# Development of Strength Evaluation Methodology for Independent IMO TYPE C Tank with LH2 Carriers

## Article information

## Abstract

Given the inadequate regulatory framework for liquefied hydrogen gas storage tanks on ships and the limitations of the IGC Code, designed for liquefied natural gas, this study introduces a critical assessment procedure to ensure the safety and suitability of such tank designs. This study performed a heat transfer analysis for boil-off gas (BOG) calculations and established separate design load cases to evaluate the yielding and buckling strength. In addition, the study assessed methodologies for both high-cycle and low-cycle fatigue assessments, complemented by comprehensive structural integrity evaluations using finite element analysis. A comprehensive approach was developed to assess the structural integrity of Type C tanks by conducting crack propagation analysis and comparing these results with the IGC Code criteria. The practicality and efficacy of these methods were validated through their application on a 23K-class liquefied hydrogen carrier at the concept design stage. These findings may have important implications for enhancing safety standards and regulatory policies.

**Keywords:**Type C tank; Cargo containment system; Liquefied hydrogen carrier; Thermal-structural analysis; Fatigue analysis; Crack propagation analysis

## Nomenclature

*L*: Rule length of the ship

*V*: Design speed

*ρ*: Density

*σ _{m}*: Membrane stress

*σ _{L}*: Local membrane stress

*σ _{g}*: The secondary stress

∑*Q _{leak}*: Total heat flux that penetrates from outside to inside of the LH2 tank

*λ*: Latent heat for vaporization

*A*: Heat transfer area

*n _{i}*: The number of cycles to fracture for the respective stress level

*n _{Loading}*: The number of loading and unloading cycles during the life of the tank is not to be less than 1,000

*C _{w}*: The maximum allowable cumulative fatigue damage ratio

*B*: Ship breadth

*C _{B}*: Block coefficient

*ρ _{r}*: Relative density of the cargo at the design temperature

*C*: Characteristics tank dimension

*σ _{b}*: Bending stress

*ρ _{LH2}*: Density of liquefied hydrogen

*V _{LH2}*: Volume of LH2 in the cargo tank

*U*: Overall heat transfer coefficient

*ΔT*: Difference in temperatures between the outer tank and LH2

*N _{i}*: The number of cycles to fracture for the respective stress level

*N _{loading}*: The number of cycles to fracture for the fatigue loads due to loading and unloading

*D _{i}*: The cumulative fatigue damage at loading condition, i means the load cases

*U _{f}*: The utilization factor based on ship profile percentage

*T _{d}*: The operating life of the ship

*K*_{2} and *m*_{2}: S-N fatigue parameters for N> 10^{7} cycles

*S _{R}*: Stress range for fatigue damage calculation

*n*_{0}: The total number of cycles associated with the stress range level, *S _{R}*

*Γ*( ): The complementary Gamma function

Δ*σ*_{0}: The maximum stress range that can occur during the life of the ship

*K _{m}*: Stress intensity factor due to misalignment

*K*_{min}: The minimum stress intensity factor

*v*_{0}: Zero up - crossing frequency

*K*_{1} and *m*_{1}: S-N fatigue parameters for N<10^{7} cycles

*S*_{0}: Stress range for which change of slope of S-N curve occur

*q*: The Weibull stress range scale distribution parameter for load condition

*k*: The Weibull stress range shape distribution parameter (1.0)

*γ*( ): Incomplete Gamma function

Δ*σ _{i}*: Arbitrary stress range

*K*_{max}: The maximum stress intensity factor

*R*: Stress ratio

## 1. Introduction

Globally, the transition to various alternative energies to replace fossil fuels is accelerating to address the issue of global warming. Currently, liquefied natural gas is attracting attention as a means to achieve the emission reduction targets for nitrogen oxides and sulfur oxides. Furthermore, for the decarbonization transition, hydrogen (H2) energy, which does not emit carbon dioxide, will be needed as a future natural resource. Nevertheless, storage and transportation methods from overseas hydrogen production sites are required to implement a hydrogen economy domestically. The volume of liquid hydrogen is approximately 1/845 of gaseous hydrogen at room temperature and atmospheric pressure, and it reduces to approximately 1/2 of the volume compared to 700-bar high-pressure hydrogen. This makes it the most suitable form for storing the largest quantity and the most suitable method for substantial storage. Differentiations exist strictly for tanks designed to store liquid hydrogen, and they must meet regulations to satisfy international standards. The independent tanks are categorized into Types A, B, and C as defined by the International Maritime Organization (IMO). As shown in Table 1, Type A tanks adhere to general liquid tank regulations. In the event of a presumed potential for liquid cargo leakage, a complete secondary barrier is needed for cases of significant leakage. This type of tank is primarily applied to LPG carriers. For Type B tanks, the structural safety of the tank must be verified through structural analysis. The leakage quantities are calculated using fatigue crack propagation analysis based on fracture mechanics, assuming crack occurrence. Partial secondary barriers are necessary for this type. Type C tanks are used for pressure vessels. They ensure the safety and integrity of the structure and pose no risk of leakage, obviating the need for a secondary barrier.

Type C tanks are typically cylindrical or spherical pressure vessels with a design pressure exceeding two bar. They are designed and manufactured to meet the requirements of recognized pressure vessel standards or codes, such as the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code (BPVC), and are further supplemented by classification society requirements and legal regulations. Research on liquid hydrogen tanks has focused primarily on transportation, storage containers, fire hazards, sloshing effects, and double-wall vacuum piping (Ahn et al., 2017; Klebanoff et al., 2017). Kim and Islam (2021) and Kim et al. (2018) proposed a structural integrity assessment procedure for Type B liquefied natural gas (LNG) fuel tanks based on the International Code for the Construction and Equipment of Ships Carrying Liquefied Cases in Bulk (IGC Code). They conducted finite element analysis under various design loads to evaluate the structural safety. Choe et al. (2016) experimentally evaluated the cryogenic compressive strength of Divinycell of the NO96-type LNG insulation system. Nho et al. (2017) performed a numerical analysis on the sloshing impact response evaluation method of the LNG carrier insulation system, considering the elastic support effect of the hull structure. Recently, Song (2022) experimentally evaluated the cryogenic material of R-PUF used in the cargo containment system of LNG carriers.

Park (2019) developed fracture strength criteria for membrane-type cargo containment systems under sloshing loads. They evaluated the strength of cargo containment facilities using the finite element method and compared the results with the DNV guidelines. On the other hand, research on the design evaluation of Type C tanks used for liquid hydrogen storage is extremely rare. Lin et al. (2018) proposed an approach to evaluate the boil-off rate (BOR) of Type C tanks at various filling ratios. They estimated the BOR based on finite element analysis and compared the results with experimental data. Lee et al. (2022) numerically analyzed the impact of sloshing on heat transfer and boil-off gas (BOG). Yao et al. (2015) verified the design thickness of a Type-C independent tank using commercial software against conventional design codes. Liu et al. (2018) also performed an optimization based on the design and application materials for Type C tanks for liquefied hydrogen, but they did not provide a reasonable procedure for the tank design itself.

The paper proposes a procedure to comprehensively evaluate the structural integrity of Type C tanks for storing and transporting liquid hydrogen. Currently, there are limitations in proposing accurate design evaluation procedures because of the absence of domestic and international regulations for the hydrogen environment. This study analyzed the design evaluation methodologies applied to ships carrying cryogenic cargo, and an evaluation procedure for liquefied hydrogen cargo holds with the IMO Type C tank was presented. This includes thermal analysis, structural and fatigue analysis, and, if necessary, crack propagation analysis. This study assessed the structural integrity assessment technique using the developed procedure and validated the suitability of the method by applying it to a finite element model.

## 2. Development of Structural Assessment Procedure for IMO TYPE C Tank

### 2.1 Introduction to Type C Tank

Type C tanks are considered leak-free because their design factors enhance the structural integrity, eliminating the need for a secondary barrier. As a result, they are commonly used in LNG fuel tanks for ships, and they have advantages that make them suitable for small-scale LNG, ammonia, or LPG carriers. Two types of tank support structures are used for cylindrical or spherical tanks: fixed and sliding. Fixed supports secure the independent tank, while sliding supports allow for tank expansion and contraction as needed.

The tanks are configured with either a single wall or a double wall, as shown in Fig. 1. In the case of a single wall tank, the exterior is covered with insulating material, and the insulating timber is placed between the saddle support and the tank structure. Double wall tanks feature vacuum insulation, and insulating material/plastic supports are placed between the internal and external tanks. They have the advantage of longer pressure retention time compared to single-wall tanks.

### 2.2 Procedure for Structural Strength Assessment

Fig. 2 presents the comprehensive strength assessment procedure for the Type C liquid hydrogen (LH2) tank. The developed methodology to check the integrity of the tank can be divided into several stages: heat transfer and BOR calculation, structural analysis, buckling analysis, fatigue, and crack-propagation analysis.

Heat transfer analysis is the critical step in designing a Type C LH2 tank because the temperature of LH2 in the liquid state is −253°C. The analysis serves twofold purposes; the first is for hull steel grade selection, and the other is for thermal load transfer in structural strength analysis. The BOR calculation also involves heat transfer analysis. On the other hand, the environmental temperature conditions are different from those of the steel grade selection conditions. Steel grade selection is governed by the IMO and USCG thermal design conditions, while the BOR is calculated under IMO warm thermal design conditions. The strength evaluation of a Type C LH2 tank requires complex thermal-structural analyses to resolve the thermal contacts among the tank shell, wood, and saddle structures. Sequentially coupled thermal-structural analysis was performed by applying thermal and mechanical loads. The design internal pressure is composed of vapor and liquid pressure. The liquid pressure results from the combined effects of gravity and acceleration, excluding sloshing loads. Structural analyses assessed each tank component under normal operating conditions with maximum acceleration, static conditions, 30° heeled conditions, collision conditions, and hydrostatic test conditions.

The buckling strength of the tank structure subjected to external pressures was calculated based on the IGC Code. The value of the design external pressure was determined, and the critical collapse pressure was calculated using finite element (FE) eigenvalue analysis. The design basis for a Type C independent tank is based on the pressure vessel criteria modified to include the fracture mechanics and crack propagation criteria. The fatigue strength was evaluated for the entire structure of the tank. In fatigue analysis, a high-cycle fatigue evaluation was performed because of repeated load histories during the design lifespan and low-cycle fatigue caused by thermal loads from cargo. The primary concern for high-cycle fatigue is the load history that acts repetitively during the design lifespan, and wave loads are a significant factor for both general vessels and independent self-support tanks. The stress distribution for long-term wave loads is directly related to fatigue failure. Typically, in the design phase, the stress long-term distribution is estimated through direct load analysis (DLA) and stochastic analysis to account for the actual environmental loads. This study applied the method outlined in international regulations (IGC Code; IMO, 2016) that utilizes the simplified load histories based on Weibull distribution to simplify the process.

Furthermore, hydrogen cargo tanks experience thermal stresses inside and around the tanks due to temperature variations during loading and unloading. Compared to high-cycle fatigue, low-cycle fatigue should also be evaluated because the stress ranges can be very high even with a few cycles. Low-cycle fatigue is typically evaluated for areas subjected to high stresses under periodic static loads. A fracture mechanics-based analysis should be carried out for the critical locations of the tank structure with high dynamic stresses. A fracture mechanics approach assumes that an idealized crack propagates in relation to the stress intensity factor range. A fatigue crack propagation analysis was conducted for the tank skin plate and internal structure to verify the tank integrity. Fatigue crack propagation was assessed from the growth of an initial existing crack to a critical size. High-stress concentration areas or large fatigue damage locations were selected for the crack propagation analysis. Detailed descriptions of each developed procedure are described in the following chapters.

## 3. Numerical Model

### 3.1 Target Vessel

The target vessel is an ocean-going LH2 carrier. Table 2 lists the principal particulars of the target vessel. Where *x* is the longitudinal distance from amidships to the center of gravity (COG) of the tank; *y* is the transverse distance from the centerline to the COG of the tank; *z* is the vertical distance from the actual waterline to the COG of the tank, *K* = 1 in general. For a particular loading condition and hull forms, *K* is determined as 13 *GM*/*B*, where *GM* is the metacentric height.

### 3.2 FE Model

The main components of the target tank included the inner tank, outer tank, inside supports (GRE G-10), and outside supports (saddle), as shown in Fig. 3. Among the components, the inner tank was the most critical because it subject to high internal pressures and cryogenic temperatures. An outer tank was designed to envelop the inner tank and safely protect it. The outer tank was glass bubble-filled vacuum insulated. The inner and outer tanks were connected through a glass-reinforced epoxy support. The entire tank was mounted on two saddles, and the outer tank and saddle were connected by welding. The cylinder diameter was approximately 18,000 mm, and the tank length was 31,500 mm. The main particulars of the target ship with a LH2 cargo tank were four (4) LH2 storage tanks with a capacity of 5,750 m^{3} × 4 ea.

The global FE model was constructed with four nodes of the shell element for the tank and saddle structures, eight nodes for the solid element for the GRE spacer, and a contact element for the interface among the tank, GRE spacer, and saddle support. The element size of the shell was set to approximately 100 mm × 100 mm, considering the convergence to the nominal stress calculated by the formula for hoop stress of the cylindrical shell. The inner and outer tanks were made of SUS304L steel. The saddle was made of mild steel, and the spacer was made of GRE G-10 material. Table 3 lists the thermal and mechanical properties of the materials.

### 3.3 Boundary Conditions

Among all the components of the target tank, the inner tank is the most critical part because it is subject to high internal pressure and cryogenic low temperature. An outer tank was designed to envelop the inner tank to protect it safely. The outer tank was glass bubble-filled and vacuum-insulated. The inner and outer tanks were connected through glass-reinforced epoxy support. The entire tank was mounted on two saddles, and the outer tank and saddle were connected by welding. The ambient temperature was set to 5°C for heat transfer analysis based on the IMO recommendations. The temperature of liquid hydrogen is −253°C, and the heat transfer coefficient, assuming natural convection, was set to 5 W/(m^{2}·K). Fig. 4(a) shows the detail of the thermal boundary. All degrees of freedom of the nodes at the bottom of the saddle supports attached to the ship hull were fixed, as shown in Fig. 4(b). The contact condition was also considered by applying a coefficient of friction between the spacer and tanks to consider the effect of contact and sliding between them.

### 3.4 Design Loads

The design loads must be determined when designing a Type C LH2 tank. The self-weight of the tank was applied as an inertial load, considering the acceleration of gravity and the density of the materials involved. The low-temperature vacuum pressure of the vacuum insulation system was applied as an internal load to the inner tank and an external load to the outer jacket. The thermal loads were derived from steady-state heat transfer analysis to calculate the temperature distribution on overall tanks and support structures, assuming the design temperature of LH2 and ambient conditions were −253°C and 5°C, respectively. The temperature distribution results calculated from heat transfer analysis were mapped to the structural analysis model to evaluate the impact of mechanical and thermal loads on the tank integrity. The IGC Code adopts the fracture mechanics, crack propagation criteria, and the traditional pressure vessel design formulae to construct the Type C tanks. The minimum design vapor pressure is calculated using the following formulae.

*σ*is the allowable dynamic membrane stress, which is 55 MPa for ferritic-pearlitic, martensitic, and austenitic steel and 25 MPa for aluminum alloys. The tank test condition is defined as 1.5 times the vapor pressure and hydrostatic pressure caused by partially filled fresh water. The forward directional acceleration under the accidental collision condition was set to 0.5 times the acceleration of gravity (9.81 m/sec

_{A}^{2}).

The dynamic loads can be determined by measuring the accelerations using accelerometers on the full-scale ship, by performing a sea-keeping analysis of the ship, or during model testing. In this study, the acceleration components were derived based on the IGC Code recommendation, which corresponds to a probability level of 10^{−8} in the North Atlantic environment.

*a*

_{x}*, a*

_{y}*,*and

*a*

_{z}are the maximum dimensionless accelerations (i.e., relative to the acceleration of gravity) in the respective directions.

*a*

_{z}does not include the component due to the static weight;

*a*includes the component due to the static weight in the transverse direction caused by rolling, and

_{y}*a*includes the component due to the static weight in the longitudinal direction due to pitching.

_{x}### 3.5 Design Load Cases

The design loads must be determined when designing a Type C LH2 tank. The self-weight of the tank was applied as an inertial load, considering the acceleration due to gravity and the density of the materials involved, and the low-temperature vacuum pressure of the vacuum insulation system was applied as an internal load to the inner tank.

All load cases mentioned in the IGC Code are specified when calculating the structural integrity of the LH2 tank. Table 4 lists seven load cases considering the pressure due to the self-weight of the structure, thermal load due to the temperature gradient in the cargo tank, vapor pressure in the inner tank, cold vacuum pressure, heeling condition (30°), liquid hydrostatic pressure, and dynamic pressure due to accelerations.

### 3.6 Acceptance Criteria

The Type C independent LH2 carrier tank is a pressurized tank. The structural stress results were assessed to determine the yield strength according to the IGC Code and other internationally recognized pressure vessel codes. For the design of Type C LH2 tanks, the calculated stress shall not exceed the corresponding allowable stress, as listed in Table 5.

where *f* is the reference allowable stress expressed as *f = min (R _{m}*

*/A, R*

_{e}*/B); R*is the specified minimum yield stress at room temperature. If the stress–strain curve does not show a defined yield stress, a 0.2% proof stress applies;

_{e}*R*is the specified minimum tensile strength at room temperature. The A and B values shall be at least the minimum values listed in Tables 6 and 7.

_{m}## 4. Thermal-Structural Analysis

### 4.1 Heat Transfer Analysis

Thermal-structural analysis was performed in two steps; the first step performed heat transfer analysis to calculate the member temperatures, and the last step accomplished structural analysis by applying the thermal loads from the previous step and all other mechanical loads. Fig. 5 shows the heat transfer analysis results for the LH2 tank. The maximum temperature of 3.3°C was estimated on saddle support, and the minimum temperature of −253°C was attained on the inner tank, which is in direct contact with the LH2. The steel foundation attached to the inner tank reached the same temperature as LH2 because of its high thermal conductivity. The temperature variation of the structure around the inner tank was minimal because the annular space between the inner and outer tank was vacuum-insulated with a glass bubble. On the other hand, the largest temperature gradient was obtained on the spacers because the two tanks are connected via GRE G-10 spacers with very low thermal conductivity, as shown in Fig. 5. Fig. 6 presents the detailed temperature distribution for each tank component.

### 4.2 Structural Analysis

Structural analysis was performed using LS-DYNA to check the movement of the tanks and associated stresses under the defined load cases. Seven load cases were analyzed, and the von Mises equivalent stresses were derived for each. The yielding check was done for each component, including the inner tank, outer tank, and two saddle supports. Figs. 7 and 8 show the stress contours under accidental collision conditions, which were intended to be the highest stress among the load conditions. The internal pressure, consisting of the vapor pressure, cargo pressure, and cold vacuum pressure, has the greatest impact on all the loads acting on the inner tank. For example, the general primary membrane stress on the inner tank is 112 MPa, which is lower than the allowable stress of 116.7 MPa. The high-temperature gradient caused the inner tank to shrink, and subsequent stresses occurred at the junction between the inner tank and the steel foundation. Maximum stress of 272MPa occurred in the inner tank where the steel foundation was attached. This stress was defined as localized stress because it was calculated at a critical location, such as a support, and was caused by the combined effects of thermal and other mechanical loads.

Table 8 lists the representative structural analysis results for the three most utilized load cases. The sum of the most critical terms (local, bending, and secondary stresses) and the corresponding allowable stresses are shown. All components of the stresses satisfied the criteria, and even for LC7, the ideal hydrostatic test conditions, the yield stress did not exceed 90% of the allowable value specified in the IGC Code. The current design of the cargo tank and its supports meet the yield strength criteria of the IGC Code.

## 5. Buckling Analysis

The buckling requirements generally apply for cylindrical shells and torispherical or ellipsoidal ends exposed to external pressure and other loads causing compressive stresses. Different buckling modes can be obtained from eigenvalue FE analysis. In addition, the critical buckling pressure of the tank can be determined using two FE simulation methods, such as linear buckling (eigenvalue) analysis and post-buckling analysis with imposed imperfection. Linear buckling (eigenvalue) analysis requires the elastic material properties of the tank and a unit buckling load distribution applied on the tank to solve the eigenvalues for the corresponding buckling modes. Generally, the first buckling mode with the lowest eigenvalue represents the critical buckling load. On the other hand, post-buckling analysis should be carried out to determine the critical buckling load when the imperfection of a tank is significant. The elastic–plastic material properties are needed, and a load distribution is applied to the tank that contains the imperfection to be considered. The imperfection field can be obtained through actual measurements, manufacturing tolerance, or buckling mode shapes derived from eigenvalue analysis.

This study examined the buckling strength of the outer tank subjected to a vacuum pressure of 0.1MPa through linear buckling analysis. Fig. 9 shows the first buckling mode from eigenvalue analysis. The FE results predicted a critical buckling pressure of 0.29 MPa and a safety factor of 2.9, which meets the IGC Code requirements.

## 6. BOR Calculation

The BOR is commonly used in the field of liquefied gas transportation and refers to the rate at which liquefied gases, such as LNG or liquefied hydrogen (LH2), vaporize and are lost from storage tanks or cargo holds. The BOR represents the quantity of gas vaporized over time, typically expressed in %/day. It plays a crucial role in the design and operation of ships or storage facilities, significantly impacting efficient gas management and economic viability. Liquefied gases evaporate at temperatures above their boiling point and generate BOG. Although there are numerous causes for BOG generation, heat ingress is the primary reason for generating BOG on ships. This study calculated BOR assuming the heat ingress into cargo tanks is the only source for generating BOG.

The BOR signifies the percentage of evaporated LH2 per day to the initial LH2 loaded amount and can be estimated using the following equation. Table 9 lists the design data for calculating the BOR of the target LH2 tank.

Local FE steady-state heat transfer analysis was performed to estimate the heat leakage into the cargo tank. The IMO warm environmental condition was applied as the thermal boundary condition where the air and seawater temperatures were assumed to be 45°C and 32°C, respectively. The convection heat transfer coefficient of 5 W/m^{2}K was applied to transfer the heat from the environment to the outer tank. The vacuum insulation system with a conductivity of 0.0018 W/(m·K) and GRE spacer of 0.29 W/(m·K) was modeled with solid elements. Fig. 10 presents the results of heat transfer analysis, and Table 10 lists the results of the BOR calculation.

The specific standards for the BOR vary according to the type of cargo being transported, the mode of transportation, the design of the storage facility, and the type of vessel. For example, in the case of ships transporting LNG, the BOR is typically calculated daily and can vary in %/day depending on the design and operation of the vessel. For other types of cargo, such as LH2, the standards for BOR are not yet widely standardized, and regulations or standards continue to evolve. The BOR is particularly important for LH2 because the vaporization of LH2 greatly affects transportation efficiency. Therefore, minimizing the BOR is crucial when designing ships or storage facilities transporting LH2.

The total heat ingress can be calculated by expanding the heat ingress calculated from the spacer and inner tank to the total area. The BOR of this tank can be calculated using Eq. (8). The calculation procedure of the BOR presented in this study is an example case, and the design BOR of an actual Type C tank may be greater than the calculated value. This study only considered the heat leakage through insulation and GRE spacers, but under real operation conditions, there may be additional heat ingress through the liquid dome, pipe penetrations, and manholes. Therefore, more precise calculations should be performed in the actual design, considering all types of heat ingress into the LH2 tank.

## 7. Fatigue Analysis

According to the IGC Code, for a large Type C independent tank, where the cargo at atmospheric pressure is below −55°C, the administration or recognized organization acting on its behalf may require additional verification to check their compliance with static and dynamic stress. The fatigue assessment was performed on welded joints, and the allowable fatigue damage in high-stress areas of the tank should be less than 0.5 for regions detectable by in-service inspection and less than 0.1 for undetectable regions. This study calculated the high cycle fatigue damage calculation caused by ship motions and low cycle fatigue damage calculation caused by loading/unloading. In Eq. (10), the first term (

The loading and unloading cycles include a complete pressure and thermal cycle, typically corresponding to 20 years of operation. In this section, the fatigue damage was calculated for areas where structural analysis predicted the maximum stresses. The high cycle fatigue damage of structurally weak points was calculated using the simplified method. Fatigue analysis considers the appropriate combination of loads for the expected life of the LH2 tank because ship motions cause high cycle fatigue. The inertial force caused by ship motion was applied as a high-cycle fatigue load in this study, as shown in Table 8. Therefore, tank accelerations (longitudinal, transverse, and vertical direction) based on the IGC Code were applied to the structural model, and a simplified method was applied to calculate fatigue damage using the maximum principal stress. This method estimates the long-term stress distribution by applying the Weibull distribution function, and the calculation method is as follows:

The critical location for the fatigue assessment was chosen based on areas of high stress in the structural analysis results. The maximum stress occurred near the tank support. Fig. 11 shows the results of the maximum vertical acceleration case.

The thermal loads based on the temperature distribution were considered for low-cycle fatigue analysis. The thermal stress range was obtained by the difference in stress between loading and unloading (Fig. 12). Fig. 13 presents the results when the temperature in the tank is −253°C.

Table 11 lists the values of the design S–N curve, and Table 12 summarizes the fatigue damage results. Even in the structural discontinuity region, the fatigue damage was calculated to be very small, and fatigue damage results satisfy the allowable criteria regardless of combining the fatigue damage by applying a conservative method.

## 8. Crack Propagation Analysis

The structural integrity can be evaluated by performing crack propagation analysis in areas where crack detection is difficult or in areas of structural weakness. This is known as ‘Engineering critical assessment (ECA) or Fracture mechanics analysis’ and is an analysis technique applied to evaluate the structural integrity and sustainability of a service. This design concept has been applied mainly to aircraft and nuclear reactors, and the concepts of damage tolerance design and leakage before failure theory are reflected in the design of cryogenic cargo tanks. ECA assumes that there is a crack inside the weld area and considers the length and depth of the crack, internal and external loads, strength and toughness of the material, and residual stress caused by the welds. In addition, the fractured joint was evaluated using a failure assessment diagram (FAD), which considers the loading characteristics and toughness characteristics, with the crack tip opening displacement (CTOD) used widely for toughness characteristics. Fig. 14 shows the flowchart for engineering a critical assessment.

The welded part of the independent tank was exposed to the internal cargo motion and the residual stress due to welding. The crack opening stress due to internal and external pressures was calculated using finite element analysis. A simplified stress history was used because the actual load and stress history cannot usually be considered accurately during the design stage, as shown in Fig. 15.

This can be determined as a long-term stress corresponding to the design life of the ship (i.e., probability level of (10^{8})). The simplified long-term stress distribution in the calculations was determined using the modified Weibull distribution in equation (12).

The total stress spectrum was divided into 20 groups to eliminate the effect of the stress sequence on the crack propagation life. The fatigue crack propagation path was assumed to be perpendicular to the principal stress direction. The stress intensity factor range was calculated from the stress range, crack shape and size, and geometry. International Institute of Welding (IIW) or equivalent standard was used to assess the stress intensity factor for a surface crack. The stress range was based on the maximum principal stress from the structural analysis results in Fig. 7.

The initial crack length and depth must be assumed when performing the surface crack propagation analysis. In this study, a crack length of 5.0 mm and a crack depth of 1.0 mm were applied for the fillet welds according to the guidelines of the Korean Register. Fig. 16 shows the crack lengths generated by applying the ASMR BPVC code over the design life of the ship. The results were calculated as non-penetrating in the thickness direction for 15 days and evaluated to satisfy the allowable criteria of the IGC Code.

## 9. Conclusion

This study developed a comprehensive structural integrity assessment procedure for Type C tanks that can store liquid hydrogen. Design load cases based on the IGC Code, which is essential for cryogenic cargo carriers, were defined. Thermal–structural analysis was conducted to calculate thermal loads, evaluate yield and buckling strengths, and propose a methodology for calculating the BOR. Furthermore, high-cycle and low-cycle fatigue analysis based on the simplified method was proposed. In addition, a procedure for crack propagation analysis based on fracture mechanics, which can be applied as needed, was presented. According to the developed procedure, the evaluation was performed on the conceptually designed 23K hydrogen carrier, and the suitability of the procedure was verified. Based on the study results, the following conclusions are derived.

(1) Heat transfer analysis was performed to calculate and transfer the thermal loads caused by the LH2 operating temperature. A similar approach can be applied for steel grade selection by changing only the thermal design conditions (i.e., IMO and USCG conditions). The temperature change in the structure around the inner tank was minimal because the annular space between the inner and outer tank was vacuum-insulated, and the largest temperature gradient was obtained at the spacer. The calculated heat loads were further exported to account for the thermal effects of LH2 in the structural analysis phase.

(2) Structural strength evaluation based on the IGC requirements was performed by analyzing seven load cases. Each satisfied the minimum criteria, and the sum of the most critical terms (local stress, bending stress, and secondary stress) was compared with the corresponding allowable stresses. The maximum stress was identified at a critical location, was a local stress, and was caused by the combined effects of thermal and other mechanical loads.

(3) After predicting the buckling strength through a linear eigenvalue analysis, a safety factor of 2.93 was obtained, indicating that the outer tank has sufficient buckling capacity against the cold vacuum pressure. Assuming that heat leakage is the only cause of BOG generation, the procedure applied to the BOR calculation was presented with an application case. Further refinement in calculation could be applied in the actual design phase, considering all types of heat ingress into the LH2 tank, including liquid dome, pipe penetrations, and manholes.

(4) An analysis procedure for high-cycle fatigue caused by inertia load from tank acceleration and low-cycle fatigue caused by temperature differences from loading/unloading was developed, and the analysis results were reviewed. In addition, crack propagation analysis based on fracture mechanics was accomplished to perform an integrated structural design evaluation of the LH2 tank

This study analyzes the methodology applied to tank design evaluation based on the IGC Code and presents an integrated procedure applicable to LH2 tanks. In addition, the evaluation methodology was applied to the IMO Type C tank, and the results were analyzed to examine applicability. This study provides initial research data because there is a lack of special regulations or approval procedures to apply to hydrogen tanks mounted on ships. Therefore, a special evaluation procedure that reflects the characteristics of liquefied hydrogen will be necessary.

## Notes

No potential conflict of interest relevant to this article was reported.

## Acknowledgements

This research was a part of the project titled ‘Technology application of design and exclusive materials for hydrogen cargo containment mock-up (Project NO. 20019043)’, funded by the Ministry of Trade, Industry and Energy, Korea.