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Creep fracture behavior of the Crofer 22 APU for the interconnect of solid oxide fuel cell under different temperatures
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Creep fracture behavior of the Crofer 22 APU for the interconnect of solid oxide fuel cell under different temperatures Yu-Cai Zhang a, Xin-Tong Yu a, Wenchun Jiang a,*, Shan-Tung Tu b, Xian-Cheng Zhang b, You-Jun Ye c a
College of New Energy, China University of Petroleum (East China), Qingdao, 266580, PR China Key Laboratory of Pressure Systems and Safety (MOE), School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai, 200237, PR China c Jiangsu Province Special Equipment Safety Supervision Inspection Institute, Nanjing, 210009, PR China b
highlights CCG behavior of Crofer 22 APU under different temperatures are investigated. The Liu-Murakami constitutive equations of Crofer 22 APU are established. Temperature effect of CCG behavior is more evident than that the stress effect. All the data of C*- a_ fall within the area of 95% prediction band.
article info
abstract
Article history:
Creep damage and creep crack growth (CCG) behavior of Crofer 22 APU as interconnect of
Received 31 July 2019
solid oxide fuel cell at different temperatures are investigated by the continuum damage
Received in revised form
mechanics method through CT specimen. It is illustrated that the fracture time of CT
21 November 2019
specimen reduces with temperature increasing at the same stress level, they are 1297 h,
Accepted 1 December 2019
42 h, 1.8 h and 0.25 h, respectively, at 650, 700, 750 and 800 C with stress level of 2.73 pffiffiffiffiffi MPa, m. The slopes of creep fracture mechanics parameter C* to CCG rate a_ (C*- rate of a) are nearly the same at 650 and 700 C. The slope of C*- a_ at 650 and 700 C is smaller than
Available online xxx Keywords: Solid oxide fuel cell
that at 750 and 800 C. It is concluded that the temperature effect on CCG behavior of Crofer 22 APU is more evident than that the stress effect. All the data of C*- a_ fall within the area of
Temperature effect
95% prediction band, and the obtained equation of C* and CCG rate is a_ ¼ 3:8e2C*0:91 . Therefore, the a_ of Crofer 22 APU can be predicted under different stress levels and
Crofer 22 APU
temperatures.
Creep crack growth
© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
* Corresponding author. E-mail address: [email protected] (W. Jiang). https://doi.org/10.1016/j.ijhydene.2019.12.009 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article as: Zhang Y-C et al., Creep fracture behavior of the Crofer 22 APU for the interconnect of solid oxide fuel cell under different temperatures, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.009
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Introduction With the concerning of environmental crisis and increasing of energy demands, tremendous efforts are carried out to develop the efficient energy conversion devices with low emissions. Fuel cell, as one of the electrochemical reaction facilities that can transform the chemical energy of the fuels assisted with oxidant to electricity directly with low pollution, high efficiency and noiseless, has been received a lot of attractions in recent years [1e6]. Compared with the other fuel cells such as molten carbonate fuel cell [7] and polymer electrolyte membrane fuel cell [8], PSOFC (planar solid oxide fuel cell) owns the advantages of wide fuel sources and compact structure [3,9,10], so it captures the heart of many researchers. Although the energy conversion efficiency of PSOFC is higher than those of the other fuel cells, the output power of single cell is still very small, it is only a few Watts, therefore, in order to meet the power demands, single PSOFC should be connected in series to compose the SOFC stack. A typical unit of a PSOFC includes the positive electrode, electrolyte and negative electrode. For the connection of single fuel cells, a interconnect frame is needed to support the SOFC. The interconnect acts as the electrical connection component between the single cell, and it also contains the gas channels to transport the fuel and oxidant [11]. The operating temperature of intermediate temperature PSOFC is about 600e800 C, in order to guarantee the power output and high temperature structural integrity, the materials of interconnect should satisfy the requirements of high electronic conductivity, good corrosion resistance, high mechanical and chemical stability, a feasible coefficient of thermal expansion and low permeability of the reactant gases. Therefore, the interconnect performance can greatly affect both current collection and life of the cell stack, and reasonable selection of the interconnect material should be carried out. Typical interconnect are usually fabricated by the electrically conductive ceramic materials such as LaCrO3. However, these ceramic materials are expensive and difficult to manufacture. The metallic materials exhibit higher thermal and electrical conductivities compared to ceramic interconnect materials and are less costly [12]. Therefore, for the IT-SOFC (Intermediate temperature Solid Oxide Fuel Cell, IT-SOFC), metallic materials are extensively applied as interconnect materials to replace the more expensive ceramic based counterparts. And also, since the metallic materials present good formability, it is easier to fabricate with complex shapes. The candidate metallic materials used for the interconnect are Fe-based alloys, Ni-based alloys and metal matrix composites [13,14], the representative materials for these three kinds alloys are Crofer 22 APU, Haynes214 and TiC/Ni, respectively. For the interconnect materials applied at high temperature conditions, the oxidation resistance and chromium poisoning should be considered to decrease the electrical resistance and keep the power output of the SOFC. For the Cr-containing materials, during long-term exposure to the high temperature atmosphere in the SOFC, the chromium oxide will growth on the steel substrate. With the continuous operating of the
SOFC, Cr-containing gaseous species are formed from the oxide scales, which results in the chromium poisoning of the SOFC electrodes and thus in turn, causes the performance degradation of the SOFC. Although the TiC/Ni has the advantages of suitable thermal expansion coefficient, excellent electrical/thermal conductivity and lower chromium poisoning, its oxidation resistance is weaker than that of Haynes214 and Crofer 22 APU, and, hence, still needs to be improved. Moreover, the creep resistance is also an important factor that should be considered. Both the creep and oxidation resistance of Haynes 214 are superior to the Crofer 22 APU, and it has already been used for the PSOFC with bonded compliant seal [15,16]. For the Haynes 214 applied in the PSOFC, the results shown that the creep deformation of the Haynes 214 is very small due to the excellent creep resistance [16], Therefore, the safety allowance of the Haynes 214 used as interconnect of the PSOFC is too large. So the application of the Haynes 214 in the PSOFC field is performance wasteful. Crofer 22 APU with comparable thermal expansion coefficient to those of cell components, excellent high temperature material properties and lower cost, is extensively applied as the PSOFC interconnect material [17e19]. PSOFC is a multi-layer structure [20], and hence at high operating temperature, large thermal stress will be produced due to the material mismatch and temperature gradient [21]. Although the thermal stress may not cause damage of the PSOFC structure promptly, it could result in large deformation or cracks caused by the high temperature creep phenomenon at the long-term and high temperature operating conditions. The gas leakage or mixture due to the generated cracks would weaken the output efficiency of PSOFC. Therefore, the thermal stress cannot be ignored for the design of the PSOFC, and investigation the life prediction on Crofer 22 APU is significant, since the life of the Crofer 22 APU interconnect can directly affect the life of whole SOFC during the long-term high temperature operation. For the Crofer 22 APU, its oxidation [19,22] and corrosion resistance, long-term electrical conductivity [23,24], chemical stability [25], formability [17], thermal performance and creep deformations [26e28] have been comprehensively investigated. However, little work involved on the creep fracture behavior, such as the damage and the CCG behavior of the Crofer 22 APU. Therefore, it is imperative to investigate its CCG behavior. In present paper, the CCG of the Crofer 22 APU under different operating temperature conditions were investigated by the continuum damage mechanic method, the results can offer basic information for the reliable design of the PSOFC.
Finite element simulation information Geometrical model For the CCG investigation of the material operated at high temperatures, compact tension (CT) specimen has been widely used according to the specification of ASTM E 1457-15 [29]. Specimen sizes adopted are described in Fig. 1. The width W and thickness B are 20 mm and 10 mm, respectively. The normalized initial crack length a0/W is 0.5.
Please cite this article as: Zhang Y-C et al., Creep fracture behavior of the Crofer 22 APU for the interconnect of solid oxide fuel cell under different temperatures, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.009
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Liu-Murakami constitutive model [31,32] was employed to calculate the material’s CCG behavior, the equations of this constitutive model were listed as follows: " # 3 2ðn þ 1Þ 3=2 p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ε_ cij ¼ Bsn1 u S exp ij 2 eq p 1 þ 3=n
(4)
A 1 exp q2 ðsr Þp exp q2 u q2
(5)
u_ ¼
sr ¼ asІ þ ð1 aÞseq
Fig. 1 e Geometrical size of the CT specimen.
Meshing and applied boundary conditions Fig. 2 delineates the meshing of CT specimen, and the applied element type is C3D8R.To reduce the calculating time and guarantee the calculating precision, only local mesh at the vicinity of crack tip was refined [30], as described in Fig. 2 (a). Three sets element-node number of 30141e35155, 18920e22176 and 14441e16885, respectively, were adopted to carry out the mesh independence analysis. The geometry of CT specimen is Y-axis and Z-axis symmetry, therefore, only 1/4 of the geometrical model was adopted to save the computing time. Boundary conditions of plane 1 and plane 2 are Y-axis and Z-axis symmetry, respectively. The temperature of 650, 700, 750 and 800 C, which is the traditional operating temperature of SOFC were used to investigation the temperature effect on CCG behavior of CT specimen. The temperatures were exerted on the element nodes. The loads were characterized in the mechanical parameter of initial stress intensity factor K. It is applied on the pffiffiffiffiffi loading point, as described in Fig. 2 (b). The K ¼ 2.73 MPa, m was adopted, it can be calculated by the following equations: K¼
P 2 þ a=W f ða = WÞ BW1=2 ð1 a=WÞ3=2
(1)
where, A, B, p and q2 are material constant, n the creep stress exponent, seq the von Mises stress, sr the fracture stress, sІ the maximum principal stress. u is the damage variable, it increases with increasing creep time. a denotes the multi-axial creep parameter. For the stainless steel, the value of a is 0.43 [33]. Sij and ε_ cij are stress and creep strain rate tensor, respectively. The parameters in Eqs. (4)e(6) are usually acquired by fitting the uni-axial creep data. The uni-axial creep data of the Crofer 22 APU under different temperatures are referenced from literature [26]. Based on the Norton equation of ε_ c ¼ Bsn , the parameters of B and n can be obtained from the log-log relationship between the s and ε_ c , as illustrated in Fig. 3. The variation of the s-_εc slope in Fig. 3 demonstrates that the uniaxial ε_ c increases with enlarging of the temperature under same stress levels. The parameters A and p can be obtained by fitting the relationship between s and rupture time tf in log-log coordinate of Fig. 4. The fitting equation is expressed: tf ¼
Material constitutive model Total deformation εtotal of Crofer 22 APU at high temperatures includes elastic deformation εe , plastic deformation εp and creep deformation εc . The constitutive equation can be expressed as follows: εtotal ¼ εe þ εp þ εc
(3)
The εe is calculated by the generalized Hooke law, εp follows the von Mises yield criterion. The parameters used for calculating εe and εp are summarized in Table 1.
1 Asp
(7)
The parameter q2, it is hard to get directly. It is usually considered as that q2 ¼ f þ 2 [31]. The parameter f can be obtained by the normalized creep strain, as follows: 1n=ðfþ1Þ
ε 1 t 1 1 ¼ n Bs tf 1 nðf þ 1Þ tf
f ða = WÞ ¼ 0:886 þ 4:64ða = WÞ 13:32ða=WÞ2 þ 14:72ða=WÞ3 5:6ða=WÞ4
where, P is the applied load, the unit is N, a the instantaneous creep crack length.
(6)
(8)
(2)
All the parameter values applied in Liu-Murakami constitutive model are listed in Table 2. The Eqs. (4)e(6) were translated by the Fortran language to integrate the commercial software of ABAQUS. When the accumulated damage value of u for the Gaussian integral point attaches its critical value ucr , the mechanical strength of the related finite element decreases very quickly. It is considered as failed and its loading capability lost. For the critical failure value of ucr , 0.99 [34] is widely used in the simulation process. It has been verified that ucr ¼ 0:99 can ensure the simulation accuracy of the damage analysis [35]. To characterize the damage effect on high temperature mechanical strength, the elastic modulus E is decreased with the u accumulating based on the relationship between u and E:
Please cite this article as: Zhang Y-C et al., Creep fracture behavior of the Crofer 22 APU for the interconnect of solid oxide fuel cell under different temperatures, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.009
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Fig. 2 e CT specimen meshing and applied boundary conditions.
Eiþ1 ¼ ð1 ui ÞEi
(9)
where, Eiþ1 and Ei are the elastic modulus at the increment time of iþ1 and i, respectively. ui is the damage value at the increment time of i.
agreement with experimental data, certifying that the Eqs. (4)e(6) with the parameters in Table 2 could well forecast the creep performances of Crofer 22 APU. Therefore, the parameters in Table 2 have been adopted to calculate the CCG behaviors of this material.
Mesh independence validation
Results and discussion To verify the reliability of the parameter values applied in the Liu-Murakami constitutive equation, the prediction and experimental data of the uniaxial creep deformations at different temperatures are compared, as illustrated in Fig. 5. The comparison shows that the prediction data present good
Element size can affect the calculate precision of the numerical results. Usually, the smaller of element size, the more precise are the simulation results. However, the computation time is increased sharply with the decreasing of the element
Table 1 e Mechanical performances of Crofer 22 APU at different temperatures. T ( C)
Yield strength (MPa)
650 700 750 800
162 92 57 44
Tensile strength Elastic modulus E (MPa) (GPa) 203 102 64 48
157 91 66 44
Fig. 4 e Variation of the tf with s under different temperatures.
Table 2 e Creep parameters used in Liu-Murakami constitutive model under different temperatures.
Fig. 3 e Variation of ε_ c with s at different temperatures.
Parameter
650 C
700 C
750 C
800 C
q2 A p B n
8.21 1.47e-9 4.02 2.57e-12 4.58
9.22 2.88e-10 5.29 3.55e-12 5.86
11.20 1.20e-9 5.45 2.57e-12 6.03
12.11 4.20e-9 6.00 3.24e-12 7.67
Please cite this article as: Zhang Y-C et al., Creep fracture behavior of the Crofer 22 APU for the interconnect of solid oxide fuel cell under different temperatures, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.009
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Fig. 5 e Comparison between the prediction and experimental creep data of Crofer 22 APU at (a) 650 C；(b) 700 C；(c) 750 C；(d) 800 C.
size. Therefore, both the computation time and cost should be given consideration, and the mesh independence validation of the finite element model should be carried out to determine a suitable finite element size. Fig. 6 shows the mesh independent validation used by the sI and seq along Path 1. Path 1 is described in Fig. 7. For both the sI and seq , when the finite element size decreases to 0.1 mm, the values of the these two kinds of stress are almost keeping the same, demonstrating that the computational accuracy can be guaranteed. However, the calculating time of the finite element analysis with 0.05 mm element size is five times longer than that of the 0.1 mm. Therefore, in present paper, the 0.1 mm mesh size was applied in the finite element analysis.
Temperature effect of CCG behavior Fig. 8 illustrates the variation of sI and seq with the creep time under different temperatures along path 1. For sI , all peak stresses under different temperatures locate before the crack tip, and they are first decreasing and then increasing with time. At initial creep stage, the stresses at the crack tip are relaxed by the creep deformation. With increasing creep time, a crack occurs, and the magnitude of the stress at the nearby of the crack reduces to a small value. The reason for that is the damaged element losing the loading capability. The peak
stresses of the CT specimen are still located before the newly generated crack tip, but the magnitude of the peak stress is larger than that at the initial creep stage. With temperature increasing, the peak stresses reduce due to stress relaxation effects. In the vicinity of the crack tip region, the value of maximum principal stress is large, while at the large distance along path1, it can be seen from Fig. 8, the maximum principal stress is decreased to a small value. For the von Mises stress, the value is large, and it further increases with increasing time. The maximum principal stress distribution of CT specimen at the temperature of 650 C is illustrated in Fig. 9 (a). It is known at the large distance area of the path1, the region A in Fig. 9 (a), the maximum principal stress is small, while the value of middle principal stress (sII ) and minimum principal stress (sIII ) are large, as shown in Fig. 9 (b) and (c), respectively. Both the middle principal stress and minimum principal stress are compressive. The von Mises stress seq calculated by the maximum, middle and minimum principal stress, as follows: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 2 seq ¼ 1 2ððsI sII Þ2 þ sII sIII þ sIII sI
(10)
From the Eq. (10) and the stress distribution in Fig. 9, it is known that although the value of sI is small, the value of sII and sIII are large, therefore, the value of von Mises stress is
Please cite this article as: Zhang Y-C et al., Creep fracture behavior of the Crofer 22 APU for the interconnect of solid oxide fuel cell under different temperatures, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.009
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Fig. 6 e Mesh independence validation of the finite element analysis used by stresses along Path 1.
Fig. 7 e Path 1 in the CT specimen.
larger than that the maximum principal stress sI . With the growth of creep crack length, the effective specimen cross section area decreases, so the von Mises stress increases with increasing creep time, as shown in Fig. 10. Since the crack growth path is not always a straight line, as illustrated in Fig. 13, the length of the region that the stresses are very small could not reflect the true length of the crack. The corresponding crack length under different temperatures and creep times in Fig. 8 can be acquired from Fig. 11 (a). Creep crack growth behavior is one of the key factors that characterization the high temperature strength of the
Fig. 8 e Stress analysis of the CT specimen along Path 1 under different temperatures.
material. Fig. 11 shows the creep crack and loading point displacement (LPD) growth with time. The shapes of the CCG and LPD curves are similar to that uni-axial creep curve. At final stage, both the values of crack length and LPD grow fast, this stage includes more than 80% of the total crack length or LPD value. In the ASTM E 1457, the crack initiation (CI) time is defined as the time that crack length increase to 0.2 mm. Therefore, the CI time of CT specimen under the temperature of 650, 700, 750 and 800 C are 188 h, 19 h, 0.2 h and 0.11 h, respectively. The corresponding fracture time are 1297 h, 42 h, 1.8 h and 0.25 h, respectively. The fracture time of CT specimen decreases with temperature increasing. While the values of the LPD present the tendency of increasing firstly and then decreasing, this is mainly caused by the different yield strength and tensile strength under different temperatures. From the Fig. 8, it is known that the stresses at the nearby of crack tip decreases with increasing temperature. Based on the data in Figs. 8 and 11, it is concluded that the temperature effect on CCG behavior of Crofer 22 APU is more evident than that the stress effect. Fig. 12 shows the contour of creep damage evolution for the Crofer 22 APU at the four temperatures. The red region in
Please cite this article as: Zhang Y-C et al., Creep fracture behavior of the Crofer 22 APU for the interconnect of solid oxide fuel cell under different temperatures, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.009
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Fig. 9 e Principal stress distribution in CT specimen at the temperature of 650 C (a) maximum principal stress (b) middle principal stress (c) minimum principal stress.
damage contour represents the damage values of the gauss integration points attach to the critical failure value of 0.99, the corresponding finite elements are failed. The creep crack morphology under the four temperatures extend in the form of finger nail, so the crack length in Fig. 11 (a) was calculated by the nine-point average method. Most of the cracks extended at the symmetrical plane, and also, some cracks occurred at a certain distance from the symmetrical plane, as shown in Region B of the Fig. 12 (b) and Fig. 13. In the CCG test of high temperature materials, the CCG plane of CT specimen is also not extended along a fixed face [36], such as the CLAM steel, as illustrated in Fig. 14. For the materials statically loaded at high temperatures, the creep cavities are
usually generated along the grain boundaries or in the interior of the grains different directions and locations, the creep cavities continued to growth and at last connect with the main crack, resulting in the crack extended forward with twists and turns. Grain growth decreases in dislocation density and coarsening of precipitates during the creep process can cause the microstructure change of the material [37]. Moreover, microstructural change of the material also can result in the stress concentration along the grain boundary or in the grain, causing the twisted creep crack. The creep damage constitutive model used in present paper is established based on the creep voids nucleation and growth theory, therefore, the numerical method used in
Please cite this article as: Zhang Y-C et al., Creep fracture behavior of the Crofer 22 APU for the interconnect of solid oxide fuel cell under different temperatures, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.009
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Fig. 10 e von Mises stress distribution in the CT specimen under different times at the temperature of 650 C (a) 1199 h (b) 1297 h. present paper can reasonably reflect the creep crack growth behavior of the Crofer 22 APU steel. The creep fracture mechanics parameter C* is usually adopted to characterize material’s CCG rate [36,38,39]. For the CT specimen, it can be obtained from Eq. (11) [29]: PV_ c n h C* ¼ pffiffiffiffiffiffiffiffiffiffiffi B,Bn ðW aÞ n þ 1
(11)
where, V_ c is the time dependent displacement rate of loading point, it can obtained directly by the finite element analysis. h is the geometric function. The average value h of CT specimen is usually taken as 2.2 [29]. The CCG rate a_ is predicted by Eq. (12) with C*: a_ ¼ a0 C*z
(12)
where, a0 and z are the material constants. Only when the ratio of the time dependent LPD rate V_ c and the total LPD rate V_ t is larger than 0.5, the C* can be reasonably applied to characterize the CCG rate. Based on the data in Fig. 11, the CCG rate a_ under different temperatures can be obtained, as described in Fig. 15. The results illustrate that the slopes of C*- a_ are nearly the same under the temperature of 650 C and 700 C. The slope of C*- a_ at the temperature of 750 C is the same as that at 800 C. But the slope of C*- a_ under the temperature of 650 C and 700 C is smaller than that the 750 C and 800 C, demonstrating that the CCG rate at 750 and 800 C is larger than that the 650 C and 700 C. All the data in Fig. 15 fall within the area of 95% prediction band, and the CCG rate of this material can be predicted by a_ ¼ 3:8e2C*0:91 . For the value of z, it is usually less than 1.0 [40], in present study, z ¼ 0:91, therefore, the prediction equation is valid, and the CCG rate of Crofer 22 APU can be
Fig. 11 e (a) Creep crack length and (b) load point displacement growth with time at different temperatures.
Please cite this article as: Zhang Y-C et al., Creep fracture behavior of the Crofer 22 APU for the interconnect of solid oxide fuel cell under different temperatures, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.009
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Fig. 12 e The contour of creep damage evolution for the Crofer 22 APU at the temperature of (a) 650 C, (b) 700 C, (c) 750 C and (d) 800 C. Please cite this article as: Zhang Y-C et al., Creep fracture behavior of the Crofer 22 APU for the interconnect of solid oxide fuel cell under different temperatures, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.009
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Fig. 13 e Creep damage cross section distribution of the Crofer 22 APU at Region B in Fig. 12. predicted under different stress levels. From the Fig. 15, it also can conclude that the temperature effect on the CCG behavior of Crofer 22 APU is more evident than that the stress effect.
Conclusions In present paper, creep fracture of Crofer 22 APU for the interconnect of SOFC under different temperatures were investigated by continuum damage mechanics method. The main results and conclusions are obtained:
Fig. 14 e Creep crack extending path of the CLAM steel.
Fig. 15 e Variation of the CCG rate with C* under different temperatures.
(1) The Liu-Murakami creep damage constitutive equations of Crofer 22 APU under different temperatures are established. Compared with the experimental uniaxial creep curves, the established constitutive equations can accurately prediction the CCG of the Crofer 22 APU. (2) The crack fracture time of the CT specimen at 650, 700, 750 and 800 C are 1297 h, 42 h, 1.8 h and 0.25 h, respectively. It is concluded that the temperature effect on the creep crack growth behavior is more evident than that the stress effect. (3) The slopes of C*- a_ are nearly the same under the temperature of 650 C and 700 C. The slope of C*- a_ at the temperature of 750 C is the same as that at 800 C. But the slope of C*- a_ under the temperature of 650 C and 700 C is smaller than that the 750 C and 800 C, demonstrating that the CCG rate at 750 and 800 C is larger than that the 650 C and 700 C. All the data of C*a_ fall within the area of 95% prediction band, and the CCG rate of Crofer 22 APU can be predicted by a_ ¼ 3:8e2C*0:91 .
Please cite this article as: Zhang Y-C et al., Creep fracture behavior of the Crofer 22 APU for the interconnect of solid oxide fuel cell under different temperatures, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.009
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Acknowledgments [16]
Thanks for the supporting of the National Natural Science Foundation of China (Grant No. 51805545), the Fundamental Research Funds for the Central Universities (Grant No. 18CX02151A).
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compliant seal of planar solid oxide fuel cell. Int J Hydrogen Energy 2018;43:4492e504. Zhang YC, Jiang W, Tu ST, Wen JF. Simulation of creep and damage in the bonded compliant seal of planar solid oxide fuel cell. Int J Hydrogen Energy 2014;39:17941e51. Timurkutluk B, Toros S, Onbilgin S, Korkmaz HG. Determination of formability characteristics of Crofer 22 APU sheets as interconnector for solid oxide fuel cells. Int J Hydrogen Energy 2018;43:14638e47. Saeidpour F, Zandrahimi M, Ebrahimifar H. Evaluation of pulse electroplated cobalt/yttrium oxide composite coating on the Crofer 22 APU stainless steel interconnect. Int J Hydrogen Energy 2019;44:3157e69. € ¨ rk B, Topcu A, Oztu € ¨ rk S, Cora ON. € Oztu Oxidation, electrical and mechanical properties of Crofer®22 solid oxide fuel cell metallic interconnects manufactured through powder metallurgy. Int J Hydrogen Energy 2018;43:10822e33. Liu M, Liu Y. Multilayer tape casting of large-scale anodesupported thin-film electrolyte solid oxide fuel cells. Int J Hydrogen Energy 2019;44:16976e82. Xu YW, Wu XL, You H, Xue T, Zhao DQ, Jiang JH, et al. Modeling and simulation of temperature distribution for planar cross-flow solid oxide fuel cell. Energy Procedia 2019;158:1585e90. Park M, Shin JS, Lee S, Kim HJ, An H, Ji HI, et al. Thermal degradation mechanism of ferritic alloy (Crofer 22 APU). Corros Sci 2018;134:17e22. Chen L, Magdefrau N, Sun E, Yamanis J, Frame D, Burila C. Strontium transport and conductivity of Mn1.5Co1.5O4 coated Haynes 230 and Crofer 22 APU under simulated solid oxide fuel cell condition. Solid State Ion 2011;204205:111e9. Puranen J, Pihlatie M, Lagerbom J, Salminen T, Laakso J, € rinen L, et al. Influence of powder composition and Hyva manufacturing method on electrical and chromium barrier properties of atmospheric plasma sprayed spinel coatings prepared from MnCo2O4 and Mn2CoO4 þ Co powders on Crofer 22 APU interconnectors. Int J Hydrogen Energy 2014;39:17246e57. Kaur G, Pandey OP, Singh K. Chemical interaction study between lanthanum based different alkaline earth glass sealants with Crofer 22 APU for solid oxide fuel cell applications. Int J Hydrogen Energy 2012;37:3883e9. Chiu YT, Lin CK, Wu JC. High-temperature tensile and creep properties of a ferritic stainless steel for interconnect in solid oxide fuel cell. J Power Sources 2011;196:2005e12. Esposito L, Boccaccini DN, Pucillo GP, Frandsen HL. Secondary creep of porous metal supports for solid oxide fuel cells by a CDM approach. Mater Sci Eng A 2017;691:155e61. Chiu YT, Lin CK. Effects of Nb and W additions on hightemperature creep properties of ferritic stainless steels for solid oxide fuel cell interconnect. J Power Sources 2012;198:149e57. ASTM E1457-15. Standard test method for measurement of creep crack growth times in metals. 2015. Yang J. Micromechanical analysis of in-plane constraint effect on local fracture behavior of cracks in the weakest locations of dissimilar metal welded joint. Acta Metall Sin 2017;30:840e50. Liu Y, Murakami S. Damage localization of conventional creep damage models and proposition of a new model for creep damage analysis. JSME Int J Series A 1998;41:57e65. Zhang YC. Creep damage and crack growth analysis of the brazed joint under multi-axial stress state. East China University of Science and Technology; 2016.
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[33] Meng Q, Wang Z. Creep damage models and their applications for crack growth analysis in pipes: a review. Eng Fract Mech 2019;205:547e76. [34] Saber M, Sun W, Hyde TH. Numerical study of the effects of crack location on creep crack growth in weldment. Eng Fract Mech 2016;154:72e82. [35] Wen JF, Tu ST, Gao XL, Reddy J. New model for creep damage analysis and its application to creep crack growth simulations. Mater Sci Technol 2014;30:32e7. [36] Zhao Y, Liu S, Shi J, Mao X. Experimental and numerical simulation analysis on creep crack growth behavior of CLAM steel. Mater Sci Eng A 2018;735:260e8. [37] Abe F. Effect of fine precipitation and subsequent coarsening of Fe2W laves phase on the creep deformation behavior of
tempered martensitic 9Cr-W steels. Metall Mater Trans A 2005;36:321e32. [38] Zhang YC, Jiang W, Tu ST, Zhang XC, Ye YJ. Creep crack growth behavior analysis of the 9Cr-1Mo steel by a modified creep-damage model. Mater Sci Eng A 2017;708:68e76. [39] Zhang YC, Jiang W, Tu ST, Zhang XC, Ye YJ, Wang RZ. Experimental investigation and numerical prediction on creep crack growth behavior of the solution treated Inconel 625 superalloy. Eng Fract Mech 2018;199:327e42. [40] Davies CM, Dean DW, Nikbin KM, O’Dowd NP. Interpretation of creep crack initiation and growth data for weldments. Eng Fract Mech 2007;74:882e97.
Please cite this article as: Zhang Y-C et al., Creep fracture behavior of the Crofer 22 APU for the interconnect of solid oxide fuel cell under different temperatures, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.009
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Creep fracture behavior of the Crofer 22 APU for the interconnect of solid oxide fuel cell under different temperatures Yu-Cai Zhang a, Xin-Tong Yu a, Wenchun Jiang a,*, Shan-Tung Tu b, Xian-Cheng Zhang b, You-Jun Ye c a
College of New Energy, China University of Petroleum (East China), Qingdao, 266580, PR China Key Laboratory of Pressure Systems and Safety (MOE), School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai, 200237, PR China c Jiangsu Province Special Equipment Safety Supervision Inspection Institute, Nanjing, 210009, PR China b
highlights CCG behavior of Crofer 22 APU under different temperatures are investigated. The Liu-Murakami constitutive equations of Crofer 22 APU are established. Temperature effect of CCG behavior is more evident than that the stress effect. All the data of C*- a_ fall within the area of 95% prediction band.
article info
abstract
Article history:
Creep damage and creep crack growth (CCG) behavior of Crofer 22 APU as interconnect of
Received 31 July 2019
solid oxide fuel cell at different temperatures are investigated by the continuum damage
Received in revised form
mechanics method through CT specimen. It is illustrated that the fracture time of CT
21 November 2019
specimen reduces with temperature increasing at the same stress level, they are 1297 h,
Accepted 1 December 2019
42 h, 1.8 h and 0.25 h, respectively, at 650, 700, 750 and 800 C with stress level of 2.73 pffiffiffiffiffi MPa, m. The slopes of creep fracture mechanics parameter C* to CCG rate a_ (C*- rate of a) are nearly the same at 650 and 700 C. The slope of C*- a_ at 650 and 700 C is smaller than
Available online xxx Keywords: Solid oxide fuel cell
that at 750 and 800 C. It is concluded that the temperature effect on CCG behavior of Crofer 22 APU is more evident than that the stress effect. All the data of C*- a_ fall within the area of
Temperature effect
95% prediction band, and the obtained equation of C* and CCG rate is a_ ¼ 3:8e2C*0:91 . Therefore, the a_ of Crofer 22 APU can be predicted under different stress levels and
Crofer 22 APU
temperatures.
Creep crack growth
© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
* Corresponding author. E-mail address: [email protected] (W. Jiang). https://doi.org/10.1016/j.ijhydene.2019.12.009 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article as: Zhang Y-C et al., Creep fracture behavior of the Crofer 22 APU for the interconnect of solid oxide fuel cell under different temperatures, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.009
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Introduction With the concerning of environmental crisis and increasing of energy demands, tremendous efforts are carried out to develop the efficient energy conversion devices with low emissions. Fuel cell, as one of the electrochemical reaction facilities that can transform the chemical energy of the fuels assisted with oxidant to electricity directly with low pollution, high efficiency and noiseless, has been received a lot of attractions in recent years [1e6]. Compared with the other fuel cells such as molten carbonate fuel cell [7] and polymer electrolyte membrane fuel cell [8], PSOFC (planar solid oxide fuel cell) owns the advantages of wide fuel sources and compact structure [3,9,10], so it captures the heart of many researchers. Although the energy conversion efficiency of PSOFC is higher than those of the other fuel cells, the output power of single cell is still very small, it is only a few Watts, therefore, in order to meet the power demands, single PSOFC should be connected in series to compose the SOFC stack. A typical unit of a PSOFC includes the positive electrode, electrolyte and negative electrode. For the connection of single fuel cells, a interconnect frame is needed to support the SOFC. The interconnect acts as the electrical connection component between the single cell, and it also contains the gas channels to transport the fuel and oxidant [11]. The operating temperature of intermediate temperature PSOFC is about 600e800 C, in order to guarantee the power output and high temperature structural integrity, the materials of interconnect should satisfy the requirements of high electronic conductivity, good corrosion resistance, high mechanical and chemical stability, a feasible coefficient of thermal expansion and low permeability of the reactant gases. Therefore, the interconnect performance can greatly affect both current collection and life of the cell stack, and reasonable selection of the interconnect material should be carried out. Typical interconnect are usually fabricated by the electrically conductive ceramic materials such as LaCrO3. However, these ceramic materials are expensive and difficult to manufacture. The metallic materials exhibit higher thermal and electrical conductivities compared to ceramic interconnect materials and are less costly [12]. Therefore, for the IT-SOFC (Intermediate temperature Solid Oxide Fuel Cell, IT-SOFC), metallic materials are extensively applied as interconnect materials to replace the more expensive ceramic based counterparts. And also, since the metallic materials present good formability, it is easier to fabricate with complex shapes. The candidate metallic materials used for the interconnect are Fe-based alloys, Ni-based alloys and metal matrix composites [13,14], the representative materials for these three kinds alloys are Crofer 22 APU, Haynes214 and TiC/Ni, respectively. For the interconnect materials applied at high temperature conditions, the oxidation resistance and chromium poisoning should be considered to decrease the electrical resistance and keep the power output of the SOFC. For the Cr-containing materials, during long-term exposure to the high temperature atmosphere in the SOFC, the chromium oxide will growth on the steel substrate. With the continuous operating of the
SOFC, Cr-containing gaseous species are formed from the oxide scales, which results in the chromium poisoning of the SOFC electrodes and thus in turn, causes the performance degradation of the SOFC. Although the TiC/Ni has the advantages of suitable thermal expansion coefficient, excellent electrical/thermal conductivity and lower chromium poisoning, its oxidation resistance is weaker than that of Haynes214 and Crofer 22 APU, and, hence, still needs to be improved. Moreover, the creep resistance is also an important factor that should be considered. Both the creep and oxidation resistance of Haynes 214 are superior to the Crofer 22 APU, and it has already been used for the PSOFC with bonded compliant seal [15,16]. For the Haynes 214 applied in the PSOFC, the results shown that the creep deformation of the Haynes 214 is very small due to the excellent creep resistance [16], Therefore, the safety allowance of the Haynes 214 used as interconnect of the PSOFC is too large. So the application of the Haynes 214 in the PSOFC field is performance wasteful. Crofer 22 APU with comparable thermal expansion coefficient to those of cell components, excellent high temperature material properties and lower cost, is extensively applied as the PSOFC interconnect material [17e19]. PSOFC is a multi-layer structure [20], and hence at high operating temperature, large thermal stress will be produced due to the material mismatch and temperature gradient [21]. Although the thermal stress may not cause damage of the PSOFC structure promptly, it could result in large deformation or cracks caused by the high temperature creep phenomenon at the long-term and high temperature operating conditions. The gas leakage or mixture due to the generated cracks would weaken the output efficiency of PSOFC. Therefore, the thermal stress cannot be ignored for the design of the PSOFC, and investigation the life prediction on Crofer 22 APU is significant, since the life of the Crofer 22 APU interconnect can directly affect the life of whole SOFC during the long-term high temperature operation. For the Crofer 22 APU, its oxidation [19,22] and corrosion resistance, long-term electrical conductivity [23,24], chemical stability [25], formability [17], thermal performance and creep deformations [26e28] have been comprehensively investigated. However, little work involved on the creep fracture behavior, such as the damage and the CCG behavior of the Crofer 22 APU. Therefore, it is imperative to investigate its CCG behavior. In present paper, the CCG of the Crofer 22 APU under different operating temperature conditions were investigated by the continuum damage mechanic method, the results can offer basic information for the reliable design of the PSOFC.
Finite element simulation information Geometrical model For the CCG investigation of the material operated at high temperatures, compact tension (CT) specimen has been widely used according to the specification of ASTM E 1457-15 [29]. Specimen sizes adopted are described in Fig. 1. The width W and thickness B are 20 mm and 10 mm, respectively. The normalized initial crack length a0/W is 0.5.
Please cite this article as: Zhang Y-C et al., Creep fracture behavior of the Crofer 22 APU for the interconnect of solid oxide fuel cell under different temperatures, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.009
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Liu-Murakami constitutive model [31,32] was employed to calculate the material’s CCG behavior, the equations of this constitutive model were listed as follows: " # 3 2ðn þ 1Þ 3=2 p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ε_ cij ¼ Bsn1 u S exp ij 2 eq p 1 þ 3=n
(4)
A 1 exp q2 ðsr Þp exp q2 u q2
(5)
u_ ¼
sr ¼ asІ þ ð1 aÞseq
Fig. 1 e Geometrical size of the CT specimen.
Meshing and applied boundary conditions Fig. 2 delineates the meshing of CT specimen, and the applied element type is C3D8R.To reduce the calculating time and guarantee the calculating precision, only local mesh at the vicinity of crack tip was refined [30], as described in Fig. 2 (a). Three sets element-node number of 30141e35155, 18920e22176 and 14441e16885, respectively, were adopted to carry out the mesh independence analysis. The geometry of CT specimen is Y-axis and Z-axis symmetry, therefore, only 1/4 of the geometrical model was adopted to save the computing time. Boundary conditions of plane 1 and plane 2 are Y-axis and Z-axis symmetry, respectively. The temperature of 650, 700, 750 and 800 C, which is the traditional operating temperature of SOFC were used to investigation the temperature effect on CCG behavior of CT specimen. The temperatures were exerted on the element nodes. The loads were characterized in the mechanical parameter of initial stress intensity factor K. It is applied on the pffiffiffiffiffi loading point, as described in Fig. 2 (b). The K ¼ 2.73 MPa, m was adopted, it can be calculated by the following equations: K¼
P 2 þ a=W f ða = WÞ BW1=2 ð1 a=WÞ3=2
(1)
where, A, B, p and q2 are material constant, n the creep stress exponent, seq the von Mises stress, sr the fracture stress, sІ the maximum principal stress. u is the damage variable, it increases with increasing creep time. a denotes the multi-axial creep parameter. For the stainless steel, the value of a is 0.43 [33]. Sij and ε_ cij are stress and creep strain rate tensor, respectively. The parameters in Eqs. (4)e(6) are usually acquired by fitting the uni-axial creep data. The uni-axial creep data of the Crofer 22 APU under different temperatures are referenced from literature [26]. Based on the Norton equation of ε_ c ¼ Bsn , the parameters of B and n can be obtained from the log-log relationship between the s and ε_ c , as illustrated in Fig. 3. The variation of the s-_εc slope in Fig. 3 demonstrates that the uniaxial ε_ c increases with enlarging of the temperature under same stress levels. The parameters A and p can be obtained by fitting the relationship between s and rupture time tf in log-log coordinate of Fig. 4. The fitting equation is expressed: tf ¼
Material constitutive model Total deformation εtotal of Crofer 22 APU at high temperatures includes elastic deformation εe , plastic deformation εp and creep deformation εc . The constitutive equation can be expressed as follows: εtotal ¼ εe þ εp þ εc
(3)
The εe is calculated by the generalized Hooke law, εp follows the von Mises yield criterion. The parameters used for calculating εe and εp are summarized in Table 1.
1 Asp
(7)
The parameter q2, it is hard to get directly. It is usually considered as that q2 ¼ f þ 2 [31]. The parameter f can be obtained by the normalized creep strain, as follows: 1n=ðfþ1Þ
ε 1 t 1 1 ¼ n Bs tf 1 nðf þ 1Þ tf
f ða = WÞ ¼ 0:886 þ 4:64ða = WÞ 13:32ða=WÞ2 þ 14:72ða=WÞ3 5:6ða=WÞ4
where, P is the applied load, the unit is N, a the instantaneous creep crack length.
(6)
(8)
(2)
All the parameter values applied in Liu-Murakami constitutive model are listed in Table 2. The Eqs. (4)e(6) were translated by the Fortran language to integrate the commercial software of ABAQUS. When the accumulated damage value of u for the Gaussian integral point attaches its critical value ucr , the mechanical strength of the related finite element decreases very quickly. It is considered as failed and its loading capability lost. For the critical failure value of ucr , 0.99 [34] is widely used in the simulation process. It has been verified that ucr ¼ 0:99 can ensure the simulation accuracy of the damage analysis [35]. To characterize the damage effect on high temperature mechanical strength, the elastic modulus E is decreased with the u accumulating based on the relationship between u and E:
Please cite this article as: Zhang Y-C et al., Creep fracture behavior of the Crofer 22 APU for the interconnect of solid oxide fuel cell under different temperatures, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.009
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Fig. 2 e CT specimen meshing and applied boundary conditions.
Eiþ1 ¼ ð1 ui ÞEi
(9)
where, Eiþ1 and Ei are the elastic modulus at the increment time of iþ1 and i, respectively. ui is the damage value at the increment time of i.
agreement with experimental data, certifying that the Eqs. (4)e(6) with the parameters in Table 2 could well forecast the creep performances of Crofer 22 APU. Therefore, the parameters in Table 2 have been adopted to calculate the CCG behaviors of this material.
Mesh independence validation
Results and discussion To verify the reliability of the parameter values applied in the Liu-Murakami constitutive equation, the prediction and experimental data of the uniaxial creep deformations at different temperatures are compared, as illustrated in Fig. 5. The comparison shows that the prediction data present good
Element size can affect the calculate precision of the numerical results. Usually, the smaller of element size, the more precise are the simulation results. However, the computation time is increased sharply with the decreasing of the element
Table 1 e Mechanical performances of Crofer 22 APU at different temperatures. T ( C)
Yield strength (MPa)
650 700 750 800
162 92 57 44
Tensile strength Elastic modulus E (MPa) (GPa) 203 102 64 48
157 91 66 44
Fig. 4 e Variation of the tf with s under different temperatures.
Table 2 e Creep parameters used in Liu-Murakami constitutive model under different temperatures.
Fig. 3 e Variation of ε_ c with s at different temperatures.
Parameter
650 C
700 C
750 C
800 C
q2 A p B n
8.21 1.47e-9 4.02 2.57e-12 4.58
9.22 2.88e-10 5.29 3.55e-12 5.86
11.20 1.20e-9 5.45 2.57e-12 6.03
12.11 4.20e-9 6.00 3.24e-12 7.67
Please cite this article as: Zhang Y-C et al., Creep fracture behavior of the Crofer 22 APU for the interconnect of solid oxide fuel cell under different temperatures, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.009
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Fig. 5 e Comparison between the prediction and experimental creep data of Crofer 22 APU at (a) 650 C；(b) 700 C；(c) 750 C；(d) 800 C.
size. Therefore, both the computation time and cost should be given consideration, and the mesh independence validation of the finite element model should be carried out to determine a suitable finite element size. Fig. 6 shows the mesh independent validation used by the sI and seq along Path 1. Path 1 is described in Fig. 7. For both the sI and seq , when the finite element size decreases to 0.1 mm, the values of the these two kinds of stress are almost keeping the same, demonstrating that the computational accuracy can be guaranteed. However, the calculating time of the finite element analysis with 0.05 mm element size is five times longer than that of the 0.1 mm. Therefore, in present paper, the 0.1 mm mesh size was applied in the finite element analysis.
Temperature effect of CCG behavior Fig. 8 illustrates the variation of sI and seq with the creep time under different temperatures along path 1. For sI , all peak stresses under different temperatures locate before the crack tip, and they are first decreasing and then increasing with time. At initial creep stage, the stresses at the crack tip are relaxed by the creep deformation. With increasing creep time, a crack occurs, and the magnitude of the stress at the nearby of the crack reduces to a small value. The reason for that is the damaged element losing the loading capability. The peak
stresses of the CT specimen are still located before the newly generated crack tip, but the magnitude of the peak stress is larger than that at the initial creep stage. With temperature increasing, the peak stresses reduce due to stress relaxation effects. In the vicinity of the crack tip region, the value of maximum principal stress is large, while at the large distance along path1, it can be seen from Fig. 8, the maximum principal stress is decreased to a small value. For the von Mises stress, the value is large, and it further increases with increasing time. The maximum principal stress distribution of CT specimen at the temperature of 650 C is illustrated in Fig. 9 (a). It is known at the large distance area of the path1, the region A in Fig. 9 (a), the maximum principal stress is small, while the value of middle principal stress (sII ) and minimum principal stress (sIII ) are large, as shown in Fig. 9 (b) and (c), respectively. Both the middle principal stress and minimum principal stress are compressive. The von Mises stress seq calculated by the maximum, middle and minimum principal stress, as follows: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 2 seq ¼ 1 2ððsI sII Þ2 þ sII sIII þ sIII sI
(10)
From the Eq. (10) and the stress distribution in Fig. 9, it is known that although the value of sI is small, the value of sII and sIII are large, therefore, the value of von Mises stress is
Please cite this article as: Zhang Y-C et al., Creep fracture behavior of the Crofer 22 APU for the interconnect of solid oxide fuel cell under different temperatures, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.009
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Fig. 6 e Mesh independence validation of the finite element analysis used by stresses along Path 1.
Fig. 7 e Path 1 in the CT specimen.
larger than that the maximum principal stress sI . With the growth of creep crack length, the effective specimen cross section area decreases, so the von Mises stress increases with increasing creep time, as shown in Fig. 10. Since the crack growth path is not always a straight line, as illustrated in Fig. 13, the length of the region that the stresses are very small could not reflect the true length of the crack. The corresponding crack length under different temperatures and creep times in Fig. 8 can be acquired from Fig. 11 (a). Creep crack growth behavior is one of the key factors that characterization the high temperature strength of the
Fig. 8 e Stress analysis of the CT specimen along Path 1 under different temperatures.
material. Fig. 11 shows the creep crack and loading point displacement (LPD) growth with time. The shapes of the CCG and LPD curves are similar to that uni-axial creep curve. At final stage, both the values of crack length and LPD grow fast, this stage includes more than 80% of the total crack length or LPD value. In the ASTM E 1457, the crack initiation (CI) time is defined as the time that crack length increase to 0.2 mm. Therefore, the CI time of CT specimen under the temperature of 650, 700, 750 and 800 C are 188 h, 19 h, 0.2 h and 0.11 h, respectively. The corresponding fracture time are 1297 h, 42 h, 1.8 h and 0.25 h, respectively. The fracture time of CT specimen decreases with temperature increasing. While the values of the LPD present the tendency of increasing firstly and then decreasing, this is mainly caused by the different yield strength and tensile strength under different temperatures. From the Fig. 8, it is known that the stresses at the nearby of crack tip decreases with increasing temperature. Based on the data in Figs. 8 and 11, it is concluded that the temperature effect on CCG behavior of Crofer 22 APU is more evident than that the stress effect. Fig. 12 shows the contour of creep damage evolution for the Crofer 22 APU at the four temperatures. The red region in
Please cite this article as: Zhang Y-C et al., Creep fracture behavior of the Crofer 22 APU for the interconnect of solid oxide fuel cell under different temperatures, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.009
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Fig. 9 e Principal stress distribution in CT specimen at the temperature of 650 C (a) maximum principal stress (b) middle principal stress (c) minimum principal stress.
damage contour represents the damage values of the gauss integration points attach to the critical failure value of 0.99, the corresponding finite elements are failed. The creep crack morphology under the four temperatures extend in the form of finger nail, so the crack length in Fig. 11 (a) was calculated by the nine-point average method. Most of the cracks extended at the symmetrical plane, and also, some cracks occurred at a certain distance from the symmetrical plane, as shown in Region B of the Fig. 12 (b) and Fig. 13. In the CCG test of high temperature materials, the CCG plane of CT specimen is also not extended along a fixed face [36], such as the CLAM steel, as illustrated in Fig. 14. For the materials statically loaded at high temperatures, the creep cavities are
usually generated along the grain boundaries or in the interior of the grains different directions and locations, the creep cavities continued to growth and at last connect with the main crack, resulting in the crack extended forward with twists and turns. Grain growth decreases in dislocation density and coarsening of precipitates during the creep process can cause the microstructure change of the material [37]. Moreover, microstructural change of the material also can result in the stress concentration along the grain boundary or in the grain, causing the twisted creep crack. The creep damage constitutive model used in present paper is established based on the creep voids nucleation and growth theory, therefore, the numerical method used in
Please cite this article as: Zhang Y-C et al., Creep fracture behavior of the Crofer 22 APU for the interconnect of solid oxide fuel cell under different temperatures, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.009
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Fig. 10 e von Mises stress distribution in the CT specimen under different times at the temperature of 650 C (a) 1199 h (b) 1297 h. present paper can reasonably reflect the creep crack growth behavior of the Crofer 22 APU steel. The creep fracture mechanics parameter C* is usually adopted to characterize material’s CCG rate [36,38,39]. For the CT specimen, it can be obtained from Eq. (11) [29]: PV_ c n h C* ¼ pffiffiffiffiffiffiffiffiffiffiffi B,Bn ðW aÞ n þ 1
(11)
where, V_ c is the time dependent displacement rate of loading point, it can obtained directly by the finite element analysis. h is the geometric function. The average value h of CT specimen is usually taken as 2.2 [29]. The CCG rate a_ is predicted by Eq. (12) with C*: a_ ¼ a0 C*z
(12)
where, a0 and z are the material constants. Only when the ratio of the time dependent LPD rate V_ c and the total LPD rate V_ t is larger than 0.5, the C* can be reasonably applied to characterize the CCG rate. Based on the data in Fig. 11, the CCG rate a_ under different temperatures can be obtained, as described in Fig. 15. The results illustrate that the slopes of C*- a_ are nearly the same under the temperature of 650 C and 700 C. The slope of C*- a_ at the temperature of 750 C is the same as that at 800 C. But the slope of C*- a_ under the temperature of 650 C and 700 C is smaller than that the 750 C and 800 C, demonstrating that the CCG rate at 750 and 800 C is larger than that the 650 C and 700 C. All the data in Fig. 15 fall within the area of 95% prediction band, and the CCG rate of this material can be predicted by a_ ¼ 3:8e2C*0:91 . For the value of z, it is usually less than 1.0 [40], in present study, z ¼ 0:91, therefore, the prediction equation is valid, and the CCG rate of Crofer 22 APU can be
Fig. 11 e (a) Creep crack length and (b) load point displacement growth with time at different temperatures.
Please cite this article as: Zhang Y-C et al., Creep fracture behavior of the Crofer 22 APU for the interconnect of solid oxide fuel cell under different temperatures, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.009
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Fig. 12 e The contour of creep damage evolution for the Crofer 22 APU at the temperature of (a) 650 C, (b) 700 C, (c) 750 C and (d) 800 C. Please cite this article as: Zhang Y-C et al., Creep fracture behavior of the Crofer 22 APU for the interconnect of solid oxide fuel cell under different temperatures, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.009
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Fig. 13 e Creep damage cross section distribution of the Crofer 22 APU at Region B in Fig. 12. predicted under different stress levels. From the Fig. 15, it also can conclude that the temperature effect on the CCG behavior of Crofer 22 APU is more evident than that the stress effect.
Conclusions In present paper, creep fracture of Crofer 22 APU for the interconnect of SOFC under different temperatures were investigated by continuum damage mechanics method. The main results and conclusions are obtained:
Fig. 14 e Creep crack extending path of the CLAM steel.
Fig. 15 e Variation of the CCG rate with C* under different temperatures.
(1) The Liu-Murakami creep damage constitutive equations of Crofer 22 APU under different temperatures are established. Compared with the experimental uniaxial creep curves, the established constitutive equations can accurately prediction the CCG of the Crofer 22 APU. (2) The crack fracture time of the CT specimen at 650, 700, 750 and 800 C are 1297 h, 42 h, 1.8 h and 0.25 h, respectively. It is concluded that the temperature effect on the creep crack growth behavior is more evident than that the stress effect. (3) The slopes of C*- a_ are nearly the same under the temperature of 650 C and 700 C. The slope of C*- a_ at the temperature of 750 C is the same as that at 800 C. But the slope of C*- a_ under the temperature of 650 C and 700 C is smaller than that the 750 C and 800 C, demonstrating that the CCG rate at 750 and 800 C is larger than that the 650 C and 700 C. All the data of C*a_ fall within the area of 95% prediction band, and the CCG rate of Crofer 22 APU can be predicted by a_ ¼ 3:8e2C*0:91 .
Please cite this article as: Zhang Y-C et al., Creep fracture behavior of the Crofer 22 APU for the interconnect of solid oxide fuel cell under different temperatures, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.009
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Acknowledgments [16]
Thanks for the supporting of the National Natural Science Foundation of China (Grant No. 51805545), the Fundamental Research Funds for the Central Universities (Grant No. 18CX02151A).
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Please cite this article as: Zhang Y-C et al., Creep fracture behavior of the Crofer 22 APU for the interconnect of solid oxide fuel cell under different temperatures, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.009