8
30
3,
34
o
r
10
i
I
20 30 Austemte volume fraction (%)
Fig.3 Variation of the effective diffusion coefficient, Deft, with volume fraction of in Uranus B50 duplex stainless steel.
I 40
Fig.4 Variation of the effective diffusion coefficient, Deft, with the reciprocal of temperature for Uranus BS0 stainless steel. (Longitudinal membrane orientation)
12