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Analysis of hydrogen diffusion and trapping in a 13% chromium martensitic stainless steel
Acta metal/. Vol. 31, No. I, pp. 2039-2046,
COOI-6160/89 $3.00 + 0.00 Pergamon Press plc
1989
Printed in Great Britain
ANALYSIS OF HYDROGEN DIFFUSION AND TRAPPING IN A 13% CHROMIUM MARTENSITIC STAINLESS STEEL A. TURNBULL, Division
of Materials
M. W. CARROLL
and D. H. FERRISS
Applications, National Physical Laboratory, Middlesex TWI 1 OLW, England
Teddington,
(Receined 13 October 1988) Abstract-A theoretical analysis has been made of the combined effects of reversible and irreversible trapping, with varying degrees of occupancy, on hydrogen transport in steels. The analysis has been coupled with repetitive electrochemical permeation measurements to characterise the diffusion and trapping parameters associated with a 13% Cr martensitic stainless steel commonly used for oil production tubing. The density of reversible and irreversible traps was (3.0 + 1.0) x IO” sites cm-? and about 1.5 x lOI sites cm-’ respectively. The binding energy of the reversible traps was (-3,8.7 + 1.0) kJmol-‘. The capture rate constant for the irreversible traps was (4.8 + 1.3) x IO-” cm- 3 s-‘. Assuming the same value for the reversible traps a release rate constant for the reversible traps of about (3.4 k 1.6) x lo-? s-‘. Knowledge of these parameters enables improved calculation of hydrogen charging times, which is essential for establishing reliable test methodology. It is recommended that the use of an effective diffusion coefficient, as a quantitative parameter for characterising hydrogen transport, be abandoned in systems for which irreversible trapping is dominant. RCsumGNous avons analysk thtoriquement les effets combinis des piCgeages riversible et irr&versible. pour diffirents degrts d’occupation, sur le transport de I’hydrogine dans les aciers. Cette analyse a tt& couplbe aved des mesures ilectrochimiques rtpetitives de filtration pour caractCriser les parametres de la diffusion et du pitgeage correspondant $ un acier inoxydable martensitique $ 13% de chrome, que l’on utilise couramment pour les tuyauteries de production de petrole. La densit& des pitges rCversibles et irrtversibles est respectivement &gale B (3.0 + 1.0)’ lOI9 sites’cm-’ et environ 1,5.1019 sites.cm-3. L’tnergie de liaison des piiges rkversibles est de (-38.7 k 1.0) kJ’mol_‘. La constante de temps de capture pour les pikges irr&versibles est &gale g (4.8 + 1.3)’ lo-l9 cm3 s-‘. Si l’on suppose la m&me valeur pour les pitiges rkversibles, on obtient une constante de vitesse de lib6ration pour les pitges rtversibles &gale B environ (3,4 f. 1.6). 10-2s-‘. La connaissance de ces paramttres permet un meilleur calcul des temps de chargement en hydrogkne, ce qui est essentiel pour dCterminer une mCthodologie d’essais &ire. L’utilisation d’un coefficient de diffusion efficace, en tant que param&re quantitatif pour caracteriser le transport de I’hydrogkne, doit itre abandon& dans le cas des systtmes oti le pikgeage irrtversible domine. Zusammenfassung-Der Wasserstofftransport in Stlhlen, insbesondere die kombinierte Wirkung von reversiblem und irreversiblem Einfang bei unterschiedlichen Besetzungsgraden, wird theoretisch untersucht. Diese Untersuchung wird gekoppelt mit wiederholten Messungen der elektrochemischen Permeation, urn die Diffusions- und Einfangparameter. die einen martensitischen, fiir dlrohre vorgesehenen rostfreien Stahl mit 13% Cr charakterisieren, zu bestimmen. Die Dichte der reversiblen Fallen war (3.0 + 1.0) x lOI cmm3, die der irreversiblen etwa 1,5 x 1019. Die Bindungsenergie der reversibien Fallen war (-38,7 + 1,0) kJ Mel-‘. Die Einfangratenkonstante der irreversiblen Fallen war (4.8 + 1.3) x 10. I9 cm3 s-‘. Mit demselben Wert erhglt man fiir die Freigaberate der reversiblen Fallen etwa (3.4 k 1.6) x 10-Zs-‘. Mit der Kenntnis dieser Werte lassen sich die Berechnungen fiir die Beladungszeiten verbessern, welches fiir Definition zuverl&siger Prlfverfahren wichtig ist. Es wird darauf hingewiesen, da0 die Nutzung eines effektiven Diffusionskoeffizienten als quantitativem Parameter zur Beschreibung des Wasserstofftransportes in Systemen. bei denen irreversibles Einfangen vorwiegt, aufgegeben werden sollte.
INTRODUCTION
Analysis of hydrogen transport and the distribution of hydrogen atoms in metals in important in understanding the influence of absorbed hydrogen on the mechanical behaviour of the metal. Furthermore, the establishment of reliable laboratory test methods in relation to hydrogen assisted cracking depends on awareness of the time-dependent distribution of hydrogen in test specimens and the corresponding relationship in structural components of varying size.
Hydrogen transport is strongly influenced by the presence of hydrogen traps such as grain boundaries, dislocations, carbides and non-metallic particles [ 11. These sites can act as traps for hydrogen atoms because of deepening of the associated potential well. The consequence of trapping is a decrease in the rate of transport of hydrogen through the metal because there is a finite probability of the hydrogen atoms jumping into trap sites and because the residence time in the site will be longer than in a normal lattice diffusion site. Since these trapping sites essentially act 2039
2040
TURNBULL et
al.:
HYDROGEN DIFFUSION AND TRAPPING IN STAINLESS STEEL
as sinks or sources of hydrogen atoms, Fick’s second law [2] for conservation of the species is no longer valid and a more comprehensive treatment is required. Ideally, this treatment would embrace a complete description of all types of traps requiring a definition of the different types of sites, the number of such sites per unit volume, the distribution of sites and the average time of transfer between sites for each type of site. This problem is almost intractable particularly if distribution of sites is non-random. Accordingly, a simplified approach has been adopted by most workers 13-81 by classifying sites into three broad categories, viz diffusion sites, reversible sites and irreversible sites. The depth of the potential well is so deep in the irreversible site that at a particular temperature there is insufficient thermal energy for a hydrogen atom to surmount the energy barrier. Analysis of hydrogen diffusion with trapping has been made by McNabb and Foster [3] but no account was taken of irreversible trapping. Oriani [4] introduced a limiting solution of McNabb and Foster’s model for the case of rapid equilibrium between trapping and normal diffusion sites. Iino [S, 61 developed a diffusion model similar to that of McNabb and Foster but, in addition, considered the situation of irreversible trapping. However, the case of irreversible trapping with saturation of trap was treated only in isolation. Leblond and Dubois [7,8] appear to be first in analysing the combined effects of reversible and irreversible trapping in detail, although solutions were obtained only for low fractional occupancy of reversible trap sites. 13% Cr martensitic stainless steels are commonly used for oil-production tubing in low H, S-containing environments. Preliminary investigations of hydrogen pe~eation in this steel in H,S/brine environments indicated a significant contribution of both irreversible and reversible trapping to the transport of hydrogen [9]. Accordingly, in an extension of the work of Leblond and Dubois [7,8] a generalised model of hydrogen transport has been developed which incorporates the combined effects of reversible and irreversible traps with varying degrees of occupancy. This model has been combined with repetitive electrochemical permeation measurements to quantify the diffusion and trapping parameters associated with the particular martensitic stainless steel.
ae,= k,C(I
at
- f3,)-pe,
l?@
-;i;‘=k,C(l -ei) where C is the number of diffusing atoms per unit volume, N is the number of traps per unit volume, B is the fraction occupied of N traps, k is the capture rate per trap, p is the release rate per trap, t is the time and D is the lattice diffusion coefficient. The subscripts r and i represent reversible and irreversible traps respectively. Equation (1) indicates that the rate of change of concentration of diffusing atoms depends on diffusion and the net rate of loss of hydrogen atoms into reversible and irreversible traps. The second and third equations relate to reversible and irreversible traps respectively and contain no diffusion terms because the traps are assumed to be isolated and, hence, there is no direct path between the trap sites. Saturation ,of traps occurs as 0, or Oi approach 1. Assuming a slab of thickness a, which is being charged with hydrogen from one side fx = a) with the hydrogen atoms discharged rapidly from the exit side, the appropriate boundary conditions are 1=0
allx,
C=O
(4)
t>O
x=0
c=o
(3
x=a
C=C,.
au azu atI aw -=---_-a7 ax2 at dz MATHEMATICAL MODEL JV
;j;=Lu(l-pv)-/lv
If the diffusion coefficient and the solubility of hydrogen are assumed uniform throughout the metal (the latter assumption will be invalid if a stress gradient is present) the continuity equations, in onedimensional form, can be expressed as
ac Da2c -=: at
ae. ;iT;i-Nr$-*i$
aw - =rcu(l-VW) ax with initial and boundary
(1)
(61
A more generalised form of the boundary condition at x = a would involve the kinetics of absorption and desorption as discussed by Pumphrey [lo]. The condition C = C, (the sub-surface concentration of diffusing hydrogen atoms) assumes that rapid equilibrium is obtained at the boundary. This simplification will be adopted in this anaiysis although its limitations are recognised, particularly for thin membranes. it will be shown later that this boundary condition is applicable for the specific test conditions adopted for the experimental programme. For ease of mathematical analysis it is convenient to express equations (1) to (6) in non-dimensional form. Defining r = Dt/a2, X=x/a, u = C/C,,, v = N,tI,jC~, W = NieilC,, I = Nrk,a2/D, /J =pa2/D, K = Nikia’/o, p = CojNr and v = C,JNi the continuity equations become
r=o
u=n=w=O
conditions
(7)
TURNBULL
z>o
x=
et al.:
DIFFUSION
u=o
x=0
1
HYDROGEN
(11)
u = 1.0.
(12)
The solution to equations (7)-(9) and conditions (lot{ 12) will furnish the time dependent distribution of u, v, iv. A quantity of importance is the time dependent flux at the exit side of the slab which can be measured electrochemically by the DevanathanStachurski method [ Ill. For purposes of comparison this can be obtained from the model; in terms of the scaled variables it is represented by (~~~~~~,~=“. At steady-state the flux is independent of trapping and is given by J, = DC(,/a. The non-linear nature of the equations necessitates numerical analysis. the full details of which are described elsewhere [ 121.In brief, the three equations in u, ZJand w were reduced to a single non-linear diffusion equation in u. This was solved numerically using the Crank-Nicolson finite difference scheme and the use of simple quadrature rules for the various integrals involved. EXPERIMENTAL
The material used was an AISI 410 stainless steel supplied in a quenched and double-tem~red condition with composition and mechanical properties as specified in Table 1. The hydrogen permeation studies were carried out using an adaptation of the ~evanathan-Stachurski [ 1I] two-compartment cell (full details are described elsewhere [S]). The environment under study was a 3.5% NaCl solution of varying pH and with varying levels of H2S. and was circulated through the charging cell from a 20 litre aspirator. The smaller, discharge cell contained a deaerated solution of 0.1 M NaOH. The specimens were 40 x 40 mm2 membranes of thickness 0.5 mm or I .Omm with an exposed area of 4.83 cm”. The electrode potential on the discharge side was set to + 300 mV(SCE), for which condition the oxidation current is diffusion limited for specimens of the thickness used. The background current was typically about 0.15 PAcrn-“. For successful repetitive permeation transients it is essential that the current decays to a low value relative to the steady maximum current at each intermediate stage and that the boundary conditions are rapidly established. Several methods were used before optimisation of these conditions could be achieved and it is informative to describe briefly the different methods and associated problems.
Table 1. Composition C 0.14
Si 0.32
Mn 0.46
S 0.007
Austemsation temperature First tempering temperature Second tempering temperature
P 0.02
of AlSl Cr 13.5
AND TRAPPING
IN STAINLESS
STEEL
2041
In principle, the simplest method is to apply a cathodic current to the specimen and set to open circuit when steady-state permeation is achieved. However, for this steel the steady-state permeation current was generally less than 1 FAcrn- z despite applying currents in excess of 1 mAcm_‘. This low current is presumably a result of the incomplete reduction of the passive film which effectively hinders hydrogen entry [9]. On setting to open circuit the permeation current decayed only to about 30% of the peak current (solution pH 5.0) and in tests in mildly acidic solutions of pH 3.6 could eventually increase due to depassivation. The cathodic polarisation method was repeated but with 32&450 ppm of H,S to generate a more significant steady ~rmeation current (3-4 FAcm ‘). To diminish subsequent reaction at open circuit the solution in the charging cell was isolated from the reservoir and H,S removed by passing argon through the solution or alternatively by flushing with 5 litres of deaerated distilled water. On achievement of the steady permeation current at open circuit the solution was recirculated from the reservoir with the first litre being exhausted to waste and cathodic protection reapplied. However, the open circuit permeation current did not fall below about 30% of the cathodic polarisation value and more significantly the rise time of the second transient was actually greater than the first transient though the breakthrough time was slightly shorter. Thus. cathodic polarisation was abandoned and transients were subsequently generated under open circuit conditions using solutions of pH 2.6 with about 350 ppm of H,S. Intermediate flushing was carried out with about 5 litres of distilled water till the pH approached 6.0, a pH sufficient to passivate the steel. However. this method also proved unsuccessful because of the slow rise in potential, eventually to about -4OOmV (SCE), in the pH 6 solution as the oxide film became more protective. The subsequent recirculation of the acidjHzS solution gave very defined and reproducible transients but the breakdown of the passive film and establishment of the steady corrosion potential [ -660 and -670 mV (SCE)] was slower than the time to breakthrough of the hydrogen atoms. This implied a changing boundary condition over the important time-scale of the test. The results from these various studies suggested that the best approach was to maintain the steel in the active state at all times so that the steady potential for each condition is rapidly established.
410 stainless Ni 0.71
steel (in mass%)
Cu 0. I5
Mo
0.05
Heat treatment 980 ‘C (oil quench) 7OtYC (air cooling) 630°C (air cooling)
Tl
Fe
Eal
TURNBULL et al.:
2042
HYDROGEN
I
0 v
1st. permeatim 1st. permeation
p
1st.
0 a A
3rd. permeation 2nd permeation 2nd permeation
permeation
DIFFUSION
AND TRAPPING
1
IN STAINLESS STEEL
1
(&=2.5~10’~ atom (C0:2.8x1016 atom
cm-31 cm-a)
(C,=3.4~10’~
atom
cm-31
(Co=1.3x10” (Co=L4xlO” (Co=lkxlO”
atom cm-31 atom cm-31 atom cm-a)
Full points
I
:lmm
Open points: 0.5mm
I
0 10’
10”
10L
T (Dt/a*)
Fig. 1. Rising permeation transients for AISI 410 stainless steel in acidified NaCl at 23°C The procedure finally adopted involved the use of 3.5% NaCl at pH 2.6 [typical corrosion potential of about -660 mV (SCE)] for the first transient giving a steady permeation current density of 3.3 PAcm-*. The reservoir was then isolated and the cell flushed with 5 1 of deaerated 3.5% NaCl at a pH of 3.6. This pH was chosen to yield a relatively low permeation current (0.9 pAcme2) while maintaining the steel just in the active state. At pH 3.6 the balance between active behaviour and partial passivity is delicate. With stirring to maintain constancy of pH at the surface and in the bulk, the steel remains active [13] but a reduced flow rate of solution can cause partial repassivation. Hence, to ensure active behaviour a magnetic stirrer was used during decay of the permeation current. The high flow rate coupled with the presence of residual H2S in solution maintained the steel in the active state with a potential between -650 mV and -700 mV (SCE). To enhance the steady permeation current relative to this “background” value the reservoir solution was saturated with H,S and the solution recirculated through the cell giving a steady permeation current of 16.1 pAcme2. The process of flushing and recirculation was repeated to yield a third transient. For each solution condition the steady corrosion potential was achieved in less than or about 15 min. The current densities quoted relate to a 1 mm thick membrane. Similar tests were also carried out with membranes of 0.5 mm thickness. In principle, avoidance of some of the surface state problems could have been achieved by deposition of a palladium coating. However, attempts at etching the steel in HCI to remove the oxide film, and then plating using the method described by Driver [14]
proved unsuccessful in that the subsequent film had a very low permeability to hydrogen. RESULTS AND DISCUSSION Rising permeation transients obtained using the method described are shown for thicknesses of 0.5 and 1.0 mm in Fig. 1. In plotting the experimental data, points are used throughout to avoid confusion with theoretical curves. Nevertheless, the data were gathered continuously. For convenience, the results are expressed in terms of a normalised flux (J/J,) and dimensionless time (r) with D = 7.2 x 10e5 cm2 s’ (see later). The agreement between second and third transients suggests that all the irreversible traps are filled, as expected, in the first transient and that no voids or defects are created or grow during the course of the test. This is consistent also with the obtainment of a maximum current which remains steady in time, showing no sign of the decrease which is sometimes observed in carbon steel [ 151. It is evident from Fig. 1 that there is no significant effect of thickness on the second permeation transient within the bounds of experimental variability. Thus, the permeation transients can be considered to be determined by mass transport within the volume of the material and the assumption of a boundary condition of C,, at the reacting surface is experimentally justified. A slight increase in the steepness of the first permeation transient is expected with increasing membrane thickness (because of the thickness dependence of IC). For each set of permeation data there are essentially three parameters, including the lattice diffusion
TURNBULL
ei af.:
HYDROGEN
DIFFUSION
coefficient, involved in fitting the theoretical permeation transient to the experimental data. Hence, it is necessary to determine one of the parameters by some other means if realistic values are to be determined. Evaluation of the lattice diffusion coefficient from permeation studies is not readily possible for a steel with significant trapping such as this 13% Cr steel. Therefore, it is necessary to rely upon data obtained either from high temperature extrapolation or from permeation measurements on annealed specimens of pure iron for which trapping is less significant. Kiuchi and McLellan [ 161have reviewed a large body of data for the lattice diffusion coefficient of iron. For temperatures between -40”’ and 80°C the best representation for D for body centre cubic iron was [16]. cm’ss’
03)
where Es = 5.69 kJmol_’ and this yieids a value of D = 7.2 x 10m5cm2 s-’ at 23°C the temperature repetitive permeation associated with these experiments. Characterisation of the lattice diffusion coefficient now permits detailed computation of the magnitude of C, which is essential for quantification of the trapping parameters. Analysis of reversible trapping
The first, second and third permeation transients obtained on a 0.5 mm membrane are shown in Fig. 2 together with the theoretical curve based on ideal lattice diffusion. The experimental separation of the contribution of irreversible and reversible traps to hydrogen transport by repetitive permeation tests enables theoretical treatment of reversible trapping in
AND
TRAPPING
IN STAINLESS
STEEL
2043
isolation. The important dimensioniess parameters are /L, p and p. The effect of variations in the magnitude of these parameters on the detailed flux/time relationship was assessed in a previous report [12]. In essence, if E, is large (typically > IO”) equilibrium exists between lattice and reversible trap sites (within the time scale associated with the particular membrane thickness) and the permeation transient has a shape identical to that for lattice diffusion (on a linear/logarithmic plot) but displaced in time [4]. The actual magnitude of i cannot be assessed directly since the shape of the permeation transient is independent of i. provided that i. is sufficiently large for equilibrium to prevail. if L is small the transient is not as steep as the classical case and a plateau region may precede the final rise to steady-state. Comparison of the experimental data with the shape of the classical diffusion curve suggests that the data are more consistent with the equilibrium case but with an increased steepness indicating that the degree of occupancy of the traps cannot be neglected. Hence. as a starting point in fitting the data i, was assumed to be large. (in practice, i = 4.0 x IO’ was used) and thus the probiem is reduced to determining p and the ratio i:;f. Increasing A//t simply displaces the transient to longer times while increasing /, increases the steepness of the transient with respect to the classical curve. Thus. in fitting the data both have to be changed in tandem. The best fit to the particular experimental data shown in Fig. :! was obtained using values for i:lc = 4.5 x 10’ and p = 5.0 x 10. ?. In order to ensure that the fit was reasonably unique a sensitivity assessment was made by systematically varying A./p and p and judging qualitatively the range of uncertainty in these parameters. The resulting range of values estimated by this proI
0 1st. pcrmeatidn A 2nd 0 3rd.
permeation permeation
(C,+2.5x1016 atom cm-J) ’
- - - -
(Co~t4xlO’~ atom cm-j) (Co~l.3~10’~ atom cm-a)
Range of
uncertainty in
Theory (All points fw 0.5 mm membrane
too
10’
fit thickness).
103
102
T (Dt/a’)
Fig.
2. Rising
permeation
transients for AISI concentrations
410 of
stainless
steel in acidified
H2S at 2? ‘C.
NaCl
with
varying
2044
TURNBULL et al.:
HYDROGEN
DIFFUSION
cedure is expressed by 1/p = (4.5 + 1.2) x 10’ and p = (4.5 + 1.3) x 10T3. For verification, examples of the extremes of these values are shown by the dashed lines in Fig. 2. From the values of n/p, p and C, calculation of N, and k,/p can be made. In doing so account was taken of the variability associated with different experiments as well as variability in the parametric fit to individual sets of data. The density of reversible trap sites (derived from p) was (3.0 + 1.0) x lOI sites cmm3. This value is consistent with the observation by Oriani [4] that the density of trap sites in undeformed steel is about lOI sites cmW3. The ratio of rate constants, k,/p was determined to be (1.4 f 0.5) x lo-” cm3. Derivation of the binding energy, AE, (in the terminology of Oriani [4]) can be made using the relationship [ 171. (14) where NL is the density of lattice diffusion sites and K is the equilibrium constant. In similar calculations for iron-titanium-carbon alloys Pressouyre and Bernstein [18] used a value for NL of 2.6 x 2023sites cme3 corresponding to the density of octahedral sites. However, in the review by Kuicki and McLellan [16] it is concluded that hydrogen atoms occupy the larger tetrahedral sites at ambient temperatures. Since there are twice as many tetrahedral sites per unit cell the value used for N,_ was 5.2 x lo*’ sites crn3. The binding energy thus determined was (-38.7 + 1.O)kJ mol-‘. The value obtained using the density of octahedral sites was about (-37.0 f 1.0) kJ mol-’ which is only slightly different. The interaction energy, as defined by Pressouyre and Bernstein [18] has a definition distinct from that of the binding energy and represents the total energy barrier for escape of hydrogen from the trap. The interaction energy, E, is defined as E=E’+E,+IAE,J
(15)
where E, is the activation energy for diffusion between normal lattice sites and E’ is described as an additional step energy. Pressouyre and Bernstein argue that E’ is of negligible importance and using this assumption together with the value of E, from Kiuchi and McLellan [16], the interaction energy calculated is (44.4 rfr 1.O)kJ mol-‘. The value of the binding energy of - 38.7 kJ mol-’ is somewhat higher than those reported by other workers, about -34 kJ mol-‘, as summarised by Kiuchi and McLellan. The latter value was attributed to trapping by dislocations. This may be relevant for this alloy also but no direct evidence exists and the possibility of multiple trap sites (reversible) cannot be excluded although the smoothness of the permeation transients suggests that the binding energy must be fairly similar. Grain boundaries may act as reversible sites. Indeed cracking of this material in NACE solution is of an intergranular nature [19]. Further
AND TRAPPING
IN STAINLESS STEEL
insight may be gained by evaluating the effect of plastic deformation on trapping behaviour and this work is in progress. Analysis of irreversible trapping
Characterisation of irreversible trapping can be achieved readily by using the parameters derived for the reversible traps and feeding in the additional parameters required to fit the first permeation curve. The relevant dimensionless parameters are K and v. A decreasing value of v tends to shift the theoretical curve for the reversible case to longer times but the shape of the curve tends not to be affected provided v is small (typically < 0.1) [12]. However, changing K does have a significant effect on the shape of the transient with the steepness increasing as K increases. It is the distinct effects of these parameters which enables reliable characterisation. Quantification of v and K was made by obtaining a preliminary fit by varying v at constant K and having defined v, by varying K. This process was repeated to obtain an optimum fit. As before, the uncertainty was evaluated and the values determined for the data for Fig. 2 were v=(2.1+0.2)x10-3and~=(l.9f0.5)x102.The best fit is shown in Fig. 2. In calculating N, and k,, five different sets of experimental data were used yielding values of Ni between 9.8 x 10” and 1.9 x lOI sites cme3 with an average value of 1.5 x lOI sites cmm3. The calculated value of ki (capture rate for the irreversible traps) was (4.8 f 1.3) x 10-‘9cm3 s-‘. If it is assumed that there is an equal probability of jumping into an irreversible or reversible trap this would give a value for 1 of about 5.2 x 10’ which is consistent with the previous assumption of equilibrium for reversible trapping. The corresponding release rate of the reversible trap, p would be (3.4 f 1.6) x lo-‘s-l. Characterisation of the binding energy of the irreversible traps requires use of high temperature desorption techniques but no tests have been conducted as yet. Implication of results
As stated in the introduction there are two main objectives in studying hydrogen diffusion and trapping: (a) to quantify the parameters necessary in evaluating charging times, (b) to improve understanding of the relationship between cracking and hydrogen distribution. (a) In stress corrosion and corrosion fatigue failures associated with absorbed hydrogen the prime source of hydrogen in a number of cases is from charging of the external surface [20]. Accordingly, evaluation of charging times is essential if the proper interrelation is to be made between measurements from specimens of varying size, configuration and time of immersion. Evaluation of the relevant timescale for charging based on classical diffusion theory with an effective diffusion coefficient is reliable only if
TURNBULL
et al.:
HYDROGEN
DIFFUSION
three criteria are simultaneously satisfied, viz irreversible trapping has no influence on hydrogen permeation, equilibrium exists between reversible and lattice sites and the fractional occupancy of trap sites is low. These conditions derive from the derivation of the effective diffusion coefficient [4,9]. A fractional occupancy of reversible traps of 0, = 0.05, which is acceptably low. yields a lattice concentration value of less than 5.0 x 1OL5atoms crnm3 which is below the values measured in acidified H,S solutions for this steel [9]. Furthermore, by definition, the fractional occupancy of irreversible traps must become equal to unity at steady-state. For steels, it is very unlikely that irreversible traps can be neglected and the use of an effective diffusion coefficient is very unreliable. For example, it was shown previously that in analysing only one permeation transient the uncertainty in effective diffusion coefficient can span an order of magnitude depending on the method of derivation [9]. Furthermore, since the permeation transients depend on C, (through v) a different effective diffusion coefficient would have to be used for each C, value. The concept of an effective diffusion coefficient becomes meaningless in these circumstances and since it is a very poor approximation and can be very misleading, the concept should be abandoned. Its use should be restricted to providing a relative assessment of the effect of different variables (for example. heat treatment) on hydrogen transport but only on a qualitative basis. The establishment of precise parameters for hydrogen diffusion and trapping enables much more realistic estimates of charging times and hydrogen distribution. An important application for which this conclusion can be of considerable significance is in fracture mechanics testing. In circumstances for which bulk charging is likely to be important (eg. this alloy in H, S saturated NACE solution [ 191) determination of k,, may depend on the time evolution of the hydrogen distribution through the specimen thickness. In previous analysis [21] a time constant (to.s) was defined corresponding to the time to achieve 50% of the steady concentration at mid-thickness. Using the full analysis of diffusion and trapping and the relevant parameters for AISI 410 stainless steel the time constant (at 23°C) could be expressed empirically by
AND
TRAPPING
IN STAINLESS
-0.79log,,C,-log,,,(D/a’)+
15.6
(16)
2045
Applying equation (18) to a compact tension specimen of thickness 2.5 cm (a = 1.25 cm) and C,, = 1.2 x 10” atoms cm- 3the relevant time constant is about 32 days. No specific calculations have been carried out for the cylindrical geometry appropriate to tensile specimens used in slow strain rate testing. Nevertheless, assuming planar geometry (which should give slightly elevated values) and a half-thickness, a. equal to 0.125 cm the time constant for the same C, is 7.6 h. (b) Analysis of trapping characteristics can often be used to assess the effect of alloying and heat treatment on the subsequent cracking resistance of the alloy. Pressouyre and Bernstein [ 181 discuss an example of this in relation to small additions of titanium to steels in which the homogeneous distribution of reversible traps can reduce the susceptibility of the particular alloys to hydrogen-induced damage by suppressing the formation of hydrogen-rich regions. The limited analysis of the present study does not enable specific statements about the relationship between cracking resistance in this 13% Cr martensitic stainless steel and hydrogen trapping at this stage. The concentration of hydrogen atoms in trap sites is by definition significantly greater than in lattice sites. The calculated distribution of hydrogen atoms between lattice and trap sites through the thickness of a membrane ((I = 0.5 mm) is illustrated in Fig. 3. The values shown relate to HzS-saturated solution for which the sub-surface concentration of hydrogen atoms in lattice sites is about 1.5 x 10”atomscm~‘. The concentration of atoms in irreversible sites is constant throughout the thickness and is equivalent
30
‘. ‘,
Total hydrogen trap sites
\
I”
\ \ J ci
lE
25
‘\
0
Hydrogen
in reversible
0
\
\ \
\
\
I
logt,,=
STEEL
b
\ \
where t is in seconds, C, is in atoms cm-‘. D is in cm’ s- ’ and a is in cm. This equation applies for C, in the range 4.6 x lOI atoms cme3 (acidified brine at pH 3.6, no H,S) to 1.2 x 10” atoms cm--’ (acidified brine at pH2.6. saturated in H,S). At pH values higher than about 3.6 the steel becomes passive and ingress of hydrogen is considerably hindered by the passive film. For this condition, the above relationship would be invalid since permeation of hydrogen is localised to corrosion pits and is not readily detected by standard permeation tests [19].
Hydrogen trap
X=0
Fig. 3. Distribution thickness
I”
irreversible wtes
X’O
of hydrogen atoms through membrane at steady state. a = 0.05 cm.
2046
TURNBULL
et al.:
HYDROGEN
DIFFUSION
to the density of sites which for this specific example was 1.2 x lOI atoms cmm3. The concentration of hydrogen atoms in reversible trap sites varied from about 2.0 x lOI at the charging side of the membrane (Q, N 0.69) to zero at the discharge side. The concentration of hydrogen atoms in reversible trap sites can be estimated for other lattice concentration values using the equilibrium relationship (which is valid at steady state) viz
& is the fraction of lattice sites occupied and is given by CL/N, where C,_ at steady state can be evaluated from CL = C,x/a. Hence,‘trapping provides a potential means of accumulating a critical quantity of hydrogen atoms which may be necessary for crack initiation and propagation. Slow strain testing of this alloy in acidified brine containing varying levels of H2S indicates that cracking is predominantly intergranular under severe charging conditions but with transgranular modes becoming more significant for less severe environments [19]. Grain boundaries may act as traps and indeed the measured binding energy could be associated with these traps. Charging a slow strain rate specimen with hydrogen and then discharging over a long period to ensure only irreversibly trapped hydrogen remained resulted in a subsequent time to failure equivalent to that in air [22]. If the grain boundaries were acting as irreversible traps some hydrogen cracking might have been expected. Further investigations to explore the relationship between deformation and trapping and the effects of temperature on cracking resistance and trapping may yield clearer insight. CONCLUSIONS
1. Reversible and irreversible traps play a significant role in hydrogen transport in AISI 410 martensitic stainless steel. 2. The density of reversible and irreversible traps was (3.0 f 1.0) x lOi sites cme3 and about 1.5 x lOI9 sites cm-’ respectively. 3. The binding energy of the reversible traps was (-38.7 + 1.0) kJmol_’ which is close to the value associated with dislocations, but could be applicable also to grain boundaries.
AND TRAPPING
IN STAINLESS STEEL
4. The capture rate constant for the irreversible traps was (4.8 f 1.3) x lo-i9 cm3 s-i. Assuming the same value for the reversible traps yields a release rate constant for the latter of (3.4 f 1.6) x lo-* s-l. 5. The use of an effective diffusion coefficient as a quantitative parameter for characterising hydrogen transport should be abandoned in systems for which irreversible trapping is significant. 6. When using fracture mechanics specimens in acidified solutions an appropriate time should be allowed for steady-state charging from the bulk to be achieved. REFERENCES 1. G. M. Pressouyre, Metall. Trans. IOA, 1571 (1979). 2. J. Crank, The Mathematics of Diffusion. Oxford Univ. Press (1975). 3. A. McNabb, and P. K. Foster, Tram metall. Sot. A.I.M.E. 227, 4. R. A. Oriani, 5. M. Iino, Acta 6. M. Iino. Acta
618 (1963). Acta metall. 18, 147 (1970). metall. 30, 367 (1982). metall. 30. 377 (1982). 7. J. B. Leblond and D. Dubois, A& metall. 31, 1459 (1983). 8. J. B. Leblond and D. Dubois, Acta mefall. 31, 1471 (1983). 9. A. Turnbull, M. Saenz de Santa Maria, and N. D.
Thomas, Corros. Sci. (1988). To be published. 10. P. H. Pumphrey, Scripta metall. 14,695 (1980). 11. M. A. V. Devanathan and Z. Stachurski. Proc. R. Sot. A270, 90 (1962). 12. D. H. Ferriss. and A. Turnbull, NPL Report DMA(A)l54 (1988). 13. A. Turnbull and M. Saenz de Santa Maria, Proc. Conf on Environment Induced Cracking of Metals, Wisconsin (1988). To be published. 14. R. Driver J. Elecrrochem. Sot. 128, 2367 (1981). 15. K. Van Gelder, M. J. J. Simon Thomas and C. J. Kroese, Corrosion 85, Paper 235. NACE, Houston, Texas (1985). 16. K. Kiuchi and R. B. McLellan, Acta metall. 31, 961 (1983). 17. A. J. Kumnick and H. H. Johnson, Acta mefall. 28, 33 (1980). 18. G. M. Pressouyre and I. M. Bernstein, Metall. Trans. 9A, 1571 (1978). 19. M. Saenz de Santa Maria and A. Turnbull, Corros. Sci.
(1988). To be published. 20. A. Turnbull and M. Saenz de Santa Maria. Proc. conf. on Environment-Assisted Fatigue, Sheffield (1988). To be published. 21. A. Turnbull and M. Saenz de Santa Maria, Metall. Trans. 19A, 1795 (1988). 22.
A. Turnbull, unpublished work (1988).
COOI-6160/89 $3.00 + 0.00 Pergamon Press plc
1989
Printed in Great Britain
ANALYSIS OF HYDROGEN DIFFUSION AND TRAPPING IN A 13% CHROMIUM MARTENSITIC STAINLESS STEEL A. TURNBULL, Division
of Materials
M. W. CARROLL
and D. H. FERRISS
Applications, National Physical Laboratory, Middlesex TWI 1 OLW, England
Teddington,
(Receined 13 October 1988) Abstract-A theoretical analysis has been made of the combined effects of reversible and irreversible trapping, with varying degrees of occupancy, on hydrogen transport in steels. The analysis has been coupled with repetitive electrochemical permeation measurements to characterise the diffusion and trapping parameters associated with a 13% Cr martensitic stainless steel commonly used for oil production tubing. The density of reversible and irreversible traps was (3.0 + 1.0) x IO” sites cm-? and about 1.5 x lOI sites cm-’ respectively. The binding energy of the reversible traps was (-3,8.7 + 1.0) kJmol-‘. The capture rate constant for the irreversible traps was (4.8 + 1.3) x IO-” cm- 3 s-‘. Assuming the same value for the reversible traps a release rate constant for the reversible traps of about (3.4 k 1.6) x lo-? s-‘. Knowledge of these parameters enables improved calculation of hydrogen charging times, which is essential for establishing reliable test methodology. It is recommended that the use of an effective diffusion coefficient, as a quantitative parameter for characterising hydrogen transport, be abandoned in systems for which irreversible trapping is dominant. RCsumGNous avons analysk thtoriquement les effets combinis des piCgeages riversible et irr&versible. pour diffirents degrts d’occupation, sur le transport de I’hydrogine dans les aciers. Cette analyse a tt& couplbe aved des mesures ilectrochimiques rtpetitives de filtration pour caractCriser les parametres de la diffusion et du pitgeage correspondant $ un acier inoxydable martensitique $ 13% de chrome, que l’on utilise couramment pour les tuyauteries de production de petrole. La densit& des pitges rCversibles et irrtversibles est respectivement &gale B (3.0 + 1.0)’ lOI9 sites’cm-’ et environ 1,5.1019 sites.cm-3. L’tnergie de liaison des piiges rkversibles est de (-38.7 k 1.0) kJ’mol_‘. La constante de temps de capture pour les pikges irr&versibles est &gale g (4.8 + 1.3)’ lo-l9 cm3 s-‘. Si l’on suppose la m&me valeur pour les pitiges rkversibles, on obtient une constante de vitesse de lib6ration pour les pitges rtversibles &gale B environ (3,4 f. 1.6). 10-2s-‘. La connaissance de ces paramttres permet un meilleur calcul des temps de chargement en hydrogkne, ce qui est essentiel pour dCterminer une mCthodologie d’essais &ire. L’utilisation d’un coefficient de diffusion efficace, en tant que param&re quantitatif pour caracteriser le transport de I’hydrogkne, doit itre abandon& dans le cas des systtmes oti le pikgeage irrtversible domine. Zusammenfassung-Der Wasserstofftransport in Stlhlen, insbesondere die kombinierte Wirkung von reversiblem und irreversiblem Einfang bei unterschiedlichen Besetzungsgraden, wird theoretisch untersucht. Diese Untersuchung wird gekoppelt mit wiederholten Messungen der elektrochemischen Permeation, urn die Diffusions- und Einfangparameter. die einen martensitischen, fiir dlrohre vorgesehenen rostfreien Stahl mit 13% Cr charakterisieren, zu bestimmen. Die Dichte der reversiblen Fallen war (3.0 + 1.0) x lOI cmm3, die der irreversiblen etwa 1,5 x 1019. Die Bindungsenergie der reversibien Fallen war (-38,7 + 1,0) kJ Mel-‘. Die Einfangratenkonstante der irreversiblen Fallen war (4.8 + 1.3) x 10. I9 cm3 s-‘. Mit demselben Wert erhglt man fiir die Freigaberate der reversiblen Fallen etwa (3.4 k 1.6) x 10-Zs-‘. Mit der Kenntnis dieser Werte lassen sich die Berechnungen fiir die Beladungszeiten verbessern, welches fiir Definition zuverl&siger Prlfverfahren wichtig ist. Es wird darauf hingewiesen, da0 die Nutzung eines effektiven Diffusionskoeffizienten als quantitativem Parameter zur Beschreibung des Wasserstofftransportes in Systemen. bei denen irreversibles Einfangen vorwiegt, aufgegeben werden sollte.
INTRODUCTION
Analysis of hydrogen transport and the distribution of hydrogen atoms in metals in important in understanding the influence of absorbed hydrogen on the mechanical behaviour of the metal. Furthermore, the establishment of reliable laboratory test methods in relation to hydrogen assisted cracking depends on awareness of the time-dependent distribution of hydrogen in test specimens and the corresponding relationship in structural components of varying size.
Hydrogen transport is strongly influenced by the presence of hydrogen traps such as grain boundaries, dislocations, carbides and non-metallic particles [ 11. These sites can act as traps for hydrogen atoms because of deepening of the associated potential well. The consequence of trapping is a decrease in the rate of transport of hydrogen through the metal because there is a finite probability of the hydrogen atoms jumping into trap sites and because the residence time in the site will be longer than in a normal lattice diffusion site. Since these trapping sites essentially act 2039
2040
TURNBULL et
al.:
HYDROGEN DIFFUSION AND TRAPPING IN STAINLESS STEEL
as sinks or sources of hydrogen atoms, Fick’s second law [2] for conservation of the species is no longer valid and a more comprehensive treatment is required. Ideally, this treatment would embrace a complete description of all types of traps requiring a definition of the different types of sites, the number of such sites per unit volume, the distribution of sites and the average time of transfer between sites for each type of site. This problem is almost intractable particularly if distribution of sites is non-random. Accordingly, a simplified approach has been adopted by most workers 13-81 by classifying sites into three broad categories, viz diffusion sites, reversible sites and irreversible sites. The depth of the potential well is so deep in the irreversible site that at a particular temperature there is insufficient thermal energy for a hydrogen atom to surmount the energy barrier. Analysis of hydrogen diffusion with trapping has been made by McNabb and Foster [3] but no account was taken of irreversible trapping. Oriani [4] introduced a limiting solution of McNabb and Foster’s model for the case of rapid equilibrium between trapping and normal diffusion sites. Iino [S, 61 developed a diffusion model similar to that of McNabb and Foster but, in addition, considered the situation of irreversible trapping. However, the case of irreversible trapping with saturation of trap was treated only in isolation. Leblond and Dubois [7,8] appear to be first in analysing the combined effects of reversible and irreversible trapping in detail, although solutions were obtained only for low fractional occupancy of reversible trap sites. 13% Cr martensitic stainless steels are commonly used for oil-production tubing in low H, S-containing environments. Preliminary investigations of hydrogen pe~eation in this steel in H,S/brine environments indicated a significant contribution of both irreversible and reversible trapping to the transport of hydrogen [9]. Accordingly, in an extension of the work of Leblond and Dubois [7,8] a generalised model of hydrogen transport has been developed which incorporates the combined effects of reversible and irreversible traps with varying degrees of occupancy. This model has been combined with repetitive electrochemical permeation measurements to quantify the diffusion and trapping parameters associated with the particular martensitic stainless steel.
ae,= k,C(I
at
- f3,)-pe,
l?@
-;i;‘=k,C(l -ei) where C is the number of diffusing atoms per unit volume, N is the number of traps per unit volume, B is the fraction occupied of N traps, k is the capture rate per trap, p is the release rate per trap, t is the time and D is the lattice diffusion coefficient. The subscripts r and i represent reversible and irreversible traps respectively. Equation (1) indicates that the rate of change of concentration of diffusing atoms depends on diffusion and the net rate of loss of hydrogen atoms into reversible and irreversible traps. The second and third equations relate to reversible and irreversible traps respectively and contain no diffusion terms because the traps are assumed to be isolated and, hence, there is no direct path between the trap sites. Saturation ,of traps occurs as 0, or Oi approach 1. Assuming a slab of thickness a, which is being charged with hydrogen from one side fx = a) with the hydrogen atoms discharged rapidly from the exit side, the appropriate boundary conditions are 1=0
allx,
C=O
(4)
t>O
x=0
c=o
(3
x=a
C=C,.
au azu atI aw -=---_-a7 ax2 at dz MATHEMATICAL MODEL JV
;j;=Lu(l-pv)-/lv
If the diffusion coefficient and the solubility of hydrogen are assumed uniform throughout the metal (the latter assumption will be invalid if a stress gradient is present) the continuity equations, in onedimensional form, can be expressed as
ac Da2c -=: at
ae. ;iT;i-Nr$-*i$
aw - =rcu(l-VW) ax with initial and boundary
(1)
(61
A more generalised form of the boundary condition at x = a would involve the kinetics of absorption and desorption as discussed by Pumphrey [lo]. The condition C = C, (the sub-surface concentration of diffusing hydrogen atoms) assumes that rapid equilibrium is obtained at the boundary. This simplification will be adopted in this anaiysis although its limitations are recognised, particularly for thin membranes. it will be shown later that this boundary condition is applicable for the specific test conditions adopted for the experimental programme. For ease of mathematical analysis it is convenient to express equations (1) to (6) in non-dimensional form. Defining r = Dt/a2, X=x/a, u = C/C,,, v = N,tI,jC~, W = NieilC,, I = Nrk,a2/D, /J =pa2/D, K = Nikia’/o, p = CojNr and v = C,JNi the continuity equations become
r=o
u=n=w=O
conditions
(7)
TURNBULL
z>o
x=
et al.:
DIFFUSION
u=o
x=0
1
HYDROGEN
(11)
u = 1.0.
(12)
The solution to equations (7)-(9) and conditions (lot{ 12) will furnish the time dependent distribution of u, v, iv. A quantity of importance is the time dependent flux at the exit side of the slab which can be measured electrochemically by the DevanathanStachurski method [ Ill. For purposes of comparison this can be obtained from the model; in terms of the scaled variables it is represented by (~~~~~~,~=“. At steady-state the flux is independent of trapping and is given by J, = DC(,/a. The non-linear nature of the equations necessitates numerical analysis. the full details of which are described elsewhere [ 121.In brief, the three equations in u, ZJand w were reduced to a single non-linear diffusion equation in u. This was solved numerically using the Crank-Nicolson finite difference scheme and the use of simple quadrature rules for the various integrals involved. EXPERIMENTAL
The material used was an AISI 410 stainless steel supplied in a quenched and double-tem~red condition with composition and mechanical properties as specified in Table 1. The hydrogen permeation studies were carried out using an adaptation of the ~evanathan-Stachurski [ 1I] two-compartment cell (full details are described elsewhere [S]). The environment under study was a 3.5% NaCl solution of varying pH and with varying levels of H2S. and was circulated through the charging cell from a 20 litre aspirator. The smaller, discharge cell contained a deaerated solution of 0.1 M NaOH. The specimens were 40 x 40 mm2 membranes of thickness 0.5 mm or I .Omm with an exposed area of 4.83 cm”. The electrode potential on the discharge side was set to + 300 mV(SCE), for which condition the oxidation current is diffusion limited for specimens of the thickness used. The background current was typically about 0.15 PAcrn-“. For successful repetitive permeation transients it is essential that the current decays to a low value relative to the steady maximum current at each intermediate stage and that the boundary conditions are rapidly established. Several methods were used before optimisation of these conditions could be achieved and it is informative to describe briefly the different methods and associated problems.
Table 1. Composition C 0.14
Si 0.32
Mn 0.46
S 0.007
Austemsation temperature First tempering temperature Second tempering temperature
P 0.02
of AlSl Cr 13.5
AND TRAPPING
IN STAINLESS
STEEL
2041
In principle, the simplest method is to apply a cathodic current to the specimen and set to open circuit when steady-state permeation is achieved. However, for this steel the steady-state permeation current was generally less than 1 FAcrn- z despite applying currents in excess of 1 mAcm_‘. This low current is presumably a result of the incomplete reduction of the passive film which effectively hinders hydrogen entry [9]. On setting to open circuit the permeation current decayed only to about 30% of the peak current (solution pH 5.0) and in tests in mildly acidic solutions of pH 3.6 could eventually increase due to depassivation. The cathodic polarisation method was repeated but with 32&450 ppm of H,S to generate a more significant steady ~rmeation current (3-4 FAcm ‘). To diminish subsequent reaction at open circuit the solution in the charging cell was isolated from the reservoir and H,S removed by passing argon through the solution or alternatively by flushing with 5 litres of deaerated distilled water. On achievement of the steady permeation current at open circuit the solution was recirculated from the reservoir with the first litre being exhausted to waste and cathodic protection reapplied. However, the open circuit permeation current did not fall below about 30% of the cathodic polarisation value and more significantly the rise time of the second transient was actually greater than the first transient though the breakthrough time was slightly shorter. Thus. cathodic polarisation was abandoned and transients were subsequently generated under open circuit conditions using solutions of pH 2.6 with about 350 ppm of H,S. Intermediate flushing was carried out with about 5 litres of distilled water till the pH approached 6.0, a pH sufficient to passivate the steel. However. this method also proved unsuccessful because of the slow rise in potential, eventually to about -4OOmV (SCE), in the pH 6 solution as the oxide film became more protective. The subsequent recirculation of the acidjHzS solution gave very defined and reproducible transients but the breakdown of the passive film and establishment of the steady corrosion potential [ -660 and -670 mV (SCE)] was slower than the time to breakthrough of the hydrogen atoms. This implied a changing boundary condition over the important time-scale of the test. The results from these various studies suggested that the best approach was to maintain the steel in the active state at all times so that the steady potential for each condition is rapidly established.
410 stainless Ni 0.71
steel (in mass%)
Cu 0. I5
Mo
0.05
Heat treatment 980 ‘C (oil quench) 7OtYC (air cooling) 630°C (air cooling)
Tl
Fe
Eal
TURNBULL et al.:
2042
HYDROGEN
I
0 v
1st. permeatim 1st. permeation
p
1st.
0 a A
3rd. permeation 2nd permeation 2nd permeation
permeation
DIFFUSION
AND TRAPPING
1
IN STAINLESS STEEL
1
(&=2.5~10’~ atom (C0:2.8x1016 atom
cm-31 cm-a)
(C,=3.4~10’~
atom
cm-31
(Co=1.3x10” (Co=L4xlO” (Co=lkxlO”
atom cm-31 atom cm-31 atom cm-a)
Full points
I
:lmm
Open points: 0.5mm
I
0 10’
10”
10L
T (Dt/a*)
Fig. 1. Rising permeation transients for AISI 410 stainless steel in acidified NaCl at 23°C The procedure finally adopted involved the use of 3.5% NaCl at pH 2.6 [typical corrosion potential of about -660 mV (SCE)] for the first transient giving a steady permeation current density of 3.3 PAcm-*. The reservoir was then isolated and the cell flushed with 5 1 of deaerated 3.5% NaCl at a pH of 3.6. This pH was chosen to yield a relatively low permeation current (0.9 pAcme2) while maintaining the steel just in the active state. At pH 3.6 the balance between active behaviour and partial passivity is delicate. With stirring to maintain constancy of pH at the surface and in the bulk, the steel remains active [13] but a reduced flow rate of solution can cause partial repassivation. Hence, to ensure active behaviour a magnetic stirrer was used during decay of the permeation current. The high flow rate coupled with the presence of residual H2S in solution maintained the steel in the active state with a potential between -650 mV and -700 mV (SCE). To enhance the steady permeation current relative to this “background” value the reservoir solution was saturated with H,S and the solution recirculated through the cell giving a steady permeation current of 16.1 pAcme2. The process of flushing and recirculation was repeated to yield a third transient. For each solution condition the steady corrosion potential was achieved in less than or about 15 min. The current densities quoted relate to a 1 mm thick membrane. Similar tests were also carried out with membranes of 0.5 mm thickness. In principle, avoidance of some of the surface state problems could have been achieved by deposition of a palladium coating. However, attempts at etching the steel in HCI to remove the oxide film, and then plating using the method described by Driver [14]
proved unsuccessful in that the subsequent film had a very low permeability to hydrogen. RESULTS AND DISCUSSION Rising permeation transients obtained using the method described are shown for thicknesses of 0.5 and 1.0 mm in Fig. 1. In plotting the experimental data, points are used throughout to avoid confusion with theoretical curves. Nevertheless, the data were gathered continuously. For convenience, the results are expressed in terms of a normalised flux (J/J,) and dimensionless time (r) with D = 7.2 x 10e5 cm2 s’ (see later). The agreement between second and third transients suggests that all the irreversible traps are filled, as expected, in the first transient and that no voids or defects are created or grow during the course of the test. This is consistent also with the obtainment of a maximum current which remains steady in time, showing no sign of the decrease which is sometimes observed in carbon steel [ 151. It is evident from Fig. 1 that there is no significant effect of thickness on the second permeation transient within the bounds of experimental variability. Thus, the permeation transients can be considered to be determined by mass transport within the volume of the material and the assumption of a boundary condition of C,, at the reacting surface is experimentally justified. A slight increase in the steepness of the first permeation transient is expected with increasing membrane thickness (because of the thickness dependence of IC). For each set of permeation data there are essentially three parameters, including the lattice diffusion
TURNBULL
ei af.:
HYDROGEN
DIFFUSION
coefficient, involved in fitting the theoretical permeation transient to the experimental data. Hence, it is necessary to determine one of the parameters by some other means if realistic values are to be determined. Evaluation of the lattice diffusion coefficient from permeation studies is not readily possible for a steel with significant trapping such as this 13% Cr steel. Therefore, it is necessary to rely upon data obtained either from high temperature extrapolation or from permeation measurements on annealed specimens of pure iron for which trapping is less significant. Kiuchi and McLellan [ 161have reviewed a large body of data for the lattice diffusion coefficient of iron. For temperatures between -40”’ and 80°C the best representation for D for body centre cubic iron was [16]. cm’ss’
03)
where Es = 5.69 kJmol_’ and this yieids a value of D = 7.2 x 10m5cm2 s-’ at 23°C the temperature repetitive permeation associated with these experiments. Characterisation of the lattice diffusion coefficient now permits detailed computation of the magnitude of C, which is essential for quantification of the trapping parameters. Analysis of reversible trapping
The first, second and third permeation transients obtained on a 0.5 mm membrane are shown in Fig. 2 together with the theoretical curve based on ideal lattice diffusion. The experimental separation of the contribution of irreversible and reversible traps to hydrogen transport by repetitive permeation tests enables theoretical treatment of reversible trapping in
AND
TRAPPING
IN STAINLESS
STEEL
2043
isolation. The important dimensioniess parameters are /L, p and p. The effect of variations in the magnitude of these parameters on the detailed flux/time relationship was assessed in a previous report [12]. In essence, if E, is large (typically > IO”) equilibrium exists between lattice and reversible trap sites (within the time scale associated with the particular membrane thickness) and the permeation transient has a shape identical to that for lattice diffusion (on a linear/logarithmic plot) but displaced in time [4]. The actual magnitude of i cannot be assessed directly since the shape of the permeation transient is independent of i. provided that i. is sufficiently large for equilibrium to prevail. if L is small the transient is not as steep as the classical case and a plateau region may precede the final rise to steady-state. Comparison of the experimental data with the shape of the classical diffusion curve suggests that the data are more consistent with the equilibrium case but with an increased steepness indicating that the degree of occupancy of the traps cannot be neglected. Hence. as a starting point in fitting the data i, was assumed to be large. (in practice, i = 4.0 x IO’ was used) and thus the probiem is reduced to determining p and the ratio i:;f. Increasing A//t simply displaces the transient to longer times while increasing /, increases the steepness of the transient with respect to the classical curve. Thus. in fitting the data both have to be changed in tandem. The best fit to the particular experimental data shown in Fig. :! was obtained using values for i:lc = 4.5 x 10’ and p = 5.0 x 10. ?. In order to ensure that the fit was reasonably unique a sensitivity assessment was made by systematically varying A./p and p and judging qualitatively the range of uncertainty in these parameters. The resulting range of values estimated by this proI
0 1st. pcrmeatidn A 2nd 0 3rd.
permeation permeation
(C,+2.5x1016 atom cm-J) ’
- - - -
(Co~t4xlO’~ atom cm-j) (Co~l.3~10’~ atom cm-a)
Range of
uncertainty in
Theory (All points fw 0.5 mm membrane
too
10’
fit thickness).
103
102
T (Dt/a’)
Fig.
2. Rising
permeation
transients for AISI concentrations
410 of
stainless
steel in acidified
H2S at 2? ‘C.
NaCl
with
varying
2044
TURNBULL et al.:
HYDROGEN
DIFFUSION
cedure is expressed by 1/p = (4.5 + 1.2) x 10’ and p = (4.5 + 1.3) x 10T3. For verification, examples of the extremes of these values are shown by the dashed lines in Fig. 2. From the values of n/p, p and C, calculation of N, and k,/p can be made. In doing so account was taken of the variability associated with different experiments as well as variability in the parametric fit to individual sets of data. The density of reversible trap sites (derived from p) was (3.0 + 1.0) x lOI sites cmm3. This value is consistent with the observation by Oriani [4] that the density of trap sites in undeformed steel is about lOI sites cmW3. The ratio of rate constants, k,/p was determined to be (1.4 f 0.5) x lo-” cm3. Derivation of the binding energy, AE, (in the terminology of Oriani [4]) can be made using the relationship [ 171. (14) where NL is the density of lattice diffusion sites and K is the equilibrium constant. In similar calculations for iron-titanium-carbon alloys Pressouyre and Bernstein [18] used a value for NL of 2.6 x 2023sites cme3 corresponding to the density of octahedral sites. However, in the review by Kuicki and McLellan [16] it is concluded that hydrogen atoms occupy the larger tetrahedral sites at ambient temperatures. Since there are twice as many tetrahedral sites per unit cell the value used for N,_ was 5.2 x lo*’ sites crn3. The binding energy thus determined was (-38.7 + 1.O)kJ mol-‘. The value obtained using the density of octahedral sites was about (-37.0 f 1.0) kJ mol-’ which is only slightly different. The interaction energy, as defined by Pressouyre and Bernstein [18] has a definition distinct from that of the binding energy and represents the total energy barrier for escape of hydrogen from the trap. The interaction energy, E, is defined as E=E’+E,+IAE,J
(15)
where E, is the activation energy for diffusion between normal lattice sites and E’ is described as an additional step energy. Pressouyre and Bernstein argue that E’ is of negligible importance and using this assumption together with the value of E, from Kiuchi and McLellan [16], the interaction energy calculated is (44.4 rfr 1.O)kJ mol-‘. The value of the binding energy of - 38.7 kJ mol-’ is somewhat higher than those reported by other workers, about -34 kJ mol-‘, as summarised by Kiuchi and McLellan. The latter value was attributed to trapping by dislocations. This may be relevant for this alloy also but no direct evidence exists and the possibility of multiple trap sites (reversible) cannot be excluded although the smoothness of the permeation transients suggests that the binding energy must be fairly similar. Grain boundaries may act as reversible sites. Indeed cracking of this material in NACE solution is of an intergranular nature [19]. Further
AND TRAPPING
IN STAINLESS STEEL
insight may be gained by evaluating the effect of plastic deformation on trapping behaviour and this work is in progress. Analysis of irreversible trapping
Characterisation of irreversible trapping can be achieved readily by using the parameters derived for the reversible traps and feeding in the additional parameters required to fit the first permeation curve. The relevant dimensionless parameters are K and v. A decreasing value of v tends to shift the theoretical curve for the reversible case to longer times but the shape of the curve tends not to be affected provided v is small (typically < 0.1) [12]. However, changing K does have a significant effect on the shape of the transient with the steepness increasing as K increases. It is the distinct effects of these parameters which enables reliable characterisation. Quantification of v and K was made by obtaining a preliminary fit by varying v at constant K and having defined v, by varying K. This process was repeated to obtain an optimum fit. As before, the uncertainty was evaluated and the values determined for the data for Fig. 2 were v=(2.1+0.2)x10-3and~=(l.9f0.5)x102.The best fit is shown in Fig. 2. In calculating N, and k,, five different sets of experimental data were used yielding values of Ni between 9.8 x 10” and 1.9 x lOI sites cme3 with an average value of 1.5 x lOI sites cmm3. The calculated value of ki (capture rate for the irreversible traps) was (4.8 f 1.3) x 10-‘9cm3 s-‘. If it is assumed that there is an equal probability of jumping into an irreversible or reversible trap this would give a value for 1 of about 5.2 x 10’ which is consistent with the previous assumption of equilibrium for reversible trapping. The corresponding release rate of the reversible trap, p would be (3.4 f 1.6) x lo-‘s-l. Characterisation of the binding energy of the irreversible traps requires use of high temperature desorption techniques but no tests have been conducted as yet. Implication of results
As stated in the introduction there are two main objectives in studying hydrogen diffusion and trapping: (a) to quantify the parameters necessary in evaluating charging times, (b) to improve understanding of the relationship between cracking and hydrogen distribution. (a) In stress corrosion and corrosion fatigue failures associated with absorbed hydrogen the prime source of hydrogen in a number of cases is from charging of the external surface [20]. Accordingly, evaluation of charging times is essential if the proper interrelation is to be made between measurements from specimens of varying size, configuration and time of immersion. Evaluation of the relevant timescale for charging based on classical diffusion theory with an effective diffusion coefficient is reliable only if
TURNBULL
et al.:
HYDROGEN
DIFFUSION
three criteria are simultaneously satisfied, viz irreversible trapping has no influence on hydrogen permeation, equilibrium exists between reversible and lattice sites and the fractional occupancy of trap sites is low. These conditions derive from the derivation of the effective diffusion coefficient [4,9]. A fractional occupancy of reversible traps of 0, = 0.05, which is acceptably low. yields a lattice concentration value of less than 5.0 x 1OL5atoms crnm3 which is below the values measured in acidified H,S solutions for this steel [9]. Furthermore, by definition, the fractional occupancy of irreversible traps must become equal to unity at steady-state. For steels, it is very unlikely that irreversible traps can be neglected and the use of an effective diffusion coefficient is very unreliable. For example, it was shown previously that in analysing only one permeation transient the uncertainty in effective diffusion coefficient can span an order of magnitude depending on the method of derivation [9]. Furthermore, since the permeation transients depend on C, (through v) a different effective diffusion coefficient would have to be used for each C, value. The concept of an effective diffusion coefficient becomes meaningless in these circumstances and since it is a very poor approximation and can be very misleading, the concept should be abandoned. Its use should be restricted to providing a relative assessment of the effect of different variables (for example. heat treatment) on hydrogen transport but only on a qualitative basis. The establishment of precise parameters for hydrogen diffusion and trapping enables much more realistic estimates of charging times and hydrogen distribution. An important application for which this conclusion can be of considerable significance is in fracture mechanics testing. In circumstances for which bulk charging is likely to be important (eg. this alloy in H, S saturated NACE solution [ 191) determination of k,, may depend on the time evolution of the hydrogen distribution through the specimen thickness. In previous analysis [21] a time constant (to.s) was defined corresponding to the time to achieve 50% of the steady concentration at mid-thickness. Using the full analysis of diffusion and trapping and the relevant parameters for AISI 410 stainless steel the time constant (at 23°C) could be expressed empirically by
AND
TRAPPING
IN STAINLESS
-0.79log,,C,-log,,,(D/a’)+
15.6
(16)
2045
Applying equation (18) to a compact tension specimen of thickness 2.5 cm (a = 1.25 cm) and C,, = 1.2 x 10” atoms cm- 3the relevant time constant is about 32 days. No specific calculations have been carried out for the cylindrical geometry appropriate to tensile specimens used in slow strain rate testing. Nevertheless, assuming planar geometry (which should give slightly elevated values) and a half-thickness, a. equal to 0.125 cm the time constant for the same C, is 7.6 h. (b) Analysis of trapping characteristics can often be used to assess the effect of alloying and heat treatment on the subsequent cracking resistance of the alloy. Pressouyre and Bernstein [ 181 discuss an example of this in relation to small additions of titanium to steels in which the homogeneous distribution of reversible traps can reduce the susceptibility of the particular alloys to hydrogen-induced damage by suppressing the formation of hydrogen-rich regions. The limited analysis of the present study does not enable specific statements about the relationship between cracking resistance in this 13% Cr martensitic stainless steel and hydrogen trapping at this stage. The concentration of hydrogen atoms in trap sites is by definition significantly greater than in lattice sites. The calculated distribution of hydrogen atoms between lattice and trap sites through the thickness of a membrane ((I = 0.5 mm) is illustrated in Fig. 3. The values shown relate to HzS-saturated solution for which the sub-surface concentration of hydrogen atoms in lattice sites is about 1.5 x 10”atomscm~‘. The concentration of atoms in irreversible sites is constant throughout the thickness and is equivalent
30
‘. ‘,
Total hydrogen trap sites
\
I”
\ \ J ci
lE
25
‘\
0
Hydrogen
in reversible
0
\
\ \
\
\
I
logt,,=
STEEL
b
\ \
where t is in seconds, C, is in atoms cm-‘. D is in cm’ s- ’ and a is in cm. This equation applies for C, in the range 4.6 x lOI atoms cme3 (acidified brine at pH 3.6, no H,S) to 1.2 x 10” atoms cm--’ (acidified brine at pH2.6. saturated in H,S). At pH values higher than about 3.6 the steel becomes passive and ingress of hydrogen is considerably hindered by the passive film. For this condition, the above relationship would be invalid since permeation of hydrogen is localised to corrosion pits and is not readily detected by standard permeation tests [19].
Hydrogen trap
X=0
Fig. 3. Distribution thickness
I”
irreversible wtes
X’O
of hydrogen atoms through membrane at steady state. a = 0.05 cm.
2046
TURNBULL
et al.:
HYDROGEN
DIFFUSION
to the density of sites which for this specific example was 1.2 x lOI atoms cmm3. The concentration of hydrogen atoms in reversible trap sites varied from about 2.0 x lOI at the charging side of the membrane (Q, N 0.69) to zero at the discharge side. The concentration of hydrogen atoms in reversible trap sites can be estimated for other lattice concentration values using the equilibrium relationship (which is valid at steady state) viz
& is the fraction of lattice sites occupied and is given by CL/N, where C,_ at steady state can be evaluated from CL = C,x/a. Hence,‘trapping provides a potential means of accumulating a critical quantity of hydrogen atoms which may be necessary for crack initiation and propagation. Slow strain testing of this alloy in acidified brine containing varying levels of H2S indicates that cracking is predominantly intergranular under severe charging conditions but with transgranular modes becoming more significant for less severe environments [19]. Grain boundaries may act as traps and indeed the measured binding energy could be associated with these traps. Charging a slow strain rate specimen with hydrogen and then discharging over a long period to ensure only irreversibly trapped hydrogen remained resulted in a subsequent time to failure equivalent to that in air [22]. If the grain boundaries were acting as irreversible traps some hydrogen cracking might have been expected. Further investigations to explore the relationship between deformation and trapping and the effects of temperature on cracking resistance and trapping may yield clearer insight. CONCLUSIONS
1. Reversible and irreversible traps play a significant role in hydrogen transport in AISI 410 martensitic stainless steel. 2. The density of reversible and irreversible traps was (3.0 f 1.0) x lOi sites cme3 and about 1.5 x lOI9 sites cm-’ respectively. 3. The binding energy of the reversible traps was (-38.7 + 1.0) kJmol_’ which is close to the value associated with dislocations, but could be applicable also to grain boundaries.
AND TRAPPING
IN STAINLESS STEEL
4. The capture rate constant for the irreversible traps was (4.8 f 1.3) x lo-i9 cm3 s-i. Assuming the same value for the reversible traps yields a release rate constant for the latter of (3.4 f 1.6) x lo-* s-l. 5. The use of an effective diffusion coefficient as a quantitative parameter for characterising hydrogen transport should be abandoned in systems for which irreversible trapping is significant. 6. When using fracture mechanics specimens in acidified solutions an appropriate time should be allowed for steady-state charging from the bulk to be achieved. REFERENCES 1. G. M. Pressouyre, Metall. Trans. IOA, 1571 (1979). 2. J. Crank, The Mathematics of Diffusion. Oxford Univ. Press (1975). 3. A. McNabb, and P. K. Foster, Tram metall. Sot. A.I.M.E. 227, 4. R. A. Oriani, 5. M. Iino, Acta 6. M. Iino. Acta
618 (1963). Acta metall. 18, 147 (1970). metall. 30, 367 (1982). metall. 30. 377 (1982). 7. J. B. Leblond and D. Dubois, A& metall. 31, 1459 (1983). 8. J. B. Leblond and D. Dubois, Acta mefall. 31, 1471 (1983). 9. A. Turnbull, M. Saenz de Santa Maria, and N. D.
Thomas, Corros. Sci. (1988). To be published. 10. P. H. Pumphrey, Scripta metall. 14,695 (1980). 11. M. A. V. Devanathan and Z. Stachurski. Proc. R. Sot. A270, 90 (1962). 12. D. H. Ferriss. and A. Turnbull, NPL Report DMA(A)l54 (1988). 13. A. Turnbull and M. Saenz de Santa Maria, Proc. Conf on Environment Induced Cracking of Metals, Wisconsin (1988). To be published. 14. R. Driver J. Elecrrochem. Sot. 128, 2367 (1981). 15. K. Van Gelder, M. J. J. Simon Thomas and C. J. Kroese, Corrosion 85, Paper 235. NACE, Houston, Texas (1985). 16. K. Kiuchi and R. B. McLellan, Acta metall. 31, 961 (1983). 17. A. J. Kumnick and H. H. Johnson, Acta mefall. 28, 33 (1980). 18. G. M. Pressouyre and I. M. Bernstein, Metall. Trans. 9A, 1571 (1978). 19. M. Saenz de Santa Maria and A. Turnbull, Corros. Sci.
(1988). To be published. 20. A. Turnbull and M. Saenz de Santa Maria. Proc. conf. on Environment-Assisted Fatigue, Sheffield (1988). To be published. 21. A. Turnbull and M. Saenz de Santa Maria, Metall. Trans. 19A, 1795 (1988). 22.
A. Turnbull, unpublished work (1988).