See discussions, stats, and author profiles for this publication at: /publication/276966263 A quantitative description on fracture toughness of steels in hydrogen gas
Article in International Journal of Hydrogen Energy · September 2013
DOI: 10.1016/j.ijhydene.2013.07.033
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A quantitative description on fracture toughness of steels in hydrogen gas
Yanfei Wang a ,Jianming Gong a ,*,Wenchun Jiang b
a College of Mechanical and Power Engineering,Nanjing University of Technology,Nanjing 211816,C
hina b
College of Chemical Engineering,China University of Petroleum (East China),Qingdao 266555,China
a r t i c l e i n f o
Article history:
Received 29March 2013Received in revid form 1July 2013
Accepted 13July 2013
Available online 8August 2013
Keywords:
Fracture toughness
Critical stress intensity factor Hydrogen embrittlement Hydrogen gas
a b s t r a c t
Fracture toughness or critical stress intensity factor of many steels can be reduced by hydrogen gas.In this paper,a simple quantitative model to predict the fracture toughness of steels in gaous hydrogen is propod.This model is bad on the assumption that fracture of a cracked body occurs when the maximum principal stress ahead of the crack tip reaches the critical cohesive stress for crack initiation.The critical stress is inverly proportional to the accumulated hydrogen concentration.The notion is that the crack will initiate at the elastic-plastic boundary ahead of the crack tip when hydrogen concentration reaches a maximum value after a long-term hydrogen diffusion assisted by the hydrostatic stress.The model describes the dependence of fracture toughness on hydrogen pressure,temperature and yield strength of steels.It can be ud to quantitatively predict fracture toughness of steels in hydrogen gas,particularly in high pressure.Some experimental data reported in literature were ud to validate the model,and a good agreement was obtained.Crown Copyright ª2013,Hydrogen Energy Publications,LLC.Published by Elvier Ltd.All
rights rerved.
1.Introduction
Hydrogen is expected as an ideal carrier of energy for trans-portation and conversion in the near futu
re [1].As hydrogen technology becomes highly developed and popular,many storage vesls and transmission pipelines for hydrogen gas,particularly high pressure hydrogen gas [2e 5],will be con-structed.However,it is well established that hydrogen can degrade the mechanical properties of almost all steels commonly arbon steels,low alloy steels and stain-less steels [6e 9].This phenomenon has been well-known as hydrogen embrittlement (HE)for over a hundred years.There-fore,in order to ensure the safe operation of storage vesls and transport pipelines for hydrogen gas,it is esntial to perform material compatibility rearch and establish the appropriate design and monitoring plan considering the HE effect.
Fracture toughness or critical stress intensity factor is an important property of steels to characterize its resistance against crack initiation and growth,when performing design or safety asssment of a component within the framework of fracture mechanics.It has been found that hydrogen gas can reduce many steels’fracture toughness.For instance,Loginow et al.[10]studied the fracture toughness of Cr-Mo steels of AISI 4130,4145and 4147expod to hydrogen gas under pressure from 0to 100MPa.They found that gaous hydrogen signif-icantly reduced fracture toughness of the steels and the toughness was further reduced as hydrogen pressure incread.Robinson et al.[11]tested fracture toughness of A516steel under hydrogen pressures from 0to 34.5MPa and Gutierrez-Solana
et al.[12]tested the fracture toughness of X42steel under hydrogen pressures from 0to 16MPa.They also found that fracture toughness of the steels decread as
*Corresponding author .Tel./fax:þ86(0)2558139361.
E-mail address: (Y.Wang),gongjm@ (J.
Gong).
Available online at
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0360-3199/$e e front matter Crown Copyright ª2013,Hydrogen Energy Publications,LLC.Published by Elvier Ltd.All rights rerved./10.1016/j.ijhydene.2013.07.033
hydrogen pressure incread.Additionally,the decreasing effect due to hydrogen was vere at low hydrogen pressure before reaching a limiting value,but after this incread pressure had little effect on the fracture toughness.Story[13] investigated the effect of temperature(302,323and347K)on fracture toughness of AISI4340steel in hydrogen gas of various pressures(0.1e7MPa).Their results showed the reduction in fracture toughness of the steel for all three tem-peratures.Under the same hydrogen pressure,increasing the temperature markedly incread the fracture toughness.In low pressure hydrogen gas,increasing temperature by20K incread fracture toughness of the steel by about30%.Nelson and Williams[14,15]measured fracture toughness of AISI4130 steel with different yield strength(1050e1330MPa)in hydrogen gas at above and below ambient temperatures(230, 297and348K).They also found that fracture toughness incread as temperature incread,but the higher the yield strength,the lower the fracture toughness in both air and hydrogen gas.
On the other hand,many authors have made great efforts to describe the variation of fracture toughness of steels with hydrogen gas.Bad on the stress-induced diffusion of hydrogen atoms to the region of high triaxial stress ahead of a plastically strained notch,Doig et al.[16]suggested an analytical model relating the fracture toughness with gaous hydrogen,and the time dependence for crack initiation on the apparent stress intensity was derived.Gerberich et al.[17] introduced a concept of local hydrogen induced fracture toughness at the crack tip by assuming that crack tip fracture is governed by the intrinsic Griffith toughness and this local toughness can be reduced by accumulated hydrogen.The macroscopic fracture toughness can be connected to the local fracture toughness by using the discrete dislocation simula-tion of the crack tip including emission from the crack and a standoff distance to thefirst dislocation.Symons[18]gave a model bad on the concept of critical grain boundary hydrogen concentration to interpret the fracture toughness of X750steel in conditions of both internal hydrogen and gaous hydrogen environment.Kim et al.[19]suggested a predictive model bad on the assumption that fracture of a cracked body submerged in hydrogen gas occurs when the normalized hydrogen concentration(which is defined as c/s,c is the hydrogen concentration,s is the solubility which follows an Arrhenius relation:s¼s0exp(ÀD H/RT),with s0the solubility pre-exponential factor and D H the enthalpy of solution)ahead of the crack tip exceeds a critical value at a critical distance.
In this paper,we propo a simple quantitative model to describe the fracture toughness of steels in hydrogen gas.The model is bad on the hypothesis that fracture occurs when the maximum principal stress at the elastic-plastic boundary ahead of a crack tip reaches the critical cohesive stress,while the critical cohesive stress is assumed to be reduced by accumulated hydrogen.Experimental data in literature [10e15]were ud to verify the model.
2.Procedure of the model
In order to explain HE phenomenon,many mechanisms have been propod.Among them,hydrogen enhanced decohesion (HEDE)[20,21]is one of the widely accepted mechanisms. HEDE wasfirst propod by Troiano[22]and further developed by Oriani[23]and Gerberich et al.[17].It is bad on the hy-pothesis that cohesive stress of the metals can be lowered by dilatation of the atomic lattice due to the prence of inter-stitial hydrogen and hence the fracture energy is reduced. This implies that hydrogen can decrea the energy barrier for either grain boundary or cleavage plane decohesion.Fracture will initiate near the location of maximum hydrostatic stress some distance ahead of the crack tip,where hydrogen con-centration will be maximum after long-term diffusion assis-ted by the hydrostatic stress.Considering that a plastic enclave always exists ahead of the crack tip,it is expected that the maximum hydrostatic stress is at the elastic-plastic boundary.When t
he combination of stress level and hydrogen concentration at the elastic-plastic boundary is sufficient to cau decohesion of atomic lattice,crack initia-tion occurs.With the time going by and the hydrogen further diffusing,the process above is repeated as the crack grows in a ries of large and discontinuous jumps.
Bad on the HEDE mechanism stated above,as well as the classic maximum principal stress criterion for crack initiation and extension,we assume that fracture of a cracked body by exposure to hydrogen occurs when the maximum principal stress s max ahead of the crack tip reaches the local critical cohesive stress s c at elastic-plastic boundary r c where maximum hydrostatic stress exists.And s c is assumed to be decreasing proportionally to the accumulated hydrogen con-centration c[24,25],i.e.
s cH¼s c0Àb c:(1)
where s cH and s c0are the critical cohesive stress with and without hydrogen,respectively,and b is a parameter relating loss of critical cohesive stress to hydrogen.Therefore at the moment of crack initiation,Eq.(1)becomes
s maxH¼s max0Àb c(2)
where s maxH and s max0are the maximum principal stress at elastic-plastic boundary r c with and without hydrogen when the crack initiates,respectively.
The hydrogen concentration c in Eq.(1)can be calculated by Fick’s law with respect to the hydrostatic stress.An approxi-mate solution for a steady state has the following form[26,27]:
c¼c0exp
s h V H
RT
(3) Where c0is the hydrogen concentration in the unstresd state,s h is the hydrostatic stress,R is the universal gas con-stant,T is the temperature,V H is the partial molar volume of hydrogen in the steel.
According to Sievert’s law,for steels expod in hydrogen gas,by assuming equilibrium between hydrogen in the steel and gaous hydrogen in the crack,the c0can be related to the solubility s and pressure of gaous hydrogen P as:
c0¼s$
ffiffiffi
P
p
(4) Fracture toughness K IC of a material is the critical stress intensity factor at which a mode I crack(the crack is loaded by a tensile stress normal to the plane of the crack)in plane
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strain condition begins to grow.For the mode I crack with tip radius r ,the elastic-plastic stress field ahead of the crack tip along the crack plane (x axis)is generally adopted as shown in Fig.1[28].According to the theory of linear elastic fracture mechanics [29],the elastic maximum principal stress and hydrostatic stress of the mode I crack in plane strain condi-tions can be expresd as s max ¼s yy ¼K I
ffiffiffiffiffiffiffiffi
2p r p (5)
s h ¼
2ð1þn Þ3K I
ffiffiffiffiffiffiffiffi2p r
p (6)
where K I is the stress intensity factor,s yy is the stress along
the y axis and n is Poisson’s ratio.Many authors had suggested formulations to describe the plastic stress ahead of the crack tip,such as the following Eqs.(7)and (8),which were propod by Hill [30]according to the slip line field theory:s max ¼s yy
¼s y 1þln
1þ
r
!(7)
s h ¼s y 1þln 1þ
r
!(8)
where s y is the yield stress.However,the detail of the plastic
stress distribution is unimportant.Only the stress near the elastic-plastic boundary r c matters.If r c is known,the maximum stress can be obtained by inrting r c into Eqs.(5)and (6).When Moody et al.[31]investigated fracture tough-ness and analyzed the critical fracture distance ahead of the crack tip in IN903alloy as a function of hydrogen concentra-tion,they found that the location of crack initiation did not change with hydrogen concentration.Bad on this finding,we assume that the location of the crack initiation does not change either with the hydrogen pressure,that is,r c is inde-pendent of hydrogen.Therefore,we u the well-known approximate expressions relating the size of the plasticity c to stress intensity factor r c ¼
12p K 2I tri
(9)
where s tri is the plastic flow stress considering a constrained triaxial stress state,which is defined as the plastic maximum principal stress in the plastic zone [32,33].According to the
conventional J 2plasticity theory and the finite element
calculation [34,35],the plastic maximum principal stress considering work hardening is expected no more than 3e 5s y .If we take s tri equal to Q s y (Q ¼3e 5),Eq.(9)can be rewritten as r c ¼
12p K 2I
ÀQ s y Á(10)
Then inrting Eqs.(3)e (6)into Eq.(2)and considering the critical state for crack initiation,the following equation is obtained
K IH ffiffiffiffiffiffiffiffiffiffi2p r c p ¼K IC ffiffiffiffiffiffiffiffiffiffi2p r c
p Àb $s ffiffiffiP p exp 2ð1þn ÞV H K IH
ffiffiffiffiffiffiffiffiffiffi
2p r c p !
(11)
Inrting Eq.(10)into Eq.(11),Eq.(11)becomes K IH K IC ¼1Àb $s ffiffiffiP
p Q s y
exp 2ð1þn Þ3V H RT K IH K IC $Q s y
!
(12)where K IH and K IC are fracture toughness with and without
hydrogen,respectively.
Eq.(12)is the model we derived to quantitatively describe the fracture toughness of steel expod to hydrogen gas.From Eq.(12),it can be en that the fracture toughness of steels in gaous hydrogen are dependent on the hydrogen pressure,temperature and mechanical properties of the steels (yield stress and fracture toughness without hydrogen).
3.Validation with experiment data
Experimental data on fracture toughness from the literature of Loginow et al.[10],Robinson et al.[11]and Gutierrez-Solana et al.[12],as reproduced in Figs.2and 3,are first ud to validate the Eq.(12).To apply Eq.(12),parameter R,V H ,Q ,and s are needed.In the following validation,R,V H ,Q are taken as 8.314J mol À1K À1, 2.0Â10À6m 3mol À1and 4,respectively.The solubility s following the Arrhenius relation for AISI 4130,4145and 4147steel [10]is taken
as
Fig.1e Schematic diagram showing the elastic-plastic stress field ahead of a crack tip [28]
.
Fig.2e Comparisons between the predicted fracture
toughness with experimental data [10]of Cr-Mo steels as a function of hydrogen pressure (*not reported as standardized K IC measurement).
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s 1¼102:0
mol H 2m 3ÂffiffiffiffiffiffiffiffiffiffiMPa
p exp 0
B @À27:20kJ
mol RT 1
C A ;though which was reported in Refs.[6,36]just for quenched
and tempered AISI 4130steel.The s for A516steel [11]and X42steel [12]is taken as
s 2¼180:1
mol H 2
m 3
ÂffiffiffiffiffiffiffiffiffiffiMPa
p exp 0
B @À23:66kJ
mol RT
1C
A ;
which was reported in Refs.[6,37]for iron and low carbon steels.Besides the above parameters,b is also needed,but it is difficult to obtain at prent.However,it can be rever determined by inrting one experimental data into Eq.(12).Therefore,from the data in Figs.2and 3,using (P ¼62MPa,K IH ¼45,55and 67MPa m 1/2)for AISI 4130,4145and 4147steel,(P ¼3.5MPa,K IH ¼131MPa m 1/2)for A516steel and (P ¼4MPa,K IH ¼85MPa m 1/2)for X42steel,respectively,to inrt into Eq.(12),and combined with K IC ,s y ,s and T (e Figs.2and 3),b was calculated for each steel.Using this value of b as well as the K IC ,s y ,s and T ,the facture toughness for each steel under other hydrogen pressures was then predicted by Eq.(12).The predicted results are also plotted in Figs.2and 3.
Figs.2and 3show good agreement between the predicted fracture toughness values and the experimental data.This means that Eq.(12)has the capacity to predict the fracture toughness of steels in hydrogen gas as a function of hydrogen pressures.And notably,the experimental data lected to determinate b for A516and X 42steel are in the range of low hydrogen pressure (e Fig.3),however,the predicted fracture toughness at the high pressure also matches quite well with the experimental data.This implies that if we have obtained the fracture toughness of steels at low hydrogen pressure,by using Eq.(12),we can then obtain the fracture toughness over the high hydrogen pressure range.This finding may be of great significance,becau it is usually difficult and dangerous
to experimentally test the fracture toughness of steels in high pressure hydrogen gas.
It’s worth noting that b for the steels had been determined.As described by Eq.(1),this parameter reprents the sus-ceptibility of steels to hydrogen induced loss of critical cohe-sive stress for crack initiation.Take the X42steel as an example,the determined b is 1.21Â104MPa m 3(mol H 2)À840MPa $(atomic ppm)À1.This value of b indicates that increasing the hydrogen concentration by 0.1atomic ppm can reduced the steel’s critical stress for crack initiation by 84MPa.Solubility s is the parameter to determine the equilibrium hydrogen concentration c 0,e Eq.
(4),in the unstresd steel expod to hydrogen gas.In Eq.(12),it can be en that the combined b and s ,i.e.(b $s ),describes the susceptibility to critical stress loss due to gaous hydrogen.The calculated (b $s )for AISI 4130,4145and 4147steel are 1.08Â102,1.11Â102and 0.86Â102MPa 1/2,respectively.The values of (b $s )are almost equal.This is consistent with that the AISI 4130,4145and 4147steel have almost the same decreasing rate in frac-ture toughness with increasing hydrogen pressure,as shown in Fig.2.For the A516steel and X42steel,the values of (b $s )are 0.73Â102and 1.50Â102MPa 1/2,respectively.Accordingly,the decreasing rate of fracture toughness of X42steel is much higher than that of A516,e Fig.3.
It is interesting to note that the predicted fracture tough-ness model of Eq.(12)includes the temperature and yield strength term.It is therefore attractive to validate the poten-tial of the model to predict the dependence of fracture toughness on temperature and yield strength.For this pur-po,the experimental data on fracture toughness in Refs.[13e 15]were ud.Figs.4e 6give the experimental data.
Figs.4and 5show that,under the same pressure,the fracture toughness increas as the temperature is incread.For the AISI 4130steel,the increa in the fracture toughness resulting from increasing temperature from 230K to 297K (297À230¼67)is not much larger than that resulting from increasing
temperature from 297K to 348K (348À297¼51).Moreover,for the AISI 4130steel,the increa in fracture toughness resulted from increasing temperature from 302K to 323K (323À302¼21)is almost the same as that resulted
from
Fig.3e Comparisons between the predicted fracture
toughness with experimental data of A516[11]and X42[12]steels as a function of hydrogen pressure (*not reported as standardized K IC measurement).
F r a c t u r e t o u g h n e s s (M P a .m 1/2)
H 2 gas pressure (MPa)
Fig.4e Comparisons between the predicted fracture
toughness with experimental data [13,14]of AISI 4130steel as a function of hydrogen pressure and temperature.
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