Failure Analysis of a Functionally Graded Multilayer Coated Stainless Steel Pipe for Hydrogen Storage

Failure Analysis of a Functionally Graded Multilayer Coated Stainless Steel Pipe for Hydrogen Storage | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Failure Analysis of a Functionally Graded Multilayer Coated Stainless Steel Pipe for Hydrogen Storage Sanam Abedini, Foon Min Amy Chu Pui Chan, Chensong Dong, Ian Davies This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3741716/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 15 You are reading this latest preprint version Abstract In this study, a plane strain finite element analysis (FEA) was employed to investigate failure mechanisms of a hydrogen storage pipe system made of 316L stainless steel pipe coated with pure and functionally graded (FG) ceramic layers composed of Al 2 O 3 and SiC. The system was studied for different common failure mechanisms, i.e. , delamination, surface cracking and buckling delamination, upon cooling from an elevated stress-free temperature. Finally, the composition and thickness of the coating layers were considered as the main controlling factors and investigated for their influence on the studied failure mechanisms. It was observed that the most energetically favourable cracking mechanism for this type of system was surface cracking with the propagation of these cracks eventually leading to different failure paths. Buckling was found to be as less energetically favourable compared to surface cracking with the buckling resistance being enhanced by changing the coating thickness and composition factor. Finite element analysis (FEA) functionally graded (FG) coating delamination buckling crack propagation. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 1. Introduction Hydrogen is becoming a promising alternative future fuel due to its abundance and ability to be burned in a combustion engine with water being the only resultant product [ 1 , 2 ]. However, among other challenges with hydrogen fuel, the storage of hydrogen, especially with regards to vehicles, has remained one of the main issues [ 1 , 3 ], in particular due to the potential for leakage from storage containers. One of the most common methods of hydrogen storage to date has been high pressure gas cylinders known as high pressure gaseous hydrogen (HPGH2) [ 4 ]. Materials that have been mainly used for manufacturing these cylinders include austenitic stainless steel ( e.g. , AISI 316L) and alloys of aluminium or copper [ 5 ]. In order to reduce hydrogen leakage from the walls of these containers, permeation barrier coatings are usually applied [ 6 – 9 ]. Alumina (Al 2 O 3 ) and silicon carbide (SiC) are among the most promising ceramic materials for this purpose [ 10 – 13 ]. However, in the case of coatings on a different material type, e.g. , ceramics on metallic substrates, failure mainly occurs due to the mismatch of properties, such as the coefficient of thermal expansion (CTE), during heating and cooling cycles [ 14 ]. For example, the mismatch between CTE of the two layers adjacent to the interface has been considered the primary reason for delamination of ceramic coatings on metallic substrates [ 15 ]. Buckling as another failure mechanism is closely related to delamination in that, while delamination occurs mainly at thicker edges of a coating, buckling tends to occur at thinner parts away from the edge [ 16 ]. One relatively recent idea is to use a functionally graded (FG) layer between the ceramic coating and the metallic substrate, which is graded in terms of composition between dissimilar materials and helps to diminish any mismatch stress due to property changes, in particular the CTE [ 15 ]. Applying a functionally graded material (FGM) layer has proved to assist with a fundamental issue for these coatings which arises from the presence of residual stresses caused by the cooling of such a coating layer from the manufacturing temperature, thereby significantly reducing these stresses [ 15 ]. In the case of using FG layers to alleviate stress severity between coating and substrate, some researchers have studied the influence of some of the most important factors. Bao and Cai [ 15 ] have applied this idea to investigate different possible failure mechanisms of a ceramic/metallic FGM coating on a metallic substrate, including edge delamination and buckle-driven delamination. In the investigation of buckle-driven delamination, it was noticed that, as the metal volume fraction increases in the applied FGM coating, the resistance for buckling also increases in terms of the increase in the critical buckling temperature drop, i.e. , the temperature drop required for buckling. However, it was also shown that, for a fixed temperature drop, buckling is more likely to occur for delamination cracks closer to the surface of the FGM coating rather than for cracks closer to the metal/FGM coating interface. In general, it was concluded that the use of a ceramic/metallic FGM coating, instead of a pure ceramic coating, for a metal substrate decreases the driving force for buckle-driven delamination. El-Borghi et al . [ 17 ] used a plane strain model for investigating the influence of the coating thickness above a buckling delamination crack on the critical buckling strain. Eq. 1 was derived for the critical buckling strain for a graded non-homogeneous coating: $${\epsilon }_{0cr}={\pi }^{2}{\left(\frac{{h}_{2}}{a}\right)}^{2}\left[\frac{1}{{{(\beta h}_{2})}^{2}}-\frac{1}{{e}^{{\beta h}_{2}}+{e}^{{-\beta h}_{2}}-2)}\right] \beta \ne 0$$ 1 where \({\epsilon }_{0cr}\) is the critical buckling strain, h 2 is the coating thickness above the buckling delamination crack and a is the crack length. β is a non-homogeneity factor describing shear modulus change throughout the thickness of the FGM coating. El-Borghi et al . [ 17 ] also showed that Eq. 1 can be written in the following form for a homogenous coating: $${\epsilon }_{0cr}=\frac{{\pi }^{2}}{12}{\left(\frac{{h}_{2}}{a}\right)}^{2} \beta =0$$ 2 Therefore, it was noticed that, for a homogeneous coating, if delamination occurs at the interface of the coating, then the critical buckling strain increases with coating thickness, with similar results being obtained by Chiu [ 18 ]. El-Borghi et al . [ 17 ] also found Eq. 2 to be similar to the Eq. 3 derived by Chai et al . [ 19 ] for thin film delamination: $${\epsilon }_{0cr}=\frac{{\pi }^{2}}{3(1-{\nu }^{2})}{\left(\frac{{h}_{c}}{{l}_{c}}\right)}^{2}$$ 3 where ν is the Poisson’s ratio, h c = h 2 and l c = 2 a in Eq. 1 . In the study by Chai et al . [ 19 ], different scenarios associated with a delamination crack in a coating leading to buckling and further propagation of delamination were thoroughly investigated. It was mentioned in that study and others that, for buckling driven delamination, further propagation of delamination mostly occurs when thermal residual strains increase beyond the critical buckling strain, i.e. , following buckling of the delaminated layer [ 15 , 19 , 20 ]. Chai et al . [ 19 ] also argued that the subsequent propagation of delamination occurs if the energy loss of this propagation can provide the required energy for creating new delaminated surfaces. Surface cracking, as another failure mechanism of ceramic coatings, has been found to be a function of the temperature and environment to which the coating surface is exposed to [ 21 ]. This failure mechanism has been studied in the form of vertical surface cracks for thermal barrier coatings which result from thermal shock and large temperature gradients through the thickness of the brittle ceramic coating [ 22 ]. However, the presence of tensile stresses at the lower temperature has been found to be the main reason for initiation and propagation of vertical surface cracks [ 21 , 23 ]. It has been found that the density and the length of these vertical surface cracks play a crucial role in their propagation, strain tolerance of the coated system and interfacial delamination resistance of the coated system [ 22 ]. As a surface crack reaches an interface within a coating system, competitive delamination of different interfaces from the root of the surface crack can be observed. This phenomenon has also been investigated in previous studies, considering each route of delamination as a possible failure mechanism. For instance, Xu et al . [ 24 ] studied this competition for a double ceramic layer thermal barrier coating (DCL-TBC) system and showed that either of the competitive mechanisms can be dominant for different ratios of the thickness of the two ceramic coatings and fracture toughness ratio of the two interfaces [ 24 ]. Similarly, Jiang et al . [ 25 ] noticed that, for the thermal barrier coating (TBC) system they studied, two different paths of competitive crack propagation could occur depending on the elastic modulus ratio and thickness ratio of thermal coating (TC) to barrier coating (BC) [ 25 ]. 2. Finite element analysis (FEA) modelling A cylindrical model which resembles most hydrogen storage containers [ 4 , 26 ] was chosen to be the model under investigation in the present work. In order to make simulations faster, where feasible, a 2D model is always preferred for FEA, as a result of it being possible to refine the mesh size of the 2D model for crack analysis within a reasonable duration of simulation time whereas, for a 3D model with a similar level of mesh refinement, this would not be feasible. Therefore, a plane strain 2D model of a pipe quarter model cross-section was used for analysis with "Quad8" elements, i.e. , each element containing 8 nodes, being employed. A Python script was created to generate each model with Fig. 1 showing the geometry and mesh for a typical model with a 0.2 mm SiC coating. Boundary conditions used for simulations are also presented in this figure as applied to two sets of nodes parallel to the X and Y axes, thus allowing them to move freely only in the X and Y directions, respectively. The FEA was conducted considering the model to be initially stress free at 600°C and then cooled to room temperature (25°C), which was expected to result in the production significant residual thermal stresses due to the difference in CTE between the coating and substrate. The 2D model for this study was validated against model type A1 from the study by Mao et al . [ 27 ] for a substrate curvature of 4 mm. The strain energy, w , calculated by FEA for the 2D model was also validated using the following analytical formula [ 28 ]: $$w=\left(\frac{1}{2}E{\epsilon }^{2}\right)V=\left(\frac{1}{2}E{\left(\alpha \varDelta T\right)}^{2}\right)V$$ 4 The model used for validation against this analytical formula was considered to be a plane strain cylindrical geometry with an inner and outer radius of 2 m and 5 m, respectively, and a height of 1 m consisting of 960 elements for one layer of stainless steel cooled from 600°C to room temperature, i.e. , 25°C. The total energy calculated by the analytical formula and the FEA for this model was found to have a difference of less than 0.0002%. The final model for simulations was further refined for convergence of energy and also refined about the angle of 45°from the horizontal, as can be seen in Fig. 1 , as this was considered as the location of crack introduction in the model. Three models were used, each consisting of a 316L stainless steel substrate with a thickness of 25.5 mm and inner curvature radius of 175 mm, an FG layer of 316L stainless steel/ Al 2 O 3 with a thickness of 0.3 mm and a SiC top coating with three different thicknesses of 0.1 mm, 0.2 mm and 0.3 mm – these three models contained a total of 102,336, 115,456 and 128,576 elements, respectively, with the element size being the same in each of the component sections. The models were created using a Python script with the dimensions for the model being based on a previous investigation by Liu et al . [ 11 ]. All materials used for the simulations were considered to be isotropic with purely elastic behaviour and their properties were considered to be same as the properties considered in the authors’ previous study of a similar system [ 10 ], which itself was based on previous work [ 11 , 29 , 30 ]. Note that the assumption of pure elastic behaviour for the substrate was considered appropriate due to the stresses present in the substrate always being significantly below the yield strength. The FG layer was considered to be comprised of nine individual interlayers, as found appropriate by previous researchers [ 31 ], with each interlayer being of equal thickness and with a composition that changed according to Eq. 5 [ 11 ]: $${V}_{{Al}_{2}{O}_{3}}={\left(\frac{z}{{t}_{FG}}\right)}^{p}$$ 5 where \({V}_{{Al}_{2}{O}_{3}}\) is the Al 2 O 3 volume fraction of each interlayer, z is the thickness coordinate of each of the nine FG interlayers and \({t}_{FG}\) is the total thickness of the FG layer. p is a composition factor, sometimes referred to as the “ p factor”, which controls the Al 2 O 3 volume fraction in each of the individual graded interlayers, with the value of p being varied between 0.0-0.9. Using \({V}_{{Al}_{2}{O}_{3}}\) , the relevant coefficient of thermal expansion, α , Poisson’s ratio, ν , and Young’s modulus, E , were calculated for each graded interlayer according to Vegard’s rule of mixtures [ 32 ] and intermediate law of mixtures [ 33 – 35 ] as explained in detail in the authors’ previous work [ 10 ]. The method used for failure analysis of the considered model was based on energy variation calculations [ 10 ]. In this method, the energy variation of crack initiation and propagation is calculated by taking into account the added surface energy and released strain energy. The method has been explained in detail in the authors’ previous studies [ 10 , 36 ]. The maximum stable crack length is then found to be the longest crack length achievable before energy variation in the system becomes negative. This method can also be applied to competitive failure mechanisms in a system comparing the energy variation occurring as a result of each mechanism, as also explained previously [ 10 , 36 ]. Whilst the strain energy released from crack growth was achieved from the FEA, the interface energy required for crack growth was calculated using the surface energy values given in the authors’ previous study [ 10 ]. However, the accuracy of the calculated interface energy for the case of a cylindrical model was improved from the authors’ previous work in order to be able to capture the influence of p factor. In this study, the energy variation method and its competitive analysis was applied for different failure mechanisms, including buckling delamination, surface cracking and delamination initiation from the root of surface cracks all shown schematically in Fig. 2 . 2.1. Buckling delamination For the buckling delamination analysis, the interface energy for the FG/SiC interface was considered to be 2.466 J/m 2 [ 10 ]. For the substrate/FG interface, the interface energy was calculated based on Vegard’s rule of mixtures [ 32 ] and interface energy values for 316L stainless steel/Al 2 O 3 [ 10 ] and 316L stainless steel/316L stainless steel [ 37 ]. Substrate/FG interface energy = \({\left({V}_{{Al}_{2}{O}_{3}}\right)}_{1}\times 0.415+\left[1-{\left({V}_{{Al}_{2}{O}_{3}}\right)}_{1}\right]\times 2\times 1.77\) (6) where \({\left({V}_{{Al}_{2}{O}_{3}}\right)}_{1}\) is the alumina volume fraction of the first interlayer of the graded layer in the substrate/FG interface and 0.415 and 2 \(\times\) 1.77 being interface energy in J/m 2 for 316L stainless steel/Al 2 O 3 and 316L stainless steel/316L stainless steel, respectively [ 10 , 37 ]. Due to the size of the mesh, the minimum applied crack length in the interfaces for this model was about 16 µm. 2.2. Surface cracking Surface cracking was another failure mechanism that was studied in this work. For this purpose, vertical surface cracks were initiated at the surface of the SiC coating for the model with 0.2 mm SiC coating. The smallest crack length that was applicable to initiate surface cracking was 2.5 µm. The interface energy for the energy variation method for a crack in the SiC coating was defined to be 2×2.840 J/m 2 , as the surface crack created two free surfaces of SiC with γ = 2.840 J/m 2 [ 38 ]. 2.3. Delamination initiation from the root of surface cracks Two different propagation paths for a vertical surface crack reaching the FG/SiC interface were studied to investigate the energy variation of each path for the FG coating system with 0.2 mm SiC coating. Path 1 was considered to be the initiation of delamination in the FG/SiC interface from the root of the surface crack and path 2 was considered to be further vertical propagation of the surface crack into the FG layer until it reached the substrate/FG interface and initiated delamination in that interface. The interface energy for vertical propagation of the surface crack into the FG layer was calculated as 2 \(\times\) 1.13 J/m 2 for the first FG interlayer, being pure Al 2 O 3 according to Eq. 5 , and 1.13 J/m 2 being the surface energy of Al 2 O 3 [ 38 ]. For the subsequent i th FG interlayers that were 316L stainless steel/Al 2 O 3 composites, Eq. 7 was employed to calculate the interface energy based on Vegard’s rule of mixtures [ 32 ] and interface energy values for Al 2 O 3 /Al 2 O 3 [ 38 ] and 316L stainless steel/316L stainless steel [ 37 ]. FG/FG interface energy = \({\left({V}_{{Al}_{2}{O}_{3}}\right)}_{i}\times 2\times 1.13+\left[1-{\left({V}_{{Al}_{2}{O}_{3}}\right)}_{i}\right]\times 2\times 1.77\) (7) 3. Results and Discussion 3.1. Buckling delamination Figure 3 shows the total energy variation of buckling delamination versus crack length for different p factor values for 316L stainless steel/FG interface (Fig. 3 (a)) and FG/SiC interface (Fig. 3 (b)) of the model with 0.1mm SiC coating. The maximum stable crack length, e.g. , the crack lengths in Fig. 3 with the maximum total energy values, and maximum total energy values obtained from these graphs can be plotted versus p factor as shown in Fig. 4 for three different models with 0.1mm, 0.2mm and 0.3mm SiC coatings. It can be seen that both the parameters under investigation, i.e. , maximum stable crack length and maximum total energy, increased with p factor for the substrate/FG interface and that, due to the fact that buckling delamination resistance will depend on the maximum stable crack length in the interface, the buckling delamination resistance of this interface therefore increased with increasing p factor which leads to a higher 316L stainless steel volume fraction of FG layer close to the substrate, according to Eq. 5 . These results were consistent with those of Bao and Cai [ 15 ] who also studied buckling-driven delamination in a metal/ceramic FGM coating on a metallic substrate. They also observed that, at the substrate/FGM coating interface, increasing the p factor of the graded coating led to an increase in the failure resistance for buckling-driven delamination. However, in contrast to this, the influence of p factor on buckling resistance of the FG/SiC interface was found to be negligible (Fig. 3 ) due to the material in contact with the SiC coating being always pure Al 2 O 3 regardless of the p factor according to Eq. 5 . This observation was also reported in the study of critical temperature drop for buckling driven delamination by Bao and Cai [ 15 ] which showed that the influence of composition gradation factor on the buckling driven delamination resistance decreased as the location of the crack moved from the substrate/FG interface to the surface of the FG coating [ 15 ]. Figure 4 also shows that, in the competition between buckling delamination of the two interfaces, the system would be expected to delaminate from the substrate/FG interface for p values smaller than the cross-over value (inferred from each plot) and from the FG/SiC interface for p values greater than this value. The cross-over value can therefore be considered the optimum value of p factor for the FG layer in terms of buckling delamination. Finally, it can be observed in Fig. 4 that, as the SiC coating thickness above the FG layer increased, buckling delamination resistance and optimum p factor of the system also tended to increase. This result was in a good agreement with the findings of El-Borghi et al . [ 17 ] as mentioned earlier and attributed to the fact that, according to Eqs. 1 , 2 and 3 explained earlier, the presence of higher interfacial delamination resistance observed for the FG/SiC interface for the models with 0.3 mm SiC coating (compared to the models with 0.1 mm SiC coating) (Fig. 4 ), can be attributed to the increase of buckling critical strain in this interface due to the increase of coating thickness. 3.2. Surface cracking The energy variation for the surface cracking failure mode is shown in Fig. 5 for interface energy, strain energy and total energy as the surface crack grows vertically towards the interface for a typical model with SiC thickness of 0.2mm and p factor of 0.2. It can be seen in these figures that surface cracking is more likely in this system compared to buckling delamination as the total energy was negative for even the smallest crack studied. Many previous researchers have also reported and studied this failure mechanism as being a critical phenomenon, especially in thermal barrier coatings [ 39 – 41 ]. It was also observed that the change of p factor did not significantly influence this failure mechanism. Additionally, Fig. 5 shows that, for all cases studied, the decrease of total energy for surface crack initiation was lower than the total energy released due to crack propagation. This indicates that surface cracks could be expected to easily reach the interface should they propagate to a certain length, however, further investigation would be required to better understand the crack propagation behaviour. Figure 6 shows how the residual shear stress and strain energy density contour plots change in the presence of a vertical surface crack. It was observed in Fig. 6 that the introduction of the surface crack relieved the residual strain energy density and shear stress behind the crack tip whereas a concentration of both residual strain energy density and shear stress was visible ahead of the crack tip. This stress state was somewhat similar to the stress state for edge delamination in the axisymmetric model previously studied by the authors [ 42 ]. These two failure mechanisms were also similar in crack propagation mode, in that the vertical surface crack was also found to be propagating mainly in mode II as a large contact pressure was required to be applied to avoid interference of the cracked surfaces. Overall, it was expected that the presence of the stress concentration ahead of the crack tip and stress relief behind the crack, as noted in Fig. 6 , was responsible for further propagation of the surface crack. A surface crack that had reached any of the critical interfaces of the system, i.e. , substrate/FG and FG/SiC interfaces, was considered in the next section for studying interfacial delamination initiating from the root of this crack. 3.3. Delamination initiation from the root of surface cracks As the vertical surface crack reaches the critical substrate/FG and FG/SiC interfaces, it might cause delamination at the interface. Figure 7 shows the total energy versus length of a delamination crack initiating from the root of a surface crack in the substrate/FG interface and FG/SiC interface. Similar to the case of buckling delamination, higher values of p factor tended to increase delamination resistance of the substrate/FG interface whilst having a negligible influence on delamination of the FG/SiC interface. Furthermore, comparing Fig. 7 with Fig. 5 illustrates that, unlike the surface crack case, the initiation of delamination from the root of a surface crack occurs with a higher rate of energy release as compared to further propagation of the delamination crack. Therefore, it can be concluded that, unlike vertical surface cracks, delamination cracks initiating from the root of a surface crack would be expected to stop propagation beyond a certain delamination crack length. Figures 8 and 9 show the residual strain energy density and shear stress contour plots for delamination initiation from surface cracks for the substrate/FG and FG/SiC interfaces of the system, respectively. It can be seen in these two figures that, while vertical surface cracking relieved both the residual strain energy density and shear stress in the coating layers, delamination of the FG/SiC interface increased the strain energy density in the FG layer. For a surface crack reaching the FG/SiC interface, there would be a competition between further vertical propagation into the FG layer and delamination of the FG/SiC interface. Based on the residual strain energy density analysis in Fig. 8 and Fig. 9 , it was expected that vertical propagation of the crack into the FG layer would be preferable due to the strain energy density increase observed for delamination of the FG/SiC interface. These competitive failure paths were further investigated using the energy variation method in the next section. 3.4. Competitive failure paths in the coating system Figure 10 shows the energy variation versus crack length for the two competitive paths for a surface crack reaching the FG/SiC interface, as explained in Section 2.3. The solid lines show the plotted simulation data whereas the dashed lines represent the connection between simulation data in the range where no simulation was conducted. It can be seen that the surface crack initiates with a low energy release rate and propagates towards the interface with a higher energy release rate. At the FG/SiC interface, the energy release rate for delamination initiation from the root of the surface crack was initially high and then decreased upon further increases of delamination crack length. Delamination resistance at this interface was found to be slightly higher for lower p factor values, i.e. , higher alumina volume fraction in the FG layer. Comparing the energy variation for the two different paths in Fig. 10 for the surface crack reaching the FG/SiC interface, it was found that path 2 was more energetically favourable and, therefore, more likely for the studied system. This was consistent with the conclusion drawn in Section 3.3 based on the residual strain energy density and shear stress contour plots (Figs. 8 and 9 ) for these two failure paths. Therefore, the failure path for a cylindrical hydrogen storage container of 316L stainless steel coated with a 0.3 mm FG layer and a 0.2 mm SiC top coat was found to be as follows: Slow surface crack initiation ◊ fast surface crack propagation ◊ vertical propagation of the crack in the FG layer. It should be mentioned that, since the FG layer of the model in the current study was composed of metallic/ceramic composites, the influence of the metallic phase in preventing crack propagation due to plastic deformation should also be considered in future studies for a more accurate investigation, as explained in the study by Cai and Bao [ 43 ]. However, since the first FG layer, as the surface crack propagated into the FG layer, was pure Al 2 O 3 , the concluded crack propagation path 2 in the competitive failure analysis was still considered to be valid. 4. Conclusions In this paper, a coating system for hydrogen storage containers was investigated in order to further improve the applicability of these containers. The system considered was a 316L stainless steel/ Al 2 O 3 FG layer applied on a 316L stainless steel substrate with a top coat of SiC applied to the FG layer. The system was modelled using a cylindrical geometry with a focus on failure mechanisms due to thermal residual stresses resulted from cooling the system from an elevated temperature. Buckling delamination, surface cracking, delamination initiation from the root of a surface crack and competitive failure paths were considered as failure mechanisms for this system. It was observed that increasing the SiC coating thickness increased the buckling delamination resistance of the system with a maximum stable crack length for this failure mechanism within the cylindrical model being 1.5 mm. Another failure mechanism studied for the cylindrical geometry was surface cracking and it was observed that crack initiation from the surface of the SiC coating was a more probable failure mechanism in this geometry compared to buckling delamination. Finally, for a surface crack that propagated and reached the interfaces, two different propagation paths were investigated in this geometry and it was observed that vertical surface cracks tended to continue to propagate vertically into the FG layer rather than delaminate at the FG/SiC interface. The influence of the FG layer composition factor was found to be negligible on the improvement of the system resistance to surface cracking and its vertical propagation. Declarations Competing Interests The authors declare no financial interests. Funding The authors would like to acknowledge the support of a Curtin Strategic Stipend Scholarship and Australian Government Research Training Program Tuition Fee-Offset Scholarship as well as HDR PhD Completion and Publication Scholarship (partial completion and partial publication scholarship) through Curtin University for one of the authors (SA) during the course of this research. Author Contribution All authors contributed to the study conception and design. Simulation, data collection and analysis were performed by Sanam Abedini and Foon Min Amy Chu Pui Chan. The first draft of the manuscript was written by Sanam Abedini and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript. Data Availability Statement Data sets generated during the current study are available from the corresponding author on reasonable request. References Johnston B, Mayo MC, Khare A. Hydrogen: the energy source for the 21st century. Technovation. 2005;25(6):569-85. doi: https://doi.org/10.1016/j.technovation.2003.11.005. Thomas JM, Edwards PP, Dobson PJ, Owen GP. Decarbonising energy: The developing international activity in hydrogen technologies and fuel cells. Journal of Energy Chemistry. 2020;51:405-15. doi: https://doi.org/10.1016/j.jechem.2020.03.087. Apak S, Atay E, Tuncer G. 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Elsevier; 1991. p. 63-191. Kokini K, Takeuchi YR, Choules BD. Surface thermal cracking of thermal barrier coatings owing to stress relaxation: zirconia vs. mullite. Surface and Coatings Technology. 1996;82(1):77-82. doi: https://doi.org/10.1016/0257-8972(95)02647-9. Zhou B, Kokini K. Effect of preexisting surface cracks on the interfacial thermal fracture of thermal barrier coatings: an experimental study. Surface and Coatings Technology. 2004;187(1):17-25. doi: https://doi.org/10.1016/j.surfcoat.2004.01.028. Kokini K, Takeuchi YR, Choules BD. Thermal crack initiation mechanisms on the surface of functionally graded ceramic thermal barrier coatings. Ceramics International. 1996;22(5):397-401. doi: https://doi.org/10.1016/0272-8842(95)00122-0. Xu R, Fan X, Wang T. Mechanisms governing the interfacial delamination of thermal barrier coating system with double ceramic layers. Applied Surface Science. 2016;370:394-402. doi: https://doi.org/10.1016/j.apsusc.2016.02.180. Jiang P, Fan X, Sun Y, Li D, Li B, Wang T. Competition mechanism of interfacial cracks in thermal barrier coating system. Materials & Design. 2017;132:559-66. doi: https://doi.org/10.1016/j.matdes.2017.07.018. Schlapbach L, Züttel A. Hydrogen-storage materials for mobile applications. Nature. 2001;414(6861):353-8. doi: https://doi.org/10.1038/35104634. Mao WG, Jiang JP, Zhou YC, Lu C. Effects of substrate curvature radius, deposition temperature and coating thickness on the residual stress field of cylindrical thermal barrier coatings. Surface and Coatings Technology. 2011;205(8):3093-102. doi: https://doi.org/10.1016/j.surfcoat.2010.11.020. Dieter GE, Bacon DJ. Mechanical Metallurgy. SI metric ed. McGraw-Hill Series in Materials Science and Engineering. London: McGraw-Hill London; 1988. Qin S, Jiang D, Zhang J, Qin J. Design, fabrication and properties of layered SiC/TiC ceramic with graded thermal residual stress. Journal of the European Ceramic Society. 2003;23(9):1491-7. doi: https://doi.org/10.1016/S0955-2219(02)00306-0. Grujicic M, Zhao H. Optimization of 316 stainless steel/alumina functionally graded material for reduction of damage induced by thermal residual stresses. Materials Science and Engineering: A. 1998;252(1):117-32. doi: https://doi.org/10.1016/S0921-5093(98)00618-2. Yu MH, Zhou B, Bi DB, Shaw D. Preparation of graded multilayer materials and evaluation of residual stresses. Materials & Design (1980-2015). 2010;31(5):2478-82. doi: https://doi.org/10.1016/j.matdes.2009.11.047. Denton AR, Ashcroft NW. Vegard's law. Physical Review A. 1991;43(6):3161-4. doi: https://doi.org/10.1103/PhysRevA.43.3161. Tamura I, Tomota Y, Ozawa H. Strength and ductility of iron-nickel-carbon alloys composed of austenite and martensite with various strength. Proceedings of the 3rd International Conference on Strength of Metals and Alloys. Cambridge, UK1973. p. 611-5. Williamson RL, Rabin BH, Drake JT. Finite element analysis of thermal residual stresses at graded ceramic‐metal interfaces. Part I. Model description and geometrical effects. Journal of Applied Physics. 1993;74(2):1310-20. doi: https://doi.org/10.1063/1.354910. Giannakopoulos AE, Suresh S, Finot M, Olsson M. Elastoplastic analysis of thermal cycling: layered materials with compositional gradients. Acta Metallurgica et Materialia. 1995;43(4):1335-54. doi: https://doi.org/10.1016/0956-7151(94)00360-T. Abedini S, Dong C, Davies IJ. Multi-objective particle swarm optimisation of multilayer functionally graded coating systems for improved interfacial delamination resistance. Materials Today Communications. 2020;24:101202. doi: https://doi.org/10.1016/j.mtcomm.2020.101202. Brooks RF, Quested PN. The surface tension of steels. Journal of Materials Science. 2005;40(9):2233-8. doi: https://doi.org/10.1007/s10853-005-1939-2. Jiao S, Jenkins ML, Davidge RW. Interfacial fracture energy-mechanical behaviour relationship in Al2O3/SiC and Al2O3/TiN nanocomposites. Acta Materialia. 1997;45(1):149-56. doi: https://doi.org/10.1016/S1359-6454(96)00168-1. Zhu W, Yang L, Guo JW, Zhou YC, Lu C. Numerical study on interaction of surface cracking and interfacial delamination in thermal barrier coatings under tension. Applied Surface Science. 2014;315:292-8. doi: https://doi.org/10.1016/j.apsusc.2014.07.142. Balke H, Hofinger I, Häusler C, Bahr HA, Weiß HJ, Kirchhoff G. Fracture mechanical damage modelling of thermal barrier coatings. Archive of Applied Mechanics. 2000;70(1):193-200. doi: https://doi.org/10.1007/s004199900057. Fan XL, Xu R, Zhang WX, Wang TJ. Effect of periodic surface cracks on the interfacial fracture of thermal barrier coating system. Applied Surface Science. 2012;258(24):9816-23. doi: https://doi.org/10.1016/j.apsusc.2012.06.036. Abedini S, Dong C, Davies IJ. Mechanisms and control of edge interfacial delamination in a multilayer system containing a functionally graded interlayer. Surface and Coatings Technology. 2020;382:125221. doi: https://doi.org/10.1016/j.surfcoat.2019.125221. Cai H, Bao G. Crack bridging in functionally graded coatings. International Journal of Solids and Structures. 1998;35(7):701-17. doi: https://doi.org/10.1016/S0020-7683(97)00082-6. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 19 Jun, 2024 Reviews received at journal 18 Jun, 2024 Reviews received at journal 18 Jun, 2024 Reviewers agreed at journal 17 Jun, 2024 Reviews received at journal 17 Jun, 2024 Reviewers agreed at journal 14 Jun, 2024 Reviewers agreed at journal 13 Jun, 2024 Reviewers agreed at journal 12 Jun, 2024 Reviews received at journal 25 Apr, 2024 Reviewers agreed at journal 24 Apr, 2024 Reviewers agreed at journal 24 Mar, 2024 Reviewers invited by journal 18 Mar, 2024 Editor assigned by journal 06 Feb, 2024 Submission checks completed at journal 06 Feb, 2024 First submitted to journal 11 Dec, 2023 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3741716","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":271342178,"identity":"d6020a2e-47c1-4780-be5a-e1c32be7b902","order_by":0,"name":"Sanam Abedini","email":"","orcid":"","institution":"Curtin University","correspondingAuthor":false,"prefix":"","firstName":"Sanam","middleName":"","lastName":"Abedini","suffix":""},{"id":271342179,"identity":"b42a9f8c-b3c8-473f-8067-3de468f9e0d9","order_by":1,"name":"Foon Min Amy Chu Pui Chan","email":"","orcid":"","institution":"Curtin University","correspondingAuthor":false,"prefix":"","firstName":"Foon","middleName":"Min Amy Chu Pui","lastName":"Chan","suffix":""},{"id":271342180,"identity":"17072cc3-f8d7-4008-96e9-74cb2dd58783","order_by":2,"name":"Chensong Dong","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1UlEQVRIiWNgGAWjYHACAyC2AbMOADFjA5Fa0oCYmTQth8FaGIjSwt/AvPFxwa/z8ga3zx88XMBgI7vhAPMzCXxaJA6wFRvP7LttuOFcMsPhGQxpxhsOsJnh1WLAwGMmzdtzO8HgDDPDYR6Gw4kbDjAQpeUcTMt/oBb2b4S18Pw4ANNyAKiFB78tEoeBfuFtSDaceYbZ4DCPQbLxzMM8xRb4tPC3N298zPPHTp7vDOPjzzwVdrJ9x9s33sCnBRwbjG0Id8LihxD4Q5SqUTAKRsEoGKkAAOM0RI8cn8JxAAAAAElFTkSuQmCC","orcid":"","institution":"Curtin University","correspondingAuthor":true,"prefix":"","firstName":"Chensong","middleName":"","lastName":"Dong","suffix":""},{"id":271342181,"identity":"c77e214f-e8a0-4a56-925d-6c0be85e2d2e","order_by":3,"name":"Ian Davies","email":"","orcid":"","institution":"Curtin University","correspondingAuthor":false,"prefix":"","firstName":"Ian","middleName":"","lastName":"Davies","suffix":""}],"badges":[],"createdAt":"2023-12-12 04:44:31","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3741716/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3741716/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":50840979,"identity":"6019cbee-837a-43a7-b1d3-9e5e5bbc746d","added_by":"auto","created_at":"2024-02-08 07:46:51","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":106457,"visible":true,"origin":"","legend":"\u003cp\u003e2D plane strain cylindrical FEA model (a); detailed views of the substrate (b), the SiC layer (c), and the FG layer (d).\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3741716/v1/c143fe3648cf9e917661935d.jpg"},{"id":50840978,"identity":"23e7663f-5e34-4c69-96dc-81979223a843","added_by":"auto","created_at":"2024-02-08 07:46:51","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":81704,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic of (a) buckling delamination in 316L stainless steel/FG interface (b) buckling delamination in FG/SiC interface, (c) surface cracking in the SiC coating, (d) delamination initiation from the root of a surface crack at the 316L stainless steel/FG interface and (e) delamination initiation from the root of a surface crack at the FG/SiC interface.\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3741716/v1/5e5c79c38bd093dd47cf63c1.jpg"},{"id":50841322,"identity":"7d95e622-0e4a-4518-9d4f-d148c42a9423","added_by":"auto","created_at":"2024-02-08 07:54:51","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":69753,"visible":true,"origin":"","legend":"\u003cp\u003eTotal energy versus delamination crack length at the: (a) 316L stainless steel/FG interface and (b) FG/SiC interface, for the FG coating system with 0.1 mm SiC coating for different \u003cem\u003ep\u003c/em\u003evalues (as shown on the graph).\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3741716/v1/ddfb3d574341eb109490d646.jpg"},{"id":50840985,"identity":"3108b27c-0ede-4225-b293-05f96e794af8","added_by":"auto","created_at":"2024-02-08 07:46:52","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":92208,"visible":true,"origin":"","legend":"\u003cp\u003eMaximum stable crack length and maximum total energy versus composition factor for 316L stainless steel/FG and FG/SiC interfaces for the FG coating system with (a,b) 0.1 mm SiC coating, (c,d) 0.2 mm SiC coating and (e,f) 0.3 mm SiC coating.\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3741716/v1/e1565d1fc07ac890180ee262.jpg"},{"id":50840981,"identity":"e4070a5b-acc4-467d-b09f-f69e6ec9560d","added_by":"auto","created_at":"2024-02-08 07:46:51","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":87066,"visible":true,"origin":"","legend":"\u003cp\u003eInterface energy, strain energy and total energy versus surface crack length for the FG coating system with 0.2 mm SiC coating and \u003cem\u003ep\u003c/em\u003e values as shown on the graphs.\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3741716/v1/2cb028e268425f43abf0134f.jpg"},{"id":50840986,"identity":"c3bf1a07-70a3-42ba-875c-96676f11a037","added_by":"auto","created_at":"2024-02-08 07:46:52","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":42056,"visible":true,"origin":"","legend":"\u003cp\u003eContour plots showing: (a) residual strain energy density and (b) shear stress, for a 0.04 mm vertical surface crack in the SiC coating.\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3741716/v1/e60f5327d18711c1996f0a68.jpg"},{"id":50840983,"identity":"2846c202-84c2-4cd5-b1fd-b371f882e113","added_by":"auto","created_at":"2024-02-08 07:46:51","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":43798,"visible":true,"origin":"","legend":"\u003cp\u003eTotal energy versus delamination crack length in: (a) 316L stainless steel/FG interface and (b) FG/SiC interface, for the FG coating system with 0.2 mm SiC coating for different \u003cem\u003ep\u003c/em\u003evalues (as shown on the graph).\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3741716/v1/65dffa3b1414646f15ddbfd8.jpg"},{"id":50840982,"identity":"62d81417-dbf5-4f24-9a88-c48141237bd5","added_by":"auto","created_at":"2024-02-08 07:46:51","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":49481,"visible":true,"origin":"","legend":"\u003cp\u003eContour plots showing: (a) residual strain energy density and (b) shear stress for a 1.68 mm delamination crack initiated from the root of a vertical surface crack in the 316L stainless steel/FG interface.\u003c/p\u003e","description":"","filename":"8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3741716/v1/f60320eb45947f2839d5c589.jpg"},{"id":50840984,"identity":"3448c1c5-e293-401f-93b3-12ac20dc4c3d","added_by":"auto","created_at":"2024-02-08 07:46:51","extension":"jpg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":47053,"visible":true,"origin":"","legend":"\u003cp\u003eContour plots showing: (a) residual strain energy density and (b) shear stress for a 1.68 mm delamination crack initiated from the root of a vertical surface crack in the FG/SiC interface.\u003c/p\u003e","description":"","filename":"9.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3741716/v1/4ac67eeb82885f9dfb0e1507.jpg"},{"id":50840987,"identity":"b7ef8818-f2ee-4e14-afe9-c542b62fedad","added_by":"auto","created_at":"2024-02-08 07:46:52","extension":"jpg","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":73243,"visible":true,"origin":"","legend":"\u003cp\u003eTotal energy versus crack length for a crack initiated from the model surface following two different paths at the FG/SiC interface for the FG coating system with 0.2 mm SiC coating for different \u003cem\u003ep\u003c/em\u003evalues.\u003c/p\u003e","description":"","filename":"10.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3741716/v1/68f1df834752f1c307825aa8.jpg"},{"id":50841862,"identity":"3ed76bfa-046b-4ca4-8fe7-925a61ae675f","added_by":"auto","created_at":"2024-02-08 08:02:54","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":819668,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3741716/v1/5d8a7d56-2a51-4407-b54d-36f08ea11b1e.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Failure Analysis of a Functionally Graded Multilayer Coated Stainless Steel Pipe for Hydrogen Storage","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eHydrogen is becoming a promising alternative future fuel due to its abundance and ability to be burned in a combustion engine with water being the only resultant product [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. However, among other challenges with hydrogen fuel, the storage of hydrogen, especially with regards to vehicles, has remained one of the main issues [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], in particular due to the potential for leakage from storage containers. One of the most common methods of hydrogen storage to date has been high pressure gas cylinders known as high pressure gaseous hydrogen (HPGH2) [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eMaterials that have been mainly used for manufacturing these cylinders include austenitic stainless steel (\u003cem\u003ee.g.\u003c/em\u003e, AISI 316L) and alloys of aluminium or copper [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. In order to reduce hydrogen leakage from the walls of these containers, permeation barrier coatings are usually applied [\u003cspan additionalcitationids=\"CR7 CR8\" citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Alumina (Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e) and silicon carbide (SiC) are among the most promising ceramic materials for this purpose [\u003cspan additionalcitationids=\"CR11 CR12\" citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. However, in the case of coatings on a different material type, \u003cem\u003ee.g.\u003c/em\u003e, ceramics on metallic substrates, failure mainly occurs due to the mismatch of properties, such as the coefficient of thermal expansion (CTE), during heating and cooling cycles [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. For example, the mismatch between CTE of the two layers adjacent to the interface has been considered the primary reason for delamination of ceramic coatings on metallic substrates [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Buckling as another failure mechanism is closely related to delamination in that, while delamination occurs mainly at thicker edges of a coating, buckling tends to occur at thinner parts away from the edge [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eOne relatively recent idea is to use a functionally graded (FG) layer between the ceramic coating and the metallic substrate, which is graded in terms of composition between dissimilar materials and helps to diminish any mismatch stress due to property changes, in particular the CTE [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Applying a functionally graded material (FGM) layer has proved to assist with a fundamental issue for these coatings which arises from the presence of residual stresses caused by the cooling of such a coating layer from the manufacturing temperature, thereby significantly reducing these stresses [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn the case of using FG layers to alleviate stress severity between coating and substrate, some researchers have studied the influence of some of the most important factors. Bao and Cai [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] have applied this idea to investigate different possible failure mechanisms of a ceramic/metallic FGM coating on a metallic substrate, including edge delamination and buckle-driven delamination. In the investigation of buckle-driven delamination, it was noticed that, as the metal volume fraction increases in the applied FGM coating, the resistance for buckling also increases in terms of the increase in the critical buckling temperature drop, \u003cem\u003ei.e.\u003c/em\u003e, the temperature drop required for buckling. However, it was also shown that, for a fixed temperature drop, buckling is more likely to occur for delamination cracks closer to the surface of the FGM coating rather than for cracks closer to the metal/FGM coating interface. In general, it was concluded that the use of a ceramic/metallic FGM coating, instead of a pure ceramic coating, for a metal substrate decreases the driving force for buckle-driven delamination.\u003c/p\u003e \u003cp\u003eEl-Borghi \u003cem\u003eet al\u003c/em\u003e. [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] used a plane strain model for investigating the influence of the coating thickness above a buckling delamination crack on the critical buckling strain. Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e was derived for the critical buckling strain for a graded non-homogeneous coating:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$${\\epsilon }_{0cr}={\\pi }^{2}{\\left(\\frac{{h}_{2}}{a}\\right)}^{2}\\left[\\frac{1}{{{(\\beta h}_{2})}^{2}}-\\frac{1}{{e}^{{\\beta h}_{2}}+{e}^{{-\\beta h}_{2}}-2)}\\right] \\beta \\ne 0$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\epsilon }_{0cr}\\)\u003c/span\u003e\u003c/span\u003e is the critical buckling strain, \u003cem\u003eh\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e is the coating thickness above the buckling delamination crack and \u003cem\u003ea\u003c/em\u003e is the crack length. \u003cem\u003eβ\u003c/em\u003e is a non-homogeneity factor describing shear modulus change throughout the thickness of the FGM coating.\u003c/p\u003e \u003cp\u003eEl-Borghi \u003cem\u003eet al\u003c/em\u003e. [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] also showed that Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e can be written in the following form for a homogenous coating:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$${\\epsilon }_{0cr}=\\frac{{\\pi }^{2}}{12}{\\left(\\frac{{h}_{2}}{a}\\right)}^{2} \\beta =0$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eTherefore, it was noticed that, for a homogeneous coating, if delamination occurs at the interface of the coating, then the critical buckling strain increases with coating thickness, with similar results being obtained by Chiu [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. El-Borghi \u003cem\u003eet al\u003c/em\u003e. [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] also found Eq.\u0026nbsp;\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e to be similar to the Eq.\u0026nbsp;\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e derived by Chai \u003cem\u003eet al\u003c/em\u003e. [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] for thin film delamination:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$${\\epsilon }_{0cr}=\\frac{{\\pi }^{2}}{3(1-{\\nu }^{2})}{\\left(\\frac{{h}_{c}}{{l}_{c}}\\right)}^{2}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eν\u003c/em\u003e is the Poisson\u0026rsquo;s ratio, \u003cem\u003eh\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e= h\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e and \u003cem\u003el\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e = 2\u003cem\u003ea\u003c/em\u003e in Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. In the study by Chai \u003cem\u003eet al\u003c/em\u003e. [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e], different scenarios associated with a delamination crack in a coating leading to buckling and further propagation of delamination were thoroughly investigated. It was mentioned in that study and others that, for buckling driven delamination, further propagation of delamination mostly occurs when thermal residual strains increase beyond the critical buckling strain, \u003cem\u003ei.e.\u003c/em\u003e, following buckling of the delaminated layer [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. Chai \u003cem\u003eet al\u003c/em\u003e. [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] also argued that the subsequent propagation of delamination occurs if the energy loss of this propagation can provide the required energy for creating new delaminated surfaces.\u003c/p\u003e \u003cp\u003eSurface cracking, as another failure mechanism of ceramic coatings, has been found to be a function of the temperature and environment to which the coating surface is exposed to [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. This failure mechanism has been studied in the form of vertical surface cracks for thermal barrier coatings which result from thermal shock and large temperature gradients through the thickness of the brittle ceramic coating [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. However, the presence of tensile stresses at the lower temperature has been found to be the main reason for initiation and propagation of vertical surface cracks [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. It has been found that the density and the length of these vertical surface cracks play a crucial role in their propagation, strain tolerance of the coated system and interfacial delamination resistance of the coated system [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAs a surface crack reaches an interface within a coating system, competitive delamination of different interfaces from the root of the surface crack can be observed. This phenomenon has also been investigated in previous studies, considering each route of delamination as a possible failure mechanism. For instance, Xu \u003cem\u003eet al\u003c/em\u003e. [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] studied this competition for a double ceramic layer thermal barrier coating (DCL-TBC) system and showed that either of the competitive mechanisms can be dominant for different ratios of the thickness of the two ceramic coatings and fracture toughness ratio of the two interfaces [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. Similarly, Jiang \u003cem\u003eet al\u003c/em\u003e. [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e] noticed that, for the thermal barrier coating (TBC) system they studied, two different paths of competitive crack propagation could occur depending on the elastic modulus ratio and thickness ratio of thermal coating (TC) to barrier coating (BC) [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e].\u003c/p\u003e"},{"header":"2. Finite element analysis (FEA) modelling","content":"\u003cp\u003eA cylindrical model which resembles most hydrogen storage containers [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e] was chosen to be the model under investigation in the present work. In order to make simulations faster, where feasible, a 2D model is always preferred for FEA, as a result of it being possible to refine the mesh size of the 2D model for crack analysis within a reasonable duration of simulation time whereas, for a 3D model with a similar level of mesh refinement, this would not be feasible. Therefore, a plane strain 2D model of a pipe quarter model cross-section was used for analysis with \"Quad8\" elements, \u003cem\u003ei.e.\u003c/em\u003e, each element containing 8 nodes, being employed. A Python script was created to generate each model with Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e showing the geometry and mesh for a typical model with a 0.2 mm SiC coating. Boundary conditions used for simulations are also presented in this figure as applied to two sets of nodes parallel to the X and Y axes, thus allowing them to move freely only in the X and Y directions, respectively. The FEA was conducted considering the model to be initially stress free at 600\u0026deg;C and then cooled to room temperature (25\u0026deg;C), which was expected to result in the production significant residual thermal stresses due to the difference in CTE between the coating and substrate.\u003c/p\u003e \u003cp\u003eThe 2D model for this study was validated against model type A1 from the study by Mao \u003cem\u003eet al\u003c/em\u003e. [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] for a substrate curvature of 4 mm. The strain energy, \u003cem\u003ew\u003c/em\u003e, calculated by FEA for the 2D model was also validated using the following analytical formula [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$w=\\left(\\frac{1}{2}E{\\epsilon }^{2}\\right)V=\\left(\\frac{1}{2}E{\\left(\\alpha \\varDelta T\\right)}^{2}\\right)V$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe model used for validation against this analytical formula was considered to be a plane strain cylindrical geometry with an inner and outer radius of 2 m and 5 m, respectively, and a height of 1 m consisting of 960 elements for one layer of stainless steel cooled from 600\u0026deg;C to room temperature, \u003cem\u003ei.e.\u003c/em\u003e, 25\u0026deg;C. The total energy calculated by the analytical formula and the FEA for this model was found to have a difference of less than 0.0002%.\u003c/p\u003e \u003cp\u003eThe final model for simulations was further refined for convergence of energy and also refined about the angle of 45\u0026deg;from the horizontal, as can be seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, as this was considered as the location of crack introduction in the model. Three models were used, each consisting of a 316L stainless steel substrate with a thickness of 25.5 mm and inner curvature radius of 175 mm, an FG layer of 316L stainless steel/ Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e with a thickness of 0.3 mm and a SiC top coating with three different thicknesses of 0.1 mm, 0.2 mm and 0.3 mm \u0026ndash; these three models contained a total of 102,336, 115,456 and 128,576 elements, respectively, with the element size being the same in each of the component sections. The models were created using a Python script with the dimensions for the model being based on a previous investigation by Liu \u003cem\u003eet al\u003c/em\u003e. [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. All materials used for the simulations were considered to be isotropic with purely elastic behaviour and their properties were considered to be same as the properties considered in the authors\u0026rsquo; previous study of a similar system [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e], which itself was based on previous work [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. Note that the assumption of pure elastic behaviour for the substrate was considered appropriate due to the stresses present in the substrate always being significantly below the yield strength.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe FG layer was considered to be comprised of nine individual interlayers, as found appropriate by previous researchers [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e], with each interlayer being of equal thickness and with a composition that changed according to Eq.\u0026nbsp;\u003cspan refid=\"Equ5\" class=\"InternalRef\"\u003e5\u003c/span\u003e [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$${V}_{{Al}_{2}{O}_{3}}={\\left(\\frac{z}{{t}_{FG}}\\right)}^{p}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({V}_{{Al}_{2}{O}_{3}}\\)\u003c/span\u003e\u003c/span\u003e is the Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e volume fraction of each interlayer, \u003cem\u003ez\u003c/em\u003e is the thickness coordinate of each of the nine FG interlayers and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({t}_{FG}\\)\u003c/span\u003e\u003c/span\u003e is the total thickness of the FG layer. \u003cem\u003ep\u003c/em\u003e is a composition factor, sometimes referred to as the \u0026ldquo;\u003cem\u003ep\u003c/em\u003e factor\u0026rdquo;, which controls the Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e volume fraction in each of the individual graded interlayers, with the value of \u003cem\u003ep\u003c/em\u003e being varied between 0.0-0.9. Using \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({V}_{{Al}_{2}{O}_{3}}\\)\u003c/span\u003e\u003c/span\u003e, the relevant coefficient of thermal expansion, \u003cem\u003eα\u003c/em\u003e, Poisson\u0026rsquo;s ratio, \u003cem\u003eν\u003c/em\u003e, and Young\u0026rsquo;s modulus, \u003cem\u003eE\u003c/em\u003e, were calculated for each graded interlayer according to Vegard\u0026rsquo;s rule of mixtures [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e] and intermediate law of mixtures [\u003cspan additionalcitationids=\"CR34\" citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e] as explained in detail in the authors\u0026rsquo; previous work [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe method used for failure analysis of the considered model was based on energy variation calculations [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. In this method, the energy variation of crack initiation and propagation is calculated by taking into account the added surface energy and released strain energy. The method has been explained in detail in the authors\u0026rsquo; previous studies [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. The maximum stable crack length is then found to be the longest crack length achievable before energy variation in the system becomes negative. This method can also be applied to competitive failure mechanisms in a system comparing the energy variation occurring as a result of each mechanism, as also explained previously [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. Whilst the strain energy released from crack growth was achieved from the FEA, the interface energy required for crack growth was calculated using the surface energy values given in the authors\u0026rsquo; previous study [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. However, the accuracy of the calculated interface energy for the case of a cylindrical model was improved from the authors\u0026rsquo; previous work in order to be able to capture the influence of \u003cem\u003ep\u003c/em\u003e factor.\u003c/p\u003e \u003cp\u003eIn this study, the energy variation method and its competitive analysis was applied for different failure mechanisms, including buckling delamination, surface cracking and delamination initiation from the root of surface cracks all shown schematically in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Buckling delamination\u003c/h2\u003e \u003cp\u003eFor the buckling delamination analysis, the interface energy for the FG/SiC interface was considered to be 2.466 J/m\u003csup\u003e2\u003c/sup\u003e [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. For the substrate/FG interface, the interface energy was calculated based on Vegard\u0026rsquo;s rule of mixtures [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e] and interface energy values for 316L stainless steel/Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] and 316L stainless steel/316L stainless steel [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eSubstrate/FG interface energy = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\left({V}_{{Al}_{2}{O}_{3}}\\right)}_{1}\\times 0.415+\\left[1-{\\left({V}_{{Al}_{2}{O}_{3}}\\right)}_{1}\\right]\\times 2\\times 1.77\\)\u003c/span\u003e\u003c/span\u003e (6)\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\left({V}_{{Al}_{2}{O}_{3}}\\right)}_{1}\\)\u003c/span\u003e\u003c/span\u003e is the alumina volume fraction of the first interlayer of the graded layer in the substrate/FG interface and 0.415 and 2\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\times\\)\u003c/span\u003e\u003c/span\u003e1.77 being interface energy in J/m\u003csup\u003e2\u003c/sup\u003e for 316L stainless steel/Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e and 316L stainless steel/316L stainless steel, respectively [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. Due to the size of the mesh, the minimum applied crack length in the interfaces for this model was about 16 \u0026micro;m.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Surface cracking\u003c/h2\u003e \u003cp\u003eSurface cracking was another failure mechanism that was studied in this work. For this purpose, vertical surface cracks were initiated at the surface of the SiC coating for the model with 0.2 mm SiC coating. The smallest crack length that was applicable to initiate surface cracking was 2.5 \u0026micro;m. The interface energy for the energy variation method for a crack in the SiC coating was defined to be 2\u0026times;2.840 J/m\u003csup\u003e2\u003c/sup\u003e, as the surface crack created two free surfaces of SiC with \u003cem\u003eγ\u003c/em\u003e = 2.840 J/m\u003csup\u003e2\u003c/sup\u003e [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3. Delamination initiation from the root of surface cracks\u003c/h2\u003e \u003cp\u003eTwo different propagation paths for a vertical surface crack reaching the FG/SiC interface were studied to investigate the energy variation of each path for the FG coating system with 0.2 mm SiC coating. Path 1 was considered to be the initiation of delamination in the FG/SiC interface from the root of the surface crack and path 2 was considered to be further vertical propagation of the surface crack into the FG layer until it reached the substrate/FG interface and initiated delamination in that interface. The interface energy for vertical propagation of the surface crack into the FG layer was calculated as 2\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\times\\)\u003c/span\u003e\u003c/span\u003e1.13 J/m\u003csup\u003e2\u003c/sup\u003e for the first FG interlayer, being pure Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e according to Eq.\u0026nbsp;\u003cspan refid=\"Equ5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, and 1.13 J/m\u003csup\u003e2\u003c/sup\u003e being the surface energy of Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. For the subsequent \u003cem\u003ei\u003c/em\u003eth FG interlayers that were 316L stainless steel/Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e composites, Eq.\u0026nbsp;7 was employed to calculate the interface energy based on Vegard\u0026rsquo;s rule of mixtures [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e] and interface energy values for Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e/Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e] and 316L stainless steel/316L stainless steel [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eFG/FG interface energy = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\left({V}_{{Al}_{2}{O}_{3}}\\right)}_{i}\\times 2\\times 1.13+\\left[1-{\\left({V}_{{Al}_{2}{O}_{3}}\\right)}_{i}\\right]\\times 2\\times 1.77\\)\u003c/span\u003e\u003c/span\u003e (7)\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results and Discussion","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.1. Buckling delamination\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows the total energy variation of buckling delamination versus crack length for different \u003cem\u003ep\u003c/em\u003e factor values for 316L stainless steel/FG interface (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(a)) and FG/SiC interface (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(b)) of the model with 0.1mm SiC coating. The maximum stable crack length, \u003cem\u003ee.g.\u003c/em\u003e, the crack lengths in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e with the maximum total energy values, and maximum total energy values obtained from these graphs can be plotted versus \u003cem\u003ep\u003c/em\u003e factor as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e for three different models with 0.1mm, 0.2mm and 0.3mm SiC coatings.\u003c/p\u003e \u003cp\u003eIt can be seen that both the parameters under investigation, \u003cem\u003ei.e.\u003c/em\u003e, maximum stable crack length and maximum total energy, increased with \u003cem\u003ep\u003c/em\u003e factor for the substrate/FG interface and that, due to the fact that buckling delamination resistance will depend on the maximum stable crack length in the interface, the buckling delamination resistance of this interface therefore increased with increasing \u003cem\u003ep\u003c/em\u003e factor which leads to a higher 316L stainless steel volume fraction of FG layer close to the substrate, according to Eq.\u0026nbsp;\u003cspan refid=\"Equ5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThese results were consistent with those of Bao and Cai [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] who also studied buckling-driven delamination in a metal/ceramic FGM coating on a metallic substrate. They also observed that, at the substrate/FGM coating interface, increasing the \u003cem\u003ep\u003c/em\u003e factor of the graded coating led to an increase in the failure resistance for buckling-driven delamination.\u003c/p\u003e \u003cp\u003eHowever, in contrast to this, the influence of \u003cem\u003ep\u003c/em\u003e factor on buckling resistance of the FG/SiC interface was found to be negligible (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) due to the material in contact with the SiC coating being always pure Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e regardless of the \u003cem\u003ep\u003c/em\u003e factor according to Eq.\u0026nbsp;\u003cspan refid=\"Equ5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. This observation was also reported in the study of critical temperature drop for buckling driven delamination by Bao and Cai [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] which showed that the influence of composition gradation factor on the buckling driven delamination resistance decreased as the location of the crack moved from the substrate/FG interface to the surface of the FG coating [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e also shows that, in the competition between buckling delamination of the two interfaces, the system would be expected to delaminate from the substrate/FG interface for \u003cem\u003ep\u003c/em\u003e values smaller than the cross-over value (inferred from each plot) and from the FG/SiC interface for \u003cem\u003ep\u003c/em\u003e values greater than this value. The cross-over value can therefore be considered the optimum value of \u003cem\u003ep\u003c/em\u003e factor for the FG layer in terms of buckling delamination.\u003c/p\u003e \u003cp\u003eFinally, it can be observed in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e that, as the SiC coating thickness above the FG layer increased, buckling delamination resistance and optimum \u003cem\u003ep\u003c/em\u003e factor of the system also tended to increase. This result was in a good agreement with the findings of El-Borghi \u003cem\u003eet al\u003c/em\u003e. [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] as mentioned earlier and attributed to the fact that, according to Eqs.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, \u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and \u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e explained earlier, the presence of higher interfacial delamination resistance observed for the FG/SiC interface for the models with 0.3 mm SiC coating (compared to the models with 0.1 mm SiC coating) (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e), can be attributed to the increase of buckling critical strain in this interface due to the increase of coating thickness.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.2. Surface cracking\u003c/h2\u003e \u003cp\u003eThe energy variation for the surface cracking failure mode is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e for interface energy, strain energy and total energy as the surface crack grows vertically towards the interface for a typical model with SiC thickness of 0.2mm and \u003cem\u003ep\u003c/em\u003e factor of 0.2. It can be seen in these figures that surface cracking is more likely in this system compared to buckling delamination as the total energy was negative for even the smallest crack studied. Many previous researchers have also reported and studied this failure mechanism as being a critical phenomenon, especially in thermal barrier coatings [\u003cspan additionalcitationids=\"CR40\" citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. It was also observed that the change of \u003cem\u003ep\u003c/em\u003e factor did not significantly influence this failure mechanism.\u003c/p\u003e \u003cp\u003eAdditionally, Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e shows that, for all cases studied, the decrease of total energy for surface crack initiation was lower than the total energy released due to crack propagation. This indicates that surface cracks could be expected to easily reach the interface should they propagate to a certain length, however, further investigation would be required to better understand the crack propagation behaviour.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows how the residual shear stress and strain energy density contour plots change in the presence of a vertical surface crack. It was observed in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e that the introduction of the surface crack relieved the residual strain energy density and shear stress behind the crack tip whereas a concentration of both residual strain energy density and shear stress was visible ahead of the crack tip. This stress state was somewhat similar to the stress state for edge delamination in the axisymmetric model previously studied by the authors [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e]. These two failure mechanisms were also similar in crack propagation mode, in that the vertical surface crack was also found to be propagating mainly in mode II as a large contact pressure was required to be applied to avoid interference of the cracked surfaces.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eOverall, it was expected that the presence of the stress concentration ahead of the crack tip and stress relief behind the crack, as noted in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, was responsible for further propagation of the surface crack. A surface crack that had reached any of the critical interfaces of the system, \u003cem\u003ei.e.\u003c/em\u003e, substrate/FG and FG/SiC interfaces, was considered in the next section for studying interfacial delamination initiating from the root of this crack.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.3. Delamination initiation from the root of surface cracks\u003c/h2\u003e \u003cp\u003eAs the vertical surface crack reaches the critical substrate/FG and FG/SiC interfaces, it might cause delamination at the interface. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e shows the total energy versus length of a delamination crack initiating from the root of a surface crack in the substrate/FG interface and FG/SiC interface. Similar to the case of buckling delamination, higher values of \u003cem\u003ep\u003c/em\u003e factor tended to increase delamination resistance of the substrate/FG interface whilst having a negligible influence on delamination of the FG/SiC interface. Furthermore, comparing Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e with Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e illustrates that, unlike the surface crack case, the initiation of delamination from the root of a surface crack occurs with a higher rate of energy release as compared to further propagation of the delamination crack. Therefore, it can be concluded that, unlike vertical surface cracks, delamination cracks initiating from the root of a surface crack would be expected to stop propagation beyond a certain delamination crack length.\u003c/p\u003e \u003cp\u003eFigures\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e and \u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e show the residual strain energy density and shear stress contour plots for delamination initiation from surface cracks for the substrate/FG and FG/SiC interfaces of the system, respectively. It can be seen in these two figures that, while vertical surface cracking relieved both the residual strain energy density and shear stress in the coating layers, delamination of the FG/SiC interface increased the strain energy density in the FG layer. For a surface crack reaching the FG/SiC interface, there would be a competition between further vertical propagation into the FG layer and delamination of the FG/SiC interface. Based on the residual strain energy density analysis in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e, it was expected that vertical propagation of the crack into the FG layer would be preferable due to the strain energy density increase observed for delamination of the FG/SiC interface. These competitive failure paths were further investigated using the energy variation method in the next section.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.4. Competitive failure paths in the coating system\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e shows the energy variation versus crack length for the two competitive paths for a surface crack reaching the FG/SiC interface, as explained in Section 2.3. The solid lines show the plotted simulation data whereas the dashed lines represent the connection between simulation data in the range where no simulation was conducted. It can be seen that the surface crack initiates with a low energy release rate and propagates towards the interface with a higher energy release rate. At the FG/SiC interface, the energy release rate for delamination initiation from the root of the surface crack was initially high and then decreased upon further increases of delamination crack length. Delamination resistance at this interface was found to be slightly higher for lower \u003cem\u003ep\u003c/em\u003e factor values, \u003cem\u003ei.e.\u003c/em\u003e, higher alumina volume fraction in the FG layer.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eComparing the energy variation for the two different paths in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e for the surface crack reaching the FG/SiC interface, it was found that path 2 was more energetically favourable and, therefore, more likely for the studied system. This was consistent with the conclusion drawn in Section 3.3 based on the residual strain energy density and shear stress contour plots (Figs.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e and \u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e) for these two failure paths. Therefore, the failure path for a cylindrical hydrogen storage container of 316L stainless steel coated with a 0.3 mm FG layer and a 0.2 mm SiC top coat was found to be as follows: Slow surface crack initiation \u0026loz; fast surface crack propagation \u0026loz; vertical propagation of the crack in the FG layer.\u003c/p\u003e \u003cp\u003eIt should be mentioned that, since the FG layer of the model in the current study was composed of metallic/ceramic composites, the influence of the metallic phase in preventing crack propagation due to plastic deformation should also be considered in future studies for a more accurate investigation, as explained in the study by Cai and Bao [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e]. However, since the first FG layer, as the surface crack propagated into the FG layer, was pure Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e, the concluded crack propagation path 2 in the competitive failure analysis was still considered to be valid.\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Conclusions","content":"\u003cp\u003eIn this paper, a coating system for hydrogen storage containers was investigated in order to further improve the applicability of these containers. The system considered was a 316L stainless steel/ Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e FG layer applied on a 316L stainless steel substrate with a top coat of SiC applied to the FG layer. The system was modelled using a cylindrical geometry with a focus on failure mechanisms due to thermal residual stresses resulted from cooling the system from an elevated temperature. Buckling delamination, surface cracking, delamination initiation from the root of a surface crack and competitive failure paths were considered as failure mechanisms for this system.\u003c/p\u003e \u003cp\u003eIt was observed that increasing the SiC coating thickness increased the buckling delamination resistance of the system with a maximum stable crack length for this failure mechanism within the cylindrical model being 1.5 mm.\u003c/p\u003e \u003cp\u003eAnother failure mechanism studied for the cylindrical geometry was surface cracking and it was observed that crack initiation from the surface of the SiC coating was a more probable failure mechanism in this geometry compared to buckling delamination.\u003c/p\u003e \u003cp\u003eFinally, for a surface crack that propagated and reached the interfaces, two different propagation paths were investigated in this geometry and it was observed that vertical surface cracks tended to continue to propagate vertically into the FG layer rather than delaminate at the FG/SiC interface. The influence of the FG layer composition factor was found to be negligible on the improvement of the system resistance to surface cracking and its vertical propagation.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eCompeting Interests\u003c/h2\u003e \u003cp\u003eThe authors declare no financial interests.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThe authors would like to acknowledge the support of a Curtin Strategic Stipend Scholarship and Australian Government Research Training Program Tuition Fee-Offset Scholarship as well as HDR PhD Completion and Publication Scholarship (partial completion and partial publication scholarship) through Curtin University for one of the authors (SA) during the course of this research.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eAll authors contributed to the study conception and design. Simulation, data collection and analysis were performed by Sanam Abedini and Foon Min Amy Chu Pui Chan. The first draft of the manuscript was written by Sanam Abedini and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.\u003c/p\u003e\u003ch2\u003eData Availability Statement\u003c/h2\u003e \u003cp\u003eData sets generated during the current study are available from the corresponding author on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eJohnston B, Mayo MC, Khare A. Hydrogen: the energy source for the 21st century. Technovation. 2005;25(6):569-85. doi: https://doi.org/10.1016/j.technovation.2003.11.005.\u003c/li\u003e\n\u003cli\u003eThomas JM, Edwards PP, Dobson PJ, Owen GP. Decarbonising energy: The developing international activity in hydrogen technologies and fuel cells. 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Proceedings of the 3rd International Conference on Strength of Metals and Alloys. Cambridge, UK1973. p. 611-5.\u003c/li\u003e\n\u003cli\u003eWilliamson RL, Rabin BH, Drake JT. Finite element analysis of thermal residual stresses at graded ceramic‐metal interfaces. Part I. Model description and geometrical effects. Journal of Applied Physics. 1993;74(2):1310-20. doi: https://doi.org/10.1063/1.354910.\u003c/li\u003e\n\u003cli\u003eGiannakopoulos AE, Suresh S, Finot M, Olsson M. Elastoplastic analysis of thermal cycling: layered materials with compositional gradients. Acta Metallurgica et Materialia. 1995;43(4):1335-54. doi: https://doi.org/10.1016/0956-7151(94)00360-T.\u003c/li\u003e\n\u003cli\u003eAbedini S, Dong C, Davies IJ. Multi-objective particle swarm optimisation of multilayer functionally graded coating systems for improved interfacial delamination resistance. Materials Today Communications. 2020;24:101202. doi: https://doi.org/10.1016/j.mtcomm.2020.101202.\u003c/li\u003e\n\u003cli\u003eBrooks RF, Quested PN. The surface tension of steels. Journal of Materials Science. 2005;40(9):2233-8. doi: https://doi.org/10.1007/s10853-005-1939-2.\u003c/li\u003e\n\u003cli\u003eJiao S, Jenkins ML, Davidge RW. Interfacial fracture energy-mechanical behaviour relationship in Al2O3/SiC and Al2O3/TiN nanocomposites. Acta Materialia. 1997;45(1):149-56. doi: https://doi.org/10.1016/S1359-6454(96)00168-1.\u003c/li\u003e\n\u003cli\u003eZhu W, Yang L, Guo JW, Zhou YC, Lu C. Numerical study on interaction of surface cracking and interfacial delamination in thermal barrier coatings under tension. Applied Surface Science. 2014;315:292-8. doi: https://doi.org/10.1016/j.apsusc.2014.07.142.\u003c/li\u003e\n\u003cli\u003eBalke H, Hofinger I, H\u0026auml;usler C, Bahr HA, Wei\u0026szlig; HJ, Kirchhoff G. Fracture mechanical damage modelling of thermal barrier coatings. Archive of Applied Mechanics. 2000;70(1):193-200. doi: https://doi.org/10.1007/s004199900057.\u003c/li\u003e\n\u003cli\u003eFan XL, Xu R, Zhang WX, Wang TJ. Effect of periodic surface cracks on the interfacial fracture of thermal barrier coating system. Applied Surface Science. 2012;258(24):9816-23. doi: https://doi.org/10.1016/j.apsusc.2012.06.036.\u003c/li\u003e\n\u003cli\u003eAbedini S, Dong C, Davies IJ. Mechanisms and control of edge interfacial delamination in a multilayer system containing a functionally graded interlayer. Surface and Coatings Technology. 2020;382:125221. doi: https://doi.org/10.1016/j.surfcoat.2019.125221.\u003c/li\u003e\n\u003cli\u003eCai H, Bao G. Crack bridging in functionally graded coatings. International Journal of Solids and Structures. 1998;35(7):701-17. doi: https://doi.org/10.1016/S0020-7683(97)00082-6.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"discover-mechanical-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"discmecheng","sideBox":"Learn more about [Discover Mechanical Engineering](https://www.springer.com/journal/44245)","snPcode":"44245","submissionUrl":"https://submission.nature.com/new-submission/44245/3","title":"Discover Mechanical Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Finite element analysis (FEA), functionally graded (FG) coating, delamination, buckling, crack propagation.","lastPublishedDoi":"10.21203/rs.3.rs-3741716/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3741716/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this study, a plane strain finite element analysis (FEA) was employed to investigate failure mechanisms of a hydrogen storage pipe system made of 316L stainless steel pipe coated with pure and functionally graded (FG) ceramic layers composed of Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e and SiC. The system was studied for different common failure mechanisms, \u003cem\u003ei.e.\u003c/em\u003e, delamination, surface cracking and buckling delamination, upon cooling from an elevated stress-free temperature. Finally, the composition and thickness of the coating layers were considered as the main controlling factors and investigated for their influence on the studied failure mechanisms. It was observed that the most energetically favourable cracking mechanism for this type of system was surface cracking with the propagation of these cracks eventually leading to different failure paths. Buckling was found to be as less energetically favourable compared to surface cracking with the buckling resistance being enhanced by changing the coating thickness and composition factor.\u003c/p\u003e","manuscriptTitle":"Failure Analysis of a Functionally Graded Multilayer Coated Stainless Steel Pipe for Hydrogen Storage","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-02-08 07:46:46","doi":"10.21203/rs.3.rs-3741716/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-06-19T19:12:48+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-06-18T07:20:37+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-06-18T06:35:29+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"300608829998995040763220136125735981701","date":"2024-06-17T18:48:59+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-06-17T14:29:07+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"1656412340808901301300953012994031901","date":"2024-06-14T11:33:14+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"311401957986348337679533140469358412649","date":"2024-06-13T18:52:40+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"266408763368824471163369720769009516154","date":"2024-06-13T01:52:18+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-04-25T08:34:15+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"152702734567302228048723307522036091170","date":"2024-04-25T02:14:01+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"a38d5345-60b0-42b0-8104-75dbfe026904","date":"2024-03-24T04:45:39+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-03-18T21:21:21+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-02-06T11:56:48+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-02-06T11:56:29+00:00","index":"","fulltext":""},{"type":"submitted","content":"Discover Mechanical Engineering","date":"2023-12-12T04:19:36+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"discover-mechanical-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"discmecheng","sideBox":"Learn more about [Discover Mechanical Engineering](https://www.springer.com/journal/44245)","snPcode":"44245","submissionUrl":"https://submission.nature.com/new-submission/44245/3","title":"Discover Mechanical Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"86889b62-d0dc-470a-8d4b-744fc7fdc492","owner":[],"postedDate":"February 8th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2024-09-09T10:17:46+00:00","versionOfRecord":[],"versionCreatedAt":"2024-02-08 07:46:46","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3741716","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3741716","identity":"rs-3741716","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}