- Email: [email protected]
Second phase embrittlement of solids
Scripta METALLURGICA
Vol. I0, pp. 747-750, 1976 Printed in the United States
Pergamon Press,
Inc.
SECOND PHASE EMBRITTLEMENT OF SOLIDS H. K. Birnbaum Department of Metallurgy and Mining Engineering University of Illinois at Urbana-Champaign Urbana, Illinois 61801 (Received May 28, 1976)
Hydrogen embrittlement of niobium has been recently shown to be caused by the stress-induced formation and cleavage of the brittle 8 hydride (1-4). It is the purpose of this note to review the general requirements for this fracture mechanism and to discuss its applicability to brittle fractures caused by the formation of other phases such as oxides, nitrides, carbides, helium bubbles, etc. It will be shown that this mechanism can play a role in the slow strain rate embrittlement of a variety of different systems. The thermodynamics of stressed solids (5) leads to the result that an external tension stress reduces the chemical potential of solutes having a positive volume of solution (characteristic of most interstitial solutes). The molal free energy of second phases having positive molal volumes of formation (characteristic of most interstitial compounds) is also decreased by the external tension stress (6,7). As a result, a flux of solute to and preferential precipitation can occur at temperatures above the stress free solvus temperature in the presence of an external stress (6,7). The fracture mechanism to be considered (1,2) can be described as the stress-induced formation of a brittle second phase and the subsequent fracture of this phase. The crack progresses rapidly through the second phase or along the interface with the solid solution and it provides the stress concentration for further flux of the solute and precipitation of the second phase. The crack propagation velocity is controlled by the flux of solute to the crack tip or by the rate of formation of the second phase, whichever is slower. The general requirements for this mechanism to lead to brittle fracture are: (a) The second phase must have a positive molal volume of formation so that its free energy is reduced by an external tension stress. (b) The second phase must have low ductility. (c) The second phase must be stable in the stress field of the crack tip. (d) The solute diffusivity must be sufficiently large to allow formation of the second phase at the crack tip. The solute flux is increased if the solute has a positive volume of solution due to the stress-induced decrease in chemical potential at the crack tip. It was shown (1,2) that these conditions are satisfied for the Nb-H system and lead to fracture from stress-induced hydride formation and cleavage. Other metal-hydrogen systems which form stable hydrides appear to be susceptible to the same fracture mechanism (8). Second phase embrittlement can also result from the formation of oxides, nitrides, carbides, and other low ductility phases. The upper bound on the temperature range in which this phenomenon will be observed is the solvus temperature under the applied stress which is given by (7) 747
748
SECOND PHASE E M B R I T T L E M E N T
Vol.
i0, No. 8
T~ = [~G~ - Z . . c i j c i j ~]/RInVCs 1,3
(1)
where T ~ is the solvus temperature for a solute concentration C under an exs s ternal stress ~ij' ~G~ is the standard free energy of formation of the second phase w h i c h has a strain tensor
¢.. relative to the solid solution, V is the 13 and ¥ is the activity coefficient of solute in solid solution.
molal volume, The increase
in the solvus temperature
due to an external
stress,
AT , can be s
given by AT where s is the spherical forming the second phase. shear modulus,
AT
s~
< 10K.
~ ~s ~V/R (-~nyCs)
s
(la)
stress component and ~V is the molal volume change on For stresses of the order of 0.01~, where ~ is the We m a y therefore take T
u
~ T O , the solvus temperature s
at zero stress. The lower bound on the second phase embrittlement temperature is set by the flux of the solute to the crack tip. If the second phase forms as a cylinder of radius r at the crack tip, the c h a r a c t e r i s t i c diffusion length from which the solute
is drained to form the p r e c i p i t a t e
solute concentration
in the second phase.
(Dt) ~, where D = D O exp-(~q/RT)
is given b y
(Cp/Cs)%r , where Cp is the
This distance
is also approximated
is the solute d i f f u s i v i t y
a c t e r i s t i c of the fracture test. fore be written
by
and t is a time char-
The lower bound on the temperature m a y there(2)
TL ~ ~/R~n(CsD0t/Cpr2) •
The c h a r a c t e r i s t i c time t will depend on the type of experiment carried o u t In a tension test where the c o n s i d e r a t i o n is w h e t h e r the fracture proceeds by a O
brittle
or ductile mode t ~
O
(¢f/¢) (r/d)
where
cf is the strain to failure,
the strain rate and d is the specimen diameter. t ~ (tf) (r/d), where tf is the time to failure. terms of the brittle
crack p r o p a g a t i o n
In a creep rupture test, Equation (2) can be written
exceeds
in
v e l o c i t y V ~ (2r/t)
TL ~ ~H/R6n(2CsD0/CprV) since if the "crack" v e l o c i t y and proceed by a ductile mode.
c is
(2a)
this value it will leave the second phase
In estimating the t e m p e r a t u r e ranges for the second phase embrittlement, values for r and t (or V) must be chosen. T does not depend s e n s i t i v e l y on r L and we will take as a lower limit r ~ 10-Tem (corresponding to a lower limit for for TL). Values calculated for various systems are shown in Table I which also lists the values for T embrittlement
u
~ TO. s
can be observed,
The range of temperatures T u > T > T L, is greatest
over which second phase for small crack velo-
Vol.
i0, No.
8
SECOND PHASE EMBRITTLEMENT
749
cities or strain rates (i.e., for creep or stress rupture tests). In some systems, such as V-0, the solid s o l u b i l i t y is s u f f i c i e n t l y high so that no second phase e m b r i t t l e m e n t is expected. In the Fe-C s y s t e m e m b r i t t l e m e n t can be expected at high C c o n c e n t r a t i o n s but at low c o n c e n t r a t i o n s could only be observed at v e r y low crack v e l o c i t i e s (low strain rates). In a tension test, the strain to failure,
ef, would exhibit an inverse
o
strain rate effect,
i.e.,
¢f i n c r e a s i n g w i t h
c in the range T L < T < T u.
In
this t e m p e r a t u r e range, the d u c t i l i t y would have a m i n i m u m and the f r a c t u r e surfaces would exhibit "cleavage" characteristics. In the p r o p o s e d mechanism, f r a c t u r e will occur in the second phase or at the interface w i t h the solid solution. Solute s e g r e g a t i o n at the crack tips will not of itself lead to b r i t t l e f r a c t u r e as the increase in c o n c e n t r a t i o n caused by r e a s o n a b l e stresses is quite small. The c o n c e n t r a t i o n e n h a n c e m e n t in the stressed region,
C~/C O, s s
is g i v e n by C~/C 0 = e x p ( a V /RT) s
s
,
(3)
s
where V
is the volume of solution and a h y d r o s t a t i c stress ~ has been assumed. s For i n t e r s t i t i a l solutes Ca/C 0 ~ 1.2 for T ~ 600K and ~ ~ 0.01~. This small s s increase in c o n c e n t r a t i o n should haye little effect on the fracture behavior. The f o r m a t i o n of a "brittle" second phase formed at a stress c o n c e n t r a t i o n will have a s i g n i f i c a n t effect on the fracture b e h a v i o r as these phases have great d i f f e r e n c e s in t h e i r m e c h a n i c a l p r o p e r t i e s relative to the solid solutions. Acknowledgement This r e s e a r c h was supported by the Office of Naval R e s e a r c h contract N00014-75-C-I012. References i.
S. Gahr, M. L. G r o s s b e c k and H. K. Birnbaum, A c t a Met.
(To be published)
2.
M. L. G r o s s b e c k and H. K. Birnbaum, A c t a Met.
3.
M. L. Grossbeck, Peter Williams, phys. stat. sol. (a) 3_~4, (1976)
4.
S. G a h r and H. K. Birnbaum,
5.
J. C. M. Li, R. A. Oriani and L. S. Parken, 271 (1966)
6.
N. Paton,
7.
H . K . Birnbaum, M. L. G r o s s b e c k and M. Amano, published)
8.
H. K. Birnbaum, M. L. G r o s s b e c k and S. Gahr, H y d r o g e n In M e t a l s for Metals, M e t a l s Park), p 303 (1974)
(Submitted)
Charles A. Evans, Jr., and H. K. Birnbaum,
Scripta M e t
B. H i c k m a n and S. Leslie,
(To be published) Z. Phys. Chem. N e w Folge 49,
Net. Trans. 2, 2791
(1971)
Jnl. Less Comm. Met.
(To be
(Amer. Soc.
750
SECOND PHASE E M B R I T T L E M E N T
Vol.
I0, No. 8
Table I
System
Do
~H
M2 sec
J mole
x
x
104
10 8
C
s
Second Phase
Tu
TL
(°K)
("K) 10 -5
10 -7
i0 -9
M
M
sec
sec
M sec
Nb-O
2.1:
I. 126
0.01
NbO
1020
890
685
555
Nb-N
0.8~
1.462
0.01
Nb2N
Ll00
i170
900
725
V-O
1.3
1.214
0.01
V90
< 300
860
680
560
V-C
0.4!
1. 142
0. 001
V2C
L430
ll40
825
645
Fe-C
2.6
0.8539
0.001
Fe3C
[020
720
545
440
0.0001 Fe3C
690
860
620
485
Vol. I0, pp. 747-750, 1976 Printed in the United States
Pergamon Press,
Inc.
SECOND PHASE EMBRITTLEMENT OF SOLIDS H. K. Birnbaum Department of Metallurgy and Mining Engineering University of Illinois at Urbana-Champaign Urbana, Illinois 61801 (Received May 28, 1976)
Hydrogen embrittlement of niobium has been recently shown to be caused by the stress-induced formation and cleavage of the brittle 8 hydride (1-4). It is the purpose of this note to review the general requirements for this fracture mechanism and to discuss its applicability to brittle fractures caused by the formation of other phases such as oxides, nitrides, carbides, helium bubbles, etc. It will be shown that this mechanism can play a role in the slow strain rate embrittlement of a variety of different systems. The thermodynamics of stressed solids (5) leads to the result that an external tension stress reduces the chemical potential of solutes having a positive volume of solution (characteristic of most interstitial solutes). The molal free energy of second phases having positive molal volumes of formation (characteristic of most interstitial compounds) is also decreased by the external tension stress (6,7). As a result, a flux of solute to and preferential precipitation can occur at temperatures above the stress free solvus temperature in the presence of an external stress (6,7). The fracture mechanism to be considered (1,2) can be described as the stress-induced formation of a brittle second phase and the subsequent fracture of this phase. The crack progresses rapidly through the second phase or along the interface with the solid solution and it provides the stress concentration for further flux of the solute and precipitation of the second phase. The crack propagation velocity is controlled by the flux of solute to the crack tip or by the rate of formation of the second phase, whichever is slower. The general requirements for this mechanism to lead to brittle fracture are: (a) The second phase must have a positive molal volume of formation so that its free energy is reduced by an external tension stress. (b) The second phase must have low ductility. (c) The second phase must be stable in the stress field of the crack tip. (d) The solute diffusivity must be sufficiently large to allow formation of the second phase at the crack tip. The solute flux is increased if the solute has a positive volume of solution due to the stress-induced decrease in chemical potential at the crack tip. It was shown (1,2) that these conditions are satisfied for the Nb-H system and lead to fracture from stress-induced hydride formation and cleavage. Other metal-hydrogen systems which form stable hydrides appear to be susceptible to the same fracture mechanism (8). Second phase embrittlement can also result from the formation of oxides, nitrides, carbides, and other low ductility phases. The upper bound on the temperature range in which this phenomenon will be observed is the solvus temperature under the applied stress which is given by (7) 747
748
SECOND PHASE E M B R I T T L E M E N T
Vol.
i0, No. 8
T~ = [~G~ - Z . . c i j c i j ~]/RInVCs 1,3
(1)
where T ~ is the solvus temperature for a solute concentration C under an exs s ternal stress ~ij' ~G~ is the standard free energy of formation of the second phase w h i c h has a strain tensor
¢.. relative to the solid solution, V is the 13 and ¥ is the activity coefficient of solute in solid solution.
molal volume, The increase
in the solvus temperature
due to an external
stress,
AT , can be s
given by AT where s is the spherical forming the second phase. shear modulus,
AT
s~
< 10K.
~ ~s ~V/R (-~nyCs)
s
(la)
stress component and ~V is the molal volume change on For stresses of the order of 0.01~, where ~ is the We m a y therefore take T
u
~ T O , the solvus temperature s
at zero stress. The lower bound on the second phase embrittlement temperature is set by the flux of the solute to the crack tip. If the second phase forms as a cylinder of radius r at the crack tip, the c h a r a c t e r i s t i c diffusion length from which the solute
is drained to form the p r e c i p i t a t e
solute concentration
in the second phase.
(Dt) ~, where D = D O exp-(~q/RT)
is given b y
(Cp/Cs)%r , where Cp is the
This distance
is also approximated
is the solute d i f f u s i v i t y
a c t e r i s t i c of the fracture test. fore be written
by
and t is a time char-
The lower bound on the temperature m a y there(2)
TL ~ ~/R~n(CsD0t/Cpr2) •
The c h a r a c t e r i s t i c time t will depend on the type of experiment carried o u t In a tension test where the c o n s i d e r a t i o n is w h e t h e r the fracture proceeds by a O
brittle
or ductile mode t ~
O
(¢f/¢) (r/d)
where
cf is the strain to failure,
the strain rate and d is the specimen diameter. t ~ (tf) (r/d), where tf is the time to failure. terms of the brittle
crack p r o p a g a t i o n
In a creep rupture test, Equation (2) can be written
exceeds
in
v e l o c i t y V ~ (2r/t)
TL ~ ~H/R6n(2CsD0/CprV) since if the "crack" v e l o c i t y and proceed by a ductile mode.
c is
(2a)
this value it will leave the second phase
In estimating the t e m p e r a t u r e ranges for the second phase embrittlement, values for r and t (or V) must be chosen. T does not depend s e n s i t i v e l y on r L and we will take as a lower limit r ~ 10-Tem (corresponding to a lower limit for for TL). Values calculated for various systems are shown in Table I which also lists the values for T embrittlement
u
~ TO. s
can be observed,
The range of temperatures T u > T > T L, is greatest
over which second phase for small crack velo-
Vol.
i0, No.
8
SECOND PHASE EMBRITTLEMENT
749
cities or strain rates (i.e., for creep or stress rupture tests). In some systems, such as V-0, the solid s o l u b i l i t y is s u f f i c i e n t l y high so that no second phase e m b r i t t l e m e n t is expected. In the Fe-C s y s t e m e m b r i t t l e m e n t can be expected at high C c o n c e n t r a t i o n s but at low c o n c e n t r a t i o n s could only be observed at v e r y low crack v e l o c i t i e s (low strain rates). In a tension test, the strain to failure,
ef, would exhibit an inverse
o
strain rate effect,
i.e.,
¢f i n c r e a s i n g w i t h
c in the range T L < T < T u.
In
this t e m p e r a t u r e range, the d u c t i l i t y would have a m i n i m u m and the f r a c t u r e surfaces would exhibit "cleavage" characteristics. In the p r o p o s e d mechanism, f r a c t u r e will occur in the second phase or at the interface w i t h the solid solution. Solute s e g r e g a t i o n at the crack tips will not of itself lead to b r i t t l e f r a c t u r e as the increase in c o n c e n t r a t i o n caused by r e a s o n a b l e stresses is quite small. The c o n c e n t r a t i o n e n h a n c e m e n t in the stressed region,
C~/C O, s s
is g i v e n by C~/C 0 = e x p ( a V /RT) s
s
,
(3)
s
where V
is the volume of solution and a h y d r o s t a t i c stress ~ has been assumed. s For i n t e r s t i t i a l solutes Ca/C 0 ~ 1.2 for T ~ 600K and ~ ~ 0.01~. This small s s increase in c o n c e n t r a t i o n should haye little effect on the fracture behavior. The f o r m a t i o n of a "brittle" second phase formed at a stress c o n c e n t r a t i o n will have a s i g n i f i c a n t effect on the fracture b e h a v i o r as these phases have great d i f f e r e n c e s in t h e i r m e c h a n i c a l p r o p e r t i e s relative to the solid solutions. Acknowledgement This r e s e a r c h was supported by the Office of Naval R e s e a r c h contract N00014-75-C-I012. References i.
S. Gahr, M. L. G r o s s b e c k and H. K. Birnbaum, A c t a Met.
(To be published)
2.
M. L. G r o s s b e c k and H. K. Birnbaum, A c t a Met.
3.
M. L. Grossbeck, Peter Williams, phys. stat. sol. (a) 3_~4, (1976)
4.
S. G a h r and H. K. Birnbaum,
5.
J. C. M. Li, R. A. Oriani and L. S. Parken, 271 (1966)
6.
N. Paton,
7.
H . K . Birnbaum, M. L. G r o s s b e c k and M. Amano, published)
8.
H. K. Birnbaum, M. L. G r o s s b e c k and S. Gahr, H y d r o g e n In M e t a l s for Metals, M e t a l s Park), p 303 (1974)
(Submitted)
Charles A. Evans, Jr., and H. K. Birnbaum,
Scripta M e t
B. H i c k m a n and S. Leslie,
(To be published) Z. Phys. Chem. N e w Folge 49,
Net. Trans. 2, 2791
(1971)
Jnl. Less Comm. Met.
(To be
(Amer. Soc.
750
SECOND PHASE E M B R I T T L E M E N T
Vol.
I0, No. 8
Table I
System
Do
~H
M2 sec
J mole
x
x
104
10 8
C
s
Second Phase
Tu
TL
(°K)
("K) 10 -5
10 -7
i0 -9
M
M
sec
sec
M sec
Nb-O
2.1:
I. 126
0.01
NbO
1020
890
685
555
Nb-N
0.8~
1.462
0.01
Nb2N
Ll00
i170
900
725
V-O
1.3
1.214
0.01
V90
< 300
860
680
560
V-C
0.4!
1. 142
0. 001
V2C
L430
ll40
825
645
Fe-C
2.6
0.8539
0.001
Fe3C
[020
720
545
440
0.0001 Fe3C
690
860
620
485