Discussion of “Hydrogen induced grain boundary fracture in high purity nickel and its alloys-enhanced hydrogen diffusion along grain boundaries”

Scripta METALLURGICA

Vol. 22, pp. 1817-1820, 1988 Printed in the U.S.A.

Pergamon Press plc All rights reserved

DISCUSSION OF "HYDROGEN INDUCED GRAIN BOUNDARY FRACq'URE IN H/GH PURITY NICKEL AND ITS ALLOYS-ENHANCED HYDROGEN DIFFUSION ALONG GRAIN BOUNDARIES"* Jing Yao and J.R. Cahoon Metallurgical Sciences Laboratory Department of Mechanical Engineering, University of Manitoba Winnipeg, Manitoba, Canada R3T 2N2 ( R e c e i v e d J u n e 24, 1988) ( R e v i s e d J u l y 27, 1988) The recent communication of Kimura and Birnbaum [1], hereafter referred to as [1], presented some interesting results concerning the hydrogen embrittlement of nickel and its alloys. They concluded that the grain boundary diffusion rate of hydrogen in nickel is about double that for lattice diffusion and therefore that the kinetics of intergranular embrittlement of nickel from external hydrogen are controlled by the grain boundary diffusion of hydrogen. However, [1] appear to have made errors in the derivation of their equation used to reach their conclusions and therefore their conclusions may not be justified. This note presents corrections for the equations of [1] and advances a different interpretation of the experimental results. In their derivation [1] start with the equation of Fisher [2] for the time-distance concentration dependence, C(y,t), of hydrogen in a grain boundary:

_(2)112y C(y,t) = C,°Bexp -

1 ~ - -

(~ DLt) where Cs~

] 1/21 '

(1) **

((5DOBI DO ]

is the surface grain boundary concentration of hydrogen in equilibrium with the surface hydride, DL and

DGB are, respectively, the lattice and grain boundary diffusion coefficients for hydrogen in nickel, and ~i is the width of the high diffusivity path along the grain boundary. [1] assume that intergranular embrittlement occurs when the GB From Eq. (1), grain boundary concentration of hydrogen exceeds a critical value, Ceril.

[

1/2

[(~DLt) '(a D [ m / D 0 Solving for Ycrit, In-'

where the term

(DLt)1/4

(3)

has been inverted to remove the -ve sign.

! * A. Kimura and H.K. Birnbaum, Acta Metall., vol. 36, (3), pp. 75%766, (1988). ** Equation (8') of [1]. Also, Equation (8) of [1] from which Equation (8') is derived is reproduced from Fisher [2] incorrectly in that yi/2 is used instead of y. 1817 0056-9748/88 $3.00 + .00 Copyright (c) 1988 Pergamon Press plc

1818

DISCUSSION

Vol. 22, No. ii

Following [1], xl/2

Ycrit= 11

(4)

( DLt )114,

where 11is given by =

In

~s GB

Ccrit

(5)

'

[1] neglect the term ~5entirely and give Ycrit=ll { ~ LB) ~ )Lt)

1/2

(Eq. 9 of [1])

with 11 given by

[n/1/2 /Cc(~tit/

(Eq. 10 of [1])

[1] use this value of Ycritto calculate the GBFR (grain boundary fracture ratio), given by 2 2 na - n ( a - Yerit) GBFR = , (6) ~a 2 or

GBFR = Yerit{ 2a - Ycrit}, a

(7)

2

where a is the radius of the specimen. Substituting the correct values for Ycritfrom Eq. (4),

. GBFR = -~- ~--~-L]

.1,2

a(DLt)I/4--~/~DoB/2~ DL]

1,2) (DLt)

(8)

Using a value of ~ = l n m [3], and experimental values of GBFR from [1], the ratio (DGB/DL) ranges from 13000150,000 (depending on the hydrogen charging time) and not 2 as calculated by [1]. Lassila and Bimbaum [4] have estimated much higher values of ~ for the grain boundary diffusion of hydrogen in nickel. Using values of 8 = 104, 75 and 50 nm for temperatures of 314, 295 and 274 K respectively, the ratio (DGB / DL) varies from about 130-3000. Few values for the grain boundary diffusion coefficient of H in Ni have been reported but since H is an interstitial solute in Ni the grain boundary diffusion coefficient is not expected to be several orders of magnitude higher than the lattice diffusion coefficient. Indeed, Siderenko and Sidorak [5] reported that the grain boundary diffusion coefficient of H in Ni is slightly lower than the lattice diffusion coefficient. DGB

=

DL

=

2.27 x 10"7 exp - (34.3 kJ/RT) m2/s 1.92 x 10-13 m2/s at 295 K. 2.52 x 10-7exp - (33.3 kJ/RT) m2/s 3.2 x 10-13 m2]s at 295 K.

Vol.

22, No.

ii

DISCUSSION

1819

Ladna and Birnbaum [3] indicate (DGB/DL) ratios from 1-17 for 295 K depending on the grain boundary angle and Tsuru and Latanision [6] suggest (DGB/DL) = 60 for 295 K. In any event it appears that the results of [1] cannot be rationalized by the theory of enhanced diffusion along grain boundaries. It remains, therefore, to determine a mechanism which can account for the experimental results of [1]. If lattice diffusion is controlling the absorption of hydrogen, the GBFR is given by [1], GBFR =--4~ [a(Dt)l/2 - ~(l:)t)] . a

2

(9)

in Eq. (9) is determined from L Ccrit

--

cl

= l--err l) ,

(10)

where ccLimis the critical lattice concentration of H required to obtain CGa"cr,,,the critical grain boundary concentration of H for cracking and CsL is the surface hydrogen concentration. [1] ruled out lattice diffusion as the controlling process since the values of GBFR calculated from Eq. (9) did not satisfactorily fit the experimental data. However, [1] used a segregation factor, s, of approximately I00 in their calculations, where s is defined by GB L S = Ccrit/Cerit

(11)

The equilibrium grain boundary concentration of H, CB (fraction of grain boundary sites which contain H atoms), is related to the lattice concentration of hydrogen, CH, by [4] = ~

exp(HB/RTage),

(12)

where HB is the binding enthalpy of the hydrogen to the grain boundary sites and Tage is the aging temperature. [1] used a value of HB = 11.6 kJ/mol to calculate the segregation factor but Lee and Lee [7] suggest a value of HB = 20.5 kJ/mol. If 20.5 kJ is used in Eq. (12) the segregation factors calculated from Eq. (12) for 274K, 295K and 314K (IB are 7600, 4000 and 2400, respectively. Using these values for the segregation factor, Ccrit = .065 and cL= 2.8x10 -3, the values of GBFR obtained from Eq. (9) are compared to the experimental results of [1] in Fig. 1 which shows excellent agreement. It must be admitted that segregation factors of over 2000 are very large. It could well be that both lattice diffusion and grain boundary diffusion contribute to H grain boundary embrittlement of Ni. However, for the case where DGB is only a factor of 1-20 greater than DL (which seems likely for H in Ni) the mathematical treatment becomes complicated since the treatment of Fisher [2] for grain boundary diffusion assumes that DGB >>DL (all H in the lattice comes from the grain boundaries). A mathematical model where both lattice diffusion and grain boundary diffusion contribute to hydrogen embrittlement and where the segregation factor as well as different surface concentrations for the lattice and grain boundary are used would be of considerable interest.

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DISCUSSION

Vol.

22, No.

References 1o

2. 3. 4. 5. 6. 7.

A. Kimura and H.K. Bimbaum; Acta Mctall., 36, ?57, (1988). LC. Fisher;, J. Appl. Phys., 22, 74, (1951). B. Ladna and H.K. Birnbaum; Acta Metall., 35, 2537, (1987). DM. Lassila and H.K. Bimbaum; Acta Metall., 34, 1237, (1986). V.M. Sidor¢nko and I.I. Sidorak; Fiz.Khim. M. Mat., 9, 12, (1973). T. Tsuru and R.M. Latanision; Scripta Metall., 6, 575, (1982). Sung Man Lee and Jai-Young Lee; Met. Trans. A., 17A, 181, (1986).

1.0

.o///o

EKperlmontal Points of Klmura and Blrnbaum / Z~ 314K, 0 295K, ~ 274K

0.8

n; i,"

Calculated from EO. (9)

0.6

0,4

/

[ /'~"I

'

I

--

o.2L0.0 0.1

I

I

1.0

I0

I

I0 z

103

CHARGING TIME (Minutes)

Fig. 1. Comparison of Experimental Values of G.B.F.R. with Calculated Values Assuming Lattice Diffusion Control.

io4

ii