Research on the Creep and Fatigue Evaluation Method of the Double-Layered Annulus Metal Hydride Bed Combined with Numerical Modeling and ASME Code

Applied to a hydrogen absorption-desorption cycle, the hydrogen storage bed will experience higher exchange temperatures and variety of mechanical load. Due to the complex structure of the double-layered annulus metal hydride bed and the importance of thermal stress on the failure of a metal hydride bed, the numerical modeling of its hot spot stress was carefully carried out. Moreover, in this paper, an analysis method considering the limit failure mode condition is proposed to deal with the stress analysis in the process of hydrogen absorption and desorption. According to the proposed analysis method, the maximum stress of thermal-structural coupling in the process of hydrogen absorption occurs at about 1/3 along the diameter direction and at the geometric mutation of the connection between the cooling pipe and the main body of the hydrogen storage bed in the process of hydrogen desorption. Apart from that, the hydrogen storage bed is also subjected to thermal-mechanical fatigue by the iterative process of absorption and desorption, and its operating temperature range is in the thermal creep temperature region. Based on the distribution of the stress and temperature, evaluation hot sites were selected and the ASME-NB and ASME-NH codes were used to evaluate fatigue and fatigue creep, respectively. Te evaluation showed that the fatigue damage generated during its service life is small, while the creep damage is relatively large and the total damage generated during the service life of the hydrogen storage bed is within the safe range. Aiming at the structure and complex process of a double-layer hydrogen storage bed, creep and fatigue evaluation methods are proposed, various failure modes of hydrogen storage bed are highlighted, and the relationship between process parameters and life is established.


Introduction
As a clean, efcient and renewable energy vector, hydrogen energy has attracted much attention; however, the storage and safety of hydrogen energy are the most important factors preventing its widespread use [1]. Terefore, it is necessary to develop a hydrogen storage structure with high hydrogen storage efciency and high strength. As a safe way to achieve rapid storage and supply of hydrogen isotopes, hydrogen storage beds are an important part of hydrogen storage systems [2]. Tis device contains the hydrogen storage material in a container of a certain structure and size, and the hydrogen storage material can absorb and desorb the hydrogen isotopes to complete the absorption and desorption of hydrogen isotopes [3]. In order to improve the chargedischarge efciency, the cooling system is turned on in the hydrogen absorption process to take away the heat in time and to add heat to improve the reaction efciency during the hydrogen desorption process [4]. During this period, the hydrogen storage bed is not only subjected to the thermal cycle load but also accompanied by the hydrogen pressure and the expansion and contraction pressure caused by the charging and discharging deformation of the hydrogen storage alloy [5]. Tis can cause thermal shock and stress concentrations in the hydrogen storage bed structure. With the increase of the number of hydrogen adsorption and desorption cycles, the continuous accumulation of stress and the increase of temperature duration may lead to thermal creep and fracture failure of the hydrogen storage bed [6,7]. So, it is critical to have a deep understanding of the complex stress phenomenon caused by the hydrogen absorption and release process.
Heubner et al. found that gas pressure, temperature, and metal hydride geometry all have an efect on stress evolution [8]. Once the elastic deformation of the reactor occurred during the hydriding-dehydriding cycles, its deformation did not become larger anymore [5]; however, after the plastic deformation of the reactor, the stress continued to increase and the stress increased with each cycle [9]. Ao et al. [10] studied the relationship between the wall stress of LaNi5 hydrogen storage bed and the cycle number of hydrogen adsorption-desorption cycles, loading of hydride bed, packing fraction, and thickness of bed's walls, and the results indicated that the wall stress increased with increasing packing fraction and decreased with thickening of the wall. Moreover, diferent locations exhibit vastly diferent maximum strain levels. Dinachandran and Mohan [11] used LaNi5 as a hydrogen storage alloy to numerically simulate the wall strain distribution of a vertically placed hydrogen storage device. Te results showed that for a given charging rate, higher supply pressure and low coolant temperature were associated with higher wall strain rates. Most of the research on metal hydride hydrogen storage reactors is more focused on the hydrogen metal deformation of the hydrogen storage layer; however, it is rare for the stress characteristics investigation and safety assessments of solid-state hydrogen storage vessels in the process of hydrogen absorption-desorption. A design by the analysis approach was introduced which highlights detailed design procedures utilizing the results from stress analysis to evaluate components for plastic collapse, local failure, buckling, and cyclic loading. Due to the difculty of experimental measurement and the high economic and time cost, the experimental method is not very suitable, but the numerical simulation method solves these problems well and is widely used in the feld of structural analysis [12][13][14]. Terefore, the numerical simulation method is a favorable means to analyze the stress characteristics of hydrogen storage beds and to assist the safety assessment.
Tis paper emphasizes the analysis approach for fatigue, and the creep assessment of design is used to predict the lifetime of hydrogen storage bed which is subjected to cycles like hydrogen absorption and desorption process [15]. Hydrogen storage bed is inherently subjected to cyclic loads of pressure and temperature. Equivalent stresses and lifetime are evaluated by thermostructural analysis complying with the ASME code. Te efect of diferent operating parameters on the equivalent stress peak value of the main body of the hydrogen storage bed was analyzed. Considering the ultimate failure mode of the hydrogen storage bed in the process of hydrogen absorption and desorption, the thermal fatigue and creep assessment was carried out.

Analysis Method and Evaluation Procedure
Te overall analysis method fow of this work is shown in Figure 1. Tis process demonstrates the need for an analysis of the hydrogen storage bed's operating conditions and possible failure modes, followed by a thermal-structural analysis. In the thermal-structural coupling analysis, the interaction between the temperature feld and the stress feld needs to be considered, mainly including direct coupling and indirect coupling methods [16,17]. If the fnal result does not satisfy the relevant criteria, it is necessary to modify the relevant parameters of the hydrogen storage bed according to the analysis of stress infuencing factors and repeat the abovementioned steps until they are satisfed.
In the process of hydrogen absorption and desorption in the hydrogen storage bed, many factors such as the temperature drop rate and temperature rise rate of the hydrogen storage layer may lead to the destruction of the structure of the hydrogen storage bed. Many studies have shown that the structural damage is mainly caused by plastic yielding. Plastic yielding is the main cause of structural damage in hydrogen storage beds. In order to ensure the safety of the hydrogen storage bed structure in the process of hydrogen absorption and desorption, it is necessary to evaluate whether the stress of the hydrogen storage bed is greater than the allowable stress or not. Te Von Mises yield criterion in many investigations [18,19] has been used to assess whether a structure has undergone plastic yield failure or not. Judging from the joint cracking evaluation criteria, the initial cracking position of the hydrogen storage bed occurs at the location where the peak value of equivalent stress occurs. Terefore, this work studies the efect of the relevant parameters for the peak value of equivalent stress on the structure of the hydrogen storage bed during the hydrogen absorption and desorption process.
Te evaluation rules of metal structures are divided into ASME-NB [20] and ASME-NH [21] according to whether the temperature is in the metal creep temperature range. Figure 2 shows the specifc process and rules of structural integrity assessment.
From the description of the ASME-NB rules, the design condition, C-level condition, and D-level condition do not involve transient calculation; only one stress assessment is required, while for A-and B-level working conditions, thermal transients and pressure transients are often involved, so it is necessary to evaluate the strength range of primary and secondary stress and the cumulative service factor of fatigue.
While the hydrogen storage bed made of 316L stainless steel was subjected the high temperature and complex loading conditions, some failure modes, such as creep-fatigue damage, cyclic creep ratcheting, and excessive deformation over time should be considered [22,23]. ASME Part III provides the design criteria for evaluating the integrity of structural components requiring load-controlled stress, deformation, strain, and creep-fatigue to meet the rules of the ASME code [14,24,25]. 2 Advances in Materials Science and Engineering Te total strain amplitude ε t corresponding to the design fatigue curve was then determined by the following equation: if where the value is not less than 1, K v ′ is the plastic Poisson's ratio adjustment coefcient, which can be obtained from Figure 3 [21]; f is the coefcient determined by the triaxial coefcient, which can be obtained from Figure 4 [21].

Advances in Materials Science and Engineering
For inelastic analysis, ASME-NH provides a simplifed method. Te limits are required to satisfy any one of tests. Te efective creep stress σ c � Z•S yL is determined by the primary and secondary stresses obtained from linear elastic stress analysis. Z is obtained by the Bree Diagram [26] with stress parameters X and Y, which can be calculated by equations (5) and (6): Te Z corresponding to Tests B-1 and B-3 is determined by Figure 5 [27]. Te equations defning the boundaries of the regimes P, S1, and S2.
In regimes S2, P, Z can be obtaine as In regimes S 1 , and In regimes E, Z � X. Te Z of Test No. B-2 is determined by Figure 6 [27]. Te creep ratchet strain Δε c corresponding to 1.25 σ c is shown in Figure 7 [27].   Advances in Materials Science and Engineering Te fatigue-creep damage of the equipment was evaluated according to ASME-NH. Based on the linear cumulative damage method, the fatigue damage caused by the load cycle and the creep damage caused by hightemperature load holding are superimposed as the total damage. Te component fails when D ≫ Dcr (Dcr = 1, critical damage). Combined with the creep-fatigue interaction curve, the total damage (D) had to be within the creep-fatigue damage envelope [21]. Terefore, creep and fatigue damage had to satisfy the following equation:

Geometrical Model and
Meshing. Te geometrical model and the cross-section of the thin double-layered annulus ZrCo hydride bed are shown in Figure 8. To facilitate fnite element meshing based on Saint-Venant's principle [28], the geometric model was reasonably simplifed, and certain details such as the threaded holes, chamfers, and small fllets were removed. Te simplifed model and the specifc local details are shown in Figure 9. Te 3D representation of the hydrogen storage bed was obtained, which included inner and outer bed bodies, inner    and outer hydrogen storage layers, and inner and outer flter layers. Tere was also a cavity structure between the two stainless steel flter cartridges, which contained a gas layer for the fow of the hydrogen isotope gas. Te cavity was connected to the inlet and outlet pipes of the system. In addition, there were M-type cooling medium circulation loops drilled along the length direction on the inner and outer stainless steel bed body walls, which could be used for rapid cooling of the bed body or fow-gas calorimetry when storing tritium.
In this study, the hydrogen storage bed structure materials are all composed of 316L stainless steel. Te physical properties of 316 stainless steel are shown in Table 1. Te overall fnite element meshing of the hydrogen storage reactor structure is shown in Figure 10. Tetrahedral and hexahedral grids were used for diferent components of the hydrogen storage bed, according to their geometry and complexity. Te mesh quality was also maintained at a reasonable level to ensure a high computational speed. A total number of 1382202 elements and 2078936 nodes were generated in this model.

Termal and Structural Loads Analysis.
When the hydrogen storage layer absorbs hydrogen, a large amount of heat is released instantaneously, and the temperature of the hydrogen storage layer rapidly rises from room temperature to 200 degrees. In order to improve the hydrogen absorption efciency, the hydrogen storage bed is cooled by passing cooling water. Te temperature evolution history of the hydrogen storage layer during the hydrogen absorption process is shown in Figure 11.
Generally speaking, the higher the temperature, the higher the hydrogen release platform of the hydrogen storage material, the faster the hydrogen release kinetics, and the easier it is to release hydrogen quickly. However, since ZrCo alloy is very easy to disproportionate when the temperature is higher than 500°C and the hydrogen pressure is high than 0.5 bar, the hydrogen desorption rate and disproportionation efect should be comprehensively considered in the selection of the hydrogen desorption temperature of the ZrCo bed. Terefore, the dehydrogenation temperature of the ZrCo bed should be strictly controlled below 500°C, and the hydrogen pressure should be controlled below 1 MPa. Te   Advances in Materials Science and Engineering temperature change of the hydrogen storage layer during hydrogen desorption is shown in Figure 12.
Te calculated loads include self-weight, internal pressure, and heat load changes in the hydrogen absorption and desorption processes. In the hydrogen absorption and exothermic stage, the heat load is generated in the inner and outer hydrogen storage layers, and the cooling pipe is cooled by water. In the hydrogen desorption and endothermic stage, the internal heating rod and the external heating shell are used for heating. Te peak and valley load conditions of the corresponding parts of the hydrogen storage bed structure in the process of hydrogen absorption and desorption are shown in Table 2.

Stress Distribution.
In the hydrogen absorption process, the hydrogen storage layer is accompanied by exothermic phenomenon. In order to increase the hydrogen absorption rate, the cooling system is activated to take away heat; the hydrogen desorption process is an endothermic reaction. Te temperature distribution of the main body of the hydrogen storage bed under the two working conditions is shown in Figure 13. It can be seen from fgure that the cooling pipe system greatly afects the temperature distribution of the hydrogen storage bed. Te geometric structures of the two ends of the hydrogen storage bed are     Advances in Materials Science and Engineering diferent. During the hydrogen absorption process, the temperature distribution is afected by the cooling system on one side as a "petal shape" and on the other side as a "fame shape," while the geometric structure in the hydrogen release stage has little efect.
It is difcult to determine the heat transfer coefcient between W and the walls of the hydrogen storage bed structure under the hydrogen absorption condition. According to Mechanical User's Guide of ANSYS soft, in the convection part of boundary condition setting, we set the ambient temperature for numerical simulation as 295.15 K and obtained the heat exchange coefcient of 1200 W/m 2 ·K by importing convection data with water as the fuid. At the same time, in order to ensure the reliability of heat transfer coefcient, the heat transfer coefcient between W and the wall of hydrogen storage bed is also calculated by Liu and Winterton's correlation [30]. Te calculation result is also close to that in design condition. Terefore, the heat transfer coefcient in design condition is adopted to investigate the stress distribution of hydrogen storage bed structures. Te working conditions of the hydrogen absorption and desorption process are shown in Table 1, and the stress distribution under the two working conditions is shown in Figure 14. It can be seen from fgure that the maximum stress of the thermal-structure coupling during the hydrogen absorption process occurs about 1/3 along the diameter direction and at the geometrical abrupt change of the connection between the cooling pipe and the main body of the hydrogen storage bed during the hydrogen desorption process. Te hydrogen absorption-desorption cycle of the hydrogen storage bed is afected by many factors. In order to further understand the stress phenomenon in the hydrogen absorption and desorption process of the hydrogen storage bed, we need to study the infuence rules of these factors.

Efect of Temperature Diference on Stress.
During the hydrogen absorption and desorption process of the hydrogen storage bed, the temperature diference between TA and TW during the hydrogen absorption process is diferent, resulting in diferent stress states of the hydrogen storage bed. In order to understand the efect of temperature difference on the safety and stability of the hydrogen storage bed structure, the thermal stress distribution under diferent temperature diferences between TA and TW was analyzed. Figure 15 shows the equivalent stress peaks for diferent temperature diferences and diferent heat transfer coefcients at the temperature of 295.15 K of W. Te results show that the peak value of equivalent stress increases with the increase of the temperature diference, and the temperature diference has a signifcant efect on the stress of the hydrogen storage bed structure. Te heat transfer coefcient between W and the walls of the hydrogen storage bed has a great infuence on the stress of the hydrogen storage bed. Te larger the heat transfer coefcient, the greater the efect of the temperature diference on the stress of the hydrogen  Figure 13: Te system temperature contour of (a) hydrogen absorption process and (b) hydrogen desorption process.  Advances in Materials Science and Engineering storage bed. With the increase of the heat transfer coefcient, the efect of the heat transfer coefcient on the temperature diference is smaller. At the same time, the stress along the length of the cooling tube during the hydrogen absorption and desorption process of the hydrogen storage bed is also diferent, because the temperature from the W inlet to the outlet is diferent. Terefore, the efect of temperature diference on stress at diferent temperatures of W is also analyzed. Figure 16 shows the relationship between the equivalent stress peak value and temperature diference at diferent TW when the heat transfer coefcient is 1200 W/m 2 ·K. Te results show that with the increase of the temperature diference, the stress peak trend of the hydrogen storage bed is also larger. Te peak stress is afected by the TW. When the temperature diference is greater than 200 K, the smaller TW, the greater the peak stress TW can be appropriately increased. When the temperature diference is less than 80 K, the higher the TW, the greater the peak stress, it is better to reduce TW.

Efect of Temperature Change Rate on Stress.
Te hydrogen absorption process of the hydrogen storage bed is relatively complicated. With the progress of the chemical reaction, there is not only the process of heating and cooling but also the operation of the cooling system to reduce the temperature as soon as possible. Terefore, the efect of temperature rate change on the stress of the hydrogen storage bed can be studied by analyzing the relationship between the rise rate, drop rate, and the equivalent stress peak value. Figures 17 and 18 depict the relationship between the peak value of equivalent stress and the rate of temperature rise and temperature drop under diferent heat transfer coefcients at the initial temperature of the cooling medium at 295.15 K degrees, respectively. Te results show that the rise rate and drop rate have little efect on the stress of the hydrogen storage bed, but it is greatly afected by the heat transfer coefcient. Te greater the heat transfer coefcient, the greater the equivalent peak stress. However, as the heat transfer coefcient increases, the degree of infuence decreases. At the same time, the peak value of equivalent stress increases with the increase of the rise rate and decreases with the decrease of the drop rate. Te reason is that the hydrogen storage bed has excellent heat transfer performance. When TA increases, it has a similar rise rate to W, so it is less afected by the rise rate, but when TA decreases, W is still in a rise state.

Efect of Heat Transfer Performance on Stress.
Te heat transfer performance directly afects the hydrogen absorption-desorption efciency of the hydrogen storage bed and also afects the stress distribution. Te heat transfer coefcient between the coolant and the wall of the hydrogen storage bed is the key parameter of the heat transfer performance of the hydrogen storage bed. Terefore, the relationship between the heat transfer coefcient and the peak equivalent stress of the hydrogen storage bed was studied. Figure 19 depicts the relationship between the equivalent stress peak value and the heat transfer coefcient under diferent temperature diferences. Te results show that with the increase of the heat transfer coefcient, the corresponding peak value of equivalent stress also increases gradually, but the growth rate becomes slower and slower, and the trend gradually becomes gentle. However, as the temperature diference increases, the peak stress becomes larger and the corresponding growth rate becomes faster.

Efect of Pressure on Stress.
According to the actual working conditions of the hydrogen storage system, the hydrogen storage bed is not only subjected to the hydrogen pressure in the process of hydrogen absorption-desorption  but also the expansion and contraction pressure of the hydrogen storage layer due to the deformation of hydrogen metal. Terefore, the efect of stress on the hydrogen storage bed was analyzed. Te pressure is taken as 0.5 bar-200 bar. Figure 20 depicts the relationship between pressure and peak equivalent stress under a temperature diference of 200 K and a heat transfer coefcient of 1200 W/m 2 ·K. Te results show that 1 MPa is a turning point, and the stress curve of the pressure-to-hydrogen storage bed structure frst decreases and then increases. From Figure 21, we can see that the reason for the turning after 1 MPa is that the position where the maximum stress occurs in the hydrogen storage bed is transferred from the inner ring of the hydrogen storage bed to the outer ring. Terefore, in the actual operation of the hydrogen storage bed, it is necessary to comprehensively consider the efect of pressure on the stress of hydrogen storage bed structures in diferent operation processes.

Termal Fatigue and Creep Assessments of the Hydrogen
Storage Bed

Termal Fatigue Assessments by ASME-NB.
Te maximum stress distribution diagrams under the thermal load and pressure conditions during the hydrogen absorption are shown in Figures 22 and 23, respectively. Based on the abovementioned stress distribution results, path A-A and path B-B along the wall thickness were selected for evaluation based on the location of maximum stress. Since the maximum temperature of the hydrogen storage bed in the hydrogen absorption process was lower than 427°C, the ASME-NB standard [20] is used for evaluation. When the low temperature parts are averaged, the primary flm stress intensity used was the time-independent allowable stress S m according to ASME BPVC II-D [31]. Te stress linearization results showed that the membrane, bending, and secondary stress values were all within the allowable values of the design stress intensity of the ASME code. Te maximum cumulative use factor for 10,000 cycles was 0.0329, which showed that the temperature was relatively low and thermal fatigue was small. Te results are shown in Table 3, and Table 4 evaluates the cumulative use factors.

Termal Fatigue and Creep Assessments by ASME-NH.
Creep fatigue assessment is an important part of structural integrity assessment at elevated temperatures. To analyze the stress and deformation levels of the hydrogen storage bed under complex loads, the creep and fatigue damage levels were calculated at key locations, and the total damage of the    Advances in Materials Science and Engineering equipment during the service period should not exceed the creep-fatigue damage envelope of the material. Since the hydrogen storage bed temperature can be up to 500°C in the hydrogen desorption process, the evaluation standard followed the NH Appendix NH-T procedure.
Te maximum stress distribution diagrams under the thermal load during the hydrogen desorption are shown in Figure 24. Te maximum stress under pressure-only loading is the same as in Figure 25, where the two paths as C-C and D-D were evaluated. Conservative evaluations were carried  out according to the A-level service limit, and elastic analysis and inelastic analysis were used to check whether the strain limit in the high temperature area was satisfed.
In the evaluation of high temperature components, two variables are introduced; St and S mt , where St is the stress intensity related to time and temperature and S mt is the average stress of high temperature components during the actual service period. Te efective creep stress parameter Z was obtained by a linear interpolation from the simplifed inelastic analysis in the literature test B-2, and the efective creep stress σ c was achieved. Finally, the creep ratchet strain Δε c (%) can be obtained corresponding to 1.25 σ c from the isochronous stress-strain curve.
According to equation (2), the maximum strain range Δε max considered the stress concentration efect caused by the discontinuity of the geometric structure. Te parameters required to calculate the total strain range Δε t , which corresponded to the linear interpolation of the fatigue design      curve [21], where for ε t , the allowable number of cycles Nd was obtained. Te design life of the hydrogen storage bed was 300.00 hours, and the design start and end cycles is 300. Te calculation parameters of fatigue-creep evaluation are shown in Table 5, and the evaluation results are summarized in Table 6. Based on the abovementioned evaluation results, the accumulated creep damage during the design life was 0.1. Compared to fatigue damage, creep damage occupied a dominant proportion in the structure of the hydrogen storage bed, which was higher than fatigue damage. By not taking into account the efects of stress relaxation in the calculation process, the most dangerous transient conditions were evaluated, and an overly conservative estimate of creep damage was obtained. Te creep and fatigue damage accumulated during the service life was within the damage envelope as shown in Figure 26. Tus, the design was ASME-NH-compliant.

Efect of Primary Load on Creep-Fatigue Damage.
Te pressure afects the hydrogen absorption and desorption efciency of the hydrogen storage bed and also changes the strain range of the hydrogen storage bed, thereby afecting the creep damage, fatigue damage and life of the hydrogen storage bed. In order to clarify the potential impact mechanism, we studied the fatigue damage and creep damage of the hydrogen storage bed under diferent pressures, and the specifc evolution is shown in Figure 27. From Figure 27, we can see that when the pressure was greater than 12 MPa, the creep damage accelerates, while the fatigue damage increases signifcantly after 16 MPa.

Conclusions
Tis paper provides an overview of a conform-to-design thermal-structural creep and fatigue analysis of a doublelayered annulus metal hydride bed by an analytical approach that considers the ultimate failure mode condition. Based on the analysis method, the efect of operating parameters on the stress of the hydrogen storage bed was studied. Combined with ASME-NB and ASME-NH codes and numerical modeling, the fatigue and fatigue creep of double-layer annular metal hydride bed during hydrogen absorption and  (1) Te numerical simulation results indicate that the maximum stress of the thermal-structure coupling during the hydrogen absorption process occurs about 1/3 along the diameter direction and at the geometrical abrupt change of the connection between the cooling pipe and the main body of the hydrogen storage bed during the hydrogen desorption process. (2) Te peak value of equivalent stress increases with the increase of the temperature diference, and the temperature diference has a signifcant efect on the stress of the hydrogen storage bed structure. Te larger the heat transfer coefcient, the greater the efect of the temperature diference on the stress of the hydrogen storage bed. When the temperature diference is greater than 200 K, the smaller TW, the greater the peak stress, TW can be appropriately increased. When the temperature diference is less than 80 K, the higher the TW, the greater the peak stress, it is better to reduce TW. (3) For the hydrogen storage bed structure, the pressure has an obvious efect on the peak stress. Te stress curve of the pressure-to-hydrogen storage bed structure frst decreases and then increases. Te temperature rise rate and drop rate have little efect on the stress of the hydrogen storage bed, but it is greatly afected by the heat transfer coefcient. Te greater the heat transfer coefcient, the greater the equivalent peak stress. (4) A systematic evaluation system for the creep and fatigue of the hydrogen storage bed during the hydrogen absorption and desorption process was established. In the hydrogen storage bed, inelastic strain occurs during the hydrogen desorption process, and signifcant high temperature creep damage occurs. High temperature is an important factor afecting the structural integrity of the hydrogen storage bed. It was found that the fatigue damage generated during its service life was very small, while the creep damage was relatively large. Te accumulated creep and fatigue damage over the service life was within the damage envelope.
Under the premise of designing life, according to the process parameters proposed in this paper, the estimated life under the interaction of creep properties is higher than designing life, and the relationship between process parameters and life is established. In order to improve the operating efciency of the bed, one can consider giving up the marginal integrity of the heating and cooling rates of the hydrogen storage bed.

Abbreviations
P m : Primary membrane stress intensity P L : Local primary membrane stress intensity P b : Primary bending stress intensity S y : Averaged yield stress at the maximum and minimum wall temperatures S yL : Yield stress at the lower of the wall-averaged temperature for extreme stresses K t : Parameter accounting for bending (Q R ) max : Maximum range of secondary stress intensity N d : Number of allowable cycles T d : Allowable creep rupture time Δε mod : Modifed maximum strain range Δε cr : Creep strain increment in one cycle Δε max : Maximum equivalent strain range Δε t : Total strain range X: Primary stress parameter Y: Secondary stress parameter Z: Efective creep stress parameter σ c : Efective creep stress K: Local geometric concentration factor K v : Multiaxial plasticity and Poisson's ratio adjustment factor.

Data Availability
Te raw/processed data required to reproduce the fndings in the current manuscript cannot be shared at this time as these data also form a part of an ongoing study.

Conflicts of Interest
Te authors declare that they have no conficts of interest.