- Email: [email protected]
Effects of initial crack positions and load levels on creep failure behavior in P92 steel welded joint
Accepted Manuscript Effects of initial crack positions and load levels on creep failure behavior in P92 steel welded joint G. Chen, G.Z. Wang, J.W. Zhang, F.Z. Xuan, S.T. Tu PII: DOI: Reference:
S1350-6307(14)00305-7 http://dx.doi.org/10.1016/j.engfailanal.2014.10.005 EFA 2423
To appear in:
Engineering Failure Analysis
Received Date: Revised Date: Accepted Date:
6 June 2014 8 October 2014 9 October 2014
Please cite this article as: Chen, G., Wang, G.Z., Zhang, J.W., Xuan, F.Z., Tu, S.T., Effects of initial crack positions and load levels on creep failure behavior in P92 steel welded joint, Engineering Failure Analysis (2014), doi: http:// dx.doi.org/10.1016/j.engfailanal.2014.10.005
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Effects of initial crack positions and load levels on creep failure behavior in P92 steel welded joint G. Chen, G.Z. Wang*, J.W. Zhang, 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
Abstract: The finite element method based on ductility exhaustion damage model coupled with the stress-regime dependent creep constitutive model was used to investigate creep failure behavior at different load levels for six initial cracks at different positions in P92 welded joints. The stress states and creep damage around cracks, creep crack growth (CCG) paths and rates and rupture life have been calculated and analyzed, and the creep failure and life assessments for welded joints were discussed. The results show that for some cracks with specific positions in the welded joint, load level causes the change of CCG path due to the stress-regime dependent creep constitutive. At low load level, the significant mismatch effect in creep properties promotes the initiation and propagation of second cracks in soft materials near interfaces, and the creep rupture life is mainly determined by the incubation time of the second cracks. This result is confirmed by similar experimental observations in the literature, and the mechanism was analyzed. For the initial crack positions with a second crack, if the extrapolation of CCG rate from higher load levels is used in creep life assessment of a welded joint at lower load levels, the non-conservative (unsafe) results will be produced. In creep failure analyses and life assessments of welded joints, the effects of initial crack positions and load levels should be fully considered. Keywords: creep failure, welded joint, initial crack position, load level, creep crack growth, second crack. Corresponding author. Tel.: +86 21 64252681; fax: +86 21 64252681. E-mail address: [email protected] (Guozhen Wang). 1
1. Introduction Many experiments and theoretical evidences have shown that the multi-axial stress state ahead of crack tip or near the interface between weldment constituents due to the constraint of deformation among base metal (BM), weld metal (WM), coarse grained heat affected zone (CGHAZ) and fine grained heat affect zone (FGHAZ) plays an important role on creep failure behavior in welded joints at high temperatures [1, 2]. Experience shows that the cracks may exist anywhere in a welded joint under different load levels, and both the creep deformation properties of the zone containing the crack and those of the surrounding materials influence the creep damage and creep crack growth (CCG) paths in welded joints [3, 4]. Thus, the cracks at different positions in a welded joint would have different failure behavior. Such as, the cracks laid in the type IV region still stayed in this region, and which is the most severe form of the cracks [5]. But metallurgical observation showed 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 with a constant CCG rate using about 80% of the total rupture life [2, 6]. Similarly, a second crack (SC) formed in the soft type IV region with starter notch in the hard WM and BM in P91 [7] and P122 [8] welded joints, respectively. The creep crack initiation tests [9] for the dissimilar welded joint of 1CrMoV/Alloy 617/Alloy 625 with the pre-crack in the middle of 1CrMoV HAZ also showed that the crack propagated both ahead of starter notch and in 1CrMoV HAZ near 1CrMoV HAZ/Alloy 617 (with higher creep strength) interface where had high constraint. The experiments and theoretical evidences also show that creep deformation and fracture mechanism are different at different stress levels for alloy steels [10-12]. The difference of 2
creep deformation properties between weldment constituents was also different at different stress regime [13]. Therefore, the load levels may also have important effect on failure behavior of welded joints. Such as, experiments showed that stress levels had an obvious effect on the rupture location for the unaxial tension tests of P91 welded joints, and the rupture location changed from WM or BM at high stress (short time) to HAZ at low stress (long time). Experiments also showed that the range of transition stress of failure location from WM to HAZ increased with increasing creep strength of WM for P911 unaxial welded joints at 600℃[15]. To better understand the mechanism of effects of initial crack positions and load levels on CCG behavior and to conduct accurate creep failure analyses and life assessments, it needs systematic mechanical analyses and investigations for failure behavior of welded joints. The numerical method based on creep damage model may provide a suitable tool for these investigations. The two-regime Norton (2RN) creep model which is described by two different Norton’s equations with different parameters provides a bi-linear formulation for high- and low-stress regimes [13, 16-19]. Recently, this 2RN creep model has been used in the creep stress-state analysis in a loaded CT specimen for predicting long-time unaxial creep rupture strength of materials [17], and it also has been used in the simulation of CCG rate in the homogenous Cr-Mo-V steel [18] and 316H steel [19]. The use of the 2RN creep model in the CCG simulations in welded joints may reveal the effects and mechanism of load levels on failure behavior of cracks at different positions. In this work，the finite element method (FEM) based on ductility exhaustion damage model coupled with the stress-regime dependent creep constitutive model (2RN model) was used to investigate creep failure behavior at different load levels (initial stress intensity factors) 3
for six initial cracks at different positions in P92 welded joints. The stress states and creep damage around cracks, CCG paths and rates and rupture life were calculated and analyzed, and the creep failure and life assessments of the welded joints were discussed.
2. Finite element models and numerical procedures 2.1 Finite element models The compact tension (CT) specimens of the P92 welded joint were used in the FE analyses with ABAQUS code [20]. The welded joint is simplified to be composed of four materials, i.e. BM, WM, FGHAZ and CGHAZ. The geometry and dimensions of the CT specimen are taken to be the same as those of the experiments in Ref [2], as shown in Fig.1. The width W of the CT specimen is 50.8mm and initial crack length a0 is 26.4mm (a0/W =0.52). The width of the WM, FGHAZ and CGHAZ is 20mm, 1.2mm and 1.2mm, respectively. To investigate the effect of initial crack positions on creep failure behavior of the welded joint，the six initial cracks at different positions in the welded joint were modeled, including three center cracks and three interface cracks. The three center cracks represent that the initial crack lies in the middle of FGHAZ, CGHAZ and WM, respectively. The three interface cracks refer to that the initial cracks exist in the FGHAZ/BM, FGHAZ/CGHAZ and CGHAZ/WM interfaces, respectively. Fig.2 shows the six initial crack positions, and the typical FGHAZ/CGHAZ interface crack can be seen in Fig.1.
4
Fig.1. The geometry and dimensions of the CT specimen of P92 welded joint [2]
Fig.2. The six initial crack positions in P92 welded joint
For the WM center crack, only one half of the specimen was modeled due to symmetry, while whole CT specimens were modeled for other cracks. 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 four-node plane strain element (CPE4) was used for all FE models. A sharp crack tip with 0.009°angle was used to represent the fatigue pre-crack. The mesh dependency analyses in the CCG simulations have been carried out by Yatomi et al. [21] and Oh et al. [22] for the mesh size from 50µm to 250µm. The results show that the creep crack initiation time decreases and the CCG rate slightly increases 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 50µm×50µm were used around 5
crack tip and near interfaces between weldment constituents. The whole and local meshes for the FGHAZ center crack are typically shown in Fig.3, and the whole FE model includes 27,615 elements and 27,816 nodes.
(a)
(b)
Fig.3 The FE model of the FGHAZ center crack specimen, (a) meshes of whole model, (b) local meshes around the crack tip and near the interface between weldment constituents
2.2 Materials and creep constitutive models of the welded joint The ASME Grade P92 steel was chosen for BM. The elastic-plastic-creep material model was used in CCG simulations. The true stress and true plastic strain relation of the steel at 650℃ is taken from Ref. [6], and is approximated by the following equation: = ( + )
(1)
where c, a and α are constants (c = 162, a = 0.32×10-2, α = 0.105), and is true plastic strain. The true stress and true plastic strain data of the WM, FGHAZ and CGHAZ were assumed to be the same as those of the BM. The un-axial creep tests of the four materials show that the creep deformation obeys two-regime Norton’ (2RN) power law [13, 23], as shown in Fig 4. The 2RN creep constitutive model is composed of low-stress regime and high-stress regime Norton’ model, as shown by 6
Eq. (2), =
（ ）
（ ）
（2）
where the is the transition stress，the A1 and n1 are creep coefficient and exponent in the Norton’ model for low-stress regime，and the A2 and n2 are those for high-stress regime. The parameters of the 2RN model and elastic modulus of the four materials at 650℃ are taken from Refs. [2, 23], and they are listed in Table 1. Because the transition stress σ0 and n2 of the CGHAZ are not available, they were assumed to be the same as those of the FGHAZ. It also can be seen from Fig.4 that the FGHAZ has the highest creep strain rate at a given stress level, so it is softer than the other three materials. The 2RN creep constitutive models (Eq. (2)) of the four materials were implemented in the ABAQUS code by using the user subroutine CREEP [20].
Fig.4 Relation between minimum creep rate and unaxial tension stress for different regions (BM, WM, FGHAZ and CGHAZ) in the P92 steel welded joint at 650℃ [13, 23]
7
Table.1 Material properties for different regions (BM, WM, FGHAZ and CGHAZ) in P92 welded joint at different stress levels at 650℃ [2, 23] Material
A (MPa-nh-1)
n
σ (MPa)
E (GPa)
WM
7.28e-16
4.7
σ ≤90
92
2.57E-32
13.12
σ>90
3.77E-19
6.71
σ≤113
2.57E-32
13.12
σ>113
8.30E-13
3.68
σ≤88
3.68E-31
13.12
σ>88
2.35E-16
5.35
σ≤88
1.83E-31
13.12
σ>88
BM
FGHAZ
CGHAZ
85
88
90
2.3 Creep damage model and crack growth simulation The ductility exhaustion model was used to account for the creep damage accumulation, and then to simulate creep crack propagation [4, 18, 19, 21-24]. The rate of damage was defined by the ratio of creep strain rate and multiaxial creep ductility ∗ , as follows:
= ∗
(3)
And the total damage at any instant is the integration of the damage rate in Eq. (3) up to that time [21]: "
"
= ! = ∗ !
(4)
where is the creep damage rate, and ∗ is the equivalent creep strain rate and multi-axial creep ductility, respectively. The value of is in a range of 0-1.0. When at a Gauss point reaches 1.0, local failure occurs and progressive cracking is simulated. Thus, load-carrying capacity of the point is reduced to near zero by reducing the elastic modulus to a very small value (1E-6MPa in this work). The ABAQUS user subroutine USDFLD was 8
used to embody this failure simulation technique [20], and it has been widely used in the recent literature [4, 5, 18, 22, 24]. It is well known that multiaxial creep ductility depends on stress triaxiality (the ratio of the mean normal stress and equivalent stress) and can be obtained from a number of available creep void growth models [12,25-27] , but one of the notable models was proposed by Cocks and Ashby [27], given by Eq. (5): ∗
*.,
*., 2
= sinh '( )-.,./ /sinh '2 )-.,. 23 / 4
(5)
where ∗ and denotes the multiaxial and unaxial creep ductility, respectively, and n is the creep exponent, and the different value of n was used at different stress regime. A lot of experimental results have shown that the unaxial creep ductility depends on stress levels and was scattered [12, 21, 28], and both the elongation and reduction of areas can represent it [22]. The data of elongation and reduction of areas for P92 steel taken from NIMS materials database [29] was in a range of 0.09-0.36 and 0.1-0.91 from 40MPa to 160MPa at 650℃, respectively. In this study, for investigating the effects of initial crack positions and load levels on CCG behavior and facilitating the interpretation of the results, the unaxial creep ductility of the four materials was assumed to be the same value of 0.35. The crack growth length was calculated by the numbers of damaged regular elements. For CT specimen, the C* was calculated by following equations considering both the bending and tension in the specimen [30], and it has been used in recent literature [23, 31].
5 ∗ = -
==
678/7"
9: （;*<）
?
)= − .
(6)
(- )（-<⁄;)@- A- (*<⁄;) (-< ⁄;)- (*<⁄;)
（7）
C = -(-<⁄;)/(*<⁄;)
（8）
D = EF2⁄(G − ) + 1I + 1 − F2⁄(G − ) + 1I 9
（9）
where W is the specimen width, a is the crack length, P is the load, J is the net thickness, K/ ! is the load line displacement rate, and n is the creep exponent in Norton’s law, and the different value of n at different stress regime should be used.
3. Numerical simulation results and discussion For investigating the effects of initial crack positions and load levels on creep failure behavior of welded joints, the six initial cracks were set at different positions in the CT specimen of welded joint (Fig.2), and two load levels were analyzed. For different initial crack positions at the same load level, the creep failure behavior will be different due to the mismatch in creep properties of material zones around the crack. For the same initial crack position at different load levels, the creep failure behavior may also be different due to the difference in creep properties of materials at different stress levels (Fig.4). Thus, these different creep failure behaviors were simulated and analyzed by using 2RN model at two load levels. 3.1 Creep failure behavior in P92 welded joint at low load level Fig.5 shows the final creep damage contours and CCG paths for the six cracks at different positions in the welded joint at low load level of K=7MPa√m (K is initial stress intensity factor). It can be seen that the crack propagated nearly straight along initial crack plane for the FGHAZ/BM and FGHAZ/CGHAZ interface cracks (Figs.5(a) and (c)) and WM center crack (Fig.5(f)), and the damage mainly concentrated on the side of soft material (FGHAZ) for the two interface cracks. For the crack lying initially in the middle of FGHAZ, the crack jumped from initial crack plane to the FGHAZ/BM interface region and a second 10
crack (SC) formed after a short distance of linear extension (Fig.5 (b)). For the CGHAZ center crack and CGHAZ/WM interface crack, the SC also occurred in the soft FGHAZ of FGHAZ/CGHAZ interface (Figs.5 (d) and (e)).
(a)
(b)
(c)
(d)
(e)
(f)
Fig.5 The final damage contours (t/tr=1, tr is the rupture life) of CCG for six cracks at different positions at low load level of K= 7MPa√m , (a) FGHAZ/BM interface crack, (b) FGHAZ center crack, (c) FGHAZ/CGHAZ interface crack, (d) CGHAZ center crack, (e) CGHAZ/WM interface crack, (f) WM center crack, SDV1: damage; ICT: initial crack tip; CCT: current crack tip
Fig.6 shows the distribution of equivalent stress (Mises stress) with CCG for the CGHAZ center crack at K=7MPa√m. It can be seen that the maximum Mises stress around crack is below the transition stress of 2RN creep constitutive model for the four materials in 11
Fig.4 and Table 1. Thus, the creep deformation and damage accumulation around the crack should be determined by the low stress-regime creep constitutive in Fig.4 and Table 1. For the other cracks, the situations are similar to that of the CGHAZ center crack. Fig.4 shows that at low stress-regime, the difference of creep strain rate between the four materials is obvious. This means that the mismatch effect in creep properties between the four materials is significant, and the CCG behavior in Fig.5 should be mainly determined by the material constraint effect which is related to the mismatch effect and crack position. Because the occurrence of the SC (Figs.5 (b), (d) and (e)) during CCG process may bring difficulty for creep failure analyses and life assessments of welded joints, the mechanism is analyzed as follows for the typical CGHAZ center crack. Fig.7 shows the damage contours under K=7MPa√m at t/tr=0.896 (tr is the rupture time) for the CGHAZ center crack. It can be seen that a SC started to initiate in the soft FGHAZ of FGHAZ/CGHAZ interface at t/tr=0.896. The creep damage model in Eqs. (3) – (5) shows that high stress triaxiality and creep strain accumulation around cracks promote creep damage and crack initiation. Fig.8 shows distributions of stress triaxiality during CCG process for the CGHAZ center crack. It can be seen that the high stress triaxiality (Fig.8(a)) and high equivalent stress (Fig.6(a)) ahead of crack-tip of initial crack plane lead to the crack growing a short distance straight along the initial crack plane at the early stage of CCG. With redistribution of the stress and strain during crack growth, because the creep deformation in soft FGHAZ was constrained by the hard CGHAZ, the higher stress triaxiality appeared in the soft FGHAZ near FGHAZ/CGHAZ interface (Fig.8(b)). The higher stress triaxiality accelerates damage accumulation in the soft FGHAZ near FGHAZ/CGHAZ interface. When 12
the accumulated damage reached critical value in the soft FGHAZ, the SC would initiate at a certain location ((Fig.7). Then, it existed two cracks in the welded joint, and the two stress fields stacked, finally the two cracks coalesced together (Fig.5 (d)). For the crack lying in the middle of FGHAZ and the CGHAZ/WM interface at K=7MPa√m, the process of coalition between the crack of initial crack plane and the SC initiating in the soft FGHAZ near FGHAZ/BM or FGHAZ/CGHAZ interface was similar to that of the CGHAZ center crack. For the FGHAZ center crack in Fig.5 (b), the SC initiated in FGHAZ of FGHAZ/BM interface due to the higher constraint near FGHAZ/BM interface caused by the higher creep strength of BM than that of CGHAZ (Fig.4). For the other two interface cracks (FGHAZ/BM and FGHAZ/CGHAZ interface cracks), the cracks propagated straight in the soft FGHAZ along the interfaces due to the higher creep damage accumulation there during the whole CCG process. For the WM center crack, the crack also propagated straight in the WM due to the small material constraint effect caused by the larger distance from initial crack plane to FGHAZ/BM interface.
(a)
(b)
Fig.6 The Mises stress contours with CCG for CGHAZ center crack at K=7MPa√m, (a) t/tr=0.086, (b) t/tr=0.708, ICT: initial crack tip; CCT: current crack tip.
13
Fig.7 The damage contours for CGHAZ center crack at K=7MPa√m and t/tr=0.896, SDV1: damage; ICT： initial crack tip; CCT: current crack tip.
(a)
(b)
Fig.8 Stress triaxiality contours with CCG for the CGHAZ center crack at K=7Mpa√m (a) t/tr=0.086, (b) t/tr=0.708, SDV3: stress triaxiality; ICT: initial crack tip; CCT: current crack tip.
The simulation results with the occurrence of the SC (Figs.5 (b), (d) and (e)) during CCG process are consistent with some experimental results in the literature [7, 9], as shown in Fig.9. Fig. 9(a) shows that a SC formed in the soft typeIV region with starter notch in the middle of hard WM for P91 welded joint [7]. This case is similar to that in Fig.7 due to the hard and narrow WM produced by electron beam welding (EBW). The creep crack initiation and growth tests [9] for dissimilar metal welded joint of 1CrMoV/Alloy 617/Alloy 625 with the pre-crack in the middle of 1CrMoV HAZ also shows that the crack propagated both ahead of the starter notch and in soft 1CrMoV HAZ near the interface of 1CrMoV HAZ and Alloy 617 (creep hard material) due to high material constraint (Fig.9 (b)). The occurring mechanism of these SCs in experiments is similar to the analyses above. 14
It should be noted that the results in Fig.5 are those under plane strain condition, and they are basically consistent with the experimental results in Fig.9. This indicates that the experimental specimens of Fig.9 may approach the plane strain condition. The plane strain generally represents the highest out-of-plane constraint, and plane stress represents the lowest out-of-plane constraint [32]. The constraint of specimens with different thicknesses is located between plane strain and plane stress condition [32]. If the analyses of Fig.5 for low load level are conducted under plane stress condition, the results may be different from those under plane strain condition due to the different Mises stress and stress triaxiality distributions ahead of crack tips. This is related to the combining effects of out-of-plane constraint and material constraint on the CCG behavior of welded joints, and needs to be further studied.
(a)
(b)
Fig.9 The CCG paths for: (a) P91 electron beam welding (EBW) welded joint with starter notch in WM [7], (b) dissimilar metal welded joint of 1CrMoV/Alloy 617/Alloy 625 with the pre-crack in the middle of 1CrMoV HAZ [9]
3.2 Creep failure behavior in P92 welded joint at high load level Fig.10 shows the final damage contours and crack growth paths for the six cracks at different positions at relative higher load level (K=10MPa√m), it can be seen that all the cracks propagated straight along initial crack plane. 15
(a)
(b)
(c)
(d)
(e)
(f)
Fig.10 The final damage contours (t/tr=1, tr is the rupture time) of CCG for six cracks at different positions at high load level of K=10MPa√m, (a) FGHAZ/BM interface crack, (b) FGHAZ center crack, (c) FGHAZ/CGHAZ interface crack, (d) CGHAZ center crack, (e) CGHAZ/WM interface crack, (f) WM center crack, SDV1: damage; ICT: initial crack tip; CCT: current crack tip
Fig.11 shows the distributions of equivalent stress and stress triaxiality with CCG for the typical CGHAZ center crack at K=10MPa√m. It can be seen that the maximum Mises stress ahead of crack-tip of initial crack plane was above the transition stress of CGHAZ (88MPa) in Fig.4 and Table 1, but that near FGHAZ/CGHAZ interface was still below the transition stress (Fig.11(a)). Thus, the creep deformation and damage accumulation ahead of crack tip 16
and near FGHAZ/CGHAZ interface were determined by high stress-regime and low stress-regime creep constitutive, respectively. For the other cracks, the situations are similar to that of the CGHAZ center crack. Fig.4 shows that at high stress-regime, the difference of creep strain rate between the CGHAZ and FGHAZ is small. This indicates that the mismatch effect in creep properties between them is small, and the material constraint effect for causing higher stress triaxiality near the interface is also small. In this case, the higher Mises stress and stress triaxiality will mainly concentrate ahead of crack-tip of initial crack plane during the whole CCG process (Fig.11), and the crack propagated straight along the initial crack plane and the SC can’t form in the soft FGHAZ near FGHAZ/CGHAZ interface. The mechanism of CCG for the other cracks at high load level of K =10MPa√m is similar to that of the CGHAZ center crack.
(a)
(b)
Fig.11 The Mises stress contours (a) and stress triaxiality contours (b) for CGHAZ center crack at K=10MPa√m and t/tr=0.41, SDV3: stress triaxiality, ICT: initial crack tip, CCT: current crack tip
A comparison of CCG behavior at low load level (Fig.5) and high load level (Fig.10) shows that for some cracks with specific positions (FGHAZ center crack, CGHAZ center crack and CGHAZ/WM interface crack), the load level causes the change of CCG path due to the stress-regime dependent creep constitutive. At low stress regime, the significant mismatch effect in creep properties promotes the initiation and propagation of SC in the soft FGHAZ
17
side of interfaces which can cause changes of CCG rate and life. This will be analyzed in the following section. 3.3 Creep failure analysis and life assessment of cracks in P92 welded joint The relations between the CCG rate and C* (da/dt-C* curves) were numerically calculated for the six cracks at different load levels, as shown in Fig.12. The open points represent the CCG data after initiation of the SC for the crack positions forming a SC (FGHAZ center crack, CGHAZ center crack and CGHAZ/WM interface crack at K=7MPa√m), and the solid points were the data for the cracks propagating straight along initial crack plane. It can be seen that for the three cracks forming a SC, the CCG rate became much higher in the soft FGHAZ near the FGHAZ/BM or FGHAZ/CGHAZ interface than that in original crack plane due to high creep strain accumulation and high material constraint near the interfaces. The CCG data of SC at lower load levels lay above those at higher load levels for the same initial crack position. If the extrapolation of CCG rate at higher load levels (solid points) is used in creep life assessments at lower load levels for these cracks, the non-conservative (unsafe) results will be produced. It can also be seen from Fig.12 that the da/dt-C* curves are different for different initial crack positions due to different creep properties of materials around crack tip and the mismatch effect. The FGHAZ/BM interface crack and WM center crack have the highest and lowest CCG rate at a given value of C*, respectively, and those of other cracks are located in the middle.
18
Fig.12 The da/dt-C* curves for the six cracks at different load levels, the open and solid points represent the CCG data after initiation of SC and crack propagating straight along initial crack plane, respectively
The calculated relationship of crack length vs. time (∆a-t curves) for the cracks forming a SC (FGHAZ center crack, CGHAZ center crack and CGHAZ/WM interface crack) at K=7MPa√m is shown in Fig.13(a), and the open and solid points indicate the crack growth data before and after the initiation of the SC, respectively. It can be seen that the CCG time before initiation of the SC takes major portion of the total life, approximately 83.1%, 89.6% and 87.3% for the FGHAZ center crack, CGHAZ center crack and CGHAZ/WM interface crack, respectively, and the crack growth accelerated up to fracture as soon as the SC initiated
in the soft materials near interface. This result is consistent with the experimental results of Sugiura et al. [2, 6]. Therefore, for this type of cracks at low load level of K=7MPa√m, the rupture life is mainly determined by the incubation time of SC, and the incubation time should
be determined accurately to predict the rupture life of the welded joints. Fig.13 (b) shows ∆a-t curves for the three cracks in Fig.13 (a) at high load level of K=10MPa√m . The feature in Fig.13 (a) does not appear due to the crack just propagating along original crack plane. Thus, for some cracks at specific positions in welded joints, the effect of load levels needs to be considered in failure analysis and life assessments. 19
(a)
(b)
Fig.13 The ∆a-t curves for the three cracks with SC at different load levels, (a) K=7MPa√m, the open and
solid points indicate the data before and after initiation of the SC, respectively, (b) K=10MPa√m
All the above results show that the cracks at different positions in welded joints have
different CCG rate and rupture life at the same load level due to the different mismatch effects in creep properties of material zones around the crack. For some cracks with specific
positions, the load levels also influence CCG behavior and path. Therefore, in creep failure analyses and life assessments of welded joints, the effects of initial crack positions and load
levels should be fully considered.
4. Conclusion The finite element method (FEM) based on ductility exhaustion damage model coupled
with the stress-regime dependent creep constitutive model (2RN model) was used to investigate the creep failure behavior at different load levels for six initial cracks at different positions in P92 welded joints. The stress states and creep damage around cracks, CCG paths and rates and rupture life were calculated and analyzed, and the creep failure and life assessments of the welded joints were discussed. The main results obtained are as follows: (1) For some cracks with specific positions (FGHAZ center crack, CGHAZ center crack and CGHAZ/WM interface crack), the load level causes the change of CCG path due to the 20
stress-regime dependent creep constitutive. At low load level (low stress regime), the significant mismatch effect in creep properties promotes the initiation and propagation of SC in the soft FGHAZ side of interfaces. (2) For different initial crack positions, the da/dt-C* curves are different due to different creep properties of materials around cracks and the mismatch effects. The CCG data with SC at lower load levels lay above those at higher load levels for the same initial crack position. If the extrapolation of CCG rate from higher load levels is used in creep life assessment of a welded joint at lower load levels, the non-conservative (unsafe) results will be produced. (3) For the initial crack positions forming a SC at low load level of K=7MPa√m, the rupture life is mainly determined by the incubation time of the SC. (4) The initial crack positions and load levels influence creep failure and CCG behavior of welded joints. In creep failure analyses and life assessments of welded joints, the effects of initial crack positions and load levels should be fully considered.
Acknowledgments This work was financially supported by the Projects of the National Natural Science Foundation of China (51375165, 51325504).
Reference [1] 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 Pres Ves Pip 2013; 110: 66-71. [2] 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. [3] Segle P, Anderrson P，Samuelson LÅ. Numerical investigation of creep crack growth in 21
cross-weld CT specimens. Part I: influence of mismatch in creep deformation properties and notch tip location. Fatigue Fract Eng Mater Struct 1999; 23: 521-31. [4] Chen G, Wang GZ, Xuan FZ, Tu ST. Mismatch effect in creep properties on creep crack growth behavior in welded joints. Mater Des 2014; 23:600-608. [5] Saber M. Experimental and finite element studies of creep and creep crack growth in P91 and P92 weldments. PHD thesis; The University of Nottingham. 2011. [6] 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*, dδ/dt, K and Q* parameters. Eng Fract Mech 2007; 74: 868-81. [7] Dogan B. Creep deformation and failure assessment of steel weldments. In: Eighth international conference on creep and fatigue at elevated temperatures. SanAntonio, Texas, USA; 2007. [8] Tabuchi M, Hongo H, Watanabe T, Yokobori Jr AT. Creep crack growth analysis of welded joints for high Cr heat resisting steel. Journal of ASTM International 2006; 3: DOI: 10.1520/JAI13226. [9] Hosseini E, Holdsworth SR, Mazza E. Exploring the applicability of the LICON methodology for the creep assessment of a dissimilar metal weld. Int J Pres Ves Pip 2013; 111-112: 162-72. [10] Hosseini E, Holdsworth SR, Mazza E. Stress regime-dependent creep constitutive model considerations in finite element continuum damage mechanics. Int J Damage Mech 2013. 22: 1186-205. [11] Hosseini E, Holdsworth SR, Mazza E. Creep constitutive model considerations for 22
high-temperature finite element numerical simulations. J strain Anal Eng Des 2012. 47: 341-9. [12] Spindler MW. The multiaxial creep ductility of austenitic stainless steels. Fatigue Frac Eng Mater Struc 2004. 27: 273-81. [13] Tabuchi M, Yokobori Jr AT, Sugiura R, Yatomi M, Fuji A, Kobayashi K. Results of a Japanese round robin program for creep crack growth using Gr.92 steel welds. Eng Fract Mech 2010; 77: 3066-76. [14] Watanabe T, Tabuchi M, Yamazaki M, Hongo H, Tanabe T. Creep damage evaluation of 9Cr–1Mo–V–Nb steel welded joints showing Type IV fracture. Int J Pres Ves Pip 2006. 83: 63-71. [15] Mayr P, Mitsche S, Cerjak H, Allen SM. The impact of weld metal creep strength on the overall creep strength of 9% Cr steel weldments. J Eng Mater Technol 2011. 133: 21011 (1-7). [16] Samuel EI, Choudhary BK, Palaparti DPR, Mathew MD. Creep deformation and rupture behavior of P92 steel at 923K. Procdia Eng 2013. 55: 64-9. [17] Hosseini E, Holdsworth SR, Mazza E. The LICON methodology for predicting long-time uniaxial creep rupture strength of materials. Int J Pres Ves Pip 2013; 111-112: 27-35. [18] Zhang JW, Wang GZ, Xuan FZ, Tu ST. The influence of stress-regime dependent creep model and ductility in the prediction of creep crack growth rate in Cr-Mo-V steel, Mater. Desi. 2014, accepted. [19] Mehmanparast A, Davies CM, Webster GA, Nikbin KM. Creep crack growth rate
23
predictions in 316H steel using stress dependent creep ductility. Mater High Temp 2014. 31: 84-94. [20] Hibbitt, Karlsson & Sorensen. ABAQUS User’s Manual, Version 6.10; 2011. [21] Yatomi M, Nikbin K, O’Dowd NP. Creep crack growth prediction using a damage based approach. Int J Pres Ves Pip 2003; 80: 573-83. [22] Oh CS, Kim NH，Kim YJ, Davies CM, Nikbin KM，Dean D. Creep failure simulations of 316H at 550℃: Part I – A method and validation. Eng Fract Mech 2011. 78: 2966-77. [23] Yatomi M, Tabuchi M. Issues relating to numerical modelling of creep crack growth. Eng Fract Mech 2010; 77: 3043-52. [24] Kim NH, Oh CS, Kim YJ, Davies CM, Nikbin KM, Dean DW. Creep failure simulations of 316H at 550℃: Part II – Effects of specimen geometry and loading mode. Eng Fract Mech 2013. 105: 169-81. [25] Manjoine MJ. Creep rupture behavior of weldments. Welding J 1982. 61: 50-7. [26] Rice JR, Tracey DM. On ductile enlargement of voids in traxial stress fields. J Mech Phys Solids 1969. 17: 201-17. [27] Cocks ACF，Ashby MF. Intergranular fracture during power-law creep under multiaxial stresses. Metal Sci 1980; 14: 395-402. [28] Binda L, Holdsworth SR, Mazza E. The exhaustion of creep ductility in 1CrMoV steel. Int J Pres Ves Pip 2010; 87: 319-25. [29] Tokyo (Internet): NIMS materials database data sheets 51A, data sheets on creep- [cited 2003 Aug]. Available from: http://mits.nims.go.jp/index_en.html. [30] Ernst HA. Unified solution for J ranging continuously from pure bending to pure tension. 24
ASTM STP 791, Fract Mech. ASTM. 1983: 499–519. [31] Tabuchi M, Yokobori Jr AT, Sugiura R, Yatomi M, Kobayashi K. Evaluation of creep crack growth properties of Gr. 92 steel weldment. Strength, Fracture, Complexity 2011; 7: 137-46. [32] 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 Pres Ves Pip 2012; 96-97:78-89.
25
Figure and Table Captions Fig.1. The geometry and dimensions of the CT specimen of P92 welded joint [2] Fig.2. The six initial crack positions in P92 welded joint Fig.3. The FE model of the FGHAZ center crack specimen, (a) meshes of whole model, (b) local meshes around the crack tip and near the interface between weldment constituents Fig.4. Relation between minimum creep rate and unaxial tension stress for different regions (BM, WM, FGHAZ and CGHAZ) in the P92 steel welded joint at 650℃ [13, 23] Fig.5. The final damage contours (t/tr=1, tr is the rupture life) of CCG for six cracks at different positions at low load level of K=7MPa√m, (a) FGHAZ/BM interface crack, (b) FGHAZ center crack, (c) FGHAZ/CGHAZ interface crack, (d) CGHAZ center crack, (e) CGHAZ/WM interface crack, (f) WM center crack, SDV1: damage; ICT: initial crack tip; CCT: current crack tip. Fig.6. The Mises stress contours with CCG for CGHAZ center crack at K=7MPa√m, (a) t/tr=0.086, (b) t/tr=0.708, ICT: initial crack tip; CCT: current crack tip. Fig.7. The damage contours for CGHAZ center crack at K=7MPa√m and t/tr=0.896, SDV1: damage; ICT：initial crack tip; CCT: current crack tip. Fig.8. Stress triaxiality contours with CCG for the CGHAZ center crack at K=7Mpa√m (a) t/tr=0.086, (b) t/tr=0.708, SDV3: stress triaxiality; ICT: initial crack tip; CCT: current crack tip. Fig.9. The CCG paths for: (a) P91 electron beam welding (EBW) welded joint with starter notch in WM [7], (b) dissimilar metal welded joint of 1CrMoV/Alloy 617/Alloy 625 with the pre-crack in the middle of 1CrMoV HAZ [9] 26
Fig.10. The final damage contours (t/tr=1, tr is the rupture time) of CCG for six cracks at different positions at high load level of K=10MPa√m, (a) FGHAZ/BM interface crack, (b) FGHAZ center crack, (c) FGHAZ/CGHAZ interface crack, (d) CGHAZ center crack, (e) CGHAZ/WM interface crack, (f) WM center crack, SDV1: damage; ICT: initial crack tip; CCT: current crack tip Fig.11. The Mises stress contours (a) and stress triaxiality contours (b) for CGHAZ center crack at K=10MPa√m and t/tr=0.41, SDV3: stress triaxiality, ICT: initial crack tip, CCT: current crack tip Fig.12. The da/dt-C* curves for the six cracks at different load levels, the open and solid points represent the CCG data after initiation of SC and crack propagating straight along initial crack plane, respectively. Fig.13. The ∆a-t curves for the three cracks with SC at different load levels, (a) K=7MPa√m, the open and solid points indicate the data before and after initiation of the SC, respectively, (b) K=10MPa√m Table.1 Material properties for different regions (BM, WM, FGHAZ and CGHAZ) in P92 welded joint at different stress levels at 650℃ [2, 23]
27
Highlights > Crack position and load level cause change of creep failure behavior in welded joint. > Mechanism of this change was investigated by stress-regime dependent creep model. > Creep rupture life is mainly determined by incubation time of second crack at low load. > Effects of crack position and load level on creep life need to be fully considered.
28
S1350-6307(14)00305-7 http://dx.doi.org/10.1016/j.engfailanal.2014.10.005 EFA 2423
To appear in:
Engineering Failure Analysis
Received Date: Revised Date: Accepted Date:
6 June 2014 8 October 2014 9 October 2014
Please cite this article as: Chen, G., Wang, G.Z., Zhang, J.W., Xuan, F.Z., Tu, S.T., Effects of initial crack positions and load levels on creep failure behavior in P92 steel welded joint, Engineering Failure Analysis (2014), doi: http:// dx.doi.org/10.1016/j.engfailanal.2014.10.005
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Effects of initial crack positions and load levels on creep failure behavior in P92 steel welded joint G. Chen, G.Z. Wang*, J.W. Zhang, 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
Abstract: The finite element method based on ductility exhaustion damage model coupled with the stress-regime dependent creep constitutive model was used to investigate creep failure behavior at different load levels for six initial cracks at different positions in P92 welded joints. The stress states and creep damage around cracks, creep crack growth (CCG) paths and rates and rupture life have been calculated and analyzed, and the creep failure and life assessments for welded joints were discussed. The results show that for some cracks with specific positions in the welded joint, load level causes the change of CCG path due to the stress-regime dependent creep constitutive. At low load level, the significant mismatch effect in creep properties promotes the initiation and propagation of second cracks in soft materials near interfaces, and the creep rupture life is mainly determined by the incubation time of the second cracks. This result is confirmed by similar experimental observations in the literature, and the mechanism was analyzed. For the initial crack positions with a second crack, if the extrapolation of CCG rate from higher load levels is used in creep life assessment of a welded joint at lower load levels, the non-conservative (unsafe) results will be produced. In creep failure analyses and life assessments of welded joints, the effects of initial crack positions and load levels should be fully considered. Keywords: creep failure, welded joint, initial crack position, load level, creep crack growth, second crack. Corresponding author. Tel.: +86 21 64252681; fax: +86 21 64252681. E-mail address: [email protected] (Guozhen Wang). 1
1. Introduction Many experiments and theoretical evidences have shown that the multi-axial stress state ahead of crack tip or near the interface between weldment constituents due to the constraint of deformation among base metal (BM), weld metal (WM), coarse grained heat affected zone (CGHAZ) and fine grained heat affect zone (FGHAZ) plays an important role on creep failure behavior in welded joints at high temperatures [1, 2]. Experience shows that the cracks may exist anywhere in a welded joint under different load levels, and both the creep deformation properties of the zone containing the crack and those of the surrounding materials influence the creep damage and creep crack growth (CCG) paths in welded joints [3, 4]. Thus, the cracks at different positions in a welded joint would have different failure behavior. Such as, the cracks laid in the type IV region still stayed in this region, and which is the most severe form of the cracks [5]. But metallurgical observation showed 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 with a constant CCG rate using about 80% of the total rupture life [2, 6]. Similarly, a second crack (SC) formed in the soft type IV region with starter notch in the hard WM and BM in P91 [7] and P122 [8] welded joints, respectively. The creep crack initiation tests [9] for the dissimilar welded joint of 1CrMoV/Alloy 617/Alloy 625 with the pre-crack in the middle of 1CrMoV HAZ also showed that the crack propagated both ahead of starter notch and in 1CrMoV HAZ near 1CrMoV HAZ/Alloy 617 (with higher creep strength) interface where had high constraint. The experiments and theoretical evidences also show that creep deformation and fracture mechanism are different at different stress levels for alloy steels [10-12]. The difference of 2
creep deformation properties between weldment constituents was also different at different stress regime [13]. Therefore, the load levels may also have important effect on failure behavior of welded joints. Such as, experiments showed that stress levels had an obvious effect on the rupture location for the unaxial tension tests of P91 welded joints, and the rupture location changed from WM or BM at high stress (short time) to HAZ at low stress (long time). Experiments also showed that the range of transition stress of failure location from WM to HAZ increased with increasing creep strength of WM for P911 unaxial welded joints at 600℃[15]. To better understand the mechanism of effects of initial crack positions and load levels on CCG behavior and to conduct accurate creep failure analyses and life assessments, it needs systematic mechanical analyses and investigations for failure behavior of welded joints. The numerical method based on creep damage model may provide a suitable tool for these investigations. The two-regime Norton (2RN) creep model which is described by two different Norton’s equations with different parameters provides a bi-linear formulation for high- and low-stress regimes [13, 16-19]. Recently, this 2RN creep model has been used in the creep stress-state analysis in a loaded CT specimen for predicting long-time unaxial creep rupture strength of materials [17], and it also has been used in the simulation of CCG rate in the homogenous Cr-Mo-V steel [18] and 316H steel [19]. The use of the 2RN creep model in the CCG simulations in welded joints may reveal the effects and mechanism of load levels on failure behavior of cracks at different positions. In this work，the finite element method (FEM) based on ductility exhaustion damage model coupled with the stress-regime dependent creep constitutive model (2RN model) was used to investigate creep failure behavior at different load levels (initial stress intensity factors) 3
for six initial cracks at different positions in P92 welded joints. The stress states and creep damage around cracks, CCG paths and rates and rupture life were calculated and analyzed, and the creep failure and life assessments of the welded joints were discussed.
2. Finite element models and numerical procedures 2.1 Finite element models The compact tension (CT) specimens of the P92 welded joint were used in the FE analyses with ABAQUS code [20]. The welded joint is simplified to be composed of four materials, i.e. BM, WM, FGHAZ and CGHAZ. The geometry and dimensions of the CT specimen are taken to be the same as those of the experiments in Ref [2], as shown in Fig.1. The width W of the CT specimen is 50.8mm and initial crack length a0 is 26.4mm (a0/W =0.52). The width of the WM, FGHAZ and CGHAZ is 20mm, 1.2mm and 1.2mm, respectively. To investigate the effect of initial crack positions on creep failure behavior of the welded joint，the six initial cracks at different positions in the welded joint were modeled, including three center cracks and three interface cracks. The three center cracks represent that the initial crack lies in the middle of FGHAZ, CGHAZ and WM, respectively. The three interface cracks refer to that the initial cracks exist in the FGHAZ/BM, FGHAZ/CGHAZ and CGHAZ/WM interfaces, respectively. Fig.2 shows the six initial crack positions, and the typical FGHAZ/CGHAZ interface crack can be seen in Fig.1.
4
Fig.1. The geometry and dimensions of the CT specimen of P92 welded joint [2]
Fig.2. The six initial crack positions in P92 welded joint
For the WM center crack, only one half of the specimen was modeled due to symmetry, while whole CT specimens were modeled for other cracks. 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 four-node plane strain element (CPE4) was used for all FE models. A sharp crack tip with 0.009°angle was used to represent the fatigue pre-crack. The mesh dependency analyses in the CCG simulations have been carried out by Yatomi et al. [21] and Oh et al. [22] for the mesh size from 50µm to 250µm. The results show that the creep crack initiation time decreases and the CCG rate slightly increases 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 50µm×50µm were used around 5
crack tip and near interfaces between weldment constituents. The whole and local meshes for the FGHAZ center crack are typically shown in Fig.3, and the whole FE model includes 27,615 elements and 27,816 nodes.
(a)
(b)
Fig.3 The FE model of the FGHAZ center crack specimen, (a) meshes of whole model, (b) local meshes around the crack tip and near the interface between weldment constituents
2.2 Materials and creep constitutive models of the welded joint The ASME Grade P92 steel was chosen for BM. The elastic-plastic-creep material model was used in CCG simulations. The true stress and true plastic strain relation of the steel at 650℃ is taken from Ref. [6], and is approximated by the following equation: = ( + )
(1)
where c, a and α are constants (c = 162, a = 0.32×10-2, α = 0.105), and is true plastic strain. The true stress and true plastic strain data of the WM, FGHAZ and CGHAZ were assumed to be the same as those of the BM. The un-axial creep tests of the four materials show that the creep deformation obeys two-regime Norton’ (2RN) power law [13, 23], as shown in Fig 4. The 2RN creep constitutive model is composed of low-stress regime and high-stress regime Norton’ model, as shown by 6
Eq. (2), =
（ ）
（ ）
（2）
where the is the transition stress，the A1 and n1 are creep coefficient and exponent in the Norton’ model for low-stress regime，and the A2 and n2 are those for high-stress regime. The parameters of the 2RN model and elastic modulus of the four materials at 650℃ are taken from Refs. [2, 23], and they are listed in Table 1. Because the transition stress σ0 and n2 of the CGHAZ are not available, they were assumed to be the same as those of the FGHAZ. It also can be seen from Fig.4 that the FGHAZ has the highest creep strain rate at a given stress level, so it is softer than the other three materials. The 2RN creep constitutive models (Eq. (2)) of the four materials were implemented in the ABAQUS code by using the user subroutine CREEP [20].
Fig.4 Relation between minimum creep rate and unaxial tension stress for different regions (BM, WM, FGHAZ and CGHAZ) in the P92 steel welded joint at 650℃ [13, 23]
7
Table.1 Material properties for different regions (BM, WM, FGHAZ and CGHAZ) in P92 welded joint at different stress levels at 650℃ [2, 23] Material
A (MPa-nh-1)
n
σ (MPa)
E (GPa)
WM
7.28e-16
4.7
σ ≤90
92
2.57E-32
13.12
σ>90
3.77E-19
6.71
σ≤113
2.57E-32
13.12
σ>113
8.30E-13
3.68
σ≤88
3.68E-31
13.12
σ>88
2.35E-16
5.35
σ≤88
1.83E-31
13.12
σ>88
BM
FGHAZ
CGHAZ
85
88
90
2.3 Creep damage model and crack growth simulation The ductility exhaustion model was used to account for the creep damage accumulation, and then to simulate creep crack propagation [4, 18, 19, 21-24]. The rate of damage was defined by the ratio of creep strain rate and multiaxial creep ductility ∗ , as follows:
= ∗
(3)
And the total damage at any instant is the integration of the damage rate in Eq. (3) up to that time [21]: "
"
= ! = ∗ !
(4)
where is the creep damage rate, and ∗ is the equivalent creep strain rate and multi-axial creep ductility, respectively. The value of is in a range of 0-1.0. When at a Gauss point reaches 1.0, local failure occurs and progressive cracking is simulated. Thus, load-carrying capacity of the point is reduced to near zero by reducing the elastic modulus to a very small value (1E-6MPa in this work). The ABAQUS user subroutine USDFLD was 8
used to embody this failure simulation technique [20], and it has been widely used in the recent literature [4, 5, 18, 22, 24]. It is well known that multiaxial creep ductility depends on stress triaxiality (the ratio of the mean normal stress and equivalent stress) and can be obtained from a number of available creep void growth models [12,25-27] , but one of the notable models was proposed by Cocks and Ashby [27], given by Eq. (5): ∗
*.,
*., 2
= sinh '( )-.,./ /sinh '2 )-.,. 23 / 4
(5)
where ∗ and denotes the multiaxial and unaxial creep ductility, respectively, and n is the creep exponent, and the different value of n was used at different stress regime. A lot of experimental results have shown that the unaxial creep ductility depends on stress levels and was scattered [12, 21, 28], and both the elongation and reduction of areas can represent it [22]. The data of elongation and reduction of areas for P92 steel taken from NIMS materials database [29] was in a range of 0.09-0.36 and 0.1-0.91 from 40MPa to 160MPa at 650℃, respectively. In this study, for investigating the effects of initial crack positions and load levels on CCG behavior and facilitating the interpretation of the results, the unaxial creep ductility of the four materials was assumed to be the same value of 0.35. The crack growth length was calculated by the numbers of damaged regular elements. For CT specimen, the C* was calculated by following equations considering both the bending and tension in the specimen [30], and it has been used in recent literature [23, 31].
5 ∗ = -
==
678/7"
9: （;*<）
?
)= − .
(6)
(- )（-<⁄;)@- A- (*<⁄;) (-< ⁄;)- (*<⁄;)
（7）
C = -(-<⁄;)/(*<⁄;)
（8）
D = EF2⁄(G − ) + 1I + 1 − F2⁄(G − ) + 1I 9
（9）
where W is the specimen width, a is the crack length, P is the load, J is the net thickness, K/ ! is the load line displacement rate, and n is the creep exponent in Norton’s law, and the different value of n at different stress regime should be used.
3. Numerical simulation results and discussion For investigating the effects of initial crack positions and load levels on creep failure behavior of welded joints, the six initial cracks were set at different positions in the CT specimen of welded joint (Fig.2), and two load levels were analyzed. For different initial crack positions at the same load level, the creep failure behavior will be different due to the mismatch in creep properties of material zones around the crack. For the same initial crack position at different load levels, the creep failure behavior may also be different due to the difference in creep properties of materials at different stress levels (Fig.4). Thus, these different creep failure behaviors were simulated and analyzed by using 2RN model at two load levels. 3.1 Creep failure behavior in P92 welded joint at low load level Fig.5 shows the final creep damage contours and CCG paths for the six cracks at different positions in the welded joint at low load level of K=7MPa√m (K is initial stress intensity factor). It can be seen that the crack propagated nearly straight along initial crack plane for the FGHAZ/BM and FGHAZ/CGHAZ interface cracks (Figs.5(a) and (c)) and WM center crack (Fig.5(f)), and the damage mainly concentrated on the side of soft material (FGHAZ) for the two interface cracks. For the crack lying initially in the middle of FGHAZ, the crack jumped from initial crack plane to the FGHAZ/BM interface region and a second 10
crack (SC) formed after a short distance of linear extension (Fig.5 (b)). For the CGHAZ center crack and CGHAZ/WM interface crack, the SC also occurred in the soft FGHAZ of FGHAZ/CGHAZ interface (Figs.5 (d) and (e)).
(a)
(b)
(c)
(d)
(e)
(f)
Fig.5 The final damage contours (t/tr=1, tr is the rupture life) of CCG for six cracks at different positions at low load level of K= 7MPa√m , (a) FGHAZ/BM interface crack, (b) FGHAZ center crack, (c) FGHAZ/CGHAZ interface crack, (d) CGHAZ center crack, (e) CGHAZ/WM interface crack, (f) WM center crack, SDV1: damage; ICT: initial crack tip; CCT: current crack tip
Fig.6 shows the distribution of equivalent stress (Mises stress) with CCG for the CGHAZ center crack at K=7MPa√m. It can be seen that the maximum Mises stress around crack is below the transition stress of 2RN creep constitutive model for the four materials in 11
Fig.4 and Table 1. Thus, the creep deformation and damage accumulation around the crack should be determined by the low stress-regime creep constitutive in Fig.4 and Table 1. For the other cracks, the situations are similar to that of the CGHAZ center crack. Fig.4 shows that at low stress-regime, the difference of creep strain rate between the four materials is obvious. This means that the mismatch effect in creep properties between the four materials is significant, and the CCG behavior in Fig.5 should be mainly determined by the material constraint effect which is related to the mismatch effect and crack position. Because the occurrence of the SC (Figs.5 (b), (d) and (e)) during CCG process may bring difficulty for creep failure analyses and life assessments of welded joints, the mechanism is analyzed as follows for the typical CGHAZ center crack. Fig.7 shows the damage contours under K=7MPa√m at t/tr=0.896 (tr is the rupture time) for the CGHAZ center crack. It can be seen that a SC started to initiate in the soft FGHAZ of FGHAZ/CGHAZ interface at t/tr=0.896. The creep damage model in Eqs. (3) – (5) shows that high stress triaxiality and creep strain accumulation around cracks promote creep damage and crack initiation. Fig.8 shows distributions of stress triaxiality during CCG process for the CGHAZ center crack. It can be seen that the high stress triaxiality (Fig.8(a)) and high equivalent stress (Fig.6(a)) ahead of crack-tip of initial crack plane lead to the crack growing a short distance straight along the initial crack plane at the early stage of CCG. With redistribution of the stress and strain during crack growth, because the creep deformation in soft FGHAZ was constrained by the hard CGHAZ, the higher stress triaxiality appeared in the soft FGHAZ near FGHAZ/CGHAZ interface (Fig.8(b)). The higher stress triaxiality accelerates damage accumulation in the soft FGHAZ near FGHAZ/CGHAZ interface. When 12
the accumulated damage reached critical value in the soft FGHAZ, the SC would initiate at a certain location ((Fig.7). Then, it existed two cracks in the welded joint, and the two stress fields stacked, finally the two cracks coalesced together (Fig.5 (d)). For the crack lying in the middle of FGHAZ and the CGHAZ/WM interface at K=7MPa√m, the process of coalition between the crack of initial crack plane and the SC initiating in the soft FGHAZ near FGHAZ/BM or FGHAZ/CGHAZ interface was similar to that of the CGHAZ center crack. For the FGHAZ center crack in Fig.5 (b), the SC initiated in FGHAZ of FGHAZ/BM interface due to the higher constraint near FGHAZ/BM interface caused by the higher creep strength of BM than that of CGHAZ (Fig.4). For the other two interface cracks (FGHAZ/BM and FGHAZ/CGHAZ interface cracks), the cracks propagated straight in the soft FGHAZ along the interfaces due to the higher creep damage accumulation there during the whole CCG process. For the WM center crack, the crack also propagated straight in the WM due to the small material constraint effect caused by the larger distance from initial crack plane to FGHAZ/BM interface.
(a)
(b)
Fig.6 The Mises stress contours with CCG for CGHAZ center crack at K=7MPa√m, (a) t/tr=0.086, (b) t/tr=0.708, ICT: initial crack tip; CCT: current crack tip.
13
Fig.7 The damage contours for CGHAZ center crack at K=7MPa√m and t/tr=0.896, SDV1: damage; ICT： initial crack tip; CCT: current crack tip.
(a)
(b)
Fig.8 Stress triaxiality contours with CCG for the CGHAZ center crack at K=7Mpa√m (a) t/tr=0.086, (b) t/tr=0.708, SDV3: stress triaxiality; ICT: initial crack tip; CCT: current crack tip.
The simulation results with the occurrence of the SC (Figs.5 (b), (d) and (e)) during CCG process are consistent with some experimental results in the literature [7, 9], as shown in Fig.9. Fig. 9(a) shows that a SC formed in the soft typeIV region with starter notch in the middle of hard WM for P91 welded joint [7]. This case is similar to that in Fig.7 due to the hard and narrow WM produced by electron beam welding (EBW). The creep crack initiation and growth tests [9] for dissimilar metal welded joint of 1CrMoV/Alloy 617/Alloy 625 with the pre-crack in the middle of 1CrMoV HAZ also shows that the crack propagated both ahead of the starter notch and in soft 1CrMoV HAZ near the interface of 1CrMoV HAZ and Alloy 617 (creep hard material) due to high material constraint (Fig.9 (b)). The occurring mechanism of these SCs in experiments is similar to the analyses above. 14
It should be noted that the results in Fig.5 are those under plane strain condition, and they are basically consistent with the experimental results in Fig.9. This indicates that the experimental specimens of Fig.9 may approach the plane strain condition. The plane strain generally represents the highest out-of-plane constraint, and plane stress represents the lowest out-of-plane constraint [32]. The constraint of specimens with different thicknesses is located between plane strain and plane stress condition [32]. If the analyses of Fig.5 for low load level are conducted under plane stress condition, the results may be different from those under plane strain condition due to the different Mises stress and stress triaxiality distributions ahead of crack tips. This is related to the combining effects of out-of-plane constraint and material constraint on the CCG behavior of welded joints, and needs to be further studied.
(a)
(b)
Fig.9 The CCG paths for: (a) P91 electron beam welding (EBW) welded joint with starter notch in WM [7], (b) dissimilar metal welded joint of 1CrMoV/Alloy 617/Alloy 625 with the pre-crack in the middle of 1CrMoV HAZ [9]
3.2 Creep failure behavior in P92 welded joint at high load level Fig.10 shows the final damage contours and crack growth paths for the six cracks at different positions at relative higher load level (K=10MPa√m), it can be seen that all the cracks propagated straight along initial crack plane. 15
(a)
(b)
(c)
(d)
(e)
(f)
Fig.10 The final damage contours (t/tr=1, tr is the rupture time) of CCG for six cracks at different positions at high load level of K=10MPa√m, (a) FGHAZ/BM interface crack, (b) FGHAZ center crack, (c) FGHAZ/CGHAZ interface crack, (d) CGHAZ center crack, (e) CGHAZ/WM interface crack, (f) WM center crack, SDV1: damage; ICT: initial crack tip; CCT: current crack tip
Fig.11 shows the distributions of equivalent stress and stress triaxiality with CCG for the typical CGHAZ center crack at K=10MPa√m. It can be seen that the maximum Mises stress ahead of crack-tip of initial crack plane was above the transition stress of CGHAZ (88MPa) in Fig.4 and Table 1, but that near FGHAZ/CGHAZ interface was still below the transition stress (Fig.11(a)). Thus, the creep deformation and damage accumulation ahead of crack tip 16
and near FGHAZ/CGHAZ interface were determined by high stress-regime and low stress-regime creep constitutive, respectively. For the other cracks, the situations are similar to that of the CGHAZ center crack. Fig.4 shows that at high stress-regime, the difference of creep strain rate between the CGHAZ and FGHAZ is small. This indicates that the mismatch effect in creep properties between them is small, and the material constraint effect for causing higher stress triaxiality near the interface is also small. In this case, the higher Mises stress and stress triaxiality will mainly concentrate ahead of crack-tip of initial crack plane during the whole CCG process (Fig.11), and the crack propagated straight along the initial crack plane and the SC can’t form in the soft FGHAZ near FGHAZ/CGHAZ interface. The mechanism of CCG for the other cracks at high load level of K =10MPa√m is similar to that of the CGHAZ center crack.
(a)
(b)
Fig.11 The Mises stress contours (a) and stress triaxiality contours (b) for CGHAZ center crack at K=10MPa√m and t/tr=0.41, SDV3: stress triaxiality, ICT: initial crack tip, CCT: current crack tip
A comparison of CCG behavior at low load level (Fig.5) and high load level (Fig.10) shows that for some cracks with specific positions (FGHAZ center crack, CGHAZ center crack and CGHAZ/WM interface crack), the load level causes the change of CCG path due to the stress-regime dependent creep constitutive. At low stress regime, the significant mismatch effect in creep properties promotes the initiation and propagation of SC in the soft FGHAZ
17
side of interfaces which can cause changes of CCG rate and life. This will be analyzed in the following section. 3.3 Creep failure analysis and life assessment of cracks in P92 welded joint The relations between the CCG rate and C* (da/dt-C* curves) were numerically calculated for the six cracks at different load levels, as shown in Fig.12. The open points represent the CCG data after initiation of the SC for the crack positions forming a SC (FGHAZ center crack, CGHAZ center crack and CGHAZ/WM interface crack at K=7MPa√m), and the solid points were the data for the cracks propagating straight along initial crack plane. It can be seen that for the three cracks forming a SC, the CCG rate became much higher in the soft FGHAZ near the FGHAZ/BM or FGHAZ/CGHAZ interface than that in original crack plane due to high creep strain accumulation and high material constraint near the interfaces. The CCG data of SC at lower load levels lay above those at higher load levels for the same initial crack position. If the extrapolation of CCG rate at higher load levels (solid points) is used in creep life assessments at lower load levels for these cracks, the non-conservative (unsafe) results will be produced. It can also be seen from Fig.12 that the da/dt-C* curves are different for different initial crack positions due to different creep properties of materials around crack tip and the mismatch effect. The FGHAZ/BM interface crack and WM center crack have the highest and lowest CCG rate at a given value of C*, respectively, and those of other cracks are located in the middle.
18
Fig.12 The da/dt-C* curves for the six cracks at different load levels, the open and solid points represent the CCG data after initiation of SC and crack propagating straight along initial crack plane, respectively
The calculated relationship of crack length vs. time (∆a-t curves) for the cracks forming a SC (FGHAZ center crack, CGHAZ center crack and CGHAZ/WM interface crack) at K=7MPa√m is shown in Fig.13(a), and the open and solid points indicate the crack growth data before and after the initiation of the SC, respectively. It can be seen that the CCG time before initiation of the SC takes major portion of the total life, approximately 83.1%, 89.6% and 87.3% for the FGHAZ center crack, CGHAZ center crack and CGHAZ/WM interface crack, respectively, and the crack growth accelerated up to fracture as soon as the SC initiated
in the soft materials near interface. This result is consistent with the experimental results of Sugiura et al. [2, 6]. Therefore, for this type of cracks at low load level of K=7MPa√m, the rupture life is mainly determined by the incubation time of SC, and the incubation time should
be determined accurately to predict the rupture life of the welded joints. Fig.13 (b) shows ∆a-t curves for the three cracks in Fig.13 (a) at high load level of K=10MPa√m . The feature in Fig.13 (a) does not appear due to the crack just propagating along original crack plane. Thus, for some cracks at specific positions in welded joints, the effect of load levels needs to be considered in failure analysis and life assessments. 19
(a)
(b)
Fig.13 The ∆a-t curves for the three cracks with SC at different load levels, (a) K=7MPa√m, the open and
solid points indicate the data before and after initiation of the SC, respectively, (b) K=10MPa√m
All the above results show that the cracks at different positions in welded joints have
different CCG rate and rupture life at the same load level due to the different mismatch effects in creep properties of material zones around the crack. For some cracks with specific
positions, the load levels also influence CCG behavior and path. Therefore, in creep failure analyses and life assessments of welded joints, the effects of initial crack positions and load
levels should be fully considered.
4. Conclusion The finite element method (FEM) based on ductility exhaustion damage model coupled
with the stress-regime dependent creep constitutive model (2RN model) was used to investigate the creep failure behavior at different load levels for six initial cracks at different positions in P92 welded joints. The stress states and creep damage around cracks, CCG paths and rates and rupture life were calculated and analyzed, and the creep failure and life assessments of the welded joints were discussed. The main results obtained are as follows: (1) For some cracks with specific positions (FGHAZ center crack, CGHAZ center crack and CGHAZ/WM interface crack), the load level causes the change of CCG path due to the 20
stress-regime dependent creep constitutive. At low load level (low stress regime), the significant mismatch effect in creep properties promotes the initiation and propagation of SC in the soft FGHAZ side of interfaces. (2) For different initial crack positions, the da/dt-C* curves are different due to different creep properties of materials around cracks and the mismatch effects. The CCG data with SC at lower load levels lay above those at higher load levels for the same initial crack position. If the extrapolation of CCG rate from higher load levels is used in creep life assessment of a welded joint at lower load levels, the non-conservative (unsafe) results will be produced. (3) For the initial crack positions forming a SC at low load level of K=7MPa√m, the rupture life is mainly determined by the incubation time of the SC. (4) The initial crack positions and load levels influence creep failure and CCG behavior of welded joints. In creep failure analyses and life assessments of welded joints, the effects of initial crack positions and load levels should be fully considered.
Acknowledgments This work was financially supported by the Projects of the National Natural Science Foundation of China (51375165, 51325504).
Reference [1] 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 Pres Ves Pip 2013; 110: 66-71. [2] 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. [3] Segle P, Anderrson P，Samuelson LÅ. Numerical investigation of creep crack growth in 21
cross-weld CT specimens. Part I: influence of mismatch in creep deformation properties and notch tip location. Fatigue Fract Eng Mater Struct 1999; 23: 521-31. [4] Chen G, Wang GZ, Xuan FZ, Tu ST. Mismatch effect in creep properties on creep crack growth behavior in welded joints. Mater Des 2014; 23:600-608. [5] Saber M. Experimental and finite element studies of creep and creep crack growth in P91 and P92 weldments. PHD thesis; The University of Nottingham. 2011. [6] 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*, dδ/dt, K and Q* parameters. Eng Fract Mech 2007; 74: 868-81. [7] Dogan B. Creep deformation and failure assessment of steel weldments. In: Eighth international conference on creep and fatigue at elevated temperatures. SanAntonio, Texas, USA; 2007. [8] Tabuchi M, Hongo H, Watanabe T, Yokobori Jr AT. Creep crack growth analysis of welded joints for high Cr heat resisting steel. Journal of ASTM International 2006; 3: DOI: 10.1520/JAI13226. [9] Hosseini E, Holdsworth SR, Mazza E. Exploring the applicability of the LICON methodology for the creep assessment of a dissimilar metal weld. Int J Pres Ves Pip 2013; 111-112: 162-72. [10] Hosseini E, Holdsworth SR, Mazza E. Stress regime-dependent creep constitutive model considerations in finite element continuum damage mechanics. Int J Damage Mech 2013. 22: 1186-205. [11] Hosseini E, Holdsworth SR, Mazza E. Creep constitutive model considerations for 22
high-temperature finite element numerical simulations. J strain Anal Eng Des 2012. 47: 341-9. [12] Spindler MW. The multiaxial creep ductility of austenitic stainless steels. Fatigue Frac Eng Mater Struc 2004. 27: 273-81. [13] Tabuchi M, Yokobori Jr AT, Sugiura R, Yatomi M, Fuji A, Kobayashi K. Results of a Japanese round robin program for creep crack growth using Gr.92 steel welds. Eng Fract Mech 2010; 77: 3066-76. [14] Watanabe T, Tabuchi M, Yamazaki M, Hongo H, Tanabe T. Creep damage evaluation of 9Cr–1Mo–V–Nb steel welded joints showing Type IV fracture. Int J Pres Ves Pip 2006. 83: 63-71. [15] Mayr P, Mitsche S, Cerjak H, Allen SM. The impact of weld metal creep strength on the overall creep strength of 9% Cr steel weldments. J Eng Mater Technol 2011. 133: 21011 (1-7). [16] Samuel EI, Choudhary BK, Palaparti DPR, Mathew MD. Creep deformation and rupture behavior of P92 steel at 923K. Procdia Eng 2013. 55: 64-9. [17] Hosseini E, Holdsworth SR, Mazza E. The LICON methodology for predicting long-time uniaxial creep rupture strength of materials. Int J Pres Ves Pip 2013; 111-112: 27-35. [18] Zhang JW, Wang GZ, Xuan FZ, Tu ST. The influence of stress-regime dependent creep model and ductility in the prediction of creep crack growth rate in Cr-Mo-V steel, Mater. Desi. 2014, accepted. [19] Mehmanparast A, Davies CM, Webster GA, Nikbin KM. Creep crack growth rate
23
predictions in 316H steel using stress dependent creep ductility. Mater High Temp 2014. 31: 84-94. [20] Hibbitt, Karlsson & Sorensen. ABAQUS User’s Manual, Version 6.10; 2011. [21] Yatomi M, Nikbin K, O’Dowd NP. Creep crack growth prediction using a damage based approach. Int J Pres Ves Pip 2003; 80: 573-83. [22] Oh CS, Kim NH，Kim YJ, Davies CM, Nikbin KM，Dean D. Creep failure simulations of 316H at 550℃: Part I – A method and validation. Eng Fract Mech 2011. 78: 2966-77. [23] Yatomi M, Tabuchi M. Issues relating to numerical modelling of creep crack growth. Eng Fract Mech 2010; 77: 3043-52. [24] Kim NH, Oh CS, Kim YJ, Davies CM, Nikbin KM, Dean DW. Creep failure simulations of 316H at 550℃: Part II – Effects of specimen geometry and loading mode. Eng Fract Mech 2013. 105: 169-81. [25] Manjoine MJ. Creep rupture behavior of weldments. Welding J 1982. 61: 50-7. [26] Rice JR, Tracey DM. On ductile enlargement of voids in traxial stress fields. J Mech Phys Solids 1969. 17: 201-17. [27] Cocks ACF，Ashby MF. Intergranular fracture during power-law creep under multiaxial stresses. Metal Sci 1980; 14: 395-402. [28] Binda L, Holdsworth SR, Mazza E. The exhaustion of creep ductility in 1CrMoV steel. Int J Pres Ves Pip 2010; 87: 319-25. [29] Tokyo (Internet): NIMS materials database data sheets 51A, data sheets on creep- [cited 2003 Aug]. Available from: http://mits.nims.go.jp/index_en.html. [30] Ernst HA. Unified solution for J ranging continuously from pure bending to pure tension. 24
ASTM STP 791, Fract Mech. ASTM. 1983: 499–519. [31] Tabuchi M, Yokobori Jr AT, Sugiura R, Yatomi M, Kobayashi K. Evaluation of creep crack growth properties of Gr. 92 steel weldment. Strength, Fracture, Complexity 2011; 7: 137-46. [32] 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 Pres Ves Pip 2012; 96-97:78-89.
25
Figure and Table Captions Fig.1. The geometry and dimensions of the CT specimen of P92 welded joint [2] Fig.2. The six initial crack positions in P92 welded joint Fig.3. The FE model of the FGHAZ center crack specimen, (a) meshes of whole model, (b) local meshes around the crack tip and near the interface between weldment constituents Fig.4. Relation between minimum creep rate and unaxial tension stress for different regions (BM, WM, FGHAZ and CGHAZ) in the P92 steel welded joint at 650℃ [13, 23] Fig.5. The final damage contours (t/tr=1, tr is the rupture life) of CCG for six cracks at different positions at low load level of K=7MPa√m, (a) FGHAZ/BM interface crack, (b) FGHAZ center crack, (c) FGHAZ/CGHAZ interface crack, (d) CGHAZ center crack, (e) CGHAZ/WM interface crack, (f) WM center crack, SDV1: damage; ICT: initial crack tip; CCT: current crack tip. Fig.6. The Mises stress contours with CCG for CGHAZ center crack at K=7MPa√m, (a) t/tr=0.086, (b) t/tr=0.708, ICT: initial crack tip; CCT: current crack tip. Fig.7. The damage contours for CGHAZ center crack at K=7MPa√m and t/tr=0.896, SDV1: damage; ICT：initial crack tip; CCT: current crack tip. Fig.8. Stress triaxiality contours with CCG for the CGHAZ center crack at K=7Mpa√m (a) t/tr=0.086, (b) t/tr=0.708, SDV3: stress triaxiality; ICT: initial crack tip; CCT: current crack tip. Fig.9. The CCG paths for: (a) P91 electron beam welding (EBW) welded joint with starter notch in WM [7], (b) dissimilar metal welded joint of 1CrMoV/Alloy 617/Alloy 625 with the pre-crack in the middle of 1CrMoV HAZ [9] 26
Fig.10. The final damage contours (t/tr=1, tr is the rupture time) of CCG for six cracks at different positions at high load level of K=10MPa√m, (a) FGHAZ/BM interface crack, (b) FGHAZ center crack, (c) FGHAZ/CGHAZ interface crack, (d) CGHAZ center crack, (e) CGHAZ/WM interface crack, (f) WM center crack, SDV1: damage; ICT: initial crack tip; CCT: current crack tip Fig.11. The Mises stress contours (a) and stress triaxiality contours (b) for CGHAZ center crack at K=10MPa√m and t/tr=0.41, SDV3: stress triaxiality, ICT: initial crack tip, CCT: current crack tip Fig.12. The da/dt-C* curves for the six cracks at different load levels, the open and solid points represent the CCG data after initiation of SC and crack propagating straight along initial crack plane, respectively. Fig.13. The ∆a-t curves for the three cracks with SC at different load levels, (a) K=7MPa√m, the open and solid points indicate the data before and after initiation of the SC, respectively, (b) K=10MPa√m Table.1 Material properties for different regions (BM, WM, FGHAZ and CGHAZ) in P92 welded joint at different stress levels at 650℃ [2, 23]
27
Highlights > Crack position and load level cause change of creep failure behavior in welded joint. > Mechanism of this change was investigated by stress-regime dependent creep model. > Creep rupture life is mainly determined by incubation time of second crack at low load. > Effects of crack position and load level on creep life need to be fully considered.
28