A thermo-mechanical stress prediction model for contemporary planar sodium sulfur (NaS) cells

Journal of Power Sources 324 (2016) 665e673

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A thermo-mechanical stress prediction model for contemporary planar sodium sulfur (NaS) cells Keeyoung Jung a, Jeffrey P. Colker b, Yuzhe Cao b, Goun Kim a, Yoon-Cheol Park a, Chang-Soo Kim b, * a b

Energy Storage Materials Research Group, Research Institute of Industrial Science and Technology (RIST), Pohang, Kyungbuk 790-660, South Korea Materials Science and Engineering Department, University of Wisconsin-Milwaukee, Milwaukee, WI 53211, USA

h i g h l i g h t s

g r a p h i c a l a b s t r a c t


A comprehensive FEA model is introduced to predict stress in contemporary planar NaS cell.
Model includes relevant experimental procedures for planar NaS cell assembly and operation.
Large stresses were developed on the outer surface of insulating header and solid electrolyte.
Cell container thickness plays an important role in the stress accumulation of planar NaS cell.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 5 April 2016 Received in revised form 29 April 2016 Accepted 27 May 2016

We introduce a comprehensive finite-element analysis (FEA) computational model to accurately predict the thermo-mechanical stresses at heterogeneous joints and components of large-size sodium sulfur (NaS) cells during thermal cycling. Quantification of the thermo-mechanical stress is important because the accumulation of stress during cell assembly and/or operation is one of the critical issues in developing practical planar NaS cells. The computational model is developed based on relevant experimental assembly and operation conditions to predict the detailed stress field of a state-of-the-art planar NaS cell. Prior to the freeze-and-thaw thermal cycle simulation, residual stresses generated from the actual high temperature cell assembly procedures are calculated and implemented into the subsequent model. The calculation results show that large stresses are developed on the outer surface of the insulating header and the solid electrolyte, where component fracture is frequently observed in the experimental cell fabrication process. The impacts of the coefficients of thermal expansion (CTE) of glass materials and the thicknesses of cell container on the stress accumulation are also evaluated to improve the cell manufacturing procedure and to guide the material choices for enhanced thermo-mechanical stability of large-size NaS cells. © 2016 Elsevier B.V. All rights reserved.

Keywords: Sodium beta-alumina battery Sodium sulfur battery Thermo-mechanical stress Cell failure Finite-element analysis

1. Introduction

* Corresponding author. E-mail address: [email protected] (C.-S. Kim). http://dx.doi.org/10.1016/j.jpowsour.2016.05.128 0378-7753/© 2016 Elsevier B.V. All rights reserved.

Increasing demands toward reliable energy resources are continuously forcing the implementation of advanced technologies that can both economically and safely store large amounts of

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energy. An energy storage technology that can effectively address the spontaneous needs of the consumer while exploiting renewable clean energy sources, is vital for the future generation. Sodium sulfur (NaS) battery has received a strong attention as one of the most promising candidates for grid scale energy storage systems (ESS) because of a number of benefits, such as its high energy density, long discharge time, long lifetime, no self-discharge, and low manufacturing costs [1e5]. The NaS cell is typically comprised of characteristic molten electrodes (i.e., Na for anode and S for cathode), b/b00 -Al2O3 solid electrolyte (BASE), intricate sealing areas, and outer metallic cell container. Depending on the shapes of its BASE, two different cell geometries (i.e., tubular cells and planar cells) have been suggested for practical applications of NaS cells. For grid scale energy storage applications, large-size (1,200 Wh class) tubular sodium sulfur cells have been developed by NGK Insulators, Ltd, in 2003 [6], and their products have been being successfully operated in many countries thereafter [7,8]. Currently, a couple of other groups are also in the developing stage for the stationary energy storage systems based on tubular NaS batteries aiming to the product realization of the technology [9e16]. Other than the tubular NaS cells, another possible NaS cell design relies on a planar geometry utilizing a flat plate BASE. First practical planar cells were constructed and tested in 1970’s for automotive applications [17,18]. Since the geometry of a NaS cell is primarily determined by the shape of its BASE, as long as the BASE forming technology is available, other alternative cell designs can also be suggested including a flat tube-shaped cell or a cell with a curved solid electrolyte. Application of a tubular BASE with a clover leaf-shaped cross-section in sodium nickel chloride battery (Na/NiCl2, also known as ZEBRA battery) is a good example of different geometries to increase the active area and to reduce the thickness of the cathode compartment [19]. However, most of the contemporary technologies to build the derivatives are more or less related to one of the two extremes (i.e., tubular or planar), therefore, development of rudimentary technology for these two extreme designs is of special importance to fabricate new cells with other shapes. The planar NaS cell has a number of distinct advantages over tubular cells, such as easiness for stacking, inter-cell connection without external connectors, and geometric merits for mass production, thereby reducing the manufacturing cost. Furthermore, it is easier to eliminate the orientation and gravity effects, and therefore, the active area of the electrode and electrolytes can be sharply defined, and it is also easier to perform post-analysis for cell components [20]. With this, the planar design has been widely used in laboratory conditions. Accordingly, planar cell designs have been adopted for developing electrode materials/structures and for testing new cell chemistries with small circular plate-shaped BASE, of which diameter is typically in the range of 10e50 mm. For example, there are several recent efforts to reduce the operation temperatures of NaS battery systems from 300e350  C to intermediate temperatures (95e190  C) [21,22] or to room temperature [23e28]. In addition to these, the planar design is also useful for fundamental studies on the wetting characteristics of molten sodium on b/b00 -Al2O3 membrane [29,30], or on testing novel electrodes for sodium metal halide chemistries [31e33]. Despite these advantages, critical issues are still remained in developing practical planar NaS cells. Since 1970’s, it was wellperceived that the diameter of a BASE disk should be at least 80 mm to provide a reasonable competitive specific energy [34]. Although several pioneers delivered some insightful lessons through their efforts for the development of planar sodium betaalumina cells for high power applications [34e36], no commercial scale success has yet been reported. Common unresolved problems include the insufficient mechanical properties of

heterogeneous joints and BASE, which can result in a catastrophic cell failure from the accumulation of thermo-mechanical stresses upon cell assembly and operation (i.e., thermal cycling). The thermo-mechanical stresses are originated from the differences in the coefficients of thermal expansion (CTE) of various cell constituents (sealing glass, BASE, a-Al2O3, and metallic components). The degree of such stress accumulation increases as the cell size increases. Because there would be a competition between the accumulated thermo-mechanical stress and the bonding strength to avoid the cell failure, the maximum NaS cell size must be determined by the capability to resist the accumulated stresses. To develop a large commercial planar cell, therefore, two-way approach deems to be reasonable: (1) minimization of the thermo-mechanical stress accumulation through optimizing the cell design and materials choices and/or (2) maximization of bonding strength through applying robust joints and components to avoid undesired fracture. In an effort to resolve the thermomechanical stress issues via approach (2), recent development of commercial scale planar sodium batteries has adopted advanced joining technologies, such as electron beam welding (EBW) and laser welding for metal-metal joints, thermal compression bonding (TCB), brazing, or state-of-the-art load framing for metal-ceramic joints, and the glass sealing (GS) for ceramic-ceramic joints [37e39]. Even with the development of these state-of-the-art bonding technologies, successful experimental fabrication of large-size practical planar NaS cells presents a formidable challenge. In this study, therefore, we introduce a comprehensive in silico finiteelement analysis (FEA) model to accurately predict the thermomechanical stress concentrations at the heterogeneous joints and components of planar NaS cells. This is in line with the approach (1) addressed above to minimize the thermo-mechanical stress by optimizing the cell geometry and materials. Using this prediction model, the thermo-mechanical stress field was calculated using one of our representative prototype planar NaS cells assembled with EBW, TCB, and GS bonding techniques. In the next sections, the computational methods are detailed and the calculation results are generally discussed to estimate the possible fracture location and fracture mode. In addition, we examined the impacts of the CTE of sealing glass and the thickness of cell container on the stress concentration and the cell failure by varying the CTE values of sealing glass and the thickness of metal container. Based on the computational results, the CTE value of sealing glass and the thickness of the container materials have been identified to minimize the stress concentration at the vulnerable joints for the planar cell design considered in this work. 2. Computations 2.1. Cell design and model construction Fig. 1(a) illustrates the cross-sectional design of the representative prototype planar NaS cell. The anode and the cathode compartments of this prototype cell are filled with molten Na and S, respectively, separated by the BASE. The sealing area is composed of heterogeneous joint parts including a-Al2O3 insulating header (IH), insert metals (IM), glass sealing (GS), and surrounding cell container collars. For conveniences, the upper and lower insert metals are referred to as IM1 and IM2 in this work. The standard choice in dictating the size of planar NaS cell is to designate the diameter (i.e., disc size) of BASE. In our study, the disc size of BASE was set to 120 mm, as it was suggested that the minimum useful BASE disc size is 80 mm and the optimum disc size is 250 mm [1,34]. Also, note that, in our in-house cell fabrication and operation experiments at RIST (Research Institute of Industrial Science and

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are 23e27  106, 17e19  106, and 10e12  106/K for Al3003, STS304, and STS431 materials, respectively, in the temperature range of 20e350  C. Because the CTE values of STS431 are much closer to those of ceramic parts in the planar NaS cells in this temperature range, STS431 was used for the top and bottom caps, and the collar parts. IM parts were processed using Al3003 alloy as it was proven to show good stress absorption capabilities [13,14]. The GS materials were selected to have a constant CTE value of 6.9  106/K in the standard reference model. The elastic modulus of GS was 62 GPa. Poisson’s ratios for the Al3003, STS431, IH, BASE, and GS materials were 0.33, 0.28, 0.23, 0.23, and 0.22, respectively. The temperature-dependence of (a) CTE and (b) elastic modulus for the Al3003, SS431, a-Al2O3, and b/b00 -Al2O3 materials is plotted in Fig. 2. These material properties including the stress-strain curves at various temperatures were obtained through the previous literature [13,14,40] and in-house measurements. 2.2. Computational conditions 2.2.1. Coordinate system With the nature of circular shape of the planar NaS cell geometry, a cylindrical coordinate system was employed to conduct

Fig. 1. (a) Cross-section of prototype planar NaS cell and (b) 30 axis-symmetric planar NaS model with FEA mesh.

Technology, South Korea), much success has been encountered when developing planar cells with BASE disc size below 100 mm. The computational results on the stress concentration in the current study are, therefore, based on the representative prototype cell design with 120 mm BASE disc size. To digitize the prototype planar NaS cells, we first used Rhinoceros (version 5.0, McNeel Inc.) auto computer-aided design (CAD) software derived from an actual experimental cell structure. The height of the cell was 34 mm. Due to the cylindrical geometry of the cells, the axis-symmetric boundary condition was applied to reduce the computation time (30 cell, see Fig. 1(b)). The digitized structure contains all of the necessary cell compartments including the cell container (top and bottom caps, and collar), Na cartridge, aAl2O3 IH, BASE, and IM. The digitized model design was then imported into the hyperMesh mesh generation software (version 11.0, Altair Engineering Inc.) to generate fine quality of FEA meshes. The types and sizes of FEA mesh for each compartment of the prototype cell have been optimized to produce consistent reliable results. The 8-node linear brick, reduced integration hexahedral element (C3D8R) mesh type was used for all of the cell components except the GS compartment. The 6-node linear triangular prism element (C3D6) mesh type was used for the GS part due to its curved tip geometries. The total number of FEA meshes of the 30 slice standard reference model was 448,621. Next, the digitized structure was imported into ABAQUS (version 6.11e2, Simulia Inc.) FEA software to evaluate the accumulated thermo-mechanical stress. The container metals of contemporary NaS cells can be commonly made up of Al alloys (Al3003) or stainless steels (STS304 or STS431) due to their competitive price, good machinability, and high corrosion resistance [13,14]. Typical CTE values of these materials

Fig. 2. Temperature-dependence of (a) the coefficients of thermal expansion (CTE) and (b) the elastic modulus for Al3003, SS431, a-Al2O3, and b/b00 -Al2O3 materials.

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computations and to analyze results. As Fig. 1(b) shows, in the axissymmetric model (i.e., 30 slice model) for the standard cell, the radial (r), circumferential (q), and vertical cell height (z) directions were designated as 1, 2, and 3 tensors, respectively, in the computations. Therefore, in the cylindrical system, the vertical normal stresses for the surfaces in the cell were given by s33, while the shear stresses on horizontal surfaces within the cell were given by t13. Due to the overall radial contraction/expansion of the outer metallic container during cooling/heating, the normal stresses in BASE were measured using s11 (radial direction) in the cylindrical coordinate system. The coordinate system used to quantify the stress components on the GS tip surface is local positiondependent. In other words, the stress components in GS were determined based on the local coordinate system at individual nodal points of the curved tip surface. 2.2.2. Thermal loading conditions A sequential experimental NaS cell fabrication process must be properly incorporated into the computations as thermal loading conditions. The GS joining process that bonds the ceramic IH to the BASE component takes place at ~950  C, while the subsequent TCB joining process to add the collar components is carried out at ~520  C. In-between these separate assembly, the cell is cooled down to room temperature (20  C) and the rest of the cell compartments are assembled. After fabrication of the cell, the temperature of the NaS cell is increased to its operation temperature (350  C) and then decreased to room temperature for maintenance purpose (i.e., “thaw-and-freeze” process). Assuming the glass transition (Tg) of GS materials occurs near ~520  C and the cell operation temperature is 350  C, the resultant simulations were subdivided into three steps; 520  C / 20  C / 350  C / 20  C. It should be noted that the GS step was truncated due to the inherent elastic behavior of glass, allowing for the simulation to begin at the temperature of ~520  C, where the subsequent TCB bonding is performed to join the ceramic components to the neighboring STS431 collar case material. The temperature cycling for the experimental fabrication and the computational step is shown schematically in Fig. 3(a) and (b), respectively; in the computation (Fig. 3(b)), an initial assembly step was conducted (computation step #1) followed by the thaw-and-freeze cycles (computation steps #2 and #3). Note that, throughout the simulations conducted in the present work, thermally static computation conditions were hypothesized. Although it is known that both endothermic and exothermic electrochemical reactions occur within the electrode compartments during the charge and discharge cycles, these effects were considered as minimal, due to the slow heating and cooling cycles implemented during thaw-and-freeze (30e50 h, slower than 0.5  C/min [13,14]). These slow heating and cooling cycles are exercised to prevent thermal shock and resultant premature failure, which could potentially develop due to the CTE mismatches between the heterogeneous cell components. In addition, internal temperature gradients through the bulk of the component thicknesses were also intentionally disregarded. The cell is experimentally held at ~550  C for relatively long periods of time during the TCB bonding operation, therefore, the Al3003 IM would be in the annealed condition, free from appreciable internal residual stresses. Effects of the carbon/glass felt within the cathode compartment were also neglected. Although slow heating and cooling cycles are implemented during the thaw-and-freeze thermal cycles, continued temperature cycling for maintenance or other unforeseen reasons during the service life of the cell can lead to plastically accumulated residual stresses in the susceptible members of the cell. As illustrated in Fig. 3, only the first thaw-andfreeze cycle was implemented, leaving the door open to further

Fig. 3. Temperature profiles in (a) the experimental cell assembly and operation and (b) the computational steps with thermal loading assumptions.

work in the future for the multiple thaw-and-freeze cycles. 2.2.3. Boundary and interface conditions In the subject planar NaS cell, the dimensions of the cell should be allowed to freely expand and shrink along the radial and the height directions. Rigid body motion must however be prevented, and this is induced by the incorporation of constraints imposed on the bottom nodal plane of the cell. These elements are therefore constrained from displacement in the cell height direction. This prevents any unintended rotational or translational movement from occurring based upon the resultant thermal contraction or expansion encountered during the thermal cycles. As mentioned before, symmetric boundary conditions (i.e., axis-symmetric model) were imposed to reduce the computational resources required for each of the individual simulations. Incorporation of the axis-symmetric boundary conditions requires the nodes along the symmetric plane to maintain zero displacement in the direction normal to the symmetric plane (i.e., circumferential direction). Assigning proper interfacial conditions between the various components of the representative model is also of paramount importance. In the present work, a non-sliding, high friction (i.e., tiecondition) was assumed at all component interfaces. Such nonsliding interface is expected in contemporary NaS cell structures, because these joint interfaces comprised of metal/ceramic, metal/ metal, and ceramic/ceramic compartments are carefully controlled to tightly bond using advanced sealing techniques including TCB, EBW, and GS, as addressed in the Introduction section. With these boundary and interface conditions, an elasto-plastic behavior with a J2 flow theory and isotropic hardening was modeled for metallic components of the constituent materials.

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2.3. Cell material and design variables Because the glass materials connect IH and BASE, it is expected that GS CTE would impose high influence on the aspects of accumulated stress during thermal cycling. After running a standard reference cell, therefore, computational trials documenting changes in the CTE values for the GS materials were implemented. The GS CTE values of 5.0, 6.0, 6.9 (standard), and 8.0  106/K were tested to study the impacts of the GS material types. Geometry of the NaS cell container also greatly influences the resultant stresses. To investigate this, the thicknesses of the container materials were changed to predict the resultant stress concentrations. ±25% variations from the standard model were tested for the thickness effects of cell container; the thicknesses of the cell container were 1.5, 2.0 (standard), and 2.5 mm in different model systems. 3. Results and discussion We first address the various thermo-mechanical stresses in the individual cell components (IH, IM, GS, and BASE) of the standard cell with 6.9  106/K GS CTE and 120 mm BASE disc diameter. In the following subsections, the computational results from the planar NaS systems with various GS CTEs and cell container thicknesses are analyzed and discussed. 3.1. Standard cell Fig. 4(a) shows the von-Mises stress distributions with a same legend scale in the heterogeneous cell joint area with the prescribed temperature cycling. The von-Mises stress distributions can indicate the degree of qualitative thermo-mechanical stress accumulations after the cell assembly (computation step #1) and the thaw-and-freeze (computation step #2 and #3, respectively) processes. From Fig. 4(a), it was identified that the interface regions between IM1 and IH exhibit relatively high stress concentrations as shown using the “O” circles after the cell assembly process. In addition, although it is not as evident as this interface region, high stress concentrations on the outer and the inner surfaces of IH are anticipated based on our in-house experimental observations. For example, in Fig. 4(b), we provide an image of fractured planar NaS cell fabricated at RIST to show an experimental example of cell

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failure on the IH outer surface. From Fig. 4(a), although it is also seen that the thermo-mechanical stress concentration in the elbow region of cell collar is relatively higher after the cell assembly and the freeze process, the stress in the collar region is not focused on in the current work, because STS431 cell container has high fracture strength with relatively higher degree of plastic deformation; therefore, failure from the cell container compartment is not likely to occur. 3.1.1. Stress in a-Al2O3 insulating header (IH) In Fig. 5(a), we first present the graphical representations of the four maximum localized stresses identified on the surfaces and in the interfaces of IH as a function of the induced temperature cycling. The figure shows maximum stress profiles of s33 (normal stress component along the cell height direction) on the outer surface and in the inner interface of IH, and s33 and t13 (shear stress component along radial direction) in the IIH/IM1 interface. These stress profiles are designated by “outer s33”, “inner s33”, “top s33” and “top t13”, respectively, using different colors in the figure. As approximately indicated by the “O” circles in the cell cross section image of Fig. 5(a), these stress profiles were obtained from the local FEA nodes that exhibited the maximum stress values (i.e., “maximum local” stress). Except the shear stress (i.e., top t13), the general trend of the three normal stress components is similar; a gradual positive slope is present during the initial temperature cycle (computation step #1), followed by a much more dramatic negative slope upon heating, and a greater positive slope upon the final cooling step (computation steps #2 and #3, respectively). As mentioned before, the TCB process to bond the upper and lower container collars to the central ceramic assembly is conducted at the temperature of ~520  C. Following the TCB process, cooling to 20  C causes the radial contraction of the outer container, giving rise to the resultant normal tensile stresses along the cell height direction in the centrally located ceramic components (initial positive slope). Following joining of the upper and the lower caps at 20  C, upon heating (i.e., thaw process) to the cell operation temperature (350  C), both the container and caps expand radially, inducing the resultant compressive stresses in the normal direction (negative slope). Subsequent cooling from 350 to 20  C (i.e., freeze process) then again induces a radial contraction of the cell, producing the final tensile stresses in the ceramic compartments

Fig. 4. Examples of (a) von-Mises stress distributions in the cell joint area and (b) fractured cell.

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Fig. 5. Maximum local stress distributions with thermal cycling in (a) IH, (b) IM1, (c) GS, and (d) BASE components of the standard cell.

(positive slope). In contrast to the variations of the maximum normal stress components, the calculated maximum t13 in the IH/ IM1 interface did not show much variation with temperature cycles. This t13 was extracted from the IH/IM1 interface region close to the inner edge of IM1 as indicated by the top “O” circle of the cross-sectional image of Fig. 5(a). After assembly (520 / 20  C), the degree of contraction in IM is much higher than that in IH, therefore, a positive shear stress is observed on the IH surface. However, during the thaw-and-freeze process, it was calculated that t13 was nearly constant. The highest maximum tensile normal stresses identified were approximately 270, 130, and 90 MPa for outer s33, inner s33, and top s33, respectively. Note that these all occurred when the cell is cooled down after assembly (520 / 20  C), which implies that the assembled NaS cell may contain high residual tensile stresses even before operation. Considering that the tensile fracture strength of Al2O3 materials used in the typical NaS systems ranges in 300e500 MPa depending on the types/sizes of existing defects, grain size, and other synthesis conditions, there is a certain probability of crack initiation/propagation in this initial cell assembly procedure. If the crack propagation was initiated in IH during the cooling cycle after the cell assembly, there is a high chance of cell failure in the thaw cycle as well. This corresponds to our in-house experiments to observe the fracture of cells during the cooling process after assembly (520 / 20  C) and/or the thaw process (20 / 350  C). The high tensile stress concentrations near the top

of the outer surface of IH is an indication of the most likely region of potential thermo-mechanical failure, as exemplified in Fig. 4(b).  without 2 When the classical Griffith brittle fracture theory appreciable plastic deformation is considered, Cc ¼ p1 fK$ICs ; (where Cc , KIC , f , and s represent the critical size of embedded ellipsoidal crack, the fracture toughness, geometry factor, and applied Mode I tensile stress, respectively) for IH with assumption of a typical fracture toughness of Al2O3 material ¼ 3.0e4.0 MPa m1/2 and the geometric factor of an ellipsoidal crack ¼ 0.64, the allowable maximum critical crack size (Cc ) is estimated as ~96e170 mm on the surface of IH. In addition, the interfacial decohesion between IH/IM is probable because the predicted normal stress near the bonding edge is ~90 MPa and the normal bonding strength of IH/IM is expected as ~30e80 MPa. After the thaw cycling, the maximum compressive stress for outer s33, inner s33, and top s33 are in the range of 1700 to 1900 MPa. The typical compressive strength of Al2O3 materials falls in the order of 2500 MPa depending again on the existing defects and grain sizes, therefore, there is a small chance of fracture probability in the IH component due to these high compressive stresses when the cell temperature is increased to its operation temperature. On the other hand, the shear stress in the IH/IM interface would not result in the interfacial delamination because the calculated maximum top t33 is ~65 MPa and the shear bonding strength in IH/IM is estimated as greater than ~100 MPa.

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3.1.2. Stress in Al3003 insert metals (IM) The thermal compression bonded (TCB) Al3003 alloy IMs are located at the interfaces between IH and adjacent STS431 structural collars. Maximum local normal and shear stress components were extracted from the bottom surface of IM1 (i.e., upper IM in Fig. 1(a)) because IM1 generally showed higher stress than IM2. It was found that the normal stress concentrations were higher towards the outside edge and that the shear stress concentrations were greatest both at the outer and inner edges of the insert, as indicated by the “O” circles in the cross-sectional image of Fig. 5(b). As shown in Fig. 5(b), the maximum local shear stresses in IM1/IH interfaces were highest (~50 MPa) following both of the cooling cycles (after assembly and after freeze). Again, it is expected that ~50 MPa would not initiate the interfacial decohesion between IM/IH as the shear bonding strength is over ~100 MPa. As for the maximum local normal stress component (s33) in the IM1 surface in contact with IH, the highest s33 was identified after the freeze process with a value of ~75 MPa. This IM s33 is important because it can directly cause the “tearing” failure from the IM side in the interface between IH and IM. It is expected that ~75 MPa of normal stress can result in the tearing failure since the normal strength between IH/IM interfaces is measured as ~30e80 MPa. While a maximum compressive stress of s33 was witnessed in IH at 350  C, a slight decrease of approximately 100 MPa in the normal (compressive) stress is evident in the case of IM1 bottom s33. This decrease seems to begin at approximately ~250  C, which is associated with a stress relaxation temperature of the Al3003 alloy. In other words, the modulus values and the stress values of IM Al3003 are substantially decreased in this temperature range (as shown in Fig. 2(a) and (b)), which gives rises to a relative increase in the stress profile compared with the one in the lower temperature. Although the annealing temperature isn’t reached until approximately 400  C for Al3003, some plastic deformation will be evident before 400  C, which accounts for the “W” shape of the plots in Fig. 5(b). The highest compressive normal stress was around 490 MPa, and this would be unlikely to initiate the interfacial failure from the IM side.

3.1.3. Stress in glass sealing (GS) GS is used in the cell construction process to join IH with BASE. Like the neighboring ceramics, glass is rigid in nature and can more easily tolerate compressive stresses, but any induced tensile loading is undesired. Fig. 5(c) shows the maximum local normal stress (with respect to the local curvature) distributions on the vertical and the horizontal tip surfaces with temperature changes. As indicated in the figure, the normal tensile stress on the horizontal tip surface reaches highest values after the step #1 and step #3 of computations at ~20e25 MPa, respectively. When the Griffith brittle fracture theory is again applied with the KIC value of 0.7e0.8 MPa m1/2 for typical soda-lime glass and the geometric factor of an ellipsoidal crack of 0.64, these tensile stresses correspond to the critical crack size over 600 mm, which is much larger than the actual crack size on the surface of GS compartment. Therefore, initiation of failure from the GS tip surface is unlikely to take place for the prototype planar NaS cell. On the vertical tip surface, it was predicted that the normal stresses are all compressive throughout the three thermal cycling with the highest magnitude of 400 MPa. Because the compressive fracture strength of typical soda-lime glass is on the order of ~1 GPa, one can expect that the failure from the vertical tip surface is not likely to occur. Note that, these results are clearly different from the stress analysis reported in Ref. [14] for the tubular NaS system, in which the fracture of GS was probable depending on the CTE values and the internal crack sizes of the constituent glass materials.

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3.1.4. Stress in b/b00 Al2O3 electrolyte (BASE) When the cell container materials contract during the cooling cycles, radial compressive stresses are induced in the BASE part. The fracture of BASE must be strongly avoided in any situation because the failure of BASE will allow the direct contact between the active materials in anode and cathode. The maximum compression stresses in the radial direction were calculated on the top and the bottom surfaces of BASE materials, as shown in Fig. 5(d). The amount of stress accumulation on the top and the bottom surfaces of BASE were similar. It is seen that, unexpectedly, very high compressive stress is accumulated on the surfaces of BASE during the thaw process when the temperature is increased from 20 to 350  C. This is probably due to a large deformation amount of the top and bottom STS431 cap, of which stresses are deflected to the central IH and BASE through the collar of the cell along the radial direction. The highest concentration was around 1800 to 1900 MPa when the cell is reached at its operation temperature. Assuming that the compressive fracture strength of b/ b00 -Al2O3 is comparable to that of a-Al2O3 materials, fracture would not likely to occur. However, the compressive strength of BASE could be highly dependent upon the internal structure and the degree/size of defects. In addition, because of the thin elongated geometry of BASE, any local deflection of BASE along the cell height direction can cause a very severe high tensile stress at that deflection point, which would readily break the BASE materials. With this, it is of vital importance to fabricate the BASE materials without warping (local bumping on the surface). Based on the current results, one can expect that, if fracture occurs in BASE, it would initiate in the central region of BASE in the thaw process. 3.2. Impacts of glass sealing CTE Up to this point, we addressed the stress concentrations in the standard planar NaS cell. Now, we will present the computational results based on altering material properties and cell design variables. The first computational sets focused on varying the CTE values of GS, because the CTE of GS is anticipated to greatly influence the thermo-mechanical stress concentrations in various cell compartments. To test the impacts of GS CTEs, the values of 5.0, 6.0, 6.9, and 8.0  106/K were used for the computations of the prototype cell design. In Fig. 6, the results based upon the GS CTE variance are presented. In the figure, the data for IH inner s33 and

Fig. 6. Highest maximum local stresses in the prototype planar NaS systems with various GS CTE values.

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GS horizontal normal stress component are only summarized because all other maximum local stress variations were nearly independent of the GS CTE values. Of the stress profiles with three temperature cyclings, the highest tensile stress values are shown in Fig. 6, because the compressive stress would not result in a failure from IH inner interface and GS horizontal surface, as previously discussed. These highest maximum local stresses were obtained after the cell assembly procedure (i.e., computation step #1). From the figure, it is evident that the highest tensile IH inner s33 and GS horizontal normal stresses are decreased and increased, respectively, as the GS CTE value increases. It was calculated that when 5.0  106/K of GS CTE was used, the highest maximum local tensile stress can be as high as ~220 MPa on the inner surface of IH along the cell height direction. This value is lower than the typical tensile fracture strength of Al2O3 materials (300e500 MPa), and the critical crack size for this stress would be 144e257 mm. As for the highest maximum GS horizontal normal tensile stress, the calculated values are in the range of ~11e27 MPa with different CTEs, which would not lead to the fracture on the GS surface. Although fractures are not expected when the glass materials with CTEs of 5.0e8.0  106/K are applied to bond IH and BASE, it is suggested to use GS with CTE value of ~8.0  106/K that is closer to the those of IH and BASE materials. However, it is mentionable that fabrication of glass materials with higher CTE could be experimentally challenging.

3.3. Impacts of cell container thickness Next, we tested the impacts of cell thicknesses on the thermomechanical stress concentration in the cell components. The cell container STS431 thickness in the standard cell was 2 mm and the modifications were chosen as ±25% from this standard value, i.e., 1.5 and 2.5 mm. In general, it is speculated that the container thicknesses would contribute to significant variances at every location, because the CTE of container is much higher than that of ceramic materials in the cell. Fig. 7(a) provides important results obtained by altering the container thicknesses. Again, the highest maximum local stresses have been extracted from the corresponding computational nodes. When the thickness of the container material was reduced, the resultant highest normal tensile stress on the IH outer surface was substantially decreased; the predicted IH outer s33 values were ~187 and ~366 MPa with the container thickness of 1.5 and 2.5 mm, respectively. These highest normal tensile stresses were observed after the cell assembly (computation step #1). In Fig. 7(b), we present the estimated critical crack size range in IH that would not initiate the crack propagation under these IH outer s33 stresses. We again used the identical approach formerly introduced with assumption that the geometry factor of embedded ellipsoidal crack is 0.64 and the KIC values of IH are in the range of 3.0e4.0 MPa m1/2. From Fig. 7(b), it is seen that the critical crack size in IH must be maintained under ~52 mm when the container thickness is 2.5 mm. Other than the normal stress on the outer surface of IH, the interface between IH/ IM1 were identified as the most influenced location by changing the thickness of cell container materials. When the thicknesses are increased from 1.5 to 2.5 mm, the highest normal tensile stresses along the cell height direction in IH/IM1 interface are increased from ~68 to 128 MPa from the IH side (computation step #1, IH top s33) and from ~18 to 150 MPa from the IM1 side (computation step 3, IM1 bottom s33), respectively. Such high normal tensile stresses are likely to result in the interface failure. Therefore, application of STS431 container materials with thickness under 2 mm is highly desired during the cell fabrication.

Fig. 7. (a) Highest maximum local stresses in the prototype planar NaS systems with various cell container thicknesses and (b) critical crack sizes in IH with different cell container thicknesses.

4. Summary In this work, we present a FEA computational model to accurately evaluate the thermo-mechanical stress concentrations in the heterogeneous joint and BASE areas of contemporary planar NaS cells. Relevant material properties and cell fabrication conditions were incorporated in developing this stress prediction model. Using a prototype standard model cell, detailed stress accumulations and possible fracture scenarios are addressed and discussed. The CTE of GS and the thickness of cell container materials were changed to examine the effects of these parameters on the resultant thermo-mechanical stress concentrations in the vulnerable area within the cell. It is expected that the current computational model can be readily applied to guide the geometrical designs and the material choices of planar NaS cell fabrications with enhanced thermo-mechanical safety and stability during the cell assembly and operation. The following lists the major findings obtained through the current study using the prototype planar cell with the BASE disc size of 120 mm in diameter.

K. Jung et al. / Journal of Power Sources 324 (2016) 665e673


For the prototype planar NaS cell design considered in the present work, the weakest areas in the cell were identified as the outer surface of IH, the edge of IH/IM interface, and the center region of BASE surface.
Upon cell assembly (cooling from 520 to 20  C), there is a probability of failure in the IH outer surface with the maximum normal tensile stress of ~270 MPa.
Upon thaw (heating from 20 to 350  C), there is a probability of failure on the BASE surface with the maximum normal compressive stress of ~1900 MPa.
Upon freeze (cooling from 350 to 20  C), there is a probability of failure in the IH/IM interface with the maximum normal tensile stress of ~90 MPa on the IH surface.
The CTE of glass materials mostly influences in the stress accumulation in the inner interface of IH and on the horizontal tip surface of GS, however, the change of glass CTE would not directly result in the fracture in the heterogeneous joints area when the glass CTE values of 5.0e8.0  106/K are applied.
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