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Stress analyses for the glass joints of contemporary sodium sulfur batteries
Journal of Power Sources 269 (2014) 773e782
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Stress analyses for the glass joints of contemporary sodium sulfur batteries Keeyoung Jung a, Solki Lee b, Goun Kim a, Chang-Soo Kim b, * a b
Energy Storage Materials Research Center, Research Institute of Industrial Science and Technology (RIST), Pohang, Kyungbuk 790-330, South Korea Materials Science and Engineering Department, University of Wisconsin-Milwaukee, 3200 N. Cramer St., Milwaukee, WI 53211, USA
h i g h l i g h t s FEA model was developed to predict thermal stress concentrations of NaS batteries. Stress concentrations are highly affected by the CTEs and shapes of sealing end tip. Convex tip end shape showed the minimum stress concentration during assembly. CTE of 7.8 106 K1 showed minimum local stress concentration for a convex tip end.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 21 June 2014 Received in revised form 10 July 2014 Accepted 11 July 2014 Available online 18 July 2014
During the manufacturing and thermal cycles of advanced contemporary large sized sodium sulfur (NaS) batteries, thermally driven stresses can be applied to the glass sealing joints, which may result in catastrophic cell failure. To minimize the thermal stresses at the joints, there is a need to develop a method to properly estimate the maximum thermal stresses by varying the materials properties and shapes of the sealing area, and thereby determine the properties and shapes of sealing material at the joints. In the present study, the optimum coefficient of thermal expansion (CTE) of the glass sealant and end shape of the glass sealing area (i.e., concave, flat, and convex shapes) have been determined using the finite-element analysis (FEA) computation technique. The results showed that the CTE value of 7.8 106 K1 with a convex end shape would have the lowest stress concentration in the vicinity of glass sealing joints for the prototype tubular NaS cell design adopted in this work. © 2014 Elsevier B.V. All rights reserved.
Keywords: Sodium sulfur (NaS) cell Glass sealing Finite element analysis (FEA) Coefficient of thermal expansion (CTE) Brittle fracture
1. Introduction Recently, sodium sulfur (NaS) batteries have been considered as one of the most promising candidates for grid scale energy storage system (ESS) applications [1,2]. This highly efficient battery technology was originally developed for electric vehicles (EV) and space applications for a long time [3e6], since Ford motors has first introduced the principles of this battery in 1966 [7]. Based on this prior work, the first commercialization of NaS batteries for MW scale load leveling purposes were successfully demonstrated in 2003 by NGK (NGK Insulators, Ltd., Japan) and TEPCO (Tokyo Electric Power Company, Japan) procuring the technology for EV applications of ABB (ABB Ltd., Switzerland, formerly BBC) in 1988 [8,9]. They are expanding their applications to frequency regulation
* Corresponding author. Tel.: þ1 414 229 3085; fax: þ1 414 229 6958. E-mail address: [email protected] (C.-S. Kim). http://dx.doi.org/10.1016/j.jpowsour.2014.07.071 0378-7753/© 2014 Elsevier B.V. All rights reserved.
purposes as well. The unit cell that they developed for ESS applications had the largest nominal capacity (1200 Wh) ever. Later in 2006 and 2010, respectively, China and South Korea started to exert intensive efforts on the system level development targeting the commercialization of NaS batteries for grid scale energy storage [10e12]. As well described elsewhere [10e14], NaS batteries have a number of advantages for large scale electrochemical ESS devices, such as no use of expensive raw materials, long discharge time, capability to have high energy capacity (up to larger than 1200 Wh per cell), long lifetime and cycle life (over 15 years and up to 4500 cycles at their full power), and high specific and volumetric energy densities (222 Wh kg1 and 367 Wh L1) allowing small footprints. Fig. 1(a) shows the schematic design of a typical central (tubular) type NaS cell used in this study. As can be better seen in the enlarged image of Fig. 1(b), a glass sealing joint is comprised of an insulating ring (a-Al2O3), solid electrolyte (b/b00 -Al2O3), and glass sealant. The glass sealant is to bond between the insulating ring and
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Fig. 1. (a) Schematic design of a typical tubular NaS cell used in this study, and (b) enlarged image to show the details of the glass sealing joint area of the NaS cell.
the open end of a solid electrolyte separating anode and cathode compartments. It forms a bond between a-Al2O3 and b/b00 -Al2O3 in two directions, horizontal and vertical directions as seen in Fig. 1(b). Fig. 2(a) shows a cross-sectional optical micrograph (OM) of a glass sealing joint. Typical compositions of glass sealants for sodium sulfur and sodium nickel chloride batteries are aluminoborosilicate glass which mainly contains SiO2, Al2O3, and B2O3, along with alkali oxides, such as Li2O, K2O, Na2O, MgO, and others [4,15e16], and sometimes Bi2O3 [17]. The determination of relevant compositions of sealing glass is extremely difficult because of a number of requirements for high temperature sealing, which include (1) adequate coefficient of thermal expansion (CTE) to minimize the thermal strain via freeze/thaw cycles, (2) thermal shock resistance, (3) corrosion resistance against molten sodium, vaporized sulfur, and sodium polysulfides (Na2Sx, where x ¼ 3e5), (4) good toughness, (5) high glass transition temperature, (6) acceptable bonding strength, (7) acceptable hermiticity related with pore sizes and their distribution, and more. Among these requirements, the crack initiation at the tip of a glass sealing joint, which is one of the major failure modes, is closely related to (1) the CTE mismatches between dissimilar material types including aAl2O3, b/b00 -Al2O3, and glass sealant, (2) the pore or defect sizes at the tip of and in the bulk of the glass sealing joint, and (3) the fracture toughness of the seal glass based on Griffith's brittle fracture (Type I) criterion. Given the fracture toughness and pore/defect sizes at the tip and in the bulk, the stress concentrations resulting from the CTE differences will govern the crack initiation. In this study, a typical tubular sodium sulfur cell was digitized to conduct finite-element analyses (FEA) seeking to determine the best CTE range and seal geometry of sealing glasses. The details of the full three dimensional computational tool used in this study have been previously introduced with a successful demonstration to understand the effect of size, shape, and location of insert metals in thermal compression bonding (TCB) for tubular NaS batteries [12]. Although some attempts to theoretically quantify the stresses that can be developed during thermal cycles were made by earlier NaS cell developers, such as an FEA work by Barrow [4], the
calculation seems to be too simplified presumably due to the limited computational capability at the time in the 1980's. Although this work provides many insights, because the sizes of cells were too small to apply to the larger and more sophisticated modern NaS cells for ESS applications. Therefore, there is a need to develop an advanced in silico computational model in conjunction with contemporary computational capability and the larger cell design recently developed and optimized for energy storage purposes so that the required thermomechanical properties of sealing glasses can be better predicted. In the following sections, we will discuss the prediction of appropriate CTE values of glass sealing materials and the seal geometry to minimize the possibility of crack initiation. 2. Computational methods 2.1. Description of a glass joint and mesh generation To digitize a prototype NaS cell, Rhinoceros (version 5.0, McNeel Inc.) auto computer-aided design (CAD) software was employed, as shown in Fig. 1. The outer radius and height of this model were 43 and 375 mm, respectively. Some components of a cell, such as wick tube, cathode felt made of carbon/glass fiber, etc., were not included in the computation because their effects on thermal stress concentrations at the glass sealing joints would be negligible. In addition, the prototype design does not contain the groove of the outer container, as it was found that the groove mainly influences the stress concentration of metallic TCB bonding. Fig. 2(a) is an optical micrograph showing the example of actual geometry of a glass joint (the design is different from the modeled prototype cell used in this study). As can be seen in the figure, the geometry of a glass sealing tip on the cathode side is generally maintained in a concave shape because the vertical gap between the insulating ring and electrolyte functions as a glass reservoir to accommodate the tolerances in the amount of glass paste or tape for different cells. On the other hand, the geometry of a glass sealing tip region on the anode side can be controlled to minimize stress accumulation.
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Fig. 2. (a) Optical micrograph (OM) of a glass sealing joint, and (b) schematic illustrations of three representative shapes of glass sealing joint tips, i.e., concave, flat, and convex systems.
Three representative glass joint end tip geometries on the anode side (horizontal) are shown in Fig. 2(b). The shape of the tip can be controlled to have a concave, flat, or convex shape on the anode side by adjusting the amount of glass sealant (amount of paste or dimension of glass tape) and/or applied pressure at bonding temperatures (800e950 C). Note that the geometry of a glass joint end tip will show characteristic curvatures depending on the wettability of glass as well as the amount of sealant. Conventional wisdom is that the wettability of glass on b/b00 -Al2O3 is higher than that on a-alumina; the wetting angle of glass sealing to the electrolyte (qG/b) is smaller than that of the insulating header side (qG/a) as can be seen in Fig. 2(a). To maintain a good mesh quality to conduct sophisticated FEA computations, internal cell components having a substantially different scale and/or high aspect ratio have been subdivided into a number of mesh parts. The FEA mesh generation was accomplished through a commercial mesh generation software (hyperMesh, version 10.0, Altair Engineering Inc.). The 8-node linear brick, reduced integration hexahedral-type element (C3D8R) was used for all components except the glass sealing joint with concave and convex tips, which have adopted 6-node linear triangular prismtype element (C3D6) due to its geometric complexity. The total numbers of elements for digitized cells with concave, flat, and
convex glass joint end shapes were 1,123,923, 191,173, and 454,773, respectively. Because the disintegration of joints is observed with a much higher frequency on the anode side of the joint, and compression stress is applied to the glass tip surfaces of vertical part on the cathode side, all of the thermal stress analysis was conducted based on the tip surfaces of the horizontal part of the joints (see Fig. 1(b)). 2.2. Material properties As a NaS cell comprises of a number of different materials, and the CTE differences among the constituent materials are one of the primary causes of thermal stresses, materials properties with temperature changes to be incorporated into the FEA simulations needs to be as accurate as possible for more reliable predictions. The most common alloy for metal components of contemporary NaS cells (i.e., container, insert metal, bracket, collar, top and bottom caps, and etc.) is the aluminum alloy (Al3003). The stress absorption in the insert metals made up of Al 3003 will greatly influence the stress concentration in the glass sealing joints area [12]. As ceramic components, a-Al2O3 and b/b00 -Al2O3 are typically used for an insulating ring and solid electrolyte, respectively. Fig. 3 shows the thermo-mechanical properties of Al3003, a-Al2O3, b/b00 -
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Al2O3, and glass that were used in the computation. Poisson's ratios for Al3003, a-Al2O3, b/b00 -Al2O3, and glass were 0.33, 0.23, 0.23, and 0.22, respectively [12]. The material properties were adopted from existing literature [12,18] or measured in-house. The CTEs of glass
materials were measured by an extensometer in a vacuum furnace (Netzsch DIL 402C). The measured CTEs were close to a constant in the temperature range of 25e520 C and showed a sudden increase above the glass transition temperature, Tg. The modulus of the glass sealant was assumed to be very low above Tg. With this assumption, different values of CTEs in the range of 5.0e8.5 106 K1 were tested to study the CTE effects of the glass sealants on the thermal stress concentrations during the assembly and the thaw-and-freeze processes. 2.3. Computation conditions Throughout the FEA simulations in this work, a static computation condition was assumed, ignoring any dynamic phenomena, such as electrochemical endothermic and/or exothermic cell reactions, since the actual heating and cooling rates are maintained at slower than 0.5 C min1 to minimize any possible thermal shock. The temperature changes during glass bonding and TCB were, however, included in the computation to realistically model the residual stresses at the glass joint. The bonding process for glass sealing and TCB were conducted at 950 and 520 C, respectively. Fig. 4(a) schematically illustrates the temperature changes during the NaS cell header assembly process and thaw-and-freeze cycles. During the glass sealing assembly step, the a-Al2O3 insulating ring and b/b00 -Al2O3 electrolyte are assembled with a glass sealant at 950 C, and the temperature drops to the room temperature (i.e., 20 C). Then, the temperature of the “a-b assembly” is increased to 520 C for TCB. The TCB is to bond between metal (i.e., bracket and collar) and the ceramic components with an insert metal. The temperature decrease from 520 C to 20 C of the “TCB assembly”
Fig. 3. Material properties used in the computation to show (a) CTE (Al3003, alphaand beta-alumina), (b) elastic modulus (Al3003, alpha- and beta-alumina, and glass), and (c) true plastic stressestrain curves for Al3003.
Fig. 4. Schematic illustrations to show the temperature changes of (a) the experimental NaS cell header assembly and (b) the computational steps.
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will yield additional residual thermal stresses. With those residual stresses in the glass and TCB areas, all of the other remaining components (i.e., container and cap) are finally assembled together via the electron beam welding (EBW) technology at 20 C. The thaw-and-freeze thermal cycle has been simulated by changing the system temperatures from 20 / 350 / 20 C considering that the cell operation temperature is 350 C. Assuming that glass softening occurs near 520 C, the total simulation was subdivided into simpler 2 steps to reflect this experimental procedure, i.e., (i) the glass sealing and TCB assembly step and (ii) the thaw-and-freezing thermal cycle step, as shown in Fig. 4(b) using the solid lines. Note that the glass sealing assembly process has been simplified due to the complete elastic characteristics of glass sealing, a-Al2O3, and b/ b00 -Al2O3 in the ranges of 520e20 C and 20e520 C, and the steps in dotted/dashed lines of Fig. 4(b) were ignored. Fig. 5 presents the axisymmetric computational domain (1/12 of the entire cell) that was generated for tubular NaS cells to reduce the computational time in the present work. All of the FEA computations were carried out based on this axisymmetric model. In the assembly step, the displacement of bottom surface of the insulating header was fixed along the cell height direction to prevent the rigid body motion. Additional boundary condition constraints on the outer surface of collar and bracket were imposed in this step to represent the experimental assembly procedure; the movement of the components along the radial direction was restrained by external jigs. In the thawing step, the displacements of the top surface of the cathode material and the bottom surface of the container were fixed along the cell height direction in the temperature range of 20e119 C and 119e350 C, respectively, in order to incorporate the solid/liquid phase transformations of cathode materials. These boundary conditions in the assembly and the thaw-and-freeze thermal cycle steps are illustrated in Fig. 5. The coexistence of S and different Na2Sx in the cathode compartment after electrochemical cycles and a certain period of time may induce the slumping of sodium polysulfides, which results in the
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accumulation of heavier Na2Sx on the bottom of the cathode compartment. This slumping of Na2Sx can cause solidification of cathode material from the bottom upon freezing since the melting temperature (Tm) of the Na2Sx (Tm ¼ 235e285 C) is higher than S (Tm ¼ 119 C). Accordingly, the gap between the outer bottom of the electrolyte tube and the inner bottom of the cathode compartment could be filled with high Tm species first during cooling, and therefore higher thermal stresses would be applied to the header area. In this study, this slumping phenomenon was ignored in the computation, as it was revealed that the slumping does not much influence the stress concentrations and their distributions at the glass joints based on our previous study and other test sets in the current study [12]. As for the interface conditions, the direct contact regions of the glass sealing and TCB were all modeled as interfaces with infinite friction (i.e., tie condition), and all other interfaces were modeled to move freely (i.e., contact condition with no friction). 3. Results and discussion To adequately analyze the thermally driven stress components on the glass sealing tip surfaces with curved shapes, a relevant local coordinate system depending on the specific geometry of the particular nodal position must be defined. As shown in Fig. 6(a), an orthogonal local coordinate system has been defined at each calculation nodal point to quantify and extract the local stress components. The 1st, 2nd, and 3rd coordinates were defined to represent the in-plane and out-of-plane axes of the local surface element in the glass sealing ends; the 2nd coordinate lies along the circumferential direction of a cell, the 1st coordinate is set to be the in-plane normal direction of the 2nd coordinate, and the 3rd coordinate is defined as the surface normal (out-of-plane) direction. Fig. 6(b) shows a set of local coordinate systems along the surface of a concave-shaped glass sealing end (concave system). Using this user-defined local coordinate system at each FEA computational
Fig. 5. Boundary conditions and restrictions used during the (a) glass sealing and TCB assembly, (b) 25e119 C (solid sulfur), and (c) 119e350 C (liquid sulfur).
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Fig. 6. User-defined local coordinate system from (a) one computational node in the concave, flat, and convex systems and (b) multiple nodes in the concave system, and (c) the profiles of three normal stress components (local s11,s22, and s33) when a concave system undergoes a cooling process from 520 to 20 C after the thermal compression bonding assembly.
node, the profiles of three normal stress components (i.e., local s11,s22, and s33) from a representative node of concave tip are plotted in Fig. 6(c), when the concave system undergoes a cooling from 520 to 20 C after the TCB assembly. The local stresss were extracted from a representative nodal point indicated in Fig. 6(b). For this calculation, the CTE value of 7.0 106 K1 was selected as a reference. The stress profiles clearly show that local s33(in-plane
Mode I stress that is normal to the circumferential direction) is primarily responsible for the thermal tensile stress concentration; local s11 (out-of-plane direction) is nearly 0 and local s22 (cell circumferential direction) shows compressive characteristics. All the following stress analysis in this work is, therefore, focused on the local s33 tensile stress and the corresponding Mode I brittle fracture. The dominant crack initiation mechanisms for all other
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test cases with different CTEs and glass sealing end shapes were the tensile Mode I fracture along the local 33 direction. 3.1. Stress distributions in the concave shaped glass sealing tip Using the user-defined local coordinate systems described above, the stress accumulation was calculated for a cell with the glass sealant of a concave end shape as a reference. Fig. 7(a) shows the local s33 thermal stress distribution profiles at the nodes that have maximum s33 values for the concave systems with different CTE values of the glass sealants, 6.0, 7.9, and 8.5 106 K1. After the glass sealing and TCB joint assembly, these systems were subject to a cooling process from 520 to 20 C and a subsequent thawand-freeze thermal cycle by changing the temperatures, i.e., 20 / 350 / 20 C, as shown in the x-axis of Fig. 7(a). The results show that that the maximum tensile s33 values are strongly affected by the CTE of glass sealants, and the maximum s33 is observed in the lower area of the concave tip toward the direction of the b/b00 -Al2O3 solid electrolyte, as indicated in Fig. 6(a). It is thought that the location of maximum tensile stress positions is determined by the geometry of the header area. During cooling, the local tensile stress along the outer surface of the sealing tip in the 33 direction is expected because more contractions would occur in
the insulating ring (a-Al2O3) than in the solid electrolyte (b/b00 Al2O3). More importantly, the maximum tensile stresses exhibit the largest values after the 520 / 20 C cooling process, and they afterward simply show small variations of thermal stresses when the cells are under the subsequent thaw-and-freeze thermal cycle. In other words, the differences between maximum s33 tensile stress values between two of these three systems are almost constant during the cell operation throughout the entire thaw-and-freeze cycle. These results may lead to the following finding; minimizing the thermal residual stress accumulated in the glass sealing during cooling after assembly is the most critical to avoid crack initiation and subsequent crack propagation, joint disintegration, and the ultimate failure in the glass sealant area. The maximum thermal stress decreases during thawing and increases during freezing; however, the highest thermal stress concentration is predicted to occur at the end of the cooling before the thaw-and-freeze operation thermal cycle. The maximum thermal tensile streses are 115.5, 89.2, 93.3 MPa in tension after glass bonding and TCB joining processes at 20 C, and are 22.0, 33.4, and 4.6 MPa in compression after the 1st thaw-and-freeze at 20 C for cells with the CTE values of 6.0, 7.9, and 8.5 106 K1, respectively. Because these trends were identified for all of our test simulation cases, the analysis given below only concentrates on the stress concentrations after cooling considering that these are the maximum local tensile stress. Fig. 7(b) shows the local maximum tensile s33 at 20 C after cooling for systems with various CTE values of 5.0e8.5 106 K1. These results clearly show that when the CTE of a glass sealant is about 7.9 106 K1, the local stress concentration is minimized with a value of 89.2 MPa for a concave end shape. Therefore, it is suggested that glass sealants with a CTE of ~7.9 106 K1 would have the lowest possibility of inducing failure at the glass joints. Note that the calculated results could be influenced by different FEA meshing schemes such as sizes and element types. It is expected that the glass sealants with a larger number of FEA meshes will produce more details about the stress gradients along the surfaces. Prior to the computation, it was confirmed that the results properly represent the stress distributions on the glass sealant tip surface within the error range of less than ~5% by testing the results for a simpler cell design with a much larger number of meshes. Now that the maximum Mode I tensile stress along the tip surface can be properly estimated, it would be useful to conduct a numerical analysis to predict a critical surface defect (i.e., pores, microcracks, etc on the surface of glass sealant). The existence of the defects is practically unavoidable but the control of the maximum defect size is possible by optimizing the sealing procedure. Therefore, it is important to estimate the maximum tensile stress applied to the glass joint so that the specification of the maximum defect size (i.e. critical defect size to failure under a given thermal stress) can be determined. The critical defect size (CC) for an embedded ellipsoidal crack based on the Griffith brittle facture theory can be typically estimated by [19];
CC ¼
Fig. 7. (a) Local maximum s33 stress distribution profiles for the concave systems with 6.0, 7.9, and 8.5 106 K1 CTE, and (b) local maximum s33 stress values after the cooling process (before operation) at 20 C for concave systems with various CTE values.
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1 KIC 2 p f $s
(1)
where KIC, f, and s are the fracture toughness, geometry factor, and applied Mode I tensile stress, respectively. Since a typical fracture toughness (KIC) of glasses is known to be 0.7e0.8 MPa m1/2 [19], and the geometric factor is 0.64 for an ellipsoidal surface notch, the critical defect sizes (CC) of glass sealant can be expressed as a function of the applied tensile stress using Eq. (1). Fig. 8 presents the relationship between CC and the applied Mode I tensile stress when the glass sealants would have the fracture toughness and shape factor as mentioned. The two curves represent the upper (red
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smaller than 48e63 mm upon fabrication (blue dashed lines in Fig. 8). On the other hand, when the CTE value of the glass sealant materials is 6.0 106 K1, the thermal stress is 115.5 MPa and its corresponding critical defect size falls in the range of 29e37 mm (green dashed lines in Fig. 8), which is considerably smaller than the allowable critical defect size for the case of 7.9 106 K1. 3.2. Stress distributions in the flat and convex shaped glass sealing tips
Fig. 8. Plot of critical defect size (CC) with applied Mode I tensile stress (s).
curve) and lower (black curve) limits of the critical defect sizes with KIC values of 0.7 and 0.8 MPa m1/2, respectively. From this, the maximum defect size, CC, of the glass sealant can be readily estimated under a certain tensile stress. For a given NaS cell with the glass CTE of 7.9 106 K1, if the maximum tensile stress is 89.2 MPa, then the inherent defect size must be controlled to be
The effects of the shapes of glass sealing tips were examined next. As shown in Fig. 2(b), three representative shapes of glass sealing ends, i.e., concave, flat, and convex systems were studied. The shapes of sealant tips can be designed and controlled by adjusting the amount of glass sealants, applied pressure, heat treatment conditions, and whether to use a glass tape or paste. Again, the CTEs of 5.0e8.5 106 K1 were applied to the systems with flat and convex end shapes, and the CTEs that produce the maximum tensile stress based on the local coordinate systems at each computational point (Fig. 6(a)) have been identified. Also for the flat and convex systems, the local s33 showed higher values compared to the local s11 or s22. Much smaller stress concentrations were predicted for the out-of-plane s11 components; they were in the ranges of 10 to 4, 16 to 2, and 10 to 13 MPa for the concave, flat, and convex systems, respectively. Stresses along the circumferential direction (s22) were all negative showing the compression behaviors. In Fig. 9(a), the glass tip surfaces were illustrated to present the maximum local tensile stress (s33) areas.
Fig. 9. (a) Areas of glass sealant tip surfaces that experience the tensile and compressive stresses, and (b) maximum local tensile stresses from different systems with various tip shapes and CTE values of the glass sealing.
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Shaded ellipsoids represent the maximum local tensile s11 areas, and arrows indicate the directions of the maximum tension or maximum compression stresses, respectively. Note that stress distributions along the local 3-direction is important as the cell has a tubular geometry, and the positions for the shaded ellipsoids and arrows along the circumferential direction have been arbitrarily chosen for the purpose of visualization. From Fig. 9(a), it is clear that for all three systems, stresses of the tension and compression are predicted in the lower and upper parts of end tips, respectively. Similar to Fig. 7(b), the maximum local tensile stresses from the systems with different tip shapes are then plotted as functions of their different CTEs in Fig. 9(b). The results show that, (i) the variations of maximum s33 tensile stress can be substantially influenced by the shape of glass tip surface, and (ii) the best CTE values for the three cases are different. In particular, it was predicted that a lower glass CTE (6.8 106 K1) would lead to the best in resistance to the brittle fracture compared to relatively higher CTEs in the concave and convex systems. From the figure, it is seen that the convex system with the glass CTE of 7.8 106 K1 would show the lowest maximum local s33, which should be preferable to have more robust glass sealing joints. Although it can be intuitively inferred that the adequate CTE value of glass sealant would be 5e8 106 K1 as the CTEs of a- and b”-alumina are in the window of 5.3e8.8 106 K1 in the temperature range of 20e520 C (see Fig. 3(a)), the results can suggest better manufacturing guidance to minimize the probability of failure at the glass joints. In Fig. 10, a map is provided to guide allowable windows of critical defect sizes (CC) for concave, flat, and convex systems with various CTEs of glass sealants. It is valid for SiO2 based sealing glasses that have a fracture toughness in the range of 0.7e0.8 MPa m1/2 [19]. Different numbers of data are presented for the three cases in this figure since the computations were conducted until the best CTEs were sought in the 0.1 106 K1 CTE intervals. From Fig. 10, it is elucidated that the concave and convex systems should be mechanically more stable with the glass CTEs of 7.8e7.9 106 K1 with critical defect sizes of 62e83 mm and 48e62 mm, respectively, whereas the flat system will be most resistant to the thermal stress with the glass CTEs of 6.8 106 K1 and the critical defect size of 50e67 mm. It must be mentioned that this stress analysis is constrained to the concave, flat, and convex glass tip systems with the prototype cell geometry adopted in this study; the best CTE might be different
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among different cell designs. Through our computational study, we have demonstrated that, the optimum CTE values can be readily predicted by changing the actual cell design. It is expected that the best CTE of a glass sealant would be non-identical for a certain tip shape when different cell geometries and configurations are adopted. Although only three representative shapes of glass tips were studied as a demonstration of the tool developed in this study, it can be inferred that the amount of glass sealant as well as wetting properties are important factors because they can determine the curvature and shape of the tips, and consequently affect the mechanical of the glass joint. Therefore, during the assembly process of the glass sealing joints, the sealing glass itself and the amount of sealant should be carefully controlled toward higher stability and safety of a large sized contemporary NaS cell for EES applications. 4. Summary In the present work, we studied the effects of the CTE of glass sealants and their tip shapes on the stress accumulation at the glass joints, which is directly related to the stability of the ceramic joints and therefore the safety of NaS cells. A computational approach employing an FEA technique incorporating relevant materials properties, simulation conditions, and local coordinate systems has been developed in this study. Tensile stress concentrations using the user-defined local coordinate system at each computational point were calculated for the concave, flat, and concave end shapes of glass joints. With the FEA computational model, the results based on the representative prototype battery design adopted in the current study are summarized as follows. The glass joints will experience the largest stress accumulation during cooling in the assembly process between a- and b-Al2O3. The maximum tensile stress in the convex shape of a glass tip is smaller than those in the flat and concave systems. For a given prototype cell design, the CTE of a glass sealant of 6.8e7.9 106 K1, depending on the glass sealing tip shapes, could be suggested to minimize the probability of failure at the glass joints; the convex glass tip shape with 7.8 106 K1 CTE showed the lowest maximum tensile stress. For the concave and convex systems, the defect size on the surface of the sealing tip must be generally controlled to be smaller than 20e50 mm and 40e85 mm when the glass CTEs are 6.8 106 K1 and 7.9 106 K1, respectively. Acknowledgments This work has been supported by POSCO (Contract No. 2013A049) and the Korea Institute of Energy Technology Evaluation and Planning (KETEP) under the authority of the Ministry of Trade, Industry, and Energy of the Republic of Korea (Contract Nos. 2011201010004A and 2012T100100643). References
Fig. 10. Range of critical defect sizes (CC) for the concave, flat, and convex systems with various glass sealant CTEs.
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[9] R. Bauer, W. Haar, H. Kleinschmager, G. Weddigen, W. Fischer, J. Power Sources 1 (1976/77) 109e126. [10] Z. Wen, Y. Hu, X. Wu, J. Han, Z. Gu, Adv. Funct. Mater. 23 (2013) 1005e1018. [11] J.K. Min, C.-H. Lee, J. Power Sources 210 (2012) 101e109. [12] K. Jung, S. Lee, Y.-C. Park, C.-S. Kim, J. Power Sources 250 (2014) 1e14. [13] B.L. Ellis, L.F. Nazar, Curr. Opin. Solid State Mater. Sci. 16 (2012) 168e177. [14] X. Lu, G. Xia, J.P. Lemmon, Z. Yang, J. Power Sources 195 (2010) 2431e2442.
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Journal of Power Sources journal homepage: www.elsevier.com/locate/jpowsour
Stress analyses for the glass joints of contemporary sodium sulfur batteries Keeyoung Jung a, Solki Lee b, Goun Kim a, Chang-Soo Kim b, * a b
Energy Storage Materials Research Center, Research Institute of Industrial Science and Technology (RIST), Pohang, Kyungbuk 790-330, South Korea Materials Science and Engineering Department, University of Wisconsin-Milwaukee, 3200 N. Cramer St., Milwaukee, WI 53211, USA
h i g h l i g h t s FEA model was developed to predict thermal stress concentrations of NaS batteries. Stress concentrations are highly affected by the CTEs and shapes of sealing end tip. Convex tip end shape showed the minimum stress concentration during assembly. CTE of 7.8 106 K1 showed minimum local stress concentration for a convex tip end.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 21 June 2014 Received in revised form 10 July 2014 Accepted 11 July 2014 Available online 18 July 2014
During the manufacturing and thermal cycles of advanced contemporary large sized sodium sulfur (NaS) batteries, thermally driven stresses can be applied to the glass sealing joints, which may result in catastrophic cell failure. To minimize the thermal stresses at the joints, there is a need to develop a method to properly estimate the maximum thermal stresses by varying the materials properties and shapes of the sealing area, and thereby determine the properties and shapes of sealing material at the joints. In the present study, the optimum coefficient of thermal expansion (CTE) of the glass sealant and end shape of the glass sealing area (i.e., concave, flat, and convex shapes) have been determined using the finite-element analysis (FEA) computation technique. The results showed that the CTE value of 7.8 106 K1 with a convex end shape would have the lowest stress concentration in the vicinity of glass sealing joints for the prototype tubular NaS cell design adopted in this work. © 2014 Elsevier B.V. All rights reserved.
Keywords: Sodium sulfur (NaS) cell Glass sealing Finite element analysis (FEA) Coefficient of thermal expansion (CTE) Brittle fracture
1. Introduction Recently, sodium sulfur (NaS) batteries have been considered as one of the most promising candidates for grid scale energy storage system (ESS) applications [1,2]. This highly efficient battery technology was originally developed for electric vehicles (EV) and space applications for a long time [3e6], since Ford motors has first introduced the principles of this battery in 1966 [7]. Based on this prior work, the first commercialization of NaS batteries for MW scale load leveling purposes were successfully demonstrated in 2003 by NGK (NGK Insulators, Ltd., Japan) and TEPCO (Tokyo Electric Power Company, Japan) procuring the technology for EV applications of ABB (ABB Ltd., Switzerland, formerly BBC) in 1988 [8,9]. They are expanding their applications to frequency regulation
* Corresponding author. Tel.: þ1 414 229 3085; fax: þ1 414 229 6958. E-mail address: [email protected] (C.-S. Kim). http://dx.doi.org/10.1016/j.jpowsour.2014.07.071 0378-7753/© 2014 Elsevier B.V. All rights reserved.
purposes as well. The unit cell that they developed for ESS applications had the largest nominal capacity (1200 Wh) ever. Later in 2006 and 2010, respectively, China and South Korea started to exert intensive efforts on the system level development targeting the commercialization of NaS batteries for grid scale energy storage [10e12]. As well described elsewhere [10e14], NaS batteries have a number of advantages for large scale electrochemical ESS devices, such as no use of expensive raw materials, long discharge time, capability to have high energy capacity (up to larger than 1200 Wh per cell), long lifetime and cycle life (over 15 years and up to 4500 cycles at their full power), and high specific and volumetric energy densities (222 Wh kg1 and 367 Wh L1) allowing small footprints. Fig. 1(a) shows the schematic design of a typical central (tubular) type NaS cell used in this study. As can be better seen in the enlarged image of Fig. 1(b), a glass sealing joint is comprised of an insulating ring (a-Al2O3), solid electrolyte (b/b00 -Al2O3), and glass sealant. The glass sealant is to bond between the insulating ring and
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Fig. 1. (a) Schematic design of a typical tubular NaS cell used in this study, and (b) enlarged image to show the details of the glass sealing joint area of the NaS cell.
the open end of a solid electrolyte separating anode and cathode compartments. It forms a bond between a-Al2O3 and b/b00 -Al2O3 in two directions, horizontal and vertical directions as seen in Fig. 1(b). Fig. 2(a) shows a cross-sectional optical micrograph (OM) of a glass sealing joint. Typical compositions of glass sealants for sodium sulfur and sodium nickel chloride batteries are aluminoborosilicate glass which mainly contains SiO2, Al2O3, and B2O3, along with alkali oxides, such as Li2O, K2O, Na2O, MgO, and others [4,15e16], and sometimes Bi2O3 [17]. The determination of relevant compositions of sealing glass is extremely difficult because of a number of requirements for high temperature sealing, which include (1) adequate coefficient of thermal expansion (CTE) to minimize the thermal strain via freeze/thaw cycles, (2) thermal shock resistance, (3) corrosion resistance against molten sodium, vaporized sulfur, and sodium polysulfides (Na2Sx, where x ¼ 3e5), (4) good toughness, (5) high glass transition temperature, (6) acceptable bonding strength, (7) acceptable hermiticity related with pore sizes and their distribution, and more. Among these requirements, the crack initiation at the tip of a glass sealing joint, which is one of the major failure modes, is closely related to (1) the CTE mismatches between dissimilar material types including aAl2O3, b/b00 -Al2O3, and glass sealant, (2) the pore or defect sizes at the tip of and in the bulk of the glass sealing joint, and (3) the fracture toughness of the seal glass based on Griffith's brittle fracture (Type I) criterion. Given the fracture toughness and pore/defect sizes at the tip and in the bulk, the stress concentrations resulting from the CTE differences will govern the crack initiation. In this study, a typical tubular sodium sulfur cell was digitized to conduct finite-element analyses (FEA) seeking to determine the best CTE range and seal geometry of sealing glasses. The details of the full three dimensional computational tool used in this study have been previously introduced with a successful demonstration to understand the effect of size, shape, and location of insert metals in thermal compression bonding (TCB) for tubular NaS batteries [12]. Although some attempts to theoretically quantify the stresses that can be developed during thermal cycles were made by earlier NaS cell developers, such as an FEA work by Barrow [4], the
calculation seems to be too simplified presumably due to the limited computational capability at the time in the 1980's. Although this work provides many insights, because the sizes of cells were too small to apply to the larger and more sophisticated modern NaS cells for ESS applications. Therefore, there is a need to develop an advanced in silico computational model in conjunction with contemporary computational capability and the larger cell design recently developed and optimized for energy storage purposes so that the required thermomechanical properties of sealing glasses can be better predicted. In the following sections, we will discuss the prediction of appropriate CTE values of glass sealing materials and the seal geometry to minimize the possibility of crack initiation. 2. Computational methods 2.1. Description of a glass joint and mesh generation To digitize a prototype NaS cell, Rhinoceros (version 5.0, McNeel Inc.) auto computer-aided design (CAD) software was employed, as shown in Fig. 1. The outer radius and height of this model were 43 and 375 mm, respectively. Some components of a cell, such as wick tube, cathode felt made of carbon/glass fiber, etc., were not included in the computation because their effects on thermal stress concentrations at the glass sealing joints would be negligible. In addition, the prototype design does not contain the groove of the outer container, as it was found that the groove mainly influences the stress concentration of metallic TCB bonding. Fig. 2(a) is an optical micrograph showing the example of actual geometry of a glass joint (the design is different from the modeled prototype cell used in this study). As can be seen in the figure, the geometry of a glass sealing tip on the cathode side is generally maintained in a concave shape because the vertical gap between the insulating ring and electrolyte functions as a glass reservoir to accommodate the tolerances in the amount of glass paste or tape for different cells. On the other hand, the geometry of a glass sealing tip region on the anode side can be controlled to minimize stress accumulation.
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Fig. 2. (a) Optical micrograph (OM) of a glass sealing joint, and (b) schematic illustrations of three representative shapes of glass sealing joint tips, i.e., concave, flat, and convex systems.
Three representative glass joint end tip geometries on the anode side (horizontal) are shown in Fig. 2(b). The shape of the tip can be controlled to have a concave, flat, or convex shape on the anode side by adjusting the amount of glass sealant (amount of paste or dimension of glass tape) and/or applied pressure at bonding temperatures (800e950 C). Note that the geometry of a glass joint end tip will show characteristic curvatures depending on the wettability of glass as well as the amount of sealant. Conventional wisdom is that the wettability of glass on b/b00 -Al2O3 is higher than that on a-alumina; the wetting angle of glass sealing to the electrolyte (qG/b) is smaller than that of the insulating header side (qG/a) as can be seen in Fig. 2(a). To maintain a good mesh quality to conduct sophisticated FEA computations, internal cell components having a substantially different scale and/or high aspect ratio have been subdivided into a number of mesh parts. The FEA mesh generation was accomplished through a commercial mesh generation software (hyperMesh, version 10.0, Altair Engineering Inc.). The 8-node linear brick, reduced integration hexahedral-type element (C3D8R) was used for all components except the glass sealing joint with concave and convex tips, which have adopted 6-node linear triangular prismtype element (C3D6) due to its geometric complexity. The total numbers of elements for digitized cells with concave, flat, and
convex glass joint end shapes were 1,123,923, 191,173, and 454,773, respectively. Because the disintegration of joints is observed with a much higher frequency on the anode side of the joint, and compression stress is applied to the glass tip surfaces of vertical part on the cathode side, all of the thermal stress analysis was conducted based on the tip surfaces of the horizontal part of the joints (see Fig. 1(b)). 2.2. Material properties As a NaS cell comprises of a number of different materials, and the CTE differences among the constituent materials are one of the primary causes of thermal stresses, materials properties with temperature changes to be incorporated into the FEA simulations needs to be as accurate as possible for more reliable predictions. The most common alloy for metal components of contemporary NaS cells (i.e., container, insert metal, bracket, collar, top and bottom caps, and etc.) is the aluminum alloy (Al3003). The stress absorption in the insert metals made up of Al 3003 will greatly influence the stress concentration in the glass sealing joints area [12]. As ceramic components, a-Al2O3 and b/b00 -Al2O3 are typically used for an insulating ring and solid electrolyte, respectively. Fig. 3 shows the thermo-mechanical properties of Al3003, a-Al2O3, b/b00 -
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Al2O3, and glass that were used in the computation. Poisson's ratios for Al3003, a-Al2O3, b/b00 -Al2O3, and glass were 0.33, 0.23, 0.23, and 0.22, respectively [12]. The material properties were adopted from existing literature [12,18] or measured in-house. The CTEs of glass
materials were measured by an extensometer in a vacuum furnace (Netzsch DIL 402C). The measured CTEs were close to a constant in the temperature range of 25e520 C and showed a sudden increase above the glass transition temperature, Tg. The modulus of the glass sealant was assumed to be very low above Tg. With this assumption, different values of CTEs in the range of 5.0e8.5 106 K1 were tested to study the CTE effects of the glass sealants on the thermal stress concentrations during the assembly and the thaw-and-freeze processes. 2.3. Computation conditions Throughout the FEA simulations in this work, a static computation condition was assumed, ignoring any dynamic phenomena, such as electrochemical endothermic and/or exothermic cell reactions, since the actual heating and cooling rates are maintained at slower than 0.5 C min1 to minimize any possible thermal shock. The temperature changes during glass bonding and TCB were, however, included in the computation to realistically model the residual stresses at the glass joint. The bonding process for glass sealing and TCB were conducted at 950 and 520 C, respectively. Fig. 4(a) schematically illustrates the temperature changes during the NaS cell header assembly process and thaw-and-freeze cycles. During the glass sealing assembly step, the a-Al2O3 insulating ring and b/b00 -Al2O3 electrolyte are assembled with a glass sealant at 950 C, and the temperature drops to the room temperature (i.e., 20 C). Then, the temperature of the “a-b assembly” is increased to 520 C for TCB. The TCB is to bond between metal (i.e., bracket and collar) and the ceramic components with an insert metal. The temperature decrease from 520 C to 20 C of the “TCB assembly”
Fig. 3. Material properties used in the computation to show (a) CTE (Al3003, alphaand beta-alumina), (b) elastic modulus (Al3003, alpha- and beta-alumina, and glass), and (c) true plastic stressestrain curves for Al3003.
Fig. 4. Schematic illustrations to show the temperature changes of (a) the experimental NaS cell header assembly and (b) the computational steps.
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will yield additional residual thermal stresses. With those residual stresses in the glass and TCB areas, all of the other remaining components (i.e., container and cap) are finally assembled together via the electron beam welding (EBW) technology at 20 C. The thaw-and-freeze thermal cycle has been simulated by changing the system temperatures from 20 / 350 / 20 C considering that the cell operation temperature is 350 C. Assuming that glass softening occurs near 520 C, the total simulation was subdivided into simpler 2 steps to reflect this experimental procedure, i.e., (i) the glass sealing and TCB assembly step and (ii) the thaw-and-freezing thermal cycle step, as shown in Fig. 4(b) using the solid lines. Note that the glass sealing assembly process has been simplified due to the complete elastic characteristics of glass sealing, a-Al2O3, and b/ b00 -Al2O3 in the ranges of 520e20 C and 20e520 C, and the steps in dotted/dashed lines of Fig. 4(b) were ignored. Fig. 5 presents the axisymmetric computational domain (1/12 of the entire cell) that was generated for tubular NaS cells to reduce the computational time in the present work. All of the FEA computations were carried out based on this axisymmetric model. In the assembly step, the displacement of bottom surface of the insulating header was fixed along the cell height direction to prevent the rigid body motion. Additional boundary condition constraints on the outer surface of collar and bracket were imposed in this step to represent the experimental assembly procedure; the movement of the components along the radial direction was restrained by external jigs. In the thawing step, the displacements of the top surface of the cathode material and the bottom surface of the container were fixed along the cell height direction in the temperature range of 20e119 C and 119e350 C, respectively, in order to incorporate the solid/liquid phase transformations of cathode materials. These boundary conditions in the assembly and the thaw-and-freeze thermal cycle steps are illustrated in Fig. 5. The coexistence of S and different Na2Sx in the cathode compartment after electrochemical cycles and a certain period of time may induce the slumping of sodium polysulfides, which results in the
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accumulation of heavier Na2Sx on the bottom of the cathode compartment. This slumping of Na2Sx can cause solidification of cathode material from the bottom upon freezing since the melting temperature (Tm) of the Na2Sx (Tm ¼ 235e285 C) is higher than S (Tm ¼ 119 C). Accordingly, the gap between the outer bottom of the electrolyte tube and the inner bottom of the cathode compartment could be filled with high Tm species first during cooling, and therefore higher thermal stresses would be applied to the header area. In this study, this slumping phenomenon was ignored in the computation, as it was revealed that the slumping does not much influence the stress concentrations and their distributions at the glass joints based on our previous study and other test sets in the current study [12]. As for the interface conditions, the direct contact regions of the glass sealing and TCB were all modeled as interfaces with infinite friction (i.e., tie condition), and all other interfaces were modeled to move freely (i.e., contact condition with no friction). 3. Results and discussion To adequately analyze the thermally driven stress components on the glass sealing tip surfaces with curved shapes, a relevant local coordinate system depending on the specific geometry of the particular nodal position must be defined. As shown in Fig. 6(a), an orthogonal local coordinate system has been defined at each calculation nodal point to quantify and extract the local stress components. The 1st, 2nd, and 3rd coordinates were defined to represent the in-plane and out-of-plane axes of the local surface element in the glass sealing ends; the 2nd coordinate lies along the circumferential direction of a cell, the 1st coordinate is set to be the in-plane normal direction of the 2nd coordinate, and the 3rd coordinate is defined as the surface normal (out-of-plane) direction. Fig. 6(b) shows a set of local coordinate systems along the surface of a concave-shaped glass sealing end (concave system). Using this user-defined local coordinate system at each FEA computational
Fig. 5. Boundary conditions and restrictions used during the (a) glass sealing and TCB assembly, (b) 25e119 C (solid sulfur), and (c) 119e350 C (liquid sulfur).
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Fig. 6. User-defined local coordinate system from (a) one computational node in the concave, flat, and convex systems and (b) multiple nodes in the concave system, and (c) the profiles of three normal stress components (local s11,s22, and s33) when a concave system undergoes a cooling process from 520 to 20 C after the thermal compression bonding assembly.
node, the profiles of three normal stress components (i.e., local s11,s22, and s33) from a representative node of concave tip are plotted in Fig. 6(c), when the concave system undergoes a cooling from 520 to 20 C after the TCB assembly. The local stresss were extracted from a representative nodal point indicated in Fig. 6(b). For this calculation, the CTE value of 7.0 106 K1 was selected as a reference. The stress profiles clearly show that local s33(in-plane
Mode I stress that is normal to the circumferential direction) is primarily responsible for the thermal tensile stress concentration; local s11 (out-of-plane direction) is nearly 0 and local s22 (cell circumferential direction) shows compressive characteristics. All the following stress analysis in this work is, therefore, focused on the local s33 tensile stress and the corresponding Mode I brittle fracture. The dominant crack initiation mechanisms for all other
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test cases with different CTEs and glass sealing end shapes were the tensile Mode I fracture along the local 33 direction. 3.1. Stress distributions in the concave shaped glass sealing tip Using the user-defined local coordinate systems described above, the stress accumulation was calculated for a cell with the glass sealant of a concave end shape as a reference. Fig. 7(a) shows the local s33 thermal stress distribution profiles at the nodes that have maximum s33 values for the concave systems with different CTE values of the glass sealants, 6.0, 7.9, and 8.5 106 K1. After the glass sealing and TCB joint assembly, these systems were subject to a cooling process from 520 to 20 C and a subsequent thawand-freeze thermal cycle by changing the temperatures, i.e., 20 / 350 / 20 C, as shown in the x-axis of Fig. 7(a). The results show that that the maximum tensile s33 values are strongly affected by the CTE of glass sealants, and the maximum s33 is observed in the lower area of the concave tip toward the direction of the b/b00 -Al2O3 solid electrolyte, as indicated in Fig. 6(a). It is thought that the location of maximum tensile stress positions is determined by the geometry of the header area. During cooling, the local tensile stress along the outer surface of the sealing tip in the 33 direction is expected because more contractions would occur in
the insulating ring (a-Al2O3) than in the solid electrolyte (b/b00 Al2O3). More importantly, the maximum tensile stresses exhibit the largest values after the 520 / 20 C cooling process, and they afterward simply show small variations of thermal stresses when the cells are under the subsequent thaw-and-freeze thermal cycle. In other words, the differences between maximum s33 tensile stress values between two of these three systems are almost constant during the cell operation throughout the entire thaw-and-freeze cycle. These results may lead to the following finding; minimizing the thermal residual stress accumulated in the glass sealing during cooling after assembly is the most critical to avoid crack initiation and subsequent crack propagation, joint disintegration, and the ultimate failure in the glass sealant area. The maximum thermal stress decreases during thawing and increases during freezing; however, the highest thermal stress concentration is predicted to occur at the end of the cooling before the thaw-and-freeze operation thermal cycle. The maximum thermal tensile streses are 115.5, 89.2, 93.3 MPa in tension after glass bonding and TCB joining processes at 20 C, and are 22.0, 33.4, and 4.6 MPa in compression after the 1st thaw-and-freeze at 20 C for cells with the CTE values of 6.0, 7.9, and 8.5 106 K1, respectively. Because these trends were identified for all of our test simulation cases, the analysis given below only concentrates on the stress concentrations after cooling considering that these are the maximum local tensile stress. Fig. 7(b) shows the local maximum tensile s33 at 20 C after cooling for systems with various CTE values of 5.0e8.5 106 K1. These results clearly show that when the CTE of a glass sealant is about 7.9 106 K1, the local stress concentration is minimized with a value of 89.2 MPa for a concave end shape. Therefore, it is suggested that glass sealants with a CTE of ~7.9 106 K1 would have the lowest possibility of inducing failure at the glass joints. Note that the calculated results could be influenced by different FEA meshing schemes such as sizes and element types. It is expected that the glass sealants with a larger number of FEA meshes will produce more details about the stress gradients along the surfaces. Prior to the computation, it was confirmed that the results properly represent the stress distributions on the glass sealant tip surface within the error range of less than ~5% by testing the results for a simpler cell design with a much larger number of meshes. Now that the maximum Mode I tensile stress along the tip surface can be properly estimated, it would be useful to conduct a numerical analysis to predict a critical surface defect (i.e., pores, microcracks, etc on the surface of glass sealant). The existence of the defects is practically unavoidable but the control of the maximum defect size is possible by optimizing the sealing procedure. Therefore, it is important to estimate the maximum tensile stress applied to the glass joint so that the specification of the maximum defect size (i.e. critical defect size to failure under a given thermal stress) can be determined. The critical defect size (CC) for an embedded ellipsoidal crack based on the Griffith brittle facture theory can be typically estimated by [19];
CC ¼
Fig. 7. (a) Local maximum s33 stress distribution profiles for the concave systems with 6.0, 7.9, and 8.5 106 K1 CTE, and (b) local maximum s33 stress values after the cooling process (before operation) at 20 C for concave systems with various CTE values.
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1 KIC 2 p f $s
(1)
where KIC, f, and s are the fracture toughness, geometry factor, and applied Mode I tensile stress, respectively. Since a typical fracture toughness (KIC) of glasses is known to be 0.7e0.8 MPa m1/2 [19], and the geometric factor is 0.64 for an ellipsoidal surface notch, the critical defect sizes (CC) of glass sealant can be expressed as a function of the applied tensile stress using Eq. (1). Fig. 8 presents the relationship between CC and the applied Mode I tensile stress when the glass sealants would have the fracture toughness and shape factor as mentioned. The two curves represent the upper (red
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smaller than 48e63 mm upon fabrication (blue dashed lines in Fig. 8). On the other hand, when the CTE value of the glass sealant materials is 6.0 106 K1, the thermal stress is 115.5 MPa and its corresponding critical defect size falls in the range of 29e37 mm (green dashed lines in Fig. 8), which is considerably smaller than the allowable critical defect size for the case of 7.9 106 K1. 3.2. Stress distributions in the flat and convex shaped glass sealing tips
Fig. 8. Plot of critical defect size (CC) with applied Mode I tensile stress (s).
curve) and lower (black curve) limits of the critical defect sizes with KIC values of 0.7 and 0.8 MPa m1/2, respectively. From this, the maximum defect size, CC, of the glass sealant can be readily estimated under a certain tensile stress. For a given NaS cell with the glass CTE of 7.9 106 K1, if the maximum tensile stress is 89.2 MPa, then the inherent defect size must be controlled to be
The effects of the shapes of glass sealing tips were examined next. As shown in Fig. 2(b), three representative shapes of glass sealing ends, i.e., concave, flat, and convex systems were studied. The shapes of sealant tips can be designed and controlled by adjusting the amount of glass sealants, applied pressure, heat treatment conditions, and whether to use a glass tape or paste. Again, the CTEs of 5.0e8.5 106 K1 were applied to the systems with flat and convex end shapes, and the CTEs that produce the maximum tensile stress based on the local coordinate systems at each computational point (Fig. 6(a)) have been identified. Also for the flat and convex systems, the local s33 showed higher values compared to the local s11 or s22. Much smaller stress concentrations were predicted for the out-of-plane s11 components; they were in the ranges of 10 to 4, 16 to 2, and 10 to 13 MPa for the concave, flat, and convex systems, respectively. Stresses along the circumferential direction (s22) were all negative showing the compression behaviors. In Fig. 9(a), the glass tip surfaces were illustrated to present the maximum local tensile stress (s33) areas.
Fig. 9. (a) Areas of glass sealant tip surfaces that experience the tensile and compressive stresses, and (b) maximum local tensile stresses from different systems with various tip shapes and CTE values of the glass sealing.
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Shaded ellipsoids represent the maximum local tensile s11 areas, and arrows indicate the directions of the maximum tension or maximum compression stresses, respectively. Note that stress distributions along the local 3-direction is important as the cell has a tubular geometry, and the positions for the shaded ellipsoids and arrows along the circumferential direction have been arbitrarily chosen for the purpose of visualization. From Fig. 9(a), it is clear that for all three systems, stresses of the tension and compression are predicted in the lower and upper parts of end tips, respectively. Similar to Fig. 7(b), the maximum local tensile stresses from the systems with different tip shapes are then plotted as functions of their different CTEs in Fig. 9(b). The results show that, (i) the variations of maximum s33 tensile stress can be substantially influenced by the shape of glass tip surface, and (ii) the best CTE values for the three cases are different. In particular, it was predicted that a lower glass CTE (6.8 106 K1) would lead to the best in resistance to the brittle fracture compared to relatively higher CTEs in the concave and convex systems. From the figure, it is seen that the convex system with the glass CTE of 7.8 106 K1 would show the lowest maximum local s33, which should be preferable to have more robust glass sealing joints. Although it can be intuitively inferred that the adequate CTE value of glass sealant would be 5e8 106 K1 as the CTEs of a- and b”-alumina are in the window of 5.3e8.8 106 K1 in the temperature range of 20e520 C (see Fig. 3(a)), the results can suggest better manufacturing guidance to minimize the probability of failure at the glass joints. In Fig. 10, a map is provided to guide allowable windows of critical defect sizes (CC) for concave, flat, and convex systems with various CTEs of glass sealants. It is valid for SiO2 based sealing glasses that have a fracture toughness in the range of 0.7e0.8 MPa m1/2 [19]. Different numbers of data are presented for the three cases in this figure since the computations were conducted until the best CTEs were sought in the 0.1 106 K1 CTE intervals. From Fig. 10, it is elucidated that the concave and convex systems should be mechanically more stable with the glass CTEs of 7.8e7.9 106 K1 with critical defect sizes of 62e83 mm and 48e62 mm, respectively, whereas the flat system will be most resistant to the thermal stress with the glass CTEs of 6.8 106 K1 and the critical defect size of 50e67 mm. It must be mentioned that this stress analysis is constrained to the concave, flat, and convex glass tip systems with the prototype cell geometry adopted in this study; the best CTE might be different
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among different cell designs. Through our computational study, we have demonstrated that, the optimum CTE values can be readily predicted by changing the actual cell design. It is expected that the best CTE of a glass sealant would be non-identical for a certain tip shape when different cell geometries and configurations are adopted. Although only three representative shapes of glass tips were studied as a demonstration of the tool developed in this study, it can be inferred that the amount of glass sealant as well as wetting properties are important factors because they can determine the curvature and shape of the tips, and consequently affect the mechanical of the glass joint. Therefore, during the assembly process of the glass sealing joints, the sealing glass itself and the amount of sealant should be carefully controlled toward higher stability and safety of a large sized contemporary NaS cell for EES applications. 4. Summary In the present work, we studied the effects of the CTE of glass sealants and their tip shapes on the stress accumulation at the glass joints, which is directly related to the stability of the ceramic joints and therefore the safety of NaS cells. A computational approach employing an FEA technique incorporating relevant materials properties, simulation conditions, and local coordinate systems has been developed in this study. Tensile stress concentrations using the user-defined local coordinate system at each computational point were calculated for the concave, flat, and concave end shapes of glass joints. With the FEA computational model, the results based on the representative prototype battery design adopted in the current study are summarized as follows. The glass joints will experience the largest stress accumulation during cooling in the assembly process between a- and b-Al2O3. The maximum tensile stress in the convex shape of a glass tip is smaller than those in the flat and concave systems. For a given prototype cell design, the CTE of a glass sealant of 6.8e7.9 106 K1, depending on the glass sealing tip shapes, could be suggested to minimize the probability of failure at the glass joints; the convex glass tip shape with 7.8 106 K1 CTE showed the lowest maximum tensile stress. For the concave and convex systems, the defect size on the surface of the sealing tip must be generally controlled to be smaller than 20e50 mm and 40e85 mm when the glass CTEs are 6.8 106 K1 and 7.9 106 K1, respectively. Acknowledgments This work has been supported by POSCO (Contract No. 2013A049) and the Korea Institute of Energy Technology Evaluation and Planning (KETEP) under the authority of the Ministry of Trade, Industry, and Energy of the Republic of Korea (Contract Nos. 2011201010004A and 2012T100100643). References
Fig. 10. Range of critical defect sizes (CC) for the concave, flat, and convex systems with various glass sealant CTEs.
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