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Hydrogen diffusion and intergranular cracking in nickel
Pergamon PII: SO360-3199(97)00@01-3
HYDROGEN
DIFFUSION
AND INTERGRANULAR IN NICKEL
All rights reserved.Printed in Great Britain mo
1199
97 $I? 00 +m!
CRACKING
J. YAO and S. A. MEGUID Engineering Mechanics and Design Laboratory, Department of Mechanical Engineering. University of Toronto 5 King’s College Road, Toronto, Ontario, Canada M5S lA4
Abstract-A new dilfusion model is developed to analyze the contribution of grain boundary diffusion to total mass transport in metals. The predictions of the model are compared with experimental results concerning the effect of room temperature hydrogen precharging period upon the intergranular fracture depth in pure nickel specimens fractured at 77 K. It is shown that the fracture mode changes from transgranular into intergranular when the hydrogen concentration in grain boundaries reaches a critical value, in the range of 6.5-9.8 at%. The observed increment of’ intergranular cracking depth with the pre-charging period indicates that hydrogen transport in this material 1snot enhanced by grain boundaries. c, 1997 International Association for Hydrogen Energy
NOMENCLATURE Hydrogen diffusivity in grain boundaries Hydrogen diffusivity in lattice Ratio of above two diffusivities Hydrogen concentrationin grain boundaries Hydrogen concentrationin lattice Segregationfactor Binding energy Grain diameter Thicknessof the membrane Concentrationat input surface Grain boundary half width Critical hydrogenconcentrationin grain boundary for intergranular fracture
grain boundary ditfusivity is ordersof magnitudegreateithan the lattice diffusivity [7-91.However. little is known about grain boundary diffusion of small interstitial impurity atoms. The lattice diffusivity of hydrogen in most metals is relatively high and it is reasonableto expect that the limited extra volume available in grain boundarieswould not greatly increasethe masstransport of hydrogen. Generally speaking, a finer grain size. and consequently, a larger volume fraction of grain boundary regions,reducesthe sensitivity of an ahoy to hydrogen embrittlement. Therefore. it is important for designers involved with the emerginghydrogen energyindustry to know the role of grain boundaries in the hydrogen diffusion process. Since grain boundary
INTRODUCTION When solute hydrogen is introduced into polycrystalline nickel, the fracture modechangesfrom transgranular ductile rupture to intergranular cracking [l41.Obviously, hydrogen has to arrive at interior grain boundaries by diffusion to cause such intergranular cracking. Among the available diffusion paths, grain boundariesare suggestedby many researchersasfaster paths than the lattice for hydrogen diffusion. The reported ratio of grain boundary diffusivity to lattice diffusivity (K = 0,/01) in the literature canbe found in a wide range, from 60 by Tsuru and Latanision [5] to as high as IO8by Calder et al. [6]. It is well known for the caseof self and substitutionallattice diffusion that the
diffusion is always coupled with
lattice diffusion, there is no experimentalmeansto measuredirectly the grain boundary diffusivity. One hasto employ a mathematicalmodel to analyze the indirect measurement,The existing modelsfor masstransport concerninggrain boundaries[lo, 111,however. do not accommodategrain sizeand smallK ratios. The present paperpresentsa morerealisticanalytical modelto predict the penetrationdepth of a pre-determinedhydrogenconcentration at any given time. If this pre-determinedconcentration is the critical concentration of the fracture mode transition in nickel. then the prediction can be verified by performing tensiletestsat 77K on thin nickel specimenspre-chargedwith hydrogen. Since hydrogen atomsare “frozen” in the host lattice and thus become unableto move along with the carrying dislocations.the
1021
1022
J. YAO and S. A. ~E~UID
observedfracture modetransition issolely relatedto the segregatedhydrogen at grain boundariesduring precharging. It is with this in mind that we conduct the current investigation.
wheres is the segregationfactor given by s = exp (E,JRT) whereEbis the binding energy. The boundary conditionsfor the z direction are
THEORETICAL ANALYSIS Consider a thin membraneof polycrystalline metal with uniform grain size and ignore the effect of those grain boundariesparallel to the membrane.We assume all grain boundariesare perpendicularto the surfaceof the membrane,i.e. the membraneis composedof hexagonatprisms,asshownin Fig. 1. Becauseof symmetry, there will be no net exchangebetweenany particular grain and its neighbors.The problemof determiningthe concentrationin the aggregateis then reducedto determining the concentration of one hexagonalgrain, which is further simplifiedto a tubular cylinder with a thickness equivalent to the grain boundary width, 2~. The central radius of this equivalent tube is definedas L/2 where L is the averagegrain size. In the grain boundary, the concentrationC, satisfies
DgV2Cg =2
C,I;=, = co
(5)
ac, (?z;=/@ =0
(6)
where h is the membranethicknessand C, the concentration at the input surface. Sincethe grain boundarywidth is smallcomparedwith the grain diameter,even in microcrystallinematerial, the local curvature should be small. Therefore, it can be assumedthat the central plane of the equivalent grain boundary tube at p = L/2 is a planeof mirror symmetry for C,, i.e. c, = qyz,
t) + @y2)’
qyz, 1)
(7)
which is similarto Whipple’sapproximation [9]. Substituting equantion (7) into equations(I), (3) and (4) and usingequation(2) onecan find a singleboundary condition which must be satisfiedby C, at p = L/2-a, i.e. at the interface between grain interior and grain boundaries
and within the grain
ac, D,V2C,= at This leads to the following dimensionlessconIt is further assumedthat the equilibrium distribution centration expressionin a grain boundary, normalized of hydrogen in the lattice and grain boundariesfollows by the surfacegrain boundary concentration, for any the Boltzmann statistics;therefore, the boundary con- time t: ditions at p = L/2-a are C --kL = I + fJ jJ A,,Jo(ctn,L/2) x sinc; n=l m=, i x exp
(4)
-I?$ i
a&+
‘2”n~‘2~“)])
(9)
(
whereCr = .r x C,. The constantsanm in equation (9) can be calculated by solvingthe following transcendentalequation:
and A, can be obtainedfrom ‘4?J?3
/
\
Fig. 1. Grain boundary aggregate and the equivalent grain boundary tube. All grain boundaries are assumed perpendicular to the free surface of the membrane, i.e. into the paper. Those parallel to the surface are neglected.
In the above equations,Jr, and J1 are Besselfunctions of zero and first order, respectively.
HJ DIFFUSION
AND
INTERGRANULAR
When the hydrogen concentration in grain boundaries reaches Cz. the fracture mode changes to IG cracking. Therefore, the penetration depth of this critical concentration (or the depth of the IG fracture) at any given time can be predicted by letting C, = C: in equation (9). There are eight parameters in equation (9) that will affect the penetration rate of IG depths: a, s, K, Cz, D,, CO,L. andh (asdefinedearlier).Among theseparameters, the last two are specimenconstantsand the hydrogen diffusivity and the surfacehydrogenconcentrationunder the current prechargingconditions are already known: D, has beenfound to be 5.4 x lo- “cm’/s and Co to be about 2880appm (atomic parts per million) [12]. Although one cannot separatethe effectsof the rest four variablesin the experiments,an examinationof equation (9).-(11) revealsthat each variable will affect the penetration curve in a distinct manner.It is thus feasibleto verify the experimentaldata with the theory by adopting a parametricstudy. To start with, a critical concentration of c; = 0.065 (H/Ni) and a binding energy of &= I I .6 kJ /mol, both reported by Kimura and Birnbaum 1131, aswellasa half grain boundary width of 5 x 10m8 cm were usedin the calculationsand the resulting curves are shown in Fig. 2. Then various combinationswere accordingly adoptedto find out if other alternative combinationscould alsobe consistentwith the experimental curve. Although the percentagecontribution from the grain boundariescannot be measuredexperimentally, the lattice contribution at any time can be evaluated theoretically. This can be obtained by usingequation (9) to calculate the grain boundary concentrations at given times for a given K value. The grain boundary concentration due to lattice diffusion can be predicted by letting K = I. The ratio of thesetwo concentrationsprovidesan estimateof the percentageof hydrogen build-up at grain boundarieswhich could be attributed to lattice diffusion. By adopting suchan approach,the ratio was found to changewith time. The correspondingcurvesfor
CRACKING
11173
IN NlCKEL
each set of parameters(K> 1) are also shown in the figuresand are designatedwith the primed numbers.In this case,curves correspondingto K % 1 are not shown sincethe theoreticallattice contribution would alwaysbe 100%.
High purity Ni270(99.98%Ni) rod (a16 mm) wascold rolled to 0.25mm thicknessand annealedat 1173K 1.01 5 min, resultingin a fully recrystallized structure with a grain size of 50pm. All specimenswere electrolytically polishedin a 60% H$O, solution at 5.5V. The membrane tensile specimenshad a final cross section 01 4.5 x 0.2mm2and a gaugelength of 12mm. The specimenswere cathodically prechargedwith hydrogen at room temperature(295K) for 20, 40, 80, 160,320. 640. and 960min, respectively.A chargingcurrent density of 10mAicm’ was applied to the unmaskedgauge length area. After charging,specimens werequickly rinsedfirst in distilledwater then in alcohol, and driedusingblowing air at room temperature. For tensiletestsat 77K, specimensand the gripping assemblywere immersedin liquid nitrogen. No more than 2 min elapsedbetweenthe end of prechargingand the beginningof cooling. In order to ensurethermalequilibrium. the specimenswere held for ii further lOmill prior to loading. No strain rate effects were observed for the range 10 4s ‘tolO~~s~‘,thusanominalstrainrateoflO~~s waschosen.The fracture surfaceswereobservedand the depths of IG cracking were measuredusing
rcw1t.v
In the absenceof hydrogen,the material behavedin a ductile fashion with the crosssection of the specimen reducingto a knife-edgewith anelongationof some60%
1 .o
80.0
60.0 o Experimentnl Eel
1 .GkJ/mol,
C&0.085,
data L=O.O5mm
40.0
a=1 14. a=5x10-8c
ii 5’ (D 8 2 s 5 s s a-
20.0
0.0 L 0.0
2.0
4.0
6.0 Precharging
8.0 10.0 Time (hours)
Fig. 2. Measured IG cracking depths vs pre-charging periods. Solid curves effect of diffusivity ratio of grain boundary to lattice diffusion K. Dashed
12.0
14.0
16.0
#: L=O.Olmm
are theoretical predictlons of equation (9) shoumg line reflects the experimental result at larlrr t~mek.
1024
J. YAO and S. A. MEGUID
Large-scaleplasticdeformation is evident usingSEM by the presenceof extensiveslip bandsover the entiresurface and ridgesand groovesat grain boundaries. DiscontinuousIG cracking beganto initiate after less than 5% elongationin specimens prechargedfor 20 and 40min. When tensiledeformation wasfurther extended during testing,the central region of the membraneelongatedandfinally fractured in a ductile manner.Flat grain boundary surfacesresultingfrom intergranular cracking are observedalongthe charging surface.Beyond the flat regions,featuressimilarto thoseof hydrogen-freespecimenswereobserved. When the chargingperiod wasfurther extendedup to 640min, the IG fracture depth continued to increase. The IG cracksbecamecontinuousalong the edgeof the charging surfaces.The fracture surface of specimens becamecompletelyIG only whenthechargingperiod was further extendedto 960min. In this case,the specimens fractured at about 5% elongation and the entire cross sectionexhibited IG fracture. Again, a common occurrence of these IG fracture surfacesis the existenceof many parallel straight slip lines indicating limited and constrainedplasticdeformation. SEM observationsshow that IG fracture surfaces which formed after a short chargingperiod (20min) are similar to those formed after long charging period (960min). Furthermore, the entire crosssection of the specimens which wereprechargedfor 960min experiences the samedegree of brittleness, even though a concentration gradient is expectedto have existed in grain boundaries.Theseobservationssuggestthe existenceof a critical hydrogen concentration for IG fracture to occur, i.e. Cp*.In fact, it wasfound that most IG cracks penetratedto nearly the samedepth in all of the specimenschargedfor the sameperiod. Therefore, the boundary betweenthe flat and the severelydeformedregionsis definedasthe interface betweenIG and TG fracture, i.e. where the fracture mode transition occurred. A typical SEM micrographis givenin Fig. 3 for a specimencharged
for 320min. The measuredIG depthsfor various charging periodsare shownwith the theoreticalpredictionsin Fig. 2.
Fig. 3. SEM micrograph showing fractured cross section of a specimen which was charged with hydrogen for 320min. The arrows indicate location of the front of IG cracking.
grain boundary transport did not play a major role; being less than - 3%. In fact, a critical concentration of 0.0295 represents one hydrogen atom in 34 nickel atoms in the
DISCUSSION As can be seenin Fig. 2, the theoreticalprediction for K = 1 (curve I) agreeswith the experimentalresultsfor
charging times up to 320min. The experimentaldata deviate from the prediction only at larger times,which can be attributed to the grain boundary trapping effect. The consistencyof the data points with the predictions confirms the existence of the critical hydrogen concentration in the grain boundariesat which a changeof fracture modefrom TG to IG takesplace.Sincecurve 4, where the averagecontribution from the lattice is only about 50%, has already overestimatedthe penetration rate, it is concludedthat grain boundary transport of hydrogen doesnot play a significant role basedon the valuesusedfor Cz, &, and a. Substituting C,*,s, and C, into equation(9), one finds C,*/&, = 0.2. Usingsimilarchargingconditions,Kimura and Birnbaum [131found that when Cz/CF’ reaches about 0.22 the fracture mode of nickel changesto IG. Therefore, the presentresultsare consistentwith data reported in the literature [4, 13, 141except for the role of grain boundaries. In the parametricstudies,it isfound that the minimum values have to be usedfor K and the grain boundary width to obtain agreement with experimental data. Otherwise, the curve always shifts to the left, overestimating the penetration rate of IG depth. Conversely, changings and Ct can shift the curve to either direction. Therefore, only two alternative combinations of parameterscapableof fitting the experimentalresultsmay be possible:(i) a greaterCz coupledwith a greaterK, or a, or s, and (ii) a smallers coupledwith a greater K or a, or a smallerC,* as indicated in the appropriate figures (Fig. 4a-d). In the first alternative, an increasein C,*will shift the calculated curve from the position of curve 1 to the right, thus deviating from the experimentaldata. However, a simultaneousincreasein either K, a, or s will negatethe effect of the increasein Cz, resulting in a theoreticalpredictioncurve adjacentto curve 1.The same is alsotrue for the secondalternative. An examination of thesefiguresrevealedthat several combinationsof variables did result in curves closeto curve 1. However, the theoreticalpredictionswould deviate evenmore than curve 1from the experimentalpoints at greater chargingtimesaslong asK > 1; see curves9, 13, and 21. The only exception is curve 17 in Fig. 4c wherea smallercritical concentration?Ct = 0.0295,was used. Even in this casewhere K = IO and s = 50, the lattice contribution is dominant, being about 97%. A further increasein K would shift the curve further left of the experimentaldata points.Therefore,weconcludethat
","o~o.". 1
0.8
0.0
4.0
K 1.0 10 1.0 I.0 10
100
18
Precharging
10.0
L 0.05 0.05 0.05
Eb 11.6 11.6 11.6
Time
9.60
E llb6 12.3 14.0 9.60 9.60
(hours)
10.0
0.05
I. 0.05 0.05 0.05 0.05 0.05
12.0
s 114 114 114
12.0
50
s 114 150 300 50 50
a Experimental
Time (hours)
8.0
set 1 14 15 16 17
Precharging
8.0
K 1.0 10 100
iLo : 40 .i. ..~;-..i-.-l.-_L.,i~-i 6.0 8.0
2.0
9
set 1 8
o Experimental
5
0.098
i
20.0
40.0
.._ 16.0 J 0.0
5
0.0295
14.0
a 5 5 5 55
60.0
80.0
I 0.0
18.0
Cfg 0.065 0.096 0.096 0.0295 0.0295
data
14.0
a 5 5
C?J 0.065 0.096
data
3 a 2
o%
2 1.
G a 8 8
0.2
0.8
0.0
(d)
0.01 0.0
0.8
(b)
j
2.0
2.0
4.0
4.0
6.0 Precharging
Precharging
6.0
10.0
8.0 10.0 Time (hours)
Time (hours)
8.0
12.0
12.0
s 114 114 114 114 50
G 11.6 11.6 11.6 11.6 9.59
14.0
5 1000
a
data
14.0
0.065 0.096 0.096 0.096 0.065
c‘s
0 Experimental L=O.OSmm
16.0
0.0
80.0
80.0
1026
J. YAO
and S
grain boundary. This seems to be too low to change the local fracture mode. Therefore, any combinations with a large E;can be excluded from consideration. When K = 1, the grain boundary width would have no effect upon the penetration rate. The only possible alternative combination to fit experimental data is to increase s and C’: simultaneously. This will provide the upper and lower boundaries for Eb and Cz. Curve 14 in Fig. 4c represents such an alternative parameter set which also fits the experimental data. In this case, Eb = 12.3 k.l/mol and Cz = 0.098 (H/Ni). Further calculations show that the lower boundary of the pair is Eb = I 1.3 kJ/mol and C’z = 0.065 (H/Ni). Therefore, it is concluded that the current experimental results support a binding energy of 11.3-12.3 kJ/mol and a critical concentration of 0.06~.098 (H/Ni) for nickel to change the fracture mode from TG to IG. The SEM observation revealed ductile fracture in the central region of specimens charged with hydrogen for 640min. In this case, the analytical calculations predict that lattice diffusion alone should have caused 100% IG fracture. This inconsistency can only be explained by a weak trapping effect of grain boundaries observed in the previous work of permeation tests and the silver decoration tests [12]. If grain boundaries act as hydrogen traps, they cannot act as fast-diffusion-paths simultaneously. It is noted that curve 1 of Fig. 2 also represents the case K=O.OOl, where grain boundaries act only as hydrogen traps. This indicates that grain boundaries perpendicular to the membrane surfaces could not account for the trapping effect observed at larger times. Therefore, it must have been caused by the grain boundaries parallel to the membrane surfaces which were neglected in the present model. Such a trapping effect increased with the depth, so that at large times the experimental data points in Fig. 2 fall on the dashed line instead of curve 1. CONCLUSIONS The penetration depths of IG fracture in nickel membranes due to hydrogen pre-charging at room tem-
A. MEGUID perature were measured after fracture at 77 K and verified analytically using a grain boundary diffusion model. The primary findings of this research can be summarized as follows: 1. Grain boundaries act as weak trapping sites rather than fast-diffusion-paths for hydrogen in nickel. 2. The experimental results provide evidence that the grain boundary binding energy with hydrogen in nickel is 11.3-12.3 kJ/mol and the critical concentration for IG cracking in this material to be 0.0650.098 (H/Ni). The financial support provided by the Nafurai Sciences and E~gimeering Research Council of Canada and ~afu~a~ Resources Canada is gratefully ackno~l~edged.
REFERENCES 1. Boniszewski, T. and Smith, G. C., Actu Metallurgica, 1963, 11, 165. 2. Wilcox, B. A. and Smith, G. C., Acta Meta~iu~g~ca, 196.5, 13, 331. 3. Latanision, R. M., Opperhauser, H. Jr, Metallurgical Transactions, 1974,5(A), 483. 4. Lassila, D. and Birnbaum, H. K., Acta MetnNurgica, 1986, 34, 1237. 5. Tsuru, T. and Latanision, R. M., Scripta Metalhwgica, 1982, 16, 575. 6. Calder, R. D., Elleman,T. S. and Verghese,K., ~ff~r~a~ of Nuclear Materiafs, 1973, 46, 46. 7. Fisher, J. C., Journal qf Applied Physics, 1951,22, 74. 8. Suzuoka, T., Transactions of the Japanese Institute of Metals,
1961,2,
25.
9. Whipple, R. T. P., Philosophical Magazine, 1954,4S, 10. Gilmer, G. H. and Farrell, H. H., JournalofAppliedPies,
1225.
1976,47,4373.
1I. Levine, H. S. and MacCallum~ C. J., ~our~4~ of Aspired .. Physics, 1960,31, 595. 12. Yao. J. andCahoon. J. R.. Acta Metaliuraica. 1991.39. 119. 13. Kin&a, A. and Birnbaum, H. K., Acza %etallurgica, i988, 36, 757. 14.
La&la, D. and Birnbaum, H. K., 36, 2821.
Acta Metallurgica,
1988.
HYDROGEN
DIFFUSION
AND INTERGRANULAR IN NICKEL
All rights reserved.Printed in Great Britain mo
1199
97 $I? 00 +m!
CRACKING
J. YAO and S. A. MEGUID Engineering Mechanics and Design Laboratory, Department of Mechanical Engineering. University of Toronto 5 King’s College Road, Toronto, Ontario, Canada M5S lA4
Abstract-A new dilfusion model is developed to analyze the contribution of grain boundary diffusion to total mass transport in metals. The predictions of the model are compared with experimental results concerning the effect of room temperature hydrogen precharging period upon the intergranular fracture depth in pure nickel specimens fractured at 77 K. It is shown that the fracture mode changes from transgranular into intergranular when the hydrogen concentration in grain boundaries reaches a critical value, in the range of 6.5-9.8 at%. The observed increment of’ intergranular cracking depth with the pre-charging period indicates that hydrogen transport in this material 1snot enhanced by grain boundaries. c, 1997 International Association for Hydrogen Energy
NOMENCLATURE Hydrogen diffusivity in grain boundaries Hydrogen diffusivity in lattice Ratio of above two diffusivities Hydrogen concentrationin grain boundaries Hydrogen concentrationin lattice Segregationfactor Binding energy Grain diameter Thicknessof the membrane Concentrationat input surface Grain boundary half width Critical hydrogenconcentrationin grain boundary for intergranular fracture
grain boundary ditfusivity is ordersof magnitudegreateithan the lattice diffusivity [7-91.However. little is known about grain boundary diffusion of small interstitial impurity atoms. The lattice diffusivity of hydrogen in most metals is relatively high and it is reasonableto expect that the limited extra volume available in grain boundarieswould not greatly increasethe masstransport of hydrogen. Generally speaking, a finer grain size. and consequently, a larger volume fraction of grain boundary regions,reducesthe sensitivity of an ahoy to hydrogen embrittlement. Therefore. it is important for designers involved with the emerginghydrogen energyindustry to know the role of grain boundaries in the hydrogen diffusion process. Since grain boundary
INTRODUCTION When solute hydrogen is introduced into polycrystalline nickel, the fracture modechangesfrom transgranular ductile rupture to intergranular cracking [l41.Obviously, hydrogen has to arrive at interior grain boundaries by diffusion to cause such intergranular cracking. Among the available diffusion paths, grain boundariesare suggestedby many researchersasfaster paths than the lattice for hydrogen diffusion. The reported ratio of grain boundary diffusivity to lattice diffusivity (K = 0,/01) in the literature canbe found in a wide range, from 60 by Tsuru and Latanision [5] to as high as IO8by Calder et al. [6]. It is well known for the caseof self and substitutionallattice diffusion that the
diffusion is always coupled with
lattice diffusion, there is no experimentalmeansto measuredirectly the grain boundary diffusivity. One hasto employ a mathematicalmodel to analyze the indirect measurement,The existing modelsfor masstransport concerninggrain boundaries[lo, 111,however. do not accommodategrain sizeand smallK ratios. The present paperpresentsa morerealisticanalytical modelto predict the penetrationdepth of a pre-determinedhydrogenconcentration at any given time. If this pre-determinedconcentration is the critical concentration of the fracture mode transition in nickel. then the prediction can be verified by performing tensiletestsat 77K on thin nickel specimenspre-chargedwith hydrogen. Since hydrogen atomsare “frozen” in the host lattice and thus become unableto move along with the carrying dislocations.the
1021
1022
J. YAO and S. A. ~E~UID
observedfracture modetransition issolely relatedto the segregatedhydrogen at grain boundariesduring precharging. It is with this in mind that we conduct the current investigation.
wheres is the segregationfactor given by s = exp (E,JRT) whereEbis the binding energy. The boundary conditionsfor the z direction are
THEORETICAL ANALYSIS Consider a thin membraneof polycrystalline metal with uniform grain size and ignore the effect of those grain boundariesparallel to the membrane.We assume all grain boundariesare perpendicularto the surfaceof the membrane,i.e. the membraneis composedof hexagonatprisms,asshownin Fig. 1. Becauseof symmetry, there will be no net exchangebetweenany particular grain and its neighbors.The problemof determiningthe concentrationin the aggregateis then reducedto determining the concentration of one hexagonalgrain, which is further simplifiedto a tubular cylinder with a thickness equivalent to the grain boundary width, 2~. The central radius of this equivalent tube is definedas L/2 where L is the averagegrain size. In the grain boundary, the concentrationC, satisfies
DgV2Cg =2
C,I;=, = co
(5)
ac, (?z;=/@ =0
(6)
where h is the membranethicknessand C, the concentration at the input surface. Sincethe grain boundarywidth is smallcomparedwith the grain diameter,even in microcrystallinematerial, the local curvature should be small. Therefore, it can be assumedthat the central plane of the equivalent grain boundary tube at p = L/2 is a planeof mirror symmetry for C,, i.e. c, = qyz,
t) + @y2)’
qyz, 1)
(7)
which is similarto Whipple’sapproximation [9]. Substituting equantion (7) into equations(I), (3) and (4) and usingequation(2) onecan find a singleboundary condition which must be satisfiedby C, at p = L/2-a, i.e. at the interface between grain interior and grain boundaries
and within the grain
ac, D,V2C,= at This leads to the following dimensionlessconIt is further assumedthat the equilibrium distribution centration expressionin a grain boundary, normalized of hydrogen in the lattice and grain boundariesfollows by the surfacegrain boundary concentration, for any the Boltzmann statistics;therefore, the boundary con- time t: ditions at p = L/2-a are C --kL = I + fJ jJ A,,Jo(ctn,L/2) x sinc; n=l m=, i x exp
(4)
-I?$ i
a&+
‘2”n~‘2~“)])
(9)
(
whereCr = .r x C,. The constantsanm in equation (9) can be calculated by solvingthe following transcendentalequation:
and A, can be obtainedfrom ‘4?J?3
/
\
Fig. 1. Grain boundary aggregate and the equivalent grain boundary tube. All grain boundaries are assumed perpendicular to the free surface of the membrane, i.e. into the paper. Those parallel to the surface are neglected.
In the above equations,Jr, and J1 are Besselfunctions of zero and first order, respectively.
HJ DIFFUSION
AND
INTERGRANULAR
When the hydrogen concentration in grain boundaries reaches Cz. the fracture mode changes to IG cracking. Therefore, the penetration depth of this critical concentration (or the depth of the IG fracture) at any given time can be predicted by letting C, = C: in equation (9). There are eight parameters in equation (9) that will affect the penetration rate of IG depths: a, s, K, Cz, D,, CO,L. andh (asdefinedearlier).Among theseparameters, the last two are specimenconstantsand the hydrogen diffusivity and the surfacehydrogenconcentrationunder the current prechargingconditions are already known: D, has beenfound to be 5.4 x lo- “cm’/s and Co to be about 2880appm (atomic parts per million) [12]. Although one cannot separatethe effectsof the rest four variablesin the experiments,an examinationof equation (9).-(11) revealsthat each variable will affect the penetration curve in a distinct manner.It is thus feasibleto verify the experimentaldata with the theory by adopting a parametricstudy. To start with, a critical concentration of c; = 0.065 (H/Ni) and a binding energy of &= I I .6 kJ /mol, both reported by Kimura and Birnbaum 1131, aswellasa half grain boundary width of 5 x 10m8 cm were usedin the calculationsand the resulting curves are shown in Fig. 2. Then various combinationswere accordingly adoptedto find out if other alternative combinationscould alsobe consistentwith the experimental curve. Although the percentagecontribution from the grain boundariescannot be measuredexperimentally, the lattice contribution at any time can be evaluated theoretically. This can be obtained by usingequation (9) to calculate the grain boundary concentrations at given times for a given K value. The grain boundary concentration due to lattice diffusion can be predicted by letting K = I. The ratio of thesetwo concentrationsprovidesan estimateof the percentageof hydrogen build-up at grain boundarieswhich could be attributed to lattice diffusion. By adopting suchan approach,the ratio was found to changewith time. The correspondingcurvesfor
CRACKING
11173
IN NlCKEL
each set of parameters(K> 1) are also shown in the figuresand are designatedwith the primed numbers.In this case,curves correspondingto K % 1 are not shown sincethe theoreticallattice contribution would alwaysbe 100%.
High purity Ni270(99.98%Ni) rod (a16 mm) wascold rolled to 0.25mm thicknessand annealedat 1173K 1.01 5 min, resultingin a fully recrystallized structure with a grain size of 50pm. All specimenswere electrolytically polishedin a 60% H$O, solution at 5.5V. The membrane tensile specimenshad a final cross section 01 4.5 x 0.2mm2and a gaugelength of 12mm. The specimenswere cathodically prechargedwith hydrogen at room temperature(295K) for 20, 40, 80, 160,320. 640. and 960min, respectively.A chargingcurrent density of 10mAicm’ was applied to the unmaskedgauge length area. After charging,specimens werequickly rinsedfirst in distilledwater then in alcohol, and driedusingblowing air at room temperature. For tensiletestsat 77K, specimensand the gripping assemblywere immersedin liquid nitrogen. No more than 2 min elapsedbetweenthe end of prechargingand the beginningof cooling. In order to ensurethermalequilibrium. the specimenswere held for ii further lOmill prior to loading. No strain rate effects were observed for the range 10 4s ‘tolO~~s~‘,thusanominalstrainrateoflO~~s waschosen.The fracture surfaceswereobservedand the depths of IG cracking were measuredusing
rcw1t.v
In the absenceof hydrogen,the material behavedin a ductile fashion with the crosssection of the specimen reducingto a knife-edgewith anelongationof some60%
1 .o
80.0
60.0 o Experimentnl Eel
1 .GkJ/mol,
C&0.085,
data L=O.O5mm
40.0
a=1 14. a=5x10-8c
ii 5’ (D 8 2 s 5 s s a-
20.0
0.0 L 0.0
2.0
4.0
6.0 Precharging
8.0 10.0 Time (hours)
Fig. 2. Measured IG cracking depths vs pre-charging periods. Solid curves effect of diffusivity ratio of grain boundary to lattice diffusion K. Dashed
12.0
14.0
16.0
#: L=O.Olmm
are theoretical predictlons of equation (9) shoumg line reflects the experimental result at larlrr t~mek.
1024
J. YAO and S. A. MEGUID
Large-scaleplasticdeformation is evident usingSEM by the presenceof extensiveslip bandsover the entiresurface and ridgesand groovesat grain boundaries. DiscontinuousIG cracking beganto initiate after less than 5% elongationin specimens prechargedfor 20 and 40min. When tensiledeformation wasfurther extended during testing,the central region of the membraneelongatedandfinally fractured in a ductile manner.Flat grain boundary surfacesresultingfrom intergranular cracking are observedalongthe charging surface.Beyond the flat regions,featuressimilarto thoseof hydrogen-freespecimenswereobserved. When the chargingperiod wasfurther extendedup to 640min, the IG fracture depth continued to increase. The IG cracksbecamecontinuousalong the edgeof the charging surfaces.The fracture surface of specimens becamecompletelyIG only whenthechargingperiod was further extendedto 960min. In this case,the specimens fractured at about 5% elongation and the entire cross sectionexhibited IG fracture. Again, a common occurrence of these IG fracture surfacesis the existenceof many parallel straight slip lines indicating limited and constrainedplasticdeformation. SEM observationsshow that IG fracture surfaces which formed after a short chargingperiod (20min) are similar to those formed after long charging period (960min). Furthermore, the entire crosssection of the specimens which wereprechargedfor 960min experiences the samedegree of brittleness, even though a concentration gradient is expectedto have existed in grain boundaries.Theseobservationssuggestthe existenceof a critical hydrogen concentration for IG fracture to occur, i.e. Cp*.In fact, it wasfound that most IG cracks penetratedto nearly the samedepth in all of the specimenschargedfor the sameperiod. Therefore, the boundary betweenthe flat and the severelydeformedregionsis definedasthe interface betweenIG and TG fracture, i.e. where the fracture mode transition occurred. A typical SEM micrographis givenin Fig. 3 for a specimencharged
for 320min. The measuredIG depthsfor various charging periodsare shownwith the theoreticalpredictionsin Fig. 2.
Fig. 3. SEM micrograph showing fractured cross section of a specimen which was charged with hydrogen for 320min. The arrows indicate location of the front of IG cracking.
grain boundary transport did not play a major role; being less than - 3%. In fact, a critical concentration of 0.0295 represents one hydrogen atom in 34 nickel atoms in the
DISCUSSION As can be seenin Fig. 2, the theoreticalprediction for K = 1 (curve I) agreeswith the experimentalresultsfor
charging times up to 320min. The experimentaldata deviate from the prediction only at larger times,which can be attributed to the grain boundary trapping effect. The consistencyof the data points with the predictions confirms the existence of the critical hydrogen concentration in the grain boundariesat which a changeof fracture modefrom TG to IG takesplace.Sincecurve 4, where the averagecontribution from the lattice is only about 50%, has already overestimatedthe penetration rate, it is concludedthat grain boundary transport of hydrogen doesnot play a significant role basedon the valuesusedfor Cz, &, and a. Substituting C,*,s, and C, into equation(9), one finds C,*/&, = 0.2. Usingsimilarchargingconditions,Kimura and Birnbaum [131found that when Cz/CF’ reaches about 0.22 the fracture mode of nickel changesto IG. Therefore, the presentresultsare consistentwith data reported in the literature [4, 13, 141except for the role of grain boundaries. In the parametricstudies,it isfound that the minimum values have to be usedfor K and the grain boundary width to obtain agreement with experimental data. Otherwise, the curve always shifts to the left, overestimating the penetration rate of IG depth. Conversely, changings and Ct can shift the curve to either direction. Therefore, only two alternative combinations of parameterscapableof fitting the experimentalresultsmay be possible:(i) a greaterCz coupledwith a greaterK, or a, or s, and (ii) a smallers coupledwith a greater K or a, or a smallerC,* as indicated in the appropriate figures (Fig. 4a-d). In the first alternative, an increasein C,*will shift the calculated curve from the position of curve 1 to the right, thus deviating from the experimentaldata. However, a simultaneousincreasein either K, a, or s will negatethe effect of the increasein Cz, resulting in a theoreticalpredictioncurve adjacentto curve 1.The same is alsotrue for the secondalternative. An examination of thesefiguresrevealedthat several combinationsof variables did result in curves closeto curve 1. However, the theoreticalpredictionswould deviate evenmore than curve 1from the experimentalpoints at greater chargingtimesaslong asK > 1; see curves9, 13, and 21. The only exception is curve 17 in Fig. 4c wherea smallercritical concentration?Ct = 0.0295,was used. Even in this casewhere K = IO and s = 50, the lattice contribution is dominant, being about 97%. A further increasein K would shift the curve further left of the experimentaldata points.Therefore,weconcludethat
","o~o.". 1
0.8
0.0
4.0
K 1.0 10 1.0 I.0 10
100
18
Precharging
10.0
L 0.05 0.05 0.05
Eb 11.6 11.6 11.6
Time
9.60
E llb6 12.3 14.0 9.60 9.60
(hours)
10.0
0.05
I. 0.05 0.05 0.05 0.05 0.05
12.0
s 114 114 114
12.0
50
s 114 150 300 50 50
a Experimental
Time (hours)
8.0
set 1 14 15 16 17
Precharging
8.0
K 1.0 10 100
iLo : 40 .i. ..~;-..i-.-l.-_L.,i~-i 6.0 8.0
2.0
9
set 1 8
o Experimental
5
0.098
i
20.0
40.0
.._ 16.0 J 0.0
5
0.0295
14.0
a 5 5 5 55
60.0
80.0
I 0.0
18.0
Cfg 0.065 0.096 0.096 0.0295 0.0295
data
14.0
a 5 5
C?J 0.065 0.096
data
3 a 2
o%
2 1.
G a 8 8
0.2
0.8
0.0
(d)
0.01 0.0
0.8
(b)
j
2.0
2.0
4.0
4.0
6.0 Precharging
Precharging
6.0
10.0
8.0 10.0 Time (hours)
Time (hours)
8.0
12.0
12.0
s 114 114 114 114 50
G 11.6 11.6 11.6 11.6 9.59
14.0
5 1000
a
data
14.0
0.065 0.096 0.096 0.096 0.065
c‘s
0 Experimental L=O.OSmm
16.0
0.0
80.0
80.0
1026
J. YAO
and S
grain boundary. This seems to be too low to change the local fracture mode. Therefore, any combinations with a large E;can be excluded from consideration. When K = 1, the grain boundary width would have no effect upon the penetration rate. The only possible alternative combination to fit experimental data is to increase s and C’: simultaneously. This will provide the upper and lower boundaries for Eb and Cz. Curve 14 in Fig. 4c represents such an alternative parameter set which also fits the experimental data. In this case, Eb = 12.3 k.l/mol and Cz = 0.098 (H/Ni). Further calculations show that the lower boundary of the pair is Eb = I 1.3 kJ/mol and C’z = 0.065 (H/Ni). Therefore, it is concluded that the current experimental results support a binding energy of 11.3-12.3 kJ/mol and a critical concentration of 0.06~.098 (H/Ni) for nickel to change the fracture mode from TG to IG. The SEM observation revealed ductile fracture in the central region of specimens charged with hydrogen for 640min. In this case, the analytical calculations predict that lattice diffusion alone should have caused 100% IG fracture. This inconsistency can only be explained by a weak trapping effect of grain boundaries observed in the previous work of permeation tests and the silver decoration tests [12]. If grain boundaries act as hydrogen traps, they cannot act as fast-diffusion-paths simultaneously. It is noted that curve 1 of Fig. 2 also represents the case K=O.OOl, where grain boundaries act only as hydrogen traps. This indicates that grain boundaries perpendicular to the membrane surfaces could not account for the trapping effect observed at larger times. Therefore, it must have been caused by the grain boundaries parallel to the membrane surfaces which were neglected in the present model. Such a trapping effect increased with the depth, so that at large times the experimental data points in Fig. 2 fall on the dashed line instead of curve 1. CONCLUSIONS The penetration depths of IG fracture in nickel membranes due to hydrogen pre-charging at room tem-
A. MEGUID perature were measured after fracture at 77 K and verified analytically using a grain boundary diffusion model. The primary findings of this research can be summarized as follows: 1. Grain boundaries act as weak trapping sites rather than fast-diffusion-paths for hydrogen in nickel. 2. The experimental results provide evidence that the grain boundary binding energy with hydrogen in nickel is 11.3-12.3 kJ/mol and the critical concentration for IG cracking in this material to be 0.0650.098 (H/Ni). The financial support provided by the Nafurai Sciences and E~gimeering Research Council of Canada and ~afu~a~ Resources Canada is gratefully ackno~l~edged.
REFERENCES 1. Boniszewski, T. and Smith, G. C., Actu Metallurgica, 1963, 11, 165. 2. Wilcox, B. A. and Smith, G. C., Acta Meta~iu~g~ca, 196.5, 13, 331. 3. Latanision, R. M., Opperhauser, H. Jr, Metallurgical Transactions, 1974,5(A), 483. 4. Lassila, D. and Birnbaum, H. K., Acta MetnNurgica, 1986, 34, 1237. 5. Tsuru, T. and Latanision, R. M., Scripta Metalhwgica, 1982, 16, 575. 6. Calder, R. D., Elleman,T. S. and Verghese,K., ~ff~r~a~ of Nuclear Materiafs, 1973, 46, 46. 7. Fisher, J. C., Journal qf Applied Physics, 1951,22, 74. 8. Suzuoka, T., Transactions of the Japanese Institute of Metals,
1961,2,
25.
9. Whipple, R. T. P., Philosophical Magazine, 1954,4S, 10. Gilmer, G. H. and Farrell, H. H., JournalofAppliedPies,
1225.
1976,47,4373.
1I. Levine, H. S. and MacCallum~ C. J., ~our~4~ of Aspired .. Physics, 1960,31, 595. 12. Yao. J. andCahoon. J. R.. Acta Metaliuraica. 1991.39. 119. 13. Kin&a, A. and Birnbaum, H. K., Acza %etallurgica, i988, 36, 757. 14.
La&la, D. and Birnbaum, H. K., 36, 2821.
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1988.