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Mismatch effect in creep properties on creep crack growth behavior in welded joints
Materials and Design 63 (2014) 600–608
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Mismatch effect in creep properties on creep crack growth behavior in welded joints G. Chen, G.Z. Wang ⇑, F.Z. Xuan, S.T. Tu Key Laboratory of Pressure Systems and Safety, Ministry of Education, East China University of Science and Technology, Shanghai 200237, China
a r t i c l e
i n f o
Article history: Received 2 May 2014 Accepted 20 June 2014 Available online 7 July 2014 Keywords: Mismatch effect Creep crack growth Welded joint Constraint Rupture life
a b s t r a c t The finite element method based on ductility exhaustion model was used to systematically investigate the mismatch effect in creep properties on creep crack growth (CCG) behavior in welded joints. The crack-tip damage, stress states, CCG paths, CCG rate and rupture life were calculated for different configurations of creep properties between weldment constituents under the same load level, and the creep life assessment and design for welded joints were discussed. The results show that when the zone containing the crack is softer than at least one of the other two surrounding materials or both, the creep crack propagates straight along the initial crack plane. Otherwise, it will form a second crack in the soft material near interface. These simulation results were confirmed by the experimental observations in the literature, and the mechanism was analyzed. The harder surrounding materials can lead to higher CCG rate and shorter rupture life due to the higher constraint given from them. The early initiation and propagation of the second cracks increase CCG rate and reduce rupture life, and the incubation time of the second cracks in soft materials near interfaces should be accurately determined in the creep life assessment and design for the welded joints. A proper mismatch design with harder material containing crack and softer surrounding material can improve CCG properties of welded joints (decreasing CCG rate and prolong rupture life). Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Most problems of crack initiation and propagation in high temperature components are likely to originate from welded joints [1], which is caused by the multi stress and strain fields appearing ahead of crack-tip or near the interface of weldment constituents due to the mismatch in creep deformation properties among base metal (BM), weld metal (WM) and heat affected zone (HAZ) [2,3]. The original cracks may exist anywhere in welded joint randomly, and mainly classified into four types. The type I crack is confined in WM, the type II crack occurring in WM may grow into BM, the type III crack occurs in coarse grained HAZ and the type IV crack propagates in the critical zone of HAZ adjacent to BM/HAZ interface [4]. Experiences showed that both the deformation properties of materials containing crack and surrounding materials influence the creep crack growth (CCG) behavior in welded joints [5–7]. Such as, the type IV crack is the most severe form of cracks due to the high creep strain of type IV region where the crack is propagating and the high constraint given from hard BM of surrounding materials [4]. Sugiura et al. [1,3] and Yatomi et al. [8] found that the ⇑ Corresponding author. Tel./fax: +86 21 64252681. E-mail address: [email protected] (G.Z. Wang). http://dx.doi.org/10.1016/j.matdes.2014.06.047 0261-3069/Ó 2014 Elsevier Ltd. All rights reserved.
crack located in the middle of HAZ region can deviate from the original crack plane to the type IV crack region with minimum hardness for the P92 welded joint, and the acceleration of CCG occurred as soon as the crack started to initiate near the HAZ/BM interface. Dogan [9] observed that the crack located in the middle of WM with high creep strength formed a second crack in the type IV crack region with lower creep strength in addition to the extending of CCG straight along the initial crack-tip in P91 welded joint, and the same phenomenon was also found in P122 steel welded joint with the pre-crack located in BM [10]. Hyde et al. [11] found that the cracks laid in the type IV region still stayed in this region, and the CCG rate was about four times higher than the corresponding BM for a given value of C⁄. All the above results show that the material constraint caused by the mismatch effect in creep properties of weldment constituents plays an important role on the CCG behavior in welded joints. For accurate creep life assessment and safety design of the welded joints, it needs to investigate and understand this material constraint effect on the CCG behavior and properties. Recently, there are some investigations on the creep crack-tip constraint effect caused by specimen geometry, crack size and loading configuration for homogenous materials [12–16] and welded joints [17,18]. However, only a few mechanical analyses
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for the material constraint effect on CCG behavior due to the mismatch in creep properties between different materials in welded joints could be found in the literature. Lee et al. [19] and Han et al. [20,21] defined a mismatch factor about creep constant and exponent of Norton’s law between different materials in weldment to quantify the mismatch effect in creep properties on the distribution of steady-state stress. Tu et al. [22,23] and Xuan et al. [24] studied the influence of material mismatch on the evaluation of the time-dependent fracture mechanics parameters C(t) and C⁄. There are also some numerical investigations on the mismatch effect on C⁄ and CCG rate in welded joints [5–7]. But the actual CCG path generally could not be realized and it was assumed that all the cracks propagated straight. In real CCG process in welded joints, the crack path may change from the initial crack plane to another place [1,3,8–10], and the stress state ahead of crack tip and near the interface between different materials may change with crack growth. Therefore, the mismatch effects in creep properties on crack-tip stress state, creep damage accumulation, real crack path and CCG properties of welded joints need to be systematically investigated and understood. But it is difficult to do the experimental studies due to the difficulty of systematic change and control in creep properties of weldment constituents. The numerical method based on creep damage model may provide suitable tool for these investigations. In this paper, the finite element method (FEM) based on ductility exhaustion model was used to investigate the mismatch effect in creep properties between weldment constituents on CCG behavior in compact tension (CT) specimens of welded joints. A brief introduction to the subject is given in this section. Section 2 describes the geometry of specimen, configurations of creep properties between weldment constituents, damage model and the calculation of CCG rate. The numerical results and discussions including mismatch effects on CCG path, CCG rate, rupture life, integrity assessment and design of welded joints are given in Section 3. Section 4 is the conclusion.
2. Finite element models and numerical procedures 2.1. Finite element models In order to investigate the mismatch effect in creep properties on CCG behavior in detail, the CT specimen of welded joint was used for the FE analyses with ABAQUS code [25], which consists of three materials, i.e. BM, WM and HAZ. The geometry and dimensions of the specimen are corresponding to those of the
experiments in Ref. [3], as shown in Fig. 1. The width W of the CT specimen is 50.8 mm and the initial crack length a0 is 26.4 mm (a0/W = 0.52). The width of the WM and HAZ is 20 mm and 2.4 mm, respectively. A sharp crack tip with 0.009° angle was used to represent the fatigue pre-crack and located in the middle of HAZ. The load was applied on the centre of the upper hole using a reference point which was tied to the internal hole surface that represents the bolt in the experiments. The centre of the upper hole was constrained in X-direction, and the centre of the lower hole was constrained in X and Y-directions. The four-node plane strain element (CPE4) was used for all FE models. The mesh dependency investigations in the CCG simulations have been carried out by Yatomi et al. [26] and Oh et al. [27] for the mesh size from 50 lm to 250 lm. The results show that the creep crack initiation time decreases with decreasing mesh size due to the increased crack-tip stress and strain, and the CCG rate was not sensitive to mesh size. So, the fine meshes with size of 50 lm 50 lm were used ahead of crack tip and near the interfaces of HAZ/WM and HAZ/BM. The whole and local meshes for the CT specimen are shown in Fig. 2, which includes 20,891 elements and 21,063 nodes. 2.2. Materials and configurations of mismatch in creep properties The ASME Grade P92 steel was chosen for BM. The elastic–plastic-creep material model was used in FE calculations. The elastic modulus E and yield stress ry of the BM at 650 °C is 85GPa and 126 MPa, respectively [28]. The characteristic of work hardening for plastic deformation is taken from Ref. [1], and is approximated by Eq. (1):
r ¼ cða þ ep Þa
where c, a and a are constants (c = 162, a = 0.32 102, a = 0.105), and ep is true plastic strain. To investigate the mismatch effect in creep properties on creep crack growth behavior in welded joints and facilitate explanation of results, the elastic modulus and plastic deformation characteristics for WM and HAZ are assumed to be the same as those of BM. For the sake of simplicity and changing creep properties easily, the Norton’s law was taken as creep constitutive equation for the three materials as follows:
e_ b ¼ Ab rnb ; e_ W ¼ AW rnW ; e_ HAZ ¼ AHAZ rnHAZ
ð2Þ
where Ab, Aw and AHAZ are creep constant, and nb, nw and nHAZ are creep stress exponent for BM, WM and HAZ, respectively. The Norton’s parameters (Ab = 3.77E19 MPan h1, nb = 6.71) for the ASME Grade P92 BM at 650 °C were used, and they were taken from Ref. [28]. To examine the mismatch effect in creep properties among WM, HAZ and BM on creep crack growth behavior in welded joints, different configurations of mismatch in creep strain rates of WM, HAZ and BM should be designed. For WM and HAZ, the material properties were given that the minimum creep strain rate was higher or lower than that of BM by varying the constant A and keeping the exponent nW = nHAZ = nb = 6.71. The mismatch factors of MFW and MFHAZ shown in Eq. (3) were given to represent the mismatch effect in creep properties relative to BM for WM and HAZ, respectively. Thus, three cases of MF > 1, MF = 1 and MF < 1 refer to creep soft material, creep match and creep hard material, respectively. This type of design of configurations of mismatch in creep properties was widely used in the literature [5–7,19–21].
MF W ¼
Fig. 1. The geometry and dimensions of the CT specimen of welded joint [3].
ð1Þ
AW ; Ab
MF HAZ ¼
AHAZ Ab
ð3Þ
For investigating the mismatch effect in creep properties on CCG behavior, the MFW and MFHAZ are assumed as 10, 0.1 and 1, respectively, which means that the minimum creep strain rate is 10 times larger or smaller and the same relative to BM both for
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Fig. 2. The FE model of the CT specimen of welded joint, (a) meshes of whole model and (b) local meshes around the crack tip and interfaces of HAZ/BM and HAZ/WM.
WM and HAZ at the same value of uniaxial tension stress. Thereby, for creep soft or creep hard materials and matched materials, the value of A is 3.77E18 MPan h1, 3.77E20 MPan h1 and 3.77E19 MPan h1, respectively. The nine different configurations of mismatch in creep properties of the three materials are shown in Table 1. Based on the creep strength of HAZ, the nine configurations can be divided into three groups. The configurations 1, 2 and 3 with matched HAZ is denoted as group 1, the configurations 4, 5 and 6 with hard HAZ is denoted as group 2, and the configurations 7, 8 and 9 with soft HAZ is denoted as group 3. The CCG path, CCG rate, rupture life and local stress and strain distributions both ahead of crack-tips and near the interfaces of different materials were simulated and calculated under the same initial stress pffiffiffiffiffi intensity factor K ¼ 10 MPa m. 2.3. Creep damage model and crack growth simulation The creep damage model is based on the ductility exhaustion approach to simulate the creep crack growth [26–29]. The rate of _ was defined by the ratio of creep strain rate e_ c and muldamage x tiaxial creep ductility ef , as follows:
x_ ¼
e_ c ef
reduced to near zero by reducing the elastic modulus to a very small value (1 MPa in this work). The ABAQUS user subroutine USDFLD was employed to embody this failure simulation technique, and it has been widely used in the recent literature [4,10,27,29]. There are a number of available creep void growth models for describing the relationship between multiaxial and uniaxial creep ductility through stress triaxiality (the ratio of the mean normal stress and equivalent stress) [30–33], but one of the notable models was proposed by Cocks and Ashby [33], given by Eq. (6):
ef 2 n 0:5 n 0:5 rm sinh 2 ¼ sinh 3 n þ 0:5 n þ 0:5 re ef
where ef and ef denotes the multiaxial and uniaxial creep ductility, respectively, and n is the creep exponent. For investigating the mismatch effect and facilitating the interpretation of results, the ef values of the three materials were assumed to be the same, and it was taken to be 0.16 [34]. The crack growth length was calculated by the number of damaged regular elements. For CT specimen of welded joint, the C⁄ can be calculated by the following equations which consider the bending and tension in the specimen [35], and has been used in the recent literature [36].
ð4Þ C ¼
And the total damage at any instant is the integration of the damage rate in Eq. (4) up to that time [26]:
x¼
Z
t
x_ dt ¼
Z
0
0
t
e_ c dt ef
Table 1 Different configurations of mismatch in creep properties.
n Pdd=dt b c n þ 1 Bn ðW aÞ n
ð7Þ
c¼
2ð1 þ aÞð1 þ a=WÞð1 þ a2 Þ þ að1 a=WÞ ð1 þ a=WÞ þ að1 a=WÞ
ð8Þ
b¼
a a þ ð1 þ a=WÞ=ð1 a=WÞ
ð9Þ
ð5Þ
_ is the creep damage rate, e_ c and ef is the equivalent creep where x strain rate and multiaxial creep ductility, respectively. The value of the x is between 0 and 1. When the accumulated creep damage calculated from Eq. (5) reaches 1, local failure occurs and progressive cracking is simulated. Thus, load-carrying capacity of the point is
ð6Þ
a¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi f2a=ðW aÞ þ 1g2 þ 1 f2a=ðW aÞ þ 1g
ð10Þ
where W is the specimen width, a is the crack length, P is the load, Bn is the net thickness, dd=dt is the load line displacement rate, and n is the creep exponent in Norton’s law.
Group
Configuration
HAZ
WM
3. Numerical simulation results and discussion
1
1 2 3
Match Match Match
Hard Match Soft
3.1. Crack-tip damage and CCG paths in welded joints with different mismatches
4 5 6
Hard Hard Hard
Hard Match Soft
7 8 9
Soft Soft Soft
Hard Match Soft
2
3
It is known that both the accumulated creep strain at a period of time and stress triaxiality determine the creep damage from the ductility exhaustion model. Different distributions of creep strain and multi stress state appearing ahead of crack-tip or near the interface between weldment constituents for different material
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Fig. 3. The final damage contours (t/tr = 1, tr is rupture time) of CCG in welded joints, (a) configuration 1, (b) configuration 2, (c) configuration 7, (d) configuration 8, and (e) configuration 9, SDV1: damage variable; ICT: initial crack tip; CCT: current crack tip.
configurations can lead to different CCG behavior. Fig. 3 shows the final damage contours for the crack growth of the configurations 1, 2, 7, 8 and 9. The SDV1 represents the damage variable, ICT is the initial crack tip and the CCT represents the current crack tip. It can be seen that the damage zone around the crack tip is approximately symmetric for the configuration 2 (homogenous material), and that was also symmetric for the configuration 8 due to the symmetry of materials in specimen and the damage zone concentrated on the soft HAZ. For the other three cases (configurations 1, 7 and 9), the damaged zone mainly concentrated on the relatively soft materials. It also can be seen that the CCG paths were nearly straight along the initial crack plane for the five configurations (Fig. 3). For all of the above five configurations, the HAZ is softer than at least one of the other two materials (configurations 1, 7, 8 and 9) or matched to the other two materials (homogenous material, configuration 2). The following Fig. 4 shows the CCG process for the configuration 6 that the HAZ is hardest and the WM is softer than BM. It can be seen that the crack jumped from the original crack plane after 1.4 mm straight extension and continued to grow in the parallel WM with lower strength near the WM/HAZ interface. Fig. 4 also shows the CCG in the hard HAZ takes major portion of the total
time, approximately 82%, and then the acceleration of CCG occurs. This result is consistent with that in the literature [1,3,8]. This means that the time for the crack growing in hard HAZ dominates the rupture time. For explaining this phenomenon, the distribution of the stress triaxiality (SDV3) in CCG process was presented in Fig. 5. It can be seen that the highest stress triaxiality occurred ahead of crack-tip in the early stage of CCG (Fig. 5(a)). With the redistribution of stress and strain during the CCG process, the accumulating creep deformation in soft WM was strongly constrained by the hard HAZ so that the highest stress triaxiality occurred both ahead of crack-tip and in WM near the WM/HAZ interface (Fig. 5(b)), and thereby the more damage accumulation occurred in WM of the interface under the higher stress triaxiality. When the accumulated damage reached the critical value after a certain period of time, the crack started to initiate in the soft WM of the interface, and then the acceleration of CCG occurred in WM due to the higher accumulated creep strain in the soft WM and the highest stress triaxiality appearing on the soft WM side of the interface (Fig. 5(c)). Fig. 6 gives the final damage contours and CCG paths for the other three configurations that the HAZ is harder than one of the other two materials (the configurations 3 and 4) or both (the
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Fig. 4. The CCG process for the configuration 6 (the tr is the rupture time), SDV1: damage variable; ICT: initial crack tip; CCT: current crack tip.
( )
( )
( ) Fig. 5. The stress triaxiality contours during CCG process for the configuration 6, SDV3: stress triaxiality; ICT: initial crack tip; CCT: current crack tip.
configuration 5). It can be seen that like the configuration 6, it also formed a second crack in the soft WM and BM sides of the interfaces for the configurations 3 and 4, respectively. For the configuration 5 (MFWM = 1, MFHAZ = 0.1), the second crack grew both in the WM of HAZ/WM interface and the BM of HAZ/BM interface due to the same creep strength of the BM and WM, but the crack mainly propagated in soft WM of WM/HAZ interface due to the higher constraint near the WM/HAZ interface caused by the had HAZ on both sides of WM (Fig. 1). The results above show that both the deformation properties of the zone containing the crack and those of the surrounding materials influence the crack tip damage and CCG path in welded joints. When the zone containing the crack is softer than at least one of the other two surrounding materials or both (like the configurations 1, 2, 7, 8 and 9), the crack propagates straight along the initial crack plane. When the zone containing the crack is harder than at least one of the other two surrounding materials or both (like the configurations 3, 4, 5 and 6), it will form a second crack in the soft
material near interfaces. These simulation results are confirmed by the experimental observation results in Refs. [9,10] which show that a second crack formed in the soft type IV region with starter notch in the hard WM in P91 welded joint (Fig. 7(a)) and pre-crack in the hard BM in P122 welded joint (Fig. 7(b)). The observation result [1,3,8] of P92 welded joint with starter-notch in the middle of HAZ (Fig. 7(c)) which developed as a type IV crack in the soft zone near HAZ/BM interface is also consistent with the simulation results above. The mechanism for this CCG behavior has been analyzed by the evolution of stress triaxiality distribution around a crack during its growth process in Fig. 5. 3.2. Mismatch effect in creep properties on CCG rate and rupture life Fig. 8 gives the relationship of CCG rate vs. C⁄ (da/dt–C⁄ curves) for the nine configurations (the three groups) for cracks growing both in HAZ and soft materials near interfaces. It can be seen that for the configurations forming a second crack (the configurations 3,
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Fig. 6. The final damage contours and crack paths in welded joints, (a) configuration 3, (b) configuration 4, and (c) configuration 5, SDV1: damage variable; ICT: initial crack tip; CCT: current crack tip.
Fig. 7. The CCG paths for: (a) P91 welded joint with starter notch in WM [9], (b) P122 welded joint with starter notch in BM [10], and (c) P92 welded joint with starter notch in the middle of HAZ [1,3,8].
4, 5 and 6), the CCG rate became much higher in soft materials than that in original hard materials as soon as the cracks jumped from the original crack plane to the parallel layer of soft materials. The CCG rates of the second cracks in these soft materials near the interfaces are nearly the same as those in the configurations with cracks in corresponding soft materials. It is also interesting to find that for a given value of C⁄, the group 3 with soft HAZ and the configurations 3 and 6 with cracks propagating in soft WM have the highest CCG rate and then the group 1 with matched HAZ and the configurations 4 and 5 with cracks propagating in the matched materials have middle CCG rate, and the group 2 with hard HAZ has the lowest CCG rate. This means that the lower creep strength of the material containing the crack can lead to higher CCG rate
regardless of the constraint given from surrounding materials. The higher CCG rate in soft materials is due to more accumulated creep strain at a certain period of time in soft materials and the higher stress triaxiality on the soft material sides of the interfaces (Fig. 5(c)). In each group, the configurations with harder WM have higher CCG rate than those with softer WM. This means the higher constraint given from surrounding hard material can promote CCG due to the formation of higher stress triaxiality on the soft material side of the interface. The relationship of crack length vs. time (Da–t curves) for the nine configurations is shown in Fig. 9. The group 3 with soft HAZ has the shortest rupture life (Fig. 9(c)), and the group 1 with hard HAZ has the longest life (Fig. 9(b)). The rupture life of the group 2
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Fig. 8. The da/dt–C⁄ curves for the nine configurations (from 1 to 9) for cracks growing both in HAZ and soft materials near interfaces.
with matched HAZ is in the middle (Fig. 9 (a)). In the group 1 (configurations 1, 2 and 3), the configuration 1 has shorter rupture life due to the higher constraint given from the surrounding hard WM, but the configuration 3 was opposite. In group 2 (the configurations 4, 5 and 6), the configuration 6 with surrounding soft WM has the shortest life due to the long second crack growth in the surrounding soft WM. In the group 3 (configurations 7, 8 and 9), the configurations 7 and 8 have shorter rupture life due to the higher constraint given from surrounding harder materials. All results above imply that the configurations with original crack in soft material have the shortest rupture life (like the group 3), and the harder surrounding materials can lead to shorter rupture life due to the higher constraint given from them (like configurations 1, 4, 7 and 8). The softer surrounding materials can increase the rupture life due to lower constraint given from them (like configurations 3, 5 and 9), but much softer surrounding mate-
rials can reduce rupture life due to the early initiation and propagation of the second cracks (like configuration 6). For the configurations 3, 4, 5 and 6 forming the second crack, the CCG time in hard HAZ takes major portion of the total life, and the crack growth accelerated up to fracture as soon as the crack initiated in the soft materials. In these cases, the time of crack growth in HAZ dominates the rupture life. This simulation result is consistent with the experimental observations in Refs. [1,3,8] that the crack located in the middle of HAZ can grow an angle of 45° to the pre-crack up to the FGHAZ/BM interface using about 80% of the total life for P92 welded joints, and the CCG rate in type IV region was much higher than that in original crack plane. The mechanism for this result has been explained in Section 3.1 by the evolution of stress triaxiality distribution around a crack during its growth process in Fig. 5. 3.3. Creep life assessment and design for welded joints Since the mismatch effect in creep properties between weldment constituents can lead to different CCG paths, da/dt–C⁄ curves and rupture life of welded joints, it should be fully considered in the creep life assessment and design for the welded joints. It can be seen from Figs. 8 and 9 that if the CCG data (da/dt–C⁄ curves or rupture life) obtained from homogenous materials (such as the configuration 2) are used for the creep life assessment and design for the welded joints with different mismatches, conservative (for configurations 3, 4, 5 and 6) or non-conservative (for configurations 1, 7, 8 and 9) results will be produced. From the above results, it can also be seen that the assessment and design procedure may be similar to those given in homogenous materials for the cracks which just propagate straight along the initial crack plane using the CCG rate data in welded joints. But for the cracks
Fig. 9. The Da–t curves, (a) group 1 (configurations 1, 2 and 3), (b) group 2 (configurations 4, 5 and 6), and (c) group 3 (configuration 7, 8 and 9).
G. Chen et al. / Materials and Design 63 (2014) 600–608
jumping from initial crack plane with hard materials to soft materials of interfaces, if only the lower CCG rate data in hard materials are used, the non-conservative (unsafe) results will be produced, especially for the cracks propagating short distance in hard materials, and if only the higher CCG rate data in soft materials of interfaces are used, the conservative results will be produced, especially for the cracks mainly propagating in hard materials. Thus, for accurate creep life assessment and design for this type of cracks, the CCG rate data of hard materials and soft materials in welded joint should be both used before and after initiation of the second cracks, respectively, and the incubation time of the second cracks in soft materials of interfaces should be determined accurately to predict the rupture life. The experiments and FEM numerical simulations based on the damage mechanics (like the method used in this article) may be necessary to determine the incubation time. The results in Figs. 8 and 9 also show that a proper mismatch design between weldment constituents can improve CCG properties of welded joints (decreasing CCG rate and prolonging the rupture life). The configurations 4 and 5 have the lowest CCG rate and the longest rupture life due to the higher creep strength of materials containing crack (hard HAZ) and lower creep strength of surrounding materials (matched WM and BM). Therefore, the mismatch design with harder material containing crack and softer surrounding material can decrease CCG rate and prolong rupture life of welded joints. But the rupture life would decrease abruptly when the creep strength of surrounding material is much lower than that of material containing crack due to the extension of short distance in hard materials caused by the earlier initiation of second crack in soft materials. Thus, in order to improve the CCG properties of welded joints, a proper mismatch between weldment constituents should be designed.
4. Conclusions The finite element method based on ductility exhaustion model was used to systematically investigate the CCG behavior in CT specimens of welded joints for different configurations of creep properties between weldment constituents under the same stress pffiffiffiffiffi intensity factor of K ¼ 10 MPa m. The crack-tip stress states, ⁄ CCG paths, da/dt–C curves and rupture life were calculated for different mismatches in creep properties, and the creep life assessment and design for welded joints were discussed. The main results obtained are as follows: (1) Both the creep deformation properties of the zone containing the crack and those of the surrounding materials influence the crack-tip damage and CCG paths in welded joints. When the zone containing the crack is softer than at least one of the other two surrounding materials or both, the crack propagates straight along the initial crack plane. Otherwise, it will form a second crack in the soft material near interface. These simulation results are confirmed by the experimental observations in the literature [1,3,8–10]. (2) The configurations with original crack in soft material have the highest CCG rate and shortest rupture life. The harder surrounding materials can lead to higher CCG rate and shorter rupture life due to the higher constraint given from them. The softer surrounding materials can reduce CCG rate and prolong the rupture life, but much softer surrounding materials can increase CCG rate and reduce rupture life due to the early initiation and propagation of the second cracks. (3) The mismatch effect in creep properties between weldment constituents should be fully considered in the creep life assessment and design for the welded joints. Especially, for
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the cases forming the second cracks, the incubation time of the second cracks in soft materials near interfaces should be accurately determined to predict the rupture life of welded joints. (4) A proper mismatch design with harder material containing crack and softer surrounding material can improve CCG properties of welded joints (decreasing CCG rate and prolong rupture life).
Acknowledgments This work was financially supported by the Projects of the National Natural Science Foundation of China (51375165, 51325504). Reference [1] Sugiura R, Yokobori Jr AT, Tabuchi M, Yokobori T. Comparison of creep crack growth rate in heat affected zone of welded joint for 9%Cr ferritic heat resistant steel based on C*, dd/dt, K and Q* parameters. Eng Fract Mech 2007;74:868–81. [2] Kim WG, Park JY, Lee HY, Hong SD, Kim YW, Kim SJ. Time-dependent crack growth behavior for a SMAW weldment of Gr.91 steel. Int J Press Ves Pip 2013;110:66–71. [3] Sugiura R, Yokobori Jr AT, Suzuki K, Tabuchi M. Characterization of incubation time on creep crack growth for weldments of P92. Eng Fract Mech 2010;77:3053–65. [4] Saber M. Experimental and finite element studies of creep and creep crack growth in P91 and P92 weldments. PHD thesis. Department of Mechanical, Materials and Manufacturing Engineering, the University of Nottingham. 2011. [5] Segle P, Anderrson P, Samuelson LÅ. Numerical investigation of creep crack growth in cross-weld CT specimens. Part I: influence of mismatch in creep deformation properties and notch tip location. Fatigue Fract Eng Mater Struct 2000;23:521–31. [6] Segle P, Anderrson P, Samuelson LÅ. Numerical investigation of creep crack growth in cross-weld CT specimens. Part II: Influence of specimen size. Fatigue Fract Eng Mater Struct 2000;23:533–40. [7] Samuelson LÅ, Segle P, Anderrson P, Storesund J. Creep crack growth in welded components—a numerical study and comparison with R5 procedure. Int J Press Ves Pip 2001;78:995–1002. [8] Yatomi M, Fuji A, Kobayashi K, Tabuchi M, Yokobori T, Hasegawa Y, Yokobori T. Creep crack growth of P92 welds. In: Proceeding of the ASME 2008 pressure vessels and piping division conference. Chicago, Illinois, USA; 2008. [9] Dogan B. Creep deformation and failure assessment of steel weldments. In: Eighth international conference on creep and fatigue at elevated temperatures. San Antonio, Texas, USA; 2007. [10] Tabuchi M, Hongo H, Watanabe T, Yokobori Jr AT. Creep crack growth analysis of welded joints for high Cr heat resisting steel. ASTM Spec Techn Pub 2007;1480:93–101. [11] Hyde TH, Saber M, Sun W. Testing and modelling of creep crack growth in compact tension specimens from a P91 weld at 650 °C. Eng Fract Mech 2010;77:2946–57. [12] Wang GZ, Liu XL, Xuan FZ, Tu ST. Effect of constraint induced by crack depth on creep crack-tip stress field in CT specimens. Int J Solids Struct 2010;47:51–7. [13] Tan JP, Wang GZ, Tu ST, Xuan FZ. Load-independent creep constraint parameter and its application. Eng Fract Mech 2014;116:41–57. [14] Sun PJ, Wang GZ, Xuan FZ, Tu ST, Wang ZD. Quantitative characterization of creep constraint induced by crack depths in compact tension specimens. Eng Fract Mech 2011;78:653–65. [15] Sun PJ, Wang GZ, Xuan FZ, Tu ST, Wang ZD. Three-dimensional numerical analyses of out-of-plane creep crack-tip constraint in compact tension specimens. Int J Press Ves Pip 2012;96–97:78–89. [16] Wang GZ, Li BK, Xuan FZ, Tu ST. Numerical investigation on the creep crack-tip constraint induced by loading configuration of specimens. Eng Fract Mech 2012;79:353–62. [17] Zhao L, Jing HY, Xiu JJ, Han YD, Xu LY. Experimental investigation of specimen size effect on creep crack growth behavior in P92 steel welded joint. Mater Des 2014;57:736–43. [18] Mehmanparast A, Maleki S, Yatomi M, Nikbin KM. Specimen geometry and size effects on the creep crack growth behavior of P91weldments. In: Proceeding of the ASME 2013 pressure vessels and piping division conference. Paris, France; 2013. [19] Lee KH, Kim YJ, Yoon KB, Nikbin K, Dean D. Quantification of stress redistribution due to mismatch in creep properties in welded branch pipes. Fatigue Fract Eng Mater Struct 2010;33:238–51. [20] Han JJ, Lee KH, Kim YJ, Nikbin K, Dean D. Effects of geometry and combined loading on steady-state creep stresses in welded branches. Int J Press Ves Pip 2011;88:395–402. [21] Han JJ, Kim SH, Kim YJ, Nikbin K, Dean D. Mismatch of creep properties on steady-state stresses for welded straight pipes: quantification and application.
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Materials and Design journal homepage: www.elsevier.com/locate/matdes
Mismatch effect in creep properties on creep crack growth behavior in welded joints G. Chen, G.Z. Wang ⇑, F.Z. Xuan, S.T. Tu Key Laboratory of Pressure Systems and Safety, Ministry of Education, East China University of Science and Technology, Shanghai 200237, China
a r t i c l e
i n f o
Article history: Received 2 May 2014 Accepted 20 June 2014 Available online 7 July 2014 Keywords: Mismatch effect Creep crack growth Welded joint Constraint Rupture life
a b s t r a c t The finite element method based on ductility exhaustion model was used to systematically investigate the mismatch effect in creep properties on creep crack growth (CCG) behavior in welded joints. The crack-tip damage, stress states, CCG paths, CCG rate and rupture life were calculated for different configurations of creep properties between weldment constituents under the same load level, and the creep life assessment and design for welded joints were discussed. The results show that when the zone containing the crack is softer than at least one of the other two surrounding materials or both, the creep crack propagates straight along the initial crack plane. Otherwise, it will form a second crack in the soft material near interface. These simulation results were confirmed by the experimental observations in the literature, and the mechanism was analyzed. The harder surrounding materials can lead to higher CCG rate and shorter rupture life due to the higher constraint given from them. The early initiation and propagation of the second cracks increase CCG rate and reduce rupture life, and the incubation time of the second cracks in soft materials near interfaces should be accurately determined in the creep life assessment and design for the welded joints. A proper mismatch design with harder material containing crack and softer surrounding material can improve CCG properties of welded joints (decreasing CCG rate and prolong rupture life). Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Most problems of crack initiation and propagation in high temperature components are likely to originate from welded joints [1], which is caused by the multi stress and strain fields appearing ahead of crack-tip or near the interface of weldment constituents due to the mismatch in creep deformation properties among base metal (BM), weld metal (WM) and heat affected zone (HAZ) [2,3]. The original cracks may exist anywhere in welded joint randomly, and mainly classified into four types. The type I crack is confined in WM, the type II crack occurring in WM may grow into BM, the type III crack occurs in coarse grained HAZ and the type IV crack propagates in the critical zone of HAZ adjacent to BM/HAZ interface [4]. Experiences showed that both the deformation properties of materials containing crack and surrounding materials influence the creep crack growth (CCG) behavior in welded joints [5–7]. Such as, the type IV crack is the most severe form of cracks due to the high creep strain of type IV region where the crack is propagating and the high constraint given from hard BM of surrounding materials [4]. Sugiura et al. [1,3] and Yatomi et al. [8] found that the ⇑ Corresponding author. Tel./fax: +86 21 64252681. E-mail address: [email protected] (G.Z. Wang). http://dx.doi.org/10.1016/j.matdes.2014.06.047 0261-3069/Ó 2014 Elsevier Ltd. All rights reserved.
crack located in the middle of HAZ region can deviate from the original crack plane to the type IV crack region with minimum hardness for the P92 welded joint, and the acceleration of CCG occurred as soon as the crack started to initiate near the HAZ/BM interface. Dogan [9] observed that the crack located in the middle of WM with high creep strength formed a second crack in the type IV crack region with lower creep strength in addition to the extending of CCG straight along the initial crack-tip in P91 welded joint, and the same phenomenon was also found in P122 steel welded joint with the pre-crack located in BM [10]. Hyde et al. [11] found that the cracks laid in the type IV region still stayed in this region, and the CCG rate was about four times higher than the corresponding BM for a given value of C⁄. All the above results show that the material constraint caused by the mismatch effect in creep properties of weldment constituents plays an important role on the CCG behavior in welded joints. For accurate creep life assessment and safety design of the welded joints, it needs to investigate and understand this material constraint effect on the CCG behavior and properties. Recently, there are some investigations on the creep crack-tip constraint effect caused by specimen geometry, crack size and loading configuration for homogenous materials [12–16] and welded joints [17,18]. However, only a few mechanical analyses
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for the material constraint effect on CCG behavior due to the mismatch in creep properties between different materials in welded joints could be found in the literature. Lee et al. [19] and Han et al. [20,21] defined a mismatch factor about creep constant and exponent of Norton’s law between different materials in weldment to quantify the mismatch effect in creep properties on the distribution of steady-state stress. Tu et al. [22,23] and Xuan et al. [24] studied the influence of material mismatch on the evaluation of the time-dependent fracture mechanics parameters C(t) and C⁄. There are also some numerical investigations on the mismatch effect on C⁄ and CCG rate in welded joints [5–7]. But the actual CCG path generally could not be realized and it was assumed that all the cracks propagated straight. In real CCG process in welded joints, the crack path may change from the initial crack plane to another place [1,3,8–10], and the stress state ahead of crack tip and near the interface between different materials may change with crack growth. Therefore, the mismatch effects in creep properties on crack-tip stress state, creep damage accumulation, real crack path and CCG properties of welded joints need to be systematically investigated and understood. But it is difficult to do the experimental studies due to the difficulty of systematic change and control in creep properties of weldment constituents. The numerical method based on creep damage model may provide suitable tool for these investigations. In this paper, the finite element method (FEM) based on ductility exhaustion model was used to investigate the mismatch effect in creep properties between weldment constituents on CCG behavior in compact tension (CT) specimens of welded joints. A brief introduction to the subject is given in this section. Section 2 describes the geometry of specimen, configurations of creep properties between weldment constituents, damage model and the calculation of CCG rate. The numerical results and discussions including mismatch effects on CCG path, CCG rate, rupture life, integrity assessment and design of welded joints are given in Section 3. Section 4 is the conclusion.
2. Finite element models and numerical procedures 2.1. Finite element models In order to investigate the mismatch effect in creep properties on CCG behavior in detail, the CT specimen of welded joint was used for the FE analyses with ABAQUS code [25], which consists of three materials, i.e. BM, WM and HAZ. The geometry and dimensions of the specimen are corresponding to those of the
experiments in Ref. [3], as shown in Fig. 1. The width W of the CT specimen is 50.8 mm and the initial crack length a0 is 26.4 mm (a0/W = 0.52). The width of the WM and HAZ is 20 mm and 2.4 mm, respectively. A sharp crack tip with 0.009° angle was used to represent the fatigue pre-crack and located in the middle of HAZ. The load was applied on the centre of the upper hole using a reference point which was tied to the internal hole surface that represents the bolt in the experiments. The centre of the upper hole was constrained in X-direction, and the centre of the lower hole was constrained in X and Y-directions. The four-node plane strain element (CPE4) was used for all FE models. The mesh dependency investigations in the CCG simulations have been carried out by Yatomi et al. [26] and Oh et al. [27] for the mesh size from 50 lm to 250 lm. The results show that the creep crack initiation time decreases with decreasing mesh size due to the increased crack-tip stress and strain, and the CCG rate was not sensitive to mesh size. So, the fine meshes with size of 50 lm 50 lm were used ahead of crack tip and near the interfaces of HAZ/WM and HAZ/BM. The whole and local meshes for the CT specimen are shown in Fig. 2, which includes 20,891 elements and 21,063 nodes. 2.2. Materials and configurations of mismatch in creep properties The ASME Grade P92 steel was chosen for BM. The elastic–plastic-creep material model was used in FE calculations. The elastic modulus E and yield stress ry of the BM at 650 °C is 85GPa and 126 MPa, respectively [28]. The characteristic of work hardening for plastic deformation is taken from Ref. [1], and is approximated by Eq. (1):
r ¼ cða þ ep Þa
where c, a and a are constants (c = 162, a = 0.32 102, a = 0.105), and ep is true plastic strain. To investigate the mismatch effect in creep properties on creep crack growth behavior in welded joints and facilitate explanation of results, the elastic modulus and plastic deformation characteristics for WM and HAZ are assumed to be the same as those of BM. For the sake of simplicity and changing creep properties easily, the Norton’s law was taken as creep constitutive equation for the three materials as follows:
e_ b ¼ Ab rnb ; e_ W ¼ AW rnW ; e_ HAZ ¼ AHAZ rnHAZ
ð2Þ
where Ab, Aw and AHAZ are creep constant, and nb, nw and nHAZ are creep stress exponent for BM, WM and HAZ, respectively. The Norton’s parameters (Ab = 3.77E19 MPan h1, nb = 6.71) for the ASME Grade P92 BM at 650 °C were used, and they were taken from Ref. [28]. To examine the mismatch effect in creep properties among WM, HAZ and BM on creep crack growth behavior in welded joints, different configurations of mismatch in creep strain rates of WM, HAZ and BM should be designed. For WM and HAZ, the material properties were given that the minimum creep strain rate was higher or lower than that of BM by varying the constant A and keeping the exponent nW = nHAZ = nb = 6.71. The mismatch factors of MFW and MFHAZ shown in Eq. (3) were given to represent the mismatch effect in creep properties relative to BM for WM and HAZ, respectively. Thus, three cases of MF > 1, MF = 1 and MF < 1 refer to creep soft material, creep match and creep hard material, respectively. This type of design of configurations of mismatch in creep properties was widely used in the literature [5–7,19–21].
MF W ¼
Fig. 1. The geometry and dimensions of the CT specimen of welded joint [3].
ð1Þ
AW ; Ab
MF HAZ ¼
AHAZ Ab
ð3Þ
For investigating the mismatch effect in creep properties on CCG behavior, the MFW and MFHAZ are assumed as 10, 0.1 and 1, respectively, which means that the minimum creep strain rate is 10 times larger or smaller and the same relative to BM both for
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Fig. 2. The FE model of the CT specimen of welded joint, (a) meshes of whole model and (b) local meshes around the crack tip and interfaces of HAZ/BM and HAZ/WM.
WM and HAZ at the same value of uniaxial tension stress. Thereby, for creep soft or creep hard materials and matched materials, the value of A is 3.77E18 MPan h1, 3.77E20 MPan h1 and 3.77E19 MPan h1, respectively. The nine different configurations of mismatch in creep properties of the three materials are shown in Table 1. Based on the creep strength of HAZ, the nine configurations can be divided into three groups. The configurations 1, 2 and 3 with matched HAZ is denoted as group 1, the configurations 4, 5 and 6 with hard HAZ is denoted as group 2, and the configurations 7, 8 and 9 with soft HAZ is denoted as group 3. The CCG path, CCG rate, rupture life and local stress and strain distributions both ahead of crack-tips and near the interfaces of different materials were simulated and calculated under the same initial stress pffiffiffiffiffi intensity factor K ¼ 10 MPa m. 2.3. Creep damage model and crack growth simulation The creep damage model is based on the ductility exhaustion approach to simulate the creep crack growth [26–29]. The rate of _ was defined by the ratio of creep strain rate e_ c and muldamage x tiaxial creep ductility ef , as follows:
x_ ¼
e_ c ef
reduced to near zero by reducing the elastic modulus to a very small value (1 MPa in this work). The ABAQUS user subroutine USDFLD was employed to embody this failure simulation technique, and it has been widely used in the recent literature [4,10,27,29]. There are a number of available creep void growth models for describing the relationship between multiaxial and uniaxial creep ductility through stress triaxiality (the ratio of the mean normal stress and equivalent stress) [30–33], but one of the notable models was proposed by Cocks and Ashby [33], given by Eq. (6):
ef 2 n 0:5 n 0:5 rm sinh 2 ¼ sinh 3 n þ 0:5 n þ 0:5 re ef
where ef and ef denotes the multiaxial and uniaxial creep ductility, respectively, and n is the creep exponent. For investigating the mismatch effect and facilitating the interpretation of results, the ef values of the three materials were assumed to be the same, and it was taken to be 0.16 [34]. The crack growth length was calculated by the number of damaged regular elements. For CT specimen of welded joint, the C⁄ can be calculated by the following equations which consider the bending and tension in the specimen [35], and has been used in the recent literature [36].
ð4Þ C ¼
And the total damage at any instant is the integration of the damage rate in Eq. (4) up to that time [26]:
x¼
Z
t
x_ dt ¼
Z
0
0
t
e_ c dt ef
Table 1 Different configurations of mismatch in creep properties.
n Pdd=dt b c n þ 1 Bn ðW aÞ n
ð7Þ
c¼
2ð1 þ aÞð1 þ a=WÞð1 þ a2 Þ þ að1 a=WÞ ð1 þ a=WÞ þ að1 a=WÞ
ð8Þ
b¼
a a þ ð1 þ a=WÞ=ð1 a=WÞ
ð9Þ
ð5Þ
_ is the creep damage rate, e_ c and ef is the equivalent creep where x strain rate and multiaxial creep ductility, respectively. The value of the x is between 0 and 1. When the accumulated creep damage calculated from Eq. (5) reaches 1, local failure occurs and progressive cracking is simulated. Thus, load-carrying capacity of the point is
ð6Þ
a¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi f2a=ðW aÞ þ 1g2 þ 1 f2a=ðW aÞ þ 1g
ð10Þ
where W is the specimen width, a is the crack length, P is the load, Bn is the net thickness, dd=dt is the load line displacement rate, and n is the creep exponent in Norton’s law.
Group
Configuration
HAZ
WM
3. Numerical simulation results and discussion
1
1 2 3
Match Match Match
Hard Match Soft
3.1. Crack-tip damage and CCG paths in welded joints with different mismatches
4 5 6
Hard Hard Hard
Hard Match Soft
7 8 9
Soft Soft Soft
Hard Match Soft
2
3
It is known that both the accumulated creep strain at a period of time and stress triaxiality determine the creep damage from the ductility exhaustion model. Different distributions of creep strain and multi stress state appearing ahead of crack-tip or near the interface between weldment constituents for different material
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Fig. 3. The final damage contours (t/tr = 1, tr is rupture time) of CCG in welded joints, (a) configuration 1, (b) configuration 2, (c) configuration 7, (d) configuration 8, and (e) configuration 9, SDV1: damage variable; ICT: initial crack tip; CCT: current crack tip.
configurations can lead to different CCG behavior. Fig. 3 shows the final damage contours for the crack growth of the configurations 1, 2, 7, 8 and 9. The SDV1 represents the damage variable, ICT is the initial crack tip and the CCT represents the current crack tip. It can be seen that the damage zone around the crack tip is approximately symmetric for the configuration 2 (homogenous material), and that was also symmetric for the configuration 8 due to the symmetry of materials in specimen and the damage zone concentrated on the soft HAZ. For the other three cases (configurations 1, 7 and 9), the damaged zone mainly concentrated on the relatively soft materials. It also can be seen that the CCG paths were nearly straight along the initial crack plane for the five configurations (Fig. 3). For all of the above five configurations, the HAZ is softer than at least one of the other two materials (configurations 1, 7, 8 and 9) or matched to the other two materials (homogenous material, configuration 2). The following Fig. 4 shows the CCG process for the configuration 6 that the HAZ is hardest and the WM is softer than BM. It can be seen that the crack jumped from the original crack plane after 1.4 mm straight extension and continued to grow in the parallel WM with lower strength near the WM/HAZ interface. Fig. 4 also shows the CCG in the hard HAZ takes major portion of the total
time, approximately 82%, and then the acceleration of CCG occurs. This result is consistent with that in the literature [1,3,8]. This means that the time for the crack growing in hard HAZ dominates the rupture time. For explaining this phenomenon, the distribution of the stress triaxiality (SDV3) in CCG process was presented in Fig. 5. It can be seen that the highest stress triaxiality occurred ahead of crack-tip in the early stage of CCG (Fig. 5(a)). With the redistribution of stress and strain during the CCG process, the accumulating creep deformation in soft WM was strongly constrained by the hard HAZ so that the highest stress triaxiality occurred both ahead of crack-tip and in WM near the WM/HAZ interface (Fig. 5(b)), and thereby the more damage accumulation occurred in WM of the interface under the higher stress triaxiality. When the accumulated damage reached the critical value after a certain period of time, the crack started to initiate in the soft WM of the interface, and then the acceleration of CCG occurred in WM due to the higher accumulated creep strain in the soft WM and the highest stress triaxiality appearing on the soft WM side of the interface (Fig. 5(c)). Fig. 6 gives the final damage contours and CCG paths for the other three configurations that the HAZ is harder than one of the other two materials (the configurations 3 and 4) or both (the
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Fig. 4. The CCG process for the configuration 6 (the tr is the rupture time), SDV1: damage variable; ICT: initial crack tip; CCT: current crack tip.
( )
( )
( ) Fig. 5. The stress triaxiality contours during CCG process for the configuration 6, SDV3: stress triaxiality; ICT: initial crack tip; CCT: current crack tip.
configuration 5). It can be seen that like the configuration 6, it also formed a second crack in the soft WM and BM sides of the interfaces for the configurations 3 and 4, respectively. For the configuration 5 (MFWM = 1, MFHAZ = 0.1), the second crack grew both in the WM of HAZ/WM interface and the BM of HAZ/BM interface due to the same creep strength of the BM and WM, but the crack mainly propagated in soft WM of WM/HAZ interface due to the higher constraint near the WM/HAZ interface caused by the had HAZ on both sides of WM (Fig. 1). The results above show that both the deformation properties of the zone containing the crack and those of the surrounding materials influence the crack tip damage and CCG path in welded joints. When the zone containing the crack is softer than at least one of the other two surrounding materials or both (like the configurations 1, 2, 7, 8 and 9), the crack propagates straight along the initial crack plane. When the zone containing the crack is harder than at least one of the other two surrounding materials or both (like the configurations 3, 4, 5 and 6), it will form a second crack in the soft
material near interfaces. These simulation results are confirmed by the experimental observation results in Refs. [9,10] which show that a second crack formed in the soft type IV region with starter notch in the hard WM in P91 welded joint (Fig. 7(a)) and pre-crack in the hard BM in P122 welded joint (Fig. 7(b)). The observation result [1,3,8] of P92 welded joint with starter-notch in the middle of HAZ (Fig. 7(c)) which developed as a type IV crack in the soft zone near HAZ/BM interface is also consistent with the simulation results above. The mechanism for this CCG behavior has been analyzed by the evolution of stress triaxiality distribution around a crack during its growth process in Fig. 5. 3.2. Mismatch effect in creep properties on CCG rate and rupture life Fig. 8 gives the relationship of CCG rate vs. C⁄ (da/dt–C⁄ curves) for the nine configurations (the three groups) for cracks growing both in HAZ and soft materials near interfaces. It can be seen that for the configurations forming a second crack (the configurations 3,
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Fig. 6. The final damage contours and crack paths in welded joints, (a) configuration 3, (b) configuration 4, and (c) configuration 5, SDV1: damage variable; ICT: initial crack tip; CCT: current crack tip.
Fig. 7. The CCG paths for: (a) P91 welded joint with starter notch in WM [9], (b) P122 welded joint with starter notch in BM [10], and (c) P92 welded joint with starter notch in the middle of HAZ [1,3,8].
4, 5 and 6), the CCG rate became much higher in soft materials than that in original hard materials as soon as the cracks jumped from the original crack plane to the parallel layer of soft materials. The CCG rates of the second cracks in these soft materials near the interfaces are nearly the same as those in the configurations with cracks in corresponding soft materials. It is also interesting to find that for a given value of C⁄, the group 3 with soft HAZ and the configurations 3 and 6 with cracks propagating in soft WM have the highest CCG rate and then the group 1 with matched HAZ and the configurations 4 and 5 with cracks propagating in the matched materials have middle CCG rate, and the group 2 with hard HAZ has the lowest CCG rate. This means that the lower creep strength of the material containing the crack can lead to higher CCG rate
regardless of the constraint given from surrounding materials. The higher CCG rate in soft materials is due to more accumulated creep strain at a certain period of time in soft materials and the higher stress triaxiality on the soft material sides of the interfaces (Fig. 5(c)). In each group, the configurations with harder WM have higher CCG rate than those with softer WM. This means the higher constraint given from surrounding hard material can promote CCG due to the formation of higher stress triaxiality on the soft material side of the interface. The relationship of crack length vs. time (Da–t curves) for the nine configurations is shown in Fig. 9. The group 3 with soft HAZ has the shortest rupture life (Fig. 9(c)), and the group 1 with hard HAZ has the longest life (Fig. 9(b)). The rupture life of the group 2
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Fig. 8. The da/dt–C⁄ curves for the nine configurations (from 1 to 9) for cracks growing both in HAZ and soft materials near interfaces.
with matched HAZ is in the middle (Fig. 9 (a)). In the group 1 (configurations 1, 2 and 3), the configuration 1 has shorter rupture life due to the higher constraint given from the surrounding hard WM, but the configuration 3 was opposite. In group 2 (the configurations 4, 5 and 6), the configuration 6 with surrounding soft WM has the shortest life due to the long second crack growth in the surrounding soft WM. In the group 3 (configurations 7, 8 and 9), the configurations 7 and 8 have shorter rupture life due to the higher constraint given from surrounding harder materials. All results above imply that the configurations with original crack in soft material have the shortest rupture life (like the group 3), and the harder surrounding materials can lead to shorter rupture life due to the higher constraint given from them (like configurations 1, 4, 7 and 8). The softer surrounding materials can increase the rupture life due to lower constraint given from them (like configurations 3, 5 and 9), but much softer surrounding mate-
rials can reduce rupture life due to the early initiation and propagation of the second cracks (like configuration 6). For the configurations 3, 4, 5 and 6 forming the second crack, the CCG time in hard HAZ takes major portion of the total life, and the crack growth accelerated up to fracture as soon as the crack initiated in the soft materials. In these cases, the time of crack growth in HAZ dominates the rupture life. This simulation result is consistent with the experimental observations in Refs. [1,3,8] that the crack located in the middle of HAZ can grow an angle of 45° to the pre-crack up to the FGHAZ/BM interface using about 80% of the total life for P92 welded joints, and the CCG rate in type IV region was much higher than that in original crack plane. The mechanism for this result has been explained in Section 3.1 by the evolution of stress triaxiality distribution around a crack during its growth process in Fig. 5. 3.3. Creep life assessment and design for welded joints Since the mismatch effect in creep properties between weldment constituents can lead to different CCG paths, da/dt–C⁄ curves and rupture life of welded joints, it should be fully considered in the creep life assessment and design for the welded joints. It can be seen from Figs. 8 and 9 that if the CCG data (da/dt–C⁄ curves or rupture life) obtained from homogenous materials (such as the configuration 2) are used for the creep life assessment and design for the welded joints with different mismatches, conservative (for configurations 3, 4, 5 and 6) or non-conservative (for configurations 1, 7, 8 and 9) results will be produced. From the above results, it can also be seen that the assessment and design procedure may be similar to those given in homogenous materials for the cracks which just propagate straight along the initial crack plane using the CCG rate data in welded joints. But for the cracks
Fig. 9. The Da–t curves, (a) group 1 (configurations 1, 2 and 3), (b) group 2 (configurations 4, 5 and 6), and (c) group 3 (configuration 7, 8 and 9).
G. Chen et al. / Materials and Design 63 (2014) 600–608
jumping from initial crack plane with hard materials to soft materials of interfaces, if only the lower CCG rate data in hard materials are used, the non-conservative (unsafe) results will be produced, especially for the cracks propagating short distance in hard materials, and if only the higher CCG rate data in soft materials of interfaces are used, the conservative results will be produced, especially for the cracks mainly propagating in hard materials. Thus, for accurate creep life assessment and design for this type of cracks, the CCG rate data of hard materials and soft materials in welded joint should be both used before and after initiation of the second cracks, respectively, and the incubation time of the second cracks in soft materials of interfaces should be determined accurately to predict the rupture life. The experiments and FEM numerical simulations based on the damage mechanics (like the method used in this article) may be necessary to determine the incubation time. The results in Figs. 8 and 9 also show that a proper mismatch design between weldment constituents can improve CCG properties of welded joints (decreasing CCG rate and prolonging the rupture life). The configurations 4 and 5 have the lowest CCG rate and the longest rupture life due to the higher creep strength of materials containing crack (hard HAZ) and lower creep strength of surrounding materials (matched WM and BM). Therefore, the mismatch design with harder material containing crack and softer surrounding material can decrease CCG rate and prolong rupture life of welded joints. But the rupture life would decrease abruptly when the creep strength of surrounding material is much lower than that of material containing crack due to the extension of short distance in hard materials caused by the earlier initiation of second crack in soft materials. Thus, in order to improve the CCG properties of welded joints, a proper mismatch between weldment constituents should be designed.
4. Conclusions The finite element method based on ductility exhaustion model was used to systematically investigate the CCG behavior in CT specimens of welded joints for different configurations of creep properties between weldment constituents under the same stress pffiffiffiffiffi intensity factor of K ¼ 10 MPa m. The crack-tip stress states, ⁄ CCG paths, da/dt–C curves and rupture life were calculated for different mismatches in creep properties, and the creep life assessment and design for welded joints were discussed. The main results obtained are as follows: (1) Both the creep deformation properties of the zone containing the crack and those of the surrounding materials influence the crack-tip damage and CCG paths in welded joints. When the zone containing the crack is softer than at least one of the other two surrounding materials or both, the crack propagates straight along the initial crack plane. Otherwise, it will form a second crack in the soft material near interface. These simulation results are confirmed by the experimental observations in the literature [1,3,8–10]. (2) The configurations with original crack in soft material have the highest CCG rate and shortest rupture life. The harder surrounding materials can lead to higher CCG rate and shorter rupture life due to the higher constraint given from them. The softer surrounding materials can reduce CCG rate and prolong the rupture life, but much softer surrounding materials can increase CCG rate and reduce rupture life due to the early initiation and propagation of the second cracks. (3) The mismatch effect in creep properties between weldment constituents should be fully considered in the creep life assessment and design for the welded joints. Especially, for
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the cases forming the second cracks, the incubation time of the second cracks in soft materials near interfaces should be accurately determined to predict the rupture life of welded joints. (4) A proper mismatch design with harder material containing crack and softer surrounding material can improve CCG properties of welded joints (decreasing CCG rate and prolong rupture life).
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