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The deformation of magnetite films forming on mild steel
Corrosion Science, 1974, Vol. 14, pp. 469 to 482. Pergamon Press. Printed in Great Britain
THE DEFORMATION OF MAGNETITE FILMS FORMING O N M I L D STEEL* H. A. MCCARTHY and P. L. HARRISON Central Electricity Research Laboratories, Leatherhead, Surrey KT22 7SE, England Abstract--Crack-detection techniques, developed for room temperature studies, have been applied to the study of magnetite layers growing on mild steel in NaOH solutions at 573 K and 10 MN/m ~ pressure, when subjected to varying tensile or compressive strains. It has been found that these films are extremely resistant to failure in compression but that they crack in tension at strains of 0-05-0.08 ~. Strains, below those necessary to cause cracking, result in changes in the rate of the electrochemical reactions associated with the oxidation process. R6sum&---On a appliqu6 les techniques de d6tection de fissures ~. teml~rature ambiante & l'6tude de couches de magn6tite form6es sur acier doux darts des solutions de NaOH h 573°K et 10 MN/m 2, et sous diverses contraintes de tension ou de compression. Ces couches se sont av&6es tr~s r6sistantes ~t la compression; mais, en tension, elles c~dent fi des sollicitations de 0,05 ~t 0,08 ~. Les sollicitations subliminaires produisent des changements des vitesses des r~actions 61ectrochimiques li6es b. la r6action d'oxydation. Zusammenfassung--Rissfeststellungsmethoden, die fiir Untersuchungen bei Raumtemperatur entwickelt worden sind, wurden auf die Untersuchung yon Magnetitschichten angewendet, die auf Gussstahl in NaOH-L6sungen bei 573 K und 10 MN/m 2 Druck entstanden sind und verschiedenen Zug- oder Druckverformungen ausgesetzt wurden. Es stellte sich heraus, dass diese Schichten/iusserst bestfindig gegen Rissentstehung bei Verformung unter Druck sind, aber bei Zugverformungen yon 0,05-0,08 ~o rissig werden. Verformungen, die geringer sind als diejenigen, welche Rissbildung verursachen, haben ~,nderungen der Geschwindigkeit elektrochemischer Reaktionen zur Folge, die mit dem Oxydationsprozess verbunden sind. INTRODUCTION
CRmCAL tensile fracture-strains at room temperature for magnetite films (grown on steels in s o d i u m h y d r o x i d e solutions at 589 K ) have been previously reported, x These i n d i c a t e d t h a t the b e h a v i o u r o f such films was nearer to t h a t o f bulk m a t e r i a l t h a n to t h a t o f a thin film. I n t e r p r e t a t i o n o f these results is c o m p l i c a t e d by the fact that the difference in e x p a n s i o n coefficients o f the metal and oxide a l m o s t certainly caused the m a g n e t i t e to be p r e - l o a d e d in compression (up to a m a x i m u m strain level o f 0-1%) on cooling the c o r r o d e d specimens to r o o m temperature. T h e extent o f this prel o a d i n g is n o t likely to have been the same for all specimens as it w o u l d depend on the ratio o f oxide thickness to specimen thickness a n d on the degree to which stress relief occurred within the m a g n e t i t e layer during the cooling process. T h e crack-detection techniques developed for the r o o m t e m p e r a t u r e w o r k can be a p p l i e d to the study o f the effect o f d e f o r m a t i o n on m a g n e t i t e films growing at high temperatures. Such a s t u d y removes the uncertainties associated with r o o m t e m p e r a t u r e tests. T h e m a i n a i m o f the present investigation has been to s t u d y the effect o f d e f o r m a t i o n on b o t h the corrosion rate o f the u n d e r l y i n g metal and the *Manuscript received 14 May 1973. 469
470
H. A. McCARTHY and P. L. HARRISON
integrity of the growing magnetite films. The metal in this case was mild steel. The corrosion was monitored by measuring the potential of the specimens with respect to a platinum electrode in a two electrode cell arrangement. Corroding specimens were subjected to compressive or tensile strains. Two autoclaves have been used in these tests, one for compression-testing, the other for tension-testing. EXPERIMENTAL
The autoclaves, specimen configurations and test procedures have been described in detail elsewhere. 2 All specimens were machined from mild steel of composition C 0.23 %, M n 0.61%, S 0.016 %, Si 0.03 %, Ni 0-13 %, Cr 0.05 %, Cu 0.08 %, P 0.015 %, Mo 0.05%, V < 0.05%. The autoclaves, containing 5%NaOH solutions, were heated to 573 K with zero load applied to the specimens. Some growing oxides were tested at their temperature of formation after 2 or 3 d oxidation. Other oxidized specimens were tested after the autoclave and its contents had cooled to room temperature. Oxides were grown under both "Bloom" and "Potter-Mann" conditions? Potter-Mann conditions were obtained by connecting the specimen externally to the platinum electrode. Bloom conditions were obtained by leaving the specimen fully insulated. In all tests, after cooling and dismantling the autoclave, the surface of part of the gauge-length was examined for damage in the scanning electron microscope. The remainder of the gauge-length was sectioned and examined metallographically. RESULTS
The potential responses were the same whether specimens had been oxidized under Bloom or Potter-Mann conditions. In all the compression and tension tests, as soon as the load started to be applied to the specimen, there was an immediate change in the potential of the specimen with respect to the platinum electrode. The sign of this change was determined by whether the applied strain was compressive or tensile and the rate of change was dependent upon the strain-rate and the temperature at which the test was performed. In tension tests, when the elastic limit of the mild steel was reached, there was an immediate large change in the potential of the specimen. At room temperature this was to more positive values whilst at 573 K it was much more rapid and to negative values. Changes in the rate of change of potential also occurred when the specimens commenced to yield in compression. However, in this case, the change can adequately be accounted for by the fact that at constant cross-head speed of the testing machine, the strain rate of the specimen increased locally as part of it was strained beyond the yield point. 2 The results are tabulated qualitatively in Table 1, and typical voltage-time curves are presented in Figs. 1-3. In all compression tests, when straining ceased the potential of the specimen drifted slowly back to its original prestrain value, whereas in tension tests, the potential remained relatively steady at the value obtaining when the straining ceased. That is, under compression the response of the potential was dependent upon the strain-rate, whereas under tension it was dependent upon the strain. Figure 1 shows the influence of strain rate in compression on the potential of the specimen. The estimated true strain-rates of the specimen were: A 0.4%/min in the
471
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H. A. McCARTHYand P. L. HARRISON
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(a) (b) Potential and extension curves on tensile straining above and below the elastic limit at: (a) room temperature; (b) 573K.
VARIATION OF SPECIMEN POTENTIAL ( W I T H RESPECT TO PLATINUM) ON COMPRESSIVE AND TENSILE STRAINING
In compression Room temp. 573 K
Room temp.
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Response on yielding of metal
Change to more negative value
Small change to more negative value
Greater change to more positive value
Very large change to negative value
By c o m p a r i n g Figs. 1 and 2 it can be seen that, at r o o m t e m p e r a t u r e , the influence o f strain rate on the rate o f change o f potential was even m o r e p r o n o u n c e d t h a n at 573 K. F o r a given strain rate, the response at r o o m t e m p e r a t u r e was a b o u t ten times that at 573 K. T h e rate o f decay o f the potential back to its pre-strain value after straining had ceased was also m u c h m o r e r a p i d at r o o m t e m p e r a t u r e t h a n at 573 K. T h e influence o f oxide thickness on the m a g n i t u d e o f the potential response d u r i n g compression testing was studied by using unoxidized 18/12/1 stainless steel specimens and mild steel specimens oxidized at 573 K (either in 5 % N a O H for I0 d o r in 1 5 % N a O H for 3 d) to p r o d u c e thicker films than those p r o d u c e d b y 3 d o x i d a t i o n in
The deformation of magnetite films forming on mild steel
473
5%NaOH. The unoxidized stainless steel specimens were subjected to compressive strain in the cold autoclave immediately after assembly. The specimens were still shiny-bright when removed from the autoclave after testing. They gave much greater. potential changes when subjected to compressive strains than did the oxidized mild steel specimens tested at room temperature. This difference appeared to be caused by the lack of substantial oxide on the stainless steel. Stainless steel specimens oxidized for 2 d in 5 % N a O H at 573 K and then strained in compression at room temperature or 573 K gave potential responses similar to those obtained with oxidized mild steel specimens when these were subjected to similar compressive strains. The mild steel specimens with the thicker oxide films gave smaller potential responses than those specimens with thin films. Furthermore, the response was sluggish in that the potential continued to drift away from its pre-strain value for 30-60 s after straining had ceased. The influence of tensile strain on the potentials of specimens, which had been oxidized for 2 d in the autoclave prior to straining, is illustrated by Fig. 3. The potentials of the specimen~ after cooling to room temperature were a few hundred mV positive with respect to the platinum electrode. Tensile strains increased these potential differences in both the elastic and the plastic regions of deformation. It will be noted from Fig. 3 that the rate of extension and the rate of change of specimen potential altered abruptly at yield. As described earlier, 2 the change in the rate of extension arose because, although during elastic deformation of the specimen part of the crosshead movement was taken up by the extension of the machine pull-rods, during the plastic deformation nearly all this movement was taken up by the gauge length. Also, during the elastic deformation only part of the measured extension was due to an increase in the gauge length. Consequently for a given cross-head speed the strain rate on the gauge length during plastic deformation was nearly six times that during the elastic deformation. Since the potential response was dependent upon strain, this partly explains the rapid change in response as the specimen yielded. However, unlike the case with compressive deformation, the change in response was greater than could be accounted for by the change in strain-rate alone. At 573 K the response of the potential to tensile strains in the elastic region was very similar to that at room temperature except for the magnitudes of both the initial potential and its rate of change (Fig. 3 and Table 1). However, when plastic deformation began at this temperature, the potential swung very rapidly to negative values. Again, as in all other tests, the potential slowly returned to its pre-strain value when deformation ceased. It was found possible to separate the point of yield of the specimen from this point of large negative swing in the potential by subjecting the specimen to plastic deformation in compression before the start of the tensile test. When this was done, the specimen underwent tensile plastic deformation before the large change in potential occurred. The amount of this tensile plastic deformation appeared to be the same as the amount of compressive plastic deformation suffered by the specimen before the tensile test. The tensile yield-strain of mild steel oxidized at 573 K in N a O H was calculated from the extension curves for a series of experiments at both room temperature and 573 K. At room temperature, successive tests in the plastic region (up to a total of 0.5% strain) gave yield-strains in the range 0.10-0.13%. At 573 K, yield-strains were
474
H. A. McCAgTHVand P. L. ~ r q
in the range 0.05-0.08% (with a total strain of up to 2.4%). Cracks in the oxide surface were observed by SEM in all specimens which had been strained at room temperature to a total tensile strain of above 0.5%. No cracks were detected when straining had been confined to below the elastic limit. The extent of the cracking depended upon the magnitude of the strain to which the specimen had been subjected. Figure 4 shows the condition of the oxide surface after 2 % and 30% strain. As shown in Fig. 4(a) cracks often emanated from defects in the oxide. The first cracks grew mainly perpendicular to the gauge-length (Fig. 4a) but at higher strains there was an increased proportion of cracking at 45° to this direction (Fig. 4b). The form of the cracks was the same whether straining had taken place at room temperature or 573 K. Optical microscopy showed that cracks produced under tensile stress (such as those in Fig. 4) frequently passed through the whole of the oxide layer (~ 5 ~m thick) down to the metal. In addition, the underlying metal was found to be cracked when plastic tensile straining had taken place at 573 K (Fig. 5). These cracks in the metal were usually, but not always, associated with visible cracks in the oxide. No cracks could be detected by optical microscopy in thin oxide layers (1-2 ~tm thick) on specimens which had suffered 1% plastic strain in compression. Thicker oxides (10 i~m thick) did, however, show short longitudinal cracks after compressive strains of 1%.
DISCUSSION It is shown in the Appendix that the potential of an oxidizing specimen is strongly dependent upon the porosity of the oxide layer formed, and that this, in turn, is influenced by the ratio "autoclave wall area/specimen area". If this ratio is large, the oxide porosity will also be large and the specimen potential will be low, and vice versa. Consequently the potential difference generated within a two-electrode cell can be of either sign depending on the conditions of oxidation. In the tension autoclave, the value of the area ratio is about one-third of its value in the compression autoclave so that the catalytic effect of the magnetite-covered autoclave wall, which promotes porosity in the specimen oxide, is less in the tension autoclave. The resulting lower porosity would explain the higher potential of the specimen (with respect to the platinum electrode) in the tension autoclave compared with the compression autoclave. The fact that this raising of the potential has resulted in a potential of approximately the same magnitude but of opposite sign is considered to be quite fortuitous. The theory of the current at yielding electrodes has been discussed by Hoar. 4
Because the thermal expansion coefficient of the magnetite film is less than that of the underlying metal, cooling of the oxidized specimen causes a compressive stress in the oxide. This compression may be expected to decrease the porosity of the oxide. If the porosity is already low, such further reduction will have a far greater percentage effect than it will if the porosity is high. This could explain the large rise in potential which occurred when specimens oxidized in the tension autoclave were cooled, although cooling those oxidized in the compression autoclave produced little change in potential.
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[facing p. 474]
The deformation of magnetite films forming on mild steel
475
It is to be noted that, in all tests, the potential of the specimen responded immediately to straining. It is unlikely that this response arose from cracking of the oxide film since this would indicate breaking strains of less than 0.01% at'573 K and cracking of the oxide as the compressive stress in it diminished during the tensile tests at room temperature. The change in potential on the rupture of a film has been discussed by Jones, Stratton and Osgood.5 It is convenient to discuss this phenomenon under the two headings of compression and tension. Compression tests
At room temperature, stainless steel specimens with no oxide layer visible on them gave much greater responses than did mild steel specimens previously oxidized at 573 K, although oxidized stainless steel and mild steel showed no such difference when both had been previously oxidized at 573 K. Furthermore, increasing the thickness of the magnetite layer on mild steel caused the response at 573 K to become smaller and somewhat delayed. Both these facts suggest that this immediate response arose from a disturbance at the oxide/metal interface. Huybregts, Van Osch and Snel s and Townsend 7 have discussed in detail the various reactions possible in the Fe-H20 system under various experimental conditions. However, the former authors only considered the temperature range 333473 K and Townsend's work was at 523 K. Field, Stanley, Adams and Holmes s have postulated that there are two competing reactions occurring at the metal/bxide interface at 573 K. One of these produces magnetite in situ whilst the other produces a soluble species, both involving a net negative charging of the specimen if at least part of the cathodic reaction is taking place at a second electrode. The proportion of the oxidizing iron that dissolves is probably governed by the stress-relief necessary to accommodate the Pilling-Bedworth ratio of 2 : 1 and would therefore rise as the oxide is compressed. This could explain the strain-rate dependent movement of the potential to more negative values as the specimens were compressed. The results obtained at room temperature were very similar to, but more pronounced than, those obtained at 573 K. Consequently it is suggested that the same explanation is valid at both temperatures even though the iron soluble species are probably quite different in the two cases. It is interesting to note that any reduction of porosity consequent on compression would cause a strain dependent reduction in the anodic reaction on the steel and hence a strain dependent movement of the potential to more positive values. These results cannot, therefore, be explained in terms of reduced porosity effects. Tensile tests
In these tests, the specimens were positive with respect to the platinum electrode As has been suggested above, this is probably a consequence of the low porosity of the oxide. This would also explain the very large positive potential difference obtained at room temperature. At this temperature, the porosity of the oxide would have been even further reduced by the compression arising from the differential contraction between metal and oxide on cooling. It should be noted that, in tensile tests, the response was approximately strain dependent, not strain-rate dependent, and that the potential always moved to more positive values as the tensile strain increased.
476
H. A.
McCARTHYand P. L. HAgRLSON
This is consistent with an enhanced cathodic activity arising from an increased surface area of oxide at which cathodic reactions can take place. In all tests, yielding of the metal specimens gave rise to greatly enhanced responses of their potentials. As has been stated previously, the enhancement occurring in the compression tests can be adequately explained by the increased strain-rate of the specimen during plastic deformation (as compared with elastic deformation) for any given machine cross-head speed. Moreover, optical microscopy showed no evidence of oxide cracking under compression until strains of the order of 1% had been achieved, so that variation in the potential, due to removal of the oxide from close contact with the metal, would not be expected at the much lower strains (0.1%) at which the metal yielded. The enhancement occurring in the tensile tests, however, cannot adequately be explained by changes in strain rate at the specimen. At room temperature, though the enhanced rate of change of potential is in the same direction as the change before yield, the enhancement is too great to be explained by the increased strain rate. This additional increase in the cathodic activity of the oxidizing specimen probably arises from a greater increase in oxide surface area occasioned by cracking of the oxide. It is to be noted that all specimens strained in tension beyond the yield point showed cracks in the oxide layers, and that the extent of the cracking was greatest for those specimens which had suffered the greatest plastic strain. At 573 K, yielding of a specimen under tension gave rise to a very sharp swing of the potential to negative values. Obviously an entirely different mechanism was operating in this case. Optical microscopy showed that all such specimens had cracks in the oxide which penetrated into the metal. The conclusion to be drawn therefore is that, under these conditions of test, the metal was being subjected to stress corrosion cracking at the base of cracks within the oxide layer, and that this gave rise to the greatly enhanced anodic activity of the specimen. It is interesting to note that yielding of the metal alone was not sufficient to produce this enhanced activity. It was possible to produce yielding under tension without the enhanced activity by subjecting the specimen to prior plastic deformation in compression. When this was done, the specimen underwent an amount of tensile plastic deformation similar in extent to the previous compressive plastic deformation (before this enhanced activity became evident). This suggests that the stress corrosion cracking occurred only after the oxide had cracked and that this happened at a strain which was very close to the yield strain of the underlying metal. It seems unlikely that this coincidence was fortuitous, and is probably further evidence for the existence of a thin layer of oxide, adjacent to the metal, which is either non-porous or of a different composition, as has been postulated earlier.I, 9 Apparently the tensile properties of this layer are in part determined by the properties of the parent metal. If the above interpretations of the experimental results are accepted, the following comments can be made concerning the critical fracture strains of the oxide. Under compression, the oxides produced appeared to be extremely resistant to damage. The thicker films ( ~ 10 ~m) showed no cracking until subjected to strains in excess of 1%. The thinner films ( ~ 1 ~tm) were even more resistant to damage. Under tension, the oxides fractured at the yield strain of the underlying metal both at room temperature and at 573 K. The yield strains of oxidized metal were found to be
The deformation of magnetite films forming on mild steel
477
0.10-0-13% a n d 0-05-0.08% at r o o m t e m p e r a t u r e a n d 573 K respectively. I f in the f o r m e r case allowance is m a d e for the compressive strain induced in the oxide by cooling, a critical tensile fracture strain at r o o m t e m p e r a t u r e o f less than 0.03% is a p p a r e n t l y obtained. However, at r o o m temperature, the mild steel yielded in an i n h o m o g e n e o u s manner. T h e overall small plastic strain o f the metal consisted o f local strains o f the o r d e r o f a few per cent, arising f r o m the p r o p a g a t i o n o f Liiders bands. Consequently, under these circumstances, it is impossible to measure the true critical tensile fracture strain. In the previous w o r k by H a r r i s o n 1 the geometry o f the experiment was such t h a t no inhomogeneities in strain were a p p a r e n t in the m e t a l until after cracks had a p p e a r e d in the oxide. Consequently the values o f 0.02-0.23 % o b t a i n e d by H a r r i s o n (allowing for the compressive strain induced in cooling) represented a measure o f the true critical tensile fracture strain o f the magnetite films at r o o m temperature.
CONCLUSIONS 1. A t 573 K magnetite films, growing on mild steel in 5 % N a O H solutions, cracked u n d e r tensile strains o f 0.05-0.08 %. 2. Tensile cracking at 573 K led to very r a p i d local dissolution o f the metal a n d stress c o r r o s i o n type cracking. 3. A t 573 K magnetite films, growing on mild steel in 5 % N a O H solutions, withs t o o d compressive strains o f up to 1% w i t h o u t cracking. 4. A t strains less t h a n those necessary to fracture the films, cathodic activity was enhanced in tensile straining and a n o d i c activity enhanced in compressive straining, leading to small changes in the rates o f the electrochemical reactions. Acknowledgements--The authors would like to thank Dr. G. J. Bignold and Dr. D. R. Holmes for
their helpful comments and Mr. S. C. Ferguson for his constant advice and assistance. This work was carried out at the Central Electricity Research Laboratories and the paper is published by permission of the Central Electricity Generating Board.
REFERENCES 1. P. L. HARRISON,Corros. Sci. 7, 789 (1967). 2. H. A. McCARTHY,P. L. HARRISONand S. C. FERGUSON,J. Phys. E. Sci. h~strum. 5 (8), 790 (1972). 3. T. F. MARSH, d. electroehem. Soc. 113, 313 (1966). 4. T. P. HOAR, N A T O Conference on the Theory o f Stress Corrosion Cracking in Alloys, Brussels (Ed. J. C. SCtlLLY), p. 105 (1971). 5. R. L. JONES, L. W. STRAI'rONand E. D. OSOOOD, Corrosion 26, 399 (1970). 6. W. i . M. HUYBREGTS,G. VAN OSCH and A. SNEL,Proc. 4th Int. Congr. on Metallic Corrosion, Amsterdam, p. 501 (1969). 7. H. E. TOWNSEND, Corros. Sci. 10, 343 (1970). 8. E. M. FIELD,R. C. STANLEY,A. M. ADAMSand D. R. HOLMES,Proc. 2nd Int. Congr. on Metallic Corrosion, New York, p. 829 (1963). 9. G. J. BIGNOLD, Corros. Sei. 12, 145 (1972). 10. J. E. CASTLEand H. G. MASTERSON,Corros. ScL 6, 93 (1966). 11. G. J. BIGNOLD,R. GARNSEYand G. M. W. I~/I.A.NN,Corros. Sci. 12, 325 (1972). 12. M. PotmsnlX, Atlas o f Electrochemical Equilibria in Aqueous Solutions. Pergamon, Oxford (1966). 13. F. H. SWEE'rONand C. F. BAES,J. chem. Thermodynamics 2, 479 (1970). 14. H. E. TOWNSEND,Corros. Sci. 10, 709 (1970). 15. J. E. CASTLEand G. M. W. MANN, Corro$. Sci. 6, 253 (1966).
H. A. McCARTHY and P. L. HARRISON
478
APPENDIX NOMENCLATURE a
a (d)
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activity of an ion in an electrolyte lower limiting activity activity at oxide/electrolyte interface higher limiting activity activity at oxide/metal interface area available for cathodic reaction geometric area of specimen coefficients defined by equation (7) coefficients relating cathodic current and potential diffusion coefficient reaction potential potential of cathodic reaction equilibrium potential standard electrode potential function of a(d) and a(s) Faraday constant current density cathodic current density exchange current density ion concentration corresponding to activity a limiting ion concentration gas constant absolute temperature porosity at oxide/metal interface porosity at a distance, x, from oxide/electrolyte interface effective porosity of oxide film defined by equation (4) distance from oxide/electrolyte interface thickness of oxide ionic charge activation coefficient activation overpotential concentration overpotential
Subscripts 1 electrode cation 2 electrolyte anion To the best of our knowledge, the case of concentration polarization for an anodic process has not been treated to any extent in the literature. Castle and Masterson ~° have developed a model for the corrosion of iron in high temperature aqueous solutions in which diffusion of a soluble iron species through a porous magnetite layer is the rate-determining step. This model is based on the postulated occurrence of two competing reactions at the corroding interface, one producing Fe304 in situ and the other producing iron ions which diffuse away from the corrosion site. The model of Castle and Masterson is based on mechanisms of chemical diffusion, and electrochemical reactions are not considered. The model now to be presented attempts to bring these latter into consideration. Bignold, Garnsey and M a n n u have recently extended the theory of Castle and Masterson, and have discussed it in electrochemical terms. GENERAL CHARACTERISTICS OF THE MODEL The corrosion reactions are assumed to occur at the interface of the metal and a porous corrosion film of uniform thickness. The supply of oxidant and the removal of soluble iron are by diffusion through the pores in this film. For convenience of analysis, the pores are assumed to be cylinders whose axes lie perpendicular to the film/metal interface. They are assumed to be identical and to have a common radius which is a function only of the distance from the surface of the film. Following Castle and Masterson, it is assumed that, for the corrosion of iron in strongly alkaline solutions, the diffusion coefficient of the electrolyte anion is much higher than that of the electrode
The deformation of magnetite films forming on mild steel
479
cation and hence that the concentration of the former at the corroding metal surface is very similar to the high value obtaining in the bulk of the electrolyte. Since the oxide is a comparatively good conductor, the cathodic reaction taking place on the oxide surface will occur at essentially the same potential as the two anodic reactions. DEVELOPMENT OF THE MODEL It is assumed that the corrosion reactions occurring at the metal surface can be represented by the two simultaneous equations Fe ~-- Fe 2+ + 2e tFe+OH-~--]FesO4+
(1) ½H=O+e.
(2)
These are suggested as representational only; for example, it is generally agreed t2-t4 that in alkaline solutions iron dissolves as an amphoteric anion such as HFeO~, FeO~-, Fe(OH)~ or Fe(OH)]-. The equilibrium potentials for these two reactions can be written as EtfE
and
R T In a t ( o ) ° + 2 fRfT In [Fe z+] = E t ° +~-ff
E2 = E2° -- "~- In
[OH-]
= E ° --
(la)
~ - In a2 (o)
(lb)
&
respectively. For non-equilibrium conditions, the activation over-potentials are given by qt (a) = R T (In it -- In i01) 213tF
and
n~
(a)
(2a)
R T ( l n i2 -- In to=).
=
(2b)
It is assumed that the reactions are independent of one another and that the exchange current densities can be treated as constant. For the diffusion of an ion, the general equation is
(3)
__ v(x) D z F n(a) da. v a dx
Integration gives x iv f - v - ~ d x i v X ~
a(X) -- D z F f
o
n(a)
(4)
a(o)
(where V is the effective porosity of the oxide film). At high levels of concentration and those corresponding to saturation, small changes in concentration will give rise to large changes of activity. This can be expressed mathematically by defining a value of a ----a(s) above which the value of the ion concentration can be taken to be constant at n(s). At low values of concentration, concentration and activity are linearly related. It is possible to define a second limiting value of a = a(d) such that only below this value can the proportionality between activity and concentration be considered valid. F o r the electrode cation (Fe2+), assuming a(X') > a(s) > a(d) > a(o) a( X)
then
f
a(d)
~ a(o)
da =
f
a(s)
n(a) da +
a(o)
T
f a(d)
---- n(,) In a ( X ) -
a(X)
n(a) -a-
da +
a(o) + f l
f a(s)
n(a) ,, da
--
H. A. McCARTHY and P. L. HARRISON
480
a(s) where
./'1 ----| d
S
~
n!a-) da -- n(s) In a(s) + a(d) is a function whose value depends on the a
a(d)
relationship existing between activity at and concentration n,(a). Therefore
ilvX V
v
-I
(Sa)
= 2 D 1 F i n ( , ) In a ( X ) - a(o) + I H .
L--
For the electrolyte anion (OH-), assuming a(X) > a(o) > a(s) > a(d)
a(X) f
then
n(a) da = n(s) In a(X) a(o)
a
a(o)
therefore iz_v_X= _ D2F ~(s) In as(X) V
as(o)
(5b) "
Assuming that the thermodynamic equation for a reversible cell is applicable, the concentration overpotential is given by q(c)
= R T I n [a(X)/a(o)]. zF
Substituting for a~(X) and a2(X) from equations (5) yields rh(c)
and
= RT
ixvX
RT
i2vX
2F-[2
qa (c) --
+ al (o) _ In al (o) --
fl ]
(6a)
(6b)
F n2(s)VD2F
respectively for the two ion types. The electrode potentials, e, and e2, for the two anodic reactions are obtained by combining equations (1), (2) and (6). This gives
RTf
a,(o)
4vX
n, (s) and
RT ~ i,v X e 2 = E 0 + F-Ln,(s~-OsF
lna,(o)+
I
f' + : I n / , nt (s) ~
In/2--
]
13-1In i0x
131 1
]
~ lnios .
These can be written as ea = A, + B1 In il + C1/1
(7a)
es = As + B.. In iz + C2 is
(7b)
(where At, .4z, B~, B2, C~ and C2 are constants). Since the cathodic reaction is occurring on the extended oxide surface, it can be assumed that it is not under diffusion control and that the reaction potential can be represented by
e~ = A, -- B, lni,.
(8)
Since the corroding specimens are electrically isolated, the total anodic current must equal the cathodic current, that is
(ix + iO v a(s) = i, A(c).
(9)
The deformation of magnetite films forming on mild steel
481
Assuming both anodic reactions are strongly under diffusion control,
el = Aa -~- Cain) e= A2 + Czi2 from (7). Substituting for it and i, in (9) gives
~+ e~2]
lea
v. A(s) = I[ ~- A - +z-A~uj I
~, A(s) + ic A(c).
If the cathodic reaction occurs at the same potential as the two anodic reactions, ea = e~ = e,, therefore
e~ --
AaC2 + A~Ca Ca + C2
q- it
A(c) G G v. A(s) (Ca + C2)
therefore from (8), A , - - B, l n i c - - A , G + A2Ca ~_ ic
Ca + C,
A(c) GC2 v. A(s) ( G + G).
(10)
The two sides of equation (10) are shown plotted against it in Fig. 6. The solution to the equation is represented by the intersection of the two solid lines. B E H A V I O U R O F THE MODEL (a) Effect of porosity (V) on specimen potential In equation (10), for any given oxide thickness, (ARC2 + A=CI) / (Ca+ C~) is independent of Vwhilst the coefficient of/, is proportional to 1IV. It can therefore be seen from Fig. 6 that, for a given eldctrolyte condition, an increased porosity gives rise to a higher value of i, and hence a lower specimen potential. (b) Effect of bulk concentration of soluble iron Jan(o)] on specimen potential The coefficient Aa contains the term RTaa(o)/2Fna(s). Reduction of an(o) will therefore reduce An. Figure 6 shows that this will cause an increase in i, and hence a reduction in specimen potential. In addition, equations (5) show that a reduction in an(o) will increase ia but have no immediate effect on i=. Since iz is the current carried by the soluble iron species, an increase in its value whilst i= remains constant will cause an increased porosity at the oxide metal interface. Therefore if an(o) is low from the commencement of the corrosion reaction, the mean porosity of the film will be large, and it has already been shown that this also leads to a low specimen potential. Thus, a low value of at(o) causes a low specimen potential both directly and indirectly.
Ai C2+A2CI icA~:~CIC2
sing
V
Reducln1gAi A¢- Bctn ic
F~o. 6.
Graphical solution to the equation
Ac -- B, In ic --
A, C2 + A~ C, c , + cs
+ i,
A(c) C~ C2 v . A(s) ( G + G)"
482
H. A. McCARTHy and P. L. HARRISON
SUMMARY This Appendix has shown, from electrochemical considerations, that the potential of an oxidizing specimen can be decreased by (i) an increase in oxide porosity or (ii) a decrease in the bulk concentration of soluble iron. Castle and Mann is have shown the effectiveness of magnetite as a catalyst for the Schikorr reaction, in which soluble iron is precipitated as magnetite. From this work, it is to be expected that the presence of large, magnetite covered areas in contact with the electrolyte will cause a substantially reduced value of the bulk concentration of soluble iron for any given rate of supply, i.e. any given specimen area. Consequently, a small specimen corroding inside an autoclave with a large internal surface area already covered by magnetite, as was the case with specimens oxidized in the compression autoclave, would be expected to form oxide of comparatively high porosity and exhibit a correspondingly low corrosion potential.
THE DEFORMATION OF MAGNETITE FILMS FORMING O N M I L D STEEL* H. A. MCCARTHY and P. L. HARRISON Central Electricity Research Laboratories, Leatherhead, Surrey KT22 7SE, England Abstract--Crack-detection techniques, developed for room temperature studies, have been applied to the study of magnetite layers growing on mild steel in NaOH solutions at 573 K and 10 MN/m ~ pressure, when subjected to varying tensile or compressive strains. It has been found that these films are extremely resistant to failure in compression but that they crack in tension at strains of 0-05-0.08 ~. Strains, below those necessary to cause cracking, result in changes in the rate of the electrochemical reactions associated with the oxidation process. R6sum&---On a appliqu6 les techniques de d6tection de fissures ~. teml~rature ambiante & l'6tude de couches de magn6tite form6es sur acier doux darts des solutions de NaOH h 573°K et 10 MN/m 2, et sous diverses contraintes de tension ou de compression. Ces couches se sont av&6es tr~s r6sistantes ~t la compression; mais, en tension, elles c~dent fi des sollicitations de 0,05 ~t 0,08 ~. Les sollicitations subliminaires produisent des changements des vitesses des r~actions 61ectrochimiques li6es b. la r6action d'oxydation. Zusammenfassung--Rissfeststellungsmethoden, die fiir Untersuchungen bei Raumtemperatur entwickelt worden sind, wurden auf die Untersuchung yon Magnetitschichten angewendet, die auf Gussstahl in NaOH-L6sungen bei 573 K und 10 MN/m 2 Druck entstanden sind und verschiedenen Zug- oder Druckverformungen ausgesetzt wurden. Es stellte sich heraus, dass diese Schichten/iusserst bestfindig gegen Rissentstehung bei Verformung unter Druck sind, aber bei Zugverformungen yon 0,05-0,08 ~o rissig werden. Verformungen, die geringer sind als diejenigen, welche Rissbildung verursachen, haben ~,nderungen der Geschwindigkeit elektrochemischer Reaktionen zur Folge, die mit dem Oxydationsprozess verbunden sind. INTRODUCTION
CRmCAL tensile fracture-strains at room temperature for magnetite films (grown on steels in s o d i u m h y d r o x i d e solutions at 589 K ) have been previously reported, x These i n d i c a t e d t h a t the b e h a v i o u r o f such films was nearer to t h a t o f bulk m a t e r i a l t h a n to t h a t o f a thin film. I n t e r p r e t a t i o n o f these results is c o m p l i c a t e d by the fact that the difference in e x p a n s i o n coefficients o f the metal and oxide a l m o s t certainly caused the m a g n e t i t e to be p r e - l o a d e d in compression (up to a m a x i m u m strain level o f 0-1%) on cooling the c o r r o d e d specimens to r o o m temperature. T h e extent o f this prel o a d i n g is n o t likely to have been the same for all specimens as it w o u l d depend on the ratio o f oxide thickness to specimen thickness a n d on the degree to which stress relief occurred within the m a g n e t i t e layer during the cooling process. T h e crack-detection techniques developed for the r o o m t e m p e r a t u r e w o r k can be a p p l i e d to the study o f the effect o f d e f o r m a t i o n on m a g n e t i t e films growing at high temperatures. Such a s t u d y removes the uncertainties associated with r o o m t e m p e r a t u r e tests. T h e m a i n a i m o f the present investigation has been to s t u d y the effect o f d e f o r m a t i o n on b o t h the corrosion rate o f the u n d e r l y i n g metal and the *Manuscript received 14 May 1973. 469
470
H. A. McCARTHY and P. L. HARRISON
integrity of the growing magnetite films. The metal in this case was mild steel. The corrosion was monitored by measuring the potential of the specimens with respect to a platinum electrode in a two electrode cell arrangement. Corroding specimens were subjected to compressive or tensile strains. Two autoclaves have been used in these tests, one for compression-testing, the other for tension-testing. EXPERIMENTAL
The autoclaves, specimen configurations and test procedures have been described in detail elsewhere. 2 All specimens were machined from mild steel of composition C 0.23 %, M n 0.61%, S 0.016 %, Si 0.03 %, Ni 0-13 %, Cr 0.05 %, Cu 0.08 %, P 0.015 %, Mo 0.05%, V < 0.05%. The autoclaves, containing 5%NaOH solutions, were heated to 573 K with zero load applied to the specimens. Some growing oxides were tested at their temperature of formation after 2 or 3 d oxidation. Other oxidized specimens were tested after the autoclave and its contents had cooled to room temperature. Oxides were grown under both "Bloom" and "Potter-Mann" conditions? Potter-Mann conditions were obtained by connecting the specimen externally to the platinum electrode. Bloom conditions were obtained by leaving the specimen fully insulated. In all tests, after cooling and dismantling the autoclave, the surface of part of the gauge-length was examined for damage in the scanning electron microscope. The remainder of the gauge-length was sectioned and examined metallographically. RESULTS
The potential responses were the same whether specimens had been oxidized under Bloom or Potter-Mann conditions. In all the compression and tension tests, as soon as the load started to be applied to the specimen, there was an immediate change in the potential of the specimen with respect to the platinum electrode. The sign of this change was determined by whether the applied strain was compressive or tensile and the rate of change was dependent upon the strain-rate and the temperature at which the test was performed. In tension tests, when the elastic limit of the mild steel was reached, there was an immediate large change in the potential of the specimen. At room temperature this was to more positive values whilst at 573 K it was much more rapid and to negative values. Changes in the rate of change of potential also occurred when the specimens commenced to yield in compression. However, in this case, the change can adequately be accounted for by the fact that at constant cross-head speed of the testing machine, the strain rate of the specimen increased locally as part of it was strained beyond the yield point. 2 The results are tabulated qualitatively in Table 1, and typical voltage-time curves are presented in Figs. 1-3. In all compression tests, when straining ceased the potential of the specimen drifted slowly back to its original prestrain value, whereas in tension tests, the potential remained relatively steady at the value obtaining when the straining ceased. That is, under compression the response of the potential was dependent upon the strain-rate, whereas under tension it was dependent upon the strain. Figure 1 shows the influence of strain rate in compression on the potential of the specimen. The estimated true strain-rates of the specimen were: A 0.4%/min in the
471
The deformation of magnetite films forming on mild steel
& A 10131 ....... ~E
80C
!
"
~int
/
60C
',!\
/
I
~
i'
7..
i
!
!
"-,-
,
'
AJ B-" C D E
)
;~*~rr~in i ~/,,/rain" I 0/./rain 2 %/rain O%/min
-I-4
I
-i-6
i
i_~ I lu
I '
' %
i
,4-,,
! ",i
-I-,~ eL
"i'-"!',
' ~
"
.-i-ie ! I
I
i I- 5
Time,
F i o . 1.
!
,
, i
I I.O
,. o 5
~ I
I
i ,~.
i /
E i
',
I
i
, !
\ i
~ 4~x
ID
i
I '
',,
,.~/ lela .../
C
B
!
I 2.o
I 2~
.I
mln
Compression of mild steel oxidizing in 5 ~oNaOH at 573K.
l
I I I I
-I-6 .-
I!
f-,---- _.... ...j,...--
/-10 >
7 Machine strain rate
~E 6o( 5oo
. . . . -~
I I -I-8 ! !
I%/rnln
I
-12
32 %/rnin
E .....-
2 %/mln
. 400
~o lOCI
J, J--2, 5
I0
15;
Time,
FIG. 2.
20
25
mln
Room temperature compression of mild steel oxidized in 5 ~ l a O H at 573K.
elastic and 4%/min in the plastic region, B 2%/min, C 1%/min, D 2%/rain. During E the machine was at rest. It can be seen that the potential of the specimen was initially negative with respect to the platinum electrode and changed to more negative values under the influence of strain. It can be seen also, that the rate of this change was directly related to the rate of straining. This was particularly pronounced at the change in strain-rate of from 0.4 %/rain to 4 %/min which occurred when the specimen was strained beyond the yield point.
H. A. McCARTHYand P. L. HARRISON
472
Elostlc deformation : PIq$1"lc IK'' C;iz~ '~deformotion I
A
Ioo
,'I ! B
I
i i, ,,'I 5o
C
!I )i!t ,
i /~,
,#
....
,oo
F I G . 3.
TABLE l .
I I I I
"C
H2
-4- ....
I i
~
~',
!
li
>
3O0
"200 !,I o
e
i',
~co
i ~I
~o
E
I I
,--"
-I-2 ~ I QI I I I I
I !
;,=
-I-4
O
0
Time,
i
! i, I Ai BI
I
mln
I ! I I
I
2
Time,
min
3
(a) (b) Potential and extension curves on tensile straining above and below the elastic limit at: (a) room temperature; (b) 573K.
VARIATION OF SPECIMEN POTENTIAL ( W I T H RESPECT TO PLATINUM) ON COMPRESSIVE AND TENSILE STRAINING
In compression Room temp. 573 K
Room temp.
In tension 573 K
Initial potential (with respect to Pt) after 3 d oxidation
1-10 mV negative
1-10 mV negative
~ 200 mV positive
1-I0 mV positive
Response immediately on straining
Change to more negative value
Small change to more negative value
Change to more positive value
Small change to more positive value
Response on yielding of metal
Change to more negative value
Small change to more negative value
Greater change to more positive value
Very large change to negative value
By c o m p a r i n g Figs. 1 and 2 it can be seen that, at r o o m t e m p e r a t u r e , the influence o f strain rate on the rate o f change o f potential was even m o r e p r o n o u n c e d t h a n at 573 K. F o r a given strain rate, the response at r o o m t e m p e r a t u r e was a b o u t ten times that at 573 K. T h e rate o f decay o f the potential back to its pre-strain value after straining had ceased was also m u c h m o r e r a p i d at r o o m t e m p e r a t u r e t h a n at 573 K. T h e influence o f oxide thickness on the m a g n i t u d e o f the potential response d u r i n g compression testing was studied by using unoxidized 18/12/1 stainless steel specimens and mild steel specimens oxidized at 573 K (either in 5 % N a O H for I0 d o r in 1 5 % N a O H for 3 d) to p r o d u c e thicker films than those p r o d u c e d b y 3 d o x i d a t i o n in
The deformation of magnetite films forming on mild steel
473
5%NaOH. The unoxidized stainless steel specimens were subjected to compressive strain in the cold autoclave immediately after assembly. The specimens were still shiny-bright when removed from the autoclave after testing. They gave much greater. potential changes when subjected to compressive strains than did the oxidized mild steel specimens tested at room temperature. This difference appeared to be caused by the lack of substantial oxide on the stainless steel. Stainless steel specimens oxidized for 2 d in 5 % N a O H at 573 K and then strained in compression at room temperature or 573 K gave potential responses similar to those obtained with oxidized mild steel specimens when these were subjected to similar compressive strains. The mild steel specimens with the thicker oxide films gave smaller potential responses than those specimens with thin films. Furthermore, the response was sluggish in that the potential continued to drift away from its pre-strain value for 30-60 s after straining had ceased. The influence of tensile strain on the potentials of specimens, which had been oxidized for 2 d in the autoclave prior to straining, is illustrated by Fig. 3. The potentials of the specimen~ after cooling to room temperature were a few hundred mV positive with respect to the platinum electrode. Tensile strains increased these potential differences in both the elastic and the plastic regions of deformation. It will be noted from Fig. 3 that the rate of extension and the rate of change of specimen potential altered abruptly at yield. As described earlier, 2 the change in the rate of extension arose because, although during elastic deformation of the specimen part of the crosshead movement was taken up by the extension of the machine pull-rods, during the plastic deformation nearly all this movement was taken up by the gauge length. Also, during the elastic deformation only part of the measured extension was due to an increase in the gauge length. Consequently for a given cross-head speed the strain rate on the gauge length during plastic deformation was nearly six times that during the elastic deformation. Since the potential response was dependent upon strain, this partly explains the rapid change in response as the specimen yielded. However, unlike the case with compressive deformation, the change in response was greater than could be accounted for by the change in strain-rate alone. At 573 K the response of the potential to tensile strains in the elastic region was very similar to that at room temperature except for the magnitudes of both the initial potential and its rate of change (Fig. 3 and Table 1). However, when plastic deformation began at this temperature, the potential swung very rapidly to negative values. Again, as in all other tests, the potential slowly returned to its pre-strain value when deformation ceased. It was found possible to separate the point of yield of the specimen from this point of large negative swing in the potential by subjecting the specimen to plastic deformation in compression before the start of the tensile test. When this was done, the specimen underwent tensile plastic deformation before the large change in potential occurred. The amount of this tensile plastic deformation appeared to be the same as the amount of compressive plastic deformation suffered by the specimen before the tensile test. The tensile yield-strain of mild steel oxidized at 573 K in N a O H was calculated from the extension curves for a series of experiments at both room temperature and 573 K. At room temperature, successive tests in the plastic region (up to a total of 0.5% strain) gave yield-strains in the range 0.10-0.13%. At 573 K, yield-strains were
474
H. A. McCAgTHVand P. L. ~ r q
in the range 0.05-0.08% (with a total strain of up to 2.4%). Cracks in the oxide surface were observed by SEM in all specimens which had been strained at room temperature to a total tensile strain of above 0.5%. No cracks were detected when straining had been confined to below the elastic limit. The extent of the cracking depended upon the magnitude of the strain to which the specimen had been subjected. Figure 4 shows the condition of the oxide surface after 2 % and 30% strain. As shown in Fig. 4(a) cracks often emanated from defects in the oxide. The first cracks grew mainly perpendicular to the gauge-length (Fig. 4a) but at higher strains there was an increased proportion of cracking at 45° to this direction (Fig. 4b). The form of the cracks was the same whether straining had taken place at room temperature or 573 K. Optical microscopy showed that cracks produced under tensile stress (such as those in Fig. 4) frequently passed through the whole of the oxide layer (~ 5 ~m thick) down to the metal. In addition, the underlying metal was found to be cracked when plastic tensile straining had taken place at 573 K (Fig. 5). These cracks in the metal were usually, but not always, associated with visible cracks in the oxide. No cracks could be detected by optical microscopy in thin oxide layers (1-2 ~tm thick) on specimens which had suffered 1% plastic strain in compression. Thicker oxides (10 i~m thick) did, however, show short longitudinal cracks after compressive strains of 1%.
DISCUSSION It is shown in the Appendix that the potential of an oxidizing specimen is strongly dependent upon the porosity of the oxide layer formed, and that this, in turn, is influenced by the ratio "autoclave wall area/specimen area". If this ratio is large, the oxide porosity will also be large and the specimen potential will be low, and vice versa. Consequently the potential difference generated within a two-electrode cell can be of either sign depending on the conditions of oxidation. In the tension autoclave, the value of the area ratio is about one-third of its value in the compression autoclave so that the catalytic effect of the magnetite-covered autoclave wall, which promotes porosity in the specimen oxide, is less in the tension autoclave. The resulting lower porosity would explain the higher potential of the specimen (with respect to the platinum electrode) in the tension autoclave compared with the compression autoclave. The fact that this raising of the potential has resulted in a potential of approximately the same magnitude but of opposite sign is considered to be quite fortuitous. The theory of the current at yielding electrodes has been discussed by Hoar. 4
Because the thermal expansion coefficient of the magnetite film is less than that of the underlying metal, cooling of the oxidized specimen causes a compressive stress in the oxide. This compression may be expected to decrease the porosity of the oxide. If the porosity is already low, such further reduction will have a far greater percentage effect than it will if the porosity is high. This could explain the large rise in potential which occurred when specimens oxidized in the tension autoclave were cooled, although cooling those oxidized in the compression autoclave produced little change in potential.
,
.
I\
' 'ii
I
)
'i I
I
~
=
I
I
10 p m Gouge leng'l'h direcfion 10 p m FIG.4. Mild steel oxidized at 573K for 2 d in 5 ~oNaOH and then strained in tension: (a) 2 % at 573K; (b) 30% at room temperature.
I I I0 pm
Fio. 5.
Mild steel oxidized at 573K for 2 d in 5 %NaOH. Cracks in oxide and metal after 2 % tensile strain at 573K.
[facing p. 474]
The deformation of magnetite films forming on mild steel
475
It is to be noted that, in all tests, the potential of the specimen responded immediately to straining. It is unlikely that this response arose from cracking of the oxide film since this would indicate breaking strains of less than 0.01% at'573 K and cracking of the oxide as the compressive stress in it diminished during the tensile tests at room temperature. The change in potential on the rupture of a film has been discussed by Jones, Stratton and Osgood.5 It is convenient to discuss this phenomenon under the two headings of compression and tension. Compression tests
At room temperature, stainless steel specimens with no oxide layer visible on them gave much greater responses than did mild steel specimens previously oxidized at 573 K, although oxidized stainless steel and mild steel showed no such difference when both had been previously oxidized at 573 K. Furthermore, increasing the thickness of the magnetite layer on mild steel caused the response at 573 K to become smaller and somewhat delayed. Both these facts suggest that this immediate response arose from a disturbance at the oxide/metal interface. Huybregts, Van Osch and Snel s and Townsend 7 have discussed in detail the various reactions possible in the Fe-H20 system under various experimental conditions. However, the former authors only considered the temperature range 333473 K and Townsend's work was at 523 K. Field, Stanley, Adams and Holmes s have postulated that there are two competing reactions occurring at the metal/bxide interface at 573 K. One of these produces magnetite in situ whilst the other produces a soluble species, both involving a net negative charging of the specimen if at least part of the cathodic reaction is taking place at a second electrode. The proportion of the oxidizing iron that dissolves is probably governed by the stress-relief necessary to accommodate the Pilling-Bedworth ratio of 2 : 1 and would therefore rise as the oxide is compressed. This could explain the strain-rate dependent movement of the potential to more negative values as the specimens were compressed. The results obtained at room temperature were very similar to, but more pronounced than, those obtained at 573 K. Consequently it is suggested that the same explanation is valid at both temperatures even though the iron soluble species are probably quite different in the two cases. It is interesting to note that any reduction of porosity consequent on compression would cause a strain dependent reduction in the anodic reaction on the steel and hence a strain dependent movement of the potential to more positive values. These results cannot, therefore, be explained in terms of reduced porosity effects. Tensile tests
In these tests, the specimens were positive with respect to the platinum electrode As has been suggested above, this is probably a consequence of the low porosity of the oxide. This would also explain the very large positive potential difference obtained at room temperature. At this temperature, the porosity of the oxide would have been even further reduced by the compression arising from the differential contraction between metal and oxide on cooling. It should be noted that, in tensile tests, the response was approximately strain dependent, not strain-rate dependent, and that the potential always moved to more positive values as the tensile strain increased.
476
H. A.
McCARTHYand P. L. HAgRLSON
This is consistent with an enhanced cathodic activity arising from an increased surface area of oxide at which cathodic reactions can take place. In all tests, yielding of the metal specimens gave rise to greatly enhanced responses of their potentials. As has been stated previously, the enhancement occurring in the compression tests can be adequately explained by the increased strain-rate of the specimen during plastic deformation (as compared with elastic deformation) for any given machine cross-head speed. Moreover, optical microscopy showed no evidence of oxide cracking under compression until strains of the order of 1% had been achieved, so that variation in the potential, due to removal of the oxide from close contact with the metal, would not be expected at the much lower strains (0.1%) at which the metal yielded. The enhancement occurring in the tensile tests, however, cannot adequately be explained by changes in strain rate at the specimen. At room temperature, though the enhanced rate of change of potential is in the same direction as the change before yield, the enhancement is too great to be explained by the increased strain rate. This additional increase in the cathodic activity of the oxidizing specimen probably arises from a greater increase in oxide surface area occasioned by cracking of the oxide. It is to be noted that all specimens strained in tension beyond the yield point showed cracks in the oxide layers, and that the extent of the cracking was greatest for those specimens which had suffered the greatest plastic strain. At 573 K, yielding of a specimen under tension gave rise to a very sharp swing of the potential to negative values. Obviously an entirely different mechanism was operating in this case. Optical microscopy showed that all such specimens had cracks in the oxide which penetrated into the metal. The conclusion to be drawn therefore is that, under these conditions of test, the metal was being subjected to stress corrosion cracking at the base of cracks within the oxide layer, and that this gave rise to the greatly enhanced anodic activity of the specimen. It is interesting to note that yielding of the metal alone was not sufficient to produce this enhanced activity. It was possible to produce yielding under tension without the enhanced activity by subjecting the specimen to prior plastic deformation in compression. When this was done, the specimen underwent an amount of tensile plastic deformation similar in extent to the previous compressive plastic deformation (before this enhanced activity became evident). This suggests that the stress corrosion cracking occurred only after the oxide had cracked and that this happened at a strain which was very close to the yield strain of the underlying metal. It seems unlikely that this coincidence was fortuitous, and is probably further evidence for the existence of a thin layer of oxide, adjacent to the metal, which is either non-porous or of a different composition, as has been postulated earlier.I, 9 Apparently the tensile properties of this layer are in part determined by the properties of the parent metal. If the above interpretations of the experimental results are accepted, the following comments can be made concerning the critical fracture strains of the oxide. Under compression, the oxides produced appeared to be extremely resistant to damage. The thicker films ( ~ 10 ~m) showed no cracking until subjected to strains in excess of 1%. The thinner films ( ~ 1 ~tm) were even more resistant to damage. Under tension, the oxides fractured at the yield strain of the underlying metal both at room temperature and at 573 K. The yield strains of oxidized metal were found to be
The deformation of magnetite films forming on mild steel
477
0.10-0-13% a n d 0-05-0.08% at r o o m t e m p e r a t u r e a n d 573 K respectively. I f in the f o r m e r case allowance is m a d e for the compressive strain induced in the oxide by cooling, a critical tensile fracture strain at r o o m t e m p e r a t u r e o f less than 0.03% is a p p a r e n t l y obtained. However, at r o o m temperature, the mild steel yielded in an i n h o m o g e n e o u s manner. T h e overall small plastic strain o f the metal consisted o f local strains o f the o r d e r o f a few per cent, arising f r o m the p r o p a g a t i o n o f Liiders bands. Consequently, under these circumstances, it is impossible to measure the true critical tensile fracture strain. In the previous w o r k by H a r r i s o n 1 the geometry o f the experiment was such t h a t no inhomogeneities in strain were a p p a r e n t in the m e t a l until after cracks had a p p e a r e d in the oxide. Consequently the values o f 0.02-0.23 % o b t a i n e d by H a r r i s o n (allowing for the compressive strain induced in cooling) represented a measure o f the true critical tensile fracture strain o f the magnetite films at r o o m temperature.
CONCLUSIONS 1. A t 573 K magnetite films, growing on mild steel in 5 % N a O H solutions, cracked u n d e r tensile strains o f 0.05-0.08 %. 2. Tensile cracking at 573 K led to very r a p i d local dissolution o f the metal a n d stress c o r r o s i o n type cracking. 3. A t 573 K magnetite films, growing on mild steel in 5 % N a O H solutions, withs t o o d compressive strains o f up to 1% w i t h o u t cracking. 4. A t strains less t h a n those necessary to fracture the films, cathodic activity was enhanced in tensile straining and a n o d i c activity enhanced in compressive straining, leading to small changes in the rates o f the electrochemical reactions. Acknowledgements--The authors would like to thank Dr. G. J. Bignold and Dr. D. R. Holmes for
their helpful comments and Mr. S. C. Ferguson for his constant advice and assistance. This work was carried out at the Central Electricity Research Laboratories and the paper is published by permission of the Central Electricity Generating Board.
REFERENCES 1. P. L. HARRISON,Corros. Sci. 7, 789 (1967). 2. H. A. McCARTHY,P. L. HARRISONand S. C. FERGUSON,J. Phys. E. Sci. h~strum. 5 (8), 790 (1972). 3. T. F. MARSH, d. electroehem. Soc. 113, 313 (1966). 4. T. P. HOAR, N A T O Conference on the Theory o f Stress Corrosion Cracking in Alloys, Brussels (Ed. J. C. SCtlLLY), p. 105 (1971). 5. R. L. JONES, L. W. STRAI'rONand E. D. OSOOOD, Corrosion 26, 399 (1970). 6. W. i . M. HUYBREGTS,G. VAN OSCH and A. SNEL,Proc. 4th Int. Congr. on Metallic Corrosion, Amsterdam, p. 501 (1969). 7. H. E. TOWNSEND, Corros. Sci. 10, 343 (1970). 8. E. M. FIELD,R. C. STANLEY,A. M. ADAMSand D. R. HOLMES,Proc. 2nd Int. Congr. on Metallic Corrosion, New York, p. 829 (1963). 9. G. J. BIGNOLD, Corros. Sei. 12, 145 (1972). 10. J. E. CASTLEand H. G. MASTERSON,Corros. ScL 6, 93 (1966). 11. G. J. BIGNOLD,R. GARNSEYand G. M. W. I~/I.A.NN,Corros. Sci. 12, 325 (1972). 12. M. PotmsnlX, Atlas o f Electrochemical Equilibria in Aqueous Solutions. Pergamon, Oxford (1966). 13. F. H. SWEE'rONand C. F. BAES,J. chem. Thermodynamics 2, 479 (1970). 14. H. E. TOWNSEND,Corros. Sci. 10, 709 (1970). 15. J. E. CASTLEand G. M. W. MANN, Corro$. Sci. 6, 253 (1966).
H. A. McCARTHY and P. L. HARRISON
478
APPENDIX NOMENCLATURE a
a (d)
a a a a
(o) (s) (X) (c)
A (s) A, B, C
A,, B, D e
e, E E0
fl F i
io io n (a) n (s) R T Y
v (x) V X
X 2
n (a) n (c)
activity of an ion in an electrolyte lower limiting activity activity at oxide/electrolyte interface higher limiting activity activity at oxide/metal interface area available for cathodic reaction geometric area of specimen coefficients defined by equation (7) coefficients relating cathodic current and potential diffusion coefficient reaction potential potential of cathodic reaction equilibrium potential standard electrode potential function of a(d) and a(s) Faraday constant current density cathodic current density exchange current density ion concentration corresponding to activity a limiting ion concentration gas constant absolute temperature porosity at oxide/metal interface porosity at a distance, x, from oxide/electrolyte interface effective porosity of oxide film defined by equation (4) distance from oxide/electrolyte interface thickness of oxide ionic charge activation coefficient activation overpotential concentration overpotential
Subscripts 1 electrode cation 2 electrolyte anion To the best of our knowledge, the case of concentration polarization for an anodic process has not been treated to any extent in the literature. Castle and Masterson ~° have developed a model for the corrosion of iron in high temperature aqueous solutions in which diffusion of a soluble iron species through a porous magnetite layer is the rate-determining step. This model is based on the postulated occurrence of two competing reactions at the corroding interface, one producing Fe304 in situ and the other producing iron ions which diffuse away from the corrosion site. The model of Castle and Masterson is based on mechanisms of chemical diffusion, and electrochemical reactions are not considered. The model now to be presented attempts to bring these latter into consideration. Bignold, Garnsey and M a n n u have recently extended the theory of Castle and Masterson, and have discussed it in electrochemical terms. GENERAL CHARACTERISTICS OF THE MODEL The corrosion reactions are assumed to occur at the interface of the metal and a porous corrosion film of uniform thickness. The supply of oxidant and the removal of soluble iron are by diffusion through the pores in this film. For convenience of analysis, the pores are assumed to be cylinders whose axes lie perpendicular to the film/metal interface. They are assumed to be identical and to have a common radius which is a function only of the distance from the surface of the film. Following Castle and Masterson, it is assumed that, for the corrosion of iron in strongly alkaline solutions, the diffusion coefficient of the electrolyte anion is much higher than that of the electrode
The deformation of magnetite films forming on mild steel
479
cation and hence that the concentration of the former at the corroding metal surface is very similar to the high value obtaining in the bulk of the electrolyte. Since the oxide is a comparatively good conductor, the cathodic reaction taking place on the oxide surface will occur at essentially the same potential as the two anodic reactions. DEVELOPMENT OF THE MODEL It is assumed that the corrosion reactions occurring at the metal surface can be represented by the two simultaneous equations Fe ~-- Fe 2+ + 2e tFe+OH-~--]FesO4+
(1) ½H=O+e.
(2)
These are suggested as representational only; for example, it is generally agreed t2-t4 that in alkaline solutions iron dissolves as an amphoteric anion such as HFeO~, FeO~-, Fe(OH)~ or Fe(OH)]-. The equilibrium potentials for these two reactions can be written as EtfE
and
R T In a t ( o ) ° + 2 fRfT In [Fe z+] = E t ° +~-ff
E2 = E2° -- "~- In
[OH-]
= E ° --
(la)
~ - In a2 (o)
(lb)
&
respectively. For non-equilibrium conditions, the activation over-potentials are given by qt (a) = R T (In it -- In i01) 213tF
and
n~
(a)
(2a)
R T ( l n i2 -- In to=).
=
(2b)
It is assumed that the reactions are independent of one another and that the exchange current densities can be treated as constant. For the diffusion of an ion, the general equation is
(3)
__ v(x) D z F n(a) da. v a dx
Integration gives x iv f - v - ~ d x i v X ~
a(X) -- D z F f
o
n(a)
(4)
a(o)
(where V is the effective porosity of the oxide film). At high levels of concentration and those corresponding to saturation, small changes in concentration will give rise to large changes of activity. This can be expressed mathematically by defining a value of a ----a(s) above which the value of the ion concentration can be taken to be constant at n(s). At low values of concentration, concentration and activity are linearly related. It is possible to define a second limiting value of a = a(d) such that only below this value can the proportionality between activity and concentration be considered valid. F o r the electrode cation (Fe2+), assuming a(X') > a(s) > a(d) > a(o) a( X)
then
f
a(d)
~ a(o)
da =
f
a(s)
n(a) da +
a(o)
T
f a(d)
---- n(,) In a ( X ) -
a(X)
n(a) -a-
da +
a(o) + f l
f a(s)
n(a) ,, da
--
H. A. McCARTHY and P. L. HARRISON
480
a(s) where
./'1 ----| d
S
~
n!a-) da -- n(s) In a(s) + a(d) is a function whose value depends on the a
a(d)
relationship existing between activity at and concentration n,(a). Therefore
ilvX V
v
-I
(Sa)
= 2 D 1 F i n ( , ) In a ( X ) - a(o) + I H .
L--
For the electrolyte anion (OH-), assuming a(X) > a(o) > a(s) > a(d)
a(X) f
then
n(a) da = n(s) In a(X) a(o)
a
a(o)
therefore iz_v_X= _ D2F ~(s) In as(X) V
as(o)
(5b) "
Assuming that the thermodynamic equation for a reversible cell is applicable, the concentration overpotential is given by q(c)
= R T I n [a(X)/a(o)]. zF
Substituting for a~(X) and a2(X) from equations (5) yields rh(c)
and
= RT
ixvX
RT
i2vX
2F-[2
qa (c) --
+ al (o) _ In al (o) --
fl ]
(6a)
(6b)
F n2(s)VD2F
respectively for the two ion types. The electrode potentials, e, and e2, for the two anodic reactions are obtained by combining equations (1), (2) and (6). This gives
RTf
a,(o)
4vX
n, (s) and
RT ~ i,v X e 2 = E 0 + F-Ln,(s~-OsF
lna,(o)+
I
f' + : I n / , nt (s) ~
In/2--
]
13-1In i0x
131 1
]
~ lnios .
These can be written as ea = A, + B1 In il + C1/1
(7a)
es = As + B.. In iz + C2 is
(7b)
(where At, .4z, B~, B2, C~ and C2 are constants). Since the cathodic reaction is occurring on the extended oxide surface, it can be assumed that it is not under diffusion control and that the reaction potential can be represented by
e~ = A, -- B, lni,.
(8)
Since the corroding specimens are electrically isolated, the total anodic current must equal the cathodic current, that is
(ix + iO v a(s) = i, A(c).
(9)
The deformation of magnetite films forming on mild steel
481
Assuming both anodic reactions are strongly under diffusion control,
el = Aa -~- Cain) e= A2 + Czi2 from (7). Substituting for it and i, in (9) gives
~+ e~2]
lea
v. A(s) = I[ ~- A - +z-A~uj I
~, A(s) + ic A(c).
If the cathodic reaction occurs at the same potential as the two anodic reactions, ea = e~ = e,, therefore
e~ --
AaC2 + A~Ca Ca + C2
q- it
A(c) G G v. A(s) (Ca + C2)
therefore from (8), A , - - B, l n i c - - A , G + A2Ca ~_ ic
Ca + C,
A(c) GC2 v. A(s) ( G + G).
(10)
The two sides of equation (10) are shown plotted against it in Fig. 6. The solution to the equation is represented by the intersection of the two solid lines. B E H A V I O U R O F THE MODEL (a) Effect of porosity (V) on specimen potential In equation (10), for any given oxide thickness, (ARC2 + A=CI) / (Ca+ C~) is independent of Vwhilst the coefficient of/, is proportional to 1IV. It can therefore be seen from Fig. 6 that, for a given eldctrolyte condition, an increased porosity gives rise to a higher value of i, and hence a lower specimen potential. (b) Effect of bulk concentration of soluble iron Jan(o)] on specimen potential The coefficient Aa contains the term RTaa(o)/2Fna(s). Reduction of an(o) will therefore reduce An. Figure 6 shows that this will cause an increase in i, and hence a reduction in specimen potential. In addition, equations (5) show that a reduction in an(o) will increase ia but have no immediate effect on i=. Since iz is the current carried by the soluble iron species, an increase in its value whilst i= remains constant will cause an increased porosity at the oxide metal interface. Therefore if an(o) is low from the commencement of the corrosion reaction, the mean porosity of the film will be large, and it has already been shown that this also leads to a low specimen potential. Thus, a low value of at(o) causes a low specimen potential both directly and indirectly.
Ai C2+A2CI icA~:~CIC2
sing
V
Reducln1gAi A¢- Bctn ic
F~o. 6.
Graphical solution to the equation
Ac -- B, In ic --
A, C2 + A~ C, c , + cs
+ i,
A(c) C~ C2 v . A(s) ( G + G)"
482
H. A. McCARTHy and P. L. HARRISON
SUMMARY This Appendix has shown, from electrochemical considerations, that the potential of an oxidizing specimen can be decreased by (i) an increase in oxide porosity or (ii) a decrease in the bulk concentration of soluble iron. Castle and Mann is have shown the effectiveness of magnetite as a catalyst for the Schikorr reaction, in which soluble iron is precipitated as magnetite. From this work, it is to be expected that the presence of large, magnetite covered areas in contact with the electrolyte will cause a substantially reduced value of the bulk concentration of soluble iron for any given rate of supply, i.e. any given specimen area. Consequently, a small specimen corroding inside an autoclave with a large internal surface area already covered by magnetite, as was the case with specimens oxidized in the compression autoclave, would be expected to form oxide of comparatively high porosity and exhibit a correspondingly low corrosion potential.