Finite element analysis of self-tensioning and bursting of 210 L carbon fiber fully wound hydrogen storage cylinders

This paper focuses on a 210 L carbon fiber fully wound hydrogen storage cylinder. A 1/8 scale model is selected for analysis. Using the finite element software ANSYS APDL and secondary development language, an orthotropic material performance equation is formulated and applied to the composite material lay-up. Following DOT CFFC standards, the cylinder undergoes simulated loading and unloading analysis to determine the optimal self-tightening pressure. Subsequently, progressive failure theory and the Tsai-Wu failure criterion are employed to identify the failure modes of the composite material. Continual adjustments to the element stiffness are made during the loading process. Employing the element birth and death technique, failed elements are terminated and recorded, and based on increasing trends, the burst pressure of the cylinder can be predicted. The results closely align with experimental data, validating its applicability as the basis for burst prediction.


Introduction
The hydrogen energy industry is experiencing a rapid technological and industrial development phase, which brings new development opportunities for special equipment, including hydrogen cylinders, mobile pressure vessels, fixed pressure vessels, pressure piping, etc., and also presents an urgent need [1] .However, judging from the hydrogen energy path taken by the United States, Japan, and Europe, the global hydrogen energy industry is still in the early stages of commercialization, even though the development of hydrogen energy has gone through four rounds of nearly 40 years [2] .
This paper focuses on the currently more reliable high-pressure hydrogen storage technology.However, the strength analysis research for Type III metal liner fully wound gas cylinders is still in the developmental stage.Based on the ACP module under the ANSYS Workbench platform, Qin [3] analyzed the stress under different loading conditions of a 100 L capacity cryogenic high-pressure hydrogen storage cylinder and determined the stress distribution state of the cylinder liner and the fiber winding layer, but lacked the selection process of the self-tensioning pressure; An et al. [4] derived a reasonable lay-up for the aluminum-lined carbon fiber composites pressure vessel according to the mesh theory scheme, established a one-eighth model, carried out finite element analysis using ANSYS software, and obtained the changing trend of stress in the liner layer and the fiber winding layer with the increase of internal pressure, but there is no clear verification method of bursting pressure.This paper focuses on a 210 L aluminum-lined carbon fiber fully wound hydrogen storage cylinder.Through ANSYS finite element calculations, the aim is to determine the reasonable self-tightening pressure range and burst pressure of the cylinder under a given lay-up scheme.

Fundamentals of material parameters and mechanical analyses
As shown in Figure 1, the aluminum alloy inner liner of a factory is used as the basis, and then carbon fiber full winding lay-up is carried out on this basis, and the exact value of the drawing is used in modeling, which is divided into four parts, the air nozzle, the head, the shoulder articulation section, and the cylinder body.The inner and outer diameters of the nozzle are 51 mm and 85 mm respectively, and the lengths of the head, shoulder, and cylinder are 125 mm, 90 mm, and 1610 mm respectively.The aluminum liner is modeled as a bilinear elastoplastic reinforcement material and the composite layer is modeled as an anisotropic material.The material properties and strength limits of the inner liner and composite layer are shown in Tables 1, 2, and 3, respectively.The lay-up effect of the composite material is achieved by defining the properties of each unit of the fiber composite layer, where it is necessary to determine the strain matrix in the principal axis for each layer of material based on the material's axis transformation equation.Then the flexibility matrix is based on the basic equations of anisotropic elastic mechanics, and ultimately the stiffness matrix of the unit is obtained through Equation ( 1), which is used to define the material properties of each unit.
where [B] is the strain matrix and [D] is the elasticity matrix of the material, the values of which depend on the modulus of elasticity and Poisson's ratio of the material in each direction.The lay-up scheme selected in this paper is shown in Table 4, where each layer thickness is set to 1 mm, the total thickness is 14 mm, and the ring-spiral ratio is 8/6, where 90° is for ring winding and non-90° is for spiral winding.The order of lay-up is 1st layer for the innermost layer and 14th layer for the outermost layer.A 1/8 model is adopted, as shown in Figure 2. The inner lining is meshed with a 20node isotropic 3D Solid186 element, while the outer wound fiber layer is meshed with an 8-node 3D solid orthotropic anisotropic Solid64 element specially designed for the simulation of composite materials.At the same time, the properties of the elements should be set by using KEYOPT, 1, 6, 1 to ensure that the initial principal direction of the composite material aligns circumferentially.The mesh division results are shown in Figure 3, with a total of 36, 900 elements, of which the number of elements in the composite material layer is 25, 200, and the inner liner is 11, 700.Symmetric constraints are applied to the cutaway end face of the model, internal pressure load is applied to the inner surface of the liner, and the pressure is divided several times for pressurization and unloading through the load step.

Self-tensioning analysis
In this paper, the internationally recognized DOT CFFC standard is adopted for the design and validation of the cylinders.We select a set of self-tightening pressures as shown in the table below for calculation at a working pressure of 35 MPa to optimize the best self-tightening pressure.After calculation and analysis, the results are summarized in Table 5.It can be observed that when the self-tightening pressure is 54 MPa, the circumferential stress exceeds 60% of the yield strength under working pressure, making it undesirable.Furthermore, at a self-tightening pressure of 61 MPa, the circumferential stress after selftightening exceeds 95% of the yield strength, making it unsuitable.The performance indicators under the remaining four self-tightening pressures meet the DOT CFFC standards.6, after unloading several groups of different self-tensioning pressures and then applying the working pressure, the maximum equivalent stress of the fiber layer increases with the increase of self-tensioning pressure, but none of them exceeds 30% of its tensile strength (2800 MPa).As shown in Table 5 and Table 6, 60 MPa was selected as the self-tensioning pressure.
As shown in Figures 4 and 5, from the extracted Mises equivalent stress contour before and after self-tightening, it can be observed that when the internal pressure increases to the self-tightening pressure, the region under significant stress is the fiber layer, with the circumferential winding layer bearing the predominant load.As the internal pressure decreases to zero, the region under the maximum stress shifts towards the inner liner, and the stress increases closer to the inner side.Throughout the entire process, the circumferential winding layer consistently bears higher stress in the fiber layer, and the stress on the inner side is greater than on the outer side.Additionally, the maximum plastic deformation values of the liner under different self-tightening pressures and the corresponding circumferential stress values of the liner under the working pressure were extracted.Line graphs were then created as shown in the following figure.As depicted in Figure 6, the plastic strain of the liner increases almost linearly with the increase in self-tightening pressure.Figure 7 reveals that after self-tightening, the maximum circumferential stress of the liner under working pressure decreases almost linearly with the increase in plastic strain.

Blast analysis
The overall strength of the gas cylinder mainly depends on the carbon fiber composite winding layer.In the finite element static analysis, the composite winding layer can be regarded as a plywood treatment, and the progressive damage model [5] has been widely used to simulate the process of layer-by-layer failure of plywood since the 1990s.This paper adopts the progressive damage model for blasting failure

MAEIE-2023
Journal of Physics: Conference Series 2761 (2024) 012005 analysis of gas cylinders, and the computational process includes the calculation of stresses, the judgment of failure, and the material degradation [6] .The failure judgment is chosen by comparison with the Tsai-Wu failure criterion [7] , and for orthotropic anisotropic materials, it is defined as follows: +   +   +   +   + 2   ≥ 1 (2) where the strength coefficients F 1 , F 2 , F 11 , F 22 , and F 66 are in the following order: where σ 1 and σ 2 are the longitudinal and transverse tensile stresses.When a location within the composite layer satisfies Equation ( 2), it is judged to have failed at that location.
As for the material degradation, when the material occurs above failure, the material performance parameters need to be modified corresponding to the stiffness degradation.This paper adopts the material degradation model of Camanho et al. [8] , as shown in Table 7.
Table 7. Criteria for degradation of material properties.During the pressurization process, the recorded number of failed fiber elements is illustrated in Figure 8.When the internal pressure is below 120 MPa, no detected fiber elements exhibit failure.As the internal pressure reaches 130 MPa, a small number of failure elements appear.When the internal pressure reaches 132 MPa, the number of fiber failure elements rapidly increases to 430, and at an internal pressure of 135 MPa, the number of fiber failure elements quickly reaches 1671.This indicates that the bursting pressure of the cylinder in this case study is between 132-135 MPa, surpassing the standard requirement of 119 MPa.

Conclusion
After analysis and calculation, the optimal self-tightening pressure for the 210 L aluminum-lined carbon fiber fully wound hydrogen storage cylinder under the selected layup scheme is determined to be 60 MPa.The plastic strain of the liner increases quasi-linearly with the increase in self-tightening pressure, while the maximum circumferential stress of the liner under working pressure linearly decreases with the increase in plastic strain.
Through the integration of progressive failure criteria and the combination of material stiffness degradation with finite element secondary development language, the bursting pressure of the cylinder is predicted to be between 132 MPa and 135 MPa, satisfying the bursting requirements.

Figure 1 .
Figure 1.Dimensions of gas cylinder liner.The aluminum liner is modeled as a bilinear elastoplastic reinforcement material and the composite layer is modeled as an anisotropic material.The material properties and strength limits of the inner liner and composite layer are shown in Tables1, 2, and 3, respectively.

Figure 7 .
Figure 7. Plastic strain versus maximum circumferential stress at working pressure.

Figure 8 .
Figure 8. Graph of the number of failed fiber units.

Table 1 .
Mechanical properties of aluminum alloy lining materials.

Table 2 .
Table of mechanical properties of composite layer materials.

Table 3 .
Strength limits for composite materials.

Table 4 .
Table of paving program.

Table 5 .
Circumferential stresses in the liner after self-tensioning and at working pressure.

Table 6 .
Maximum Mises equivalent stress of cylinders at working pressure 35 MPa.