# Design of Type-IV Composite Pressure Vessel Based on Comparative Analysis of Numerical Methods for Modeling Type-III Vessels

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Micromechanics Models

#### 2.3. Constitutive Models for the Liner and the Overwrapped Composite Layers

**M**is the damage operator:

## 3. Numerical Simulations

#### 3.1. Simulation Using 3D Elements

#### 3.2. Simulation Using Conventional Shell Elements

#### 3.3. Simulation Using Continuum Shell Elements

#### 3.4. Simulation Using Mixed Method

_{3}, as illustrated in Figure 2. Each layer within this sequence has a thickness of 0.2 mm, and the properties associated with these layers are detailed in Table 1. Table 2 reports the three-dimensional effective properties for the solid-to-solid homogenization, while Equation (12) provides the upper triangular part of the symmetric ABD matrix corresponding to the solid-to-shell homogenization.

## 4. Comparison between Methods and Discussion

## 5. New Design of Type-IV Hydrogen Tank

_{2}is a molecule known for its small size and high permeability. Furthermore, HDPE stands out for its lightweight composition, durability, and minimal moisture absorption, rendering it well suited for scenarios where managing weight and moisture levels is crucial. Specifically designed to be lightweight and featuring a composite structure with a nonmetallic liner, type-VI hydrogen tanks prove to be highly adaptable for diverse transportation and storage needs. All the necessary property parameters for conducting simulations can be found in Table 3.

_{18}, we found that the tank can only withstand a maximum of 140 bar. This highlights the significance of stacking sequence and pattern as key parameters influencing the tank’s burst pressure, emphasizing the need for optimization techniques to enhance the tank’s performance.

## 6. Concluding Remarks

- In this study, we presented a comparative analysis of various numerical methods for modeling composite pressure vessels, aiming to provide a comprehensive understanding of their performance. The methods under scrutiny include finite element analysis in Abaqus with conventional shell element, continuum shell element, three-dimensional solid element, and homogenization approaches for multilayered composite pressure vessels. Through a systematic comparison, this research offers insights into the strengths and limitations of each method. It is crucial to emphasize that the results achieved could be replicated with a lower mesh density when utilizing only a quarter of the model.
- The findings of this study indicate that three-dimensional solid elements yield the highest accuracy in modeling composite pressure vessels. However, their practicality diminishes as the number of layers in the composite increases. Following closely are the continuum shell elements, which strike a balance between accuracy and computational efficiency due to their intermediate nature, combining features of both 3D and conventional shell elements. Meanwhile, the method relying solely on conventional shell elements proves to be accurate for specific applications but lacks universality.
- Moreover, this research underscores the significance of the homogenization technique used in the mixed method as an alternative, particularly for damage-free applications, as it consistently delivers highly accurate results. The approach involves treating the composite shell section of the tank as a straightforward homogenized layer.
- A new design dedicated to a type-IV hydrogen tank, composed of carbon fibers, epoxy resin, and a high-density polyethylene (HDPE) liner, is proposed. The study concentrates on predicting damage onset and behavior within the tank and burst pressure prediction. With this new design, we demonstrated that the tank can endure a pressure of 1000 bar when using 36 plies, resulting in a composite shell thickness of 7.2 mm. Undoubtedly, future optimization is essential as this exploration aligns with the broader scope of a significant project where we are concurrently working on new materials development.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Geometry of the bare liner used for comparison from reference [18].

**Figure 5.**Comparison Between the hoop strain and the applied internal pressure obtained with the conventional shell element, continuum shell element, and mixed method and the experimental and numerical results of the reference.

**Figure 6.**Comparison between the axial strain and the applied internal pressure obtained with the conventional shell element, continuum shell element, and mixed methods and the experimental and numerical results of the reference.

**Figure 7.**Comparison Equivalent stress vs. axial distance along the inner surface of the bare liner at 700 bar using conventional shell elements, continuum shell elements, and 3D elements.

**Figure 8.**The Equivalent stress vs. axial distance along the inner surface of the wound liner at 700 bar using conventional shell elements, continuum shell elements, homogenized conventional shell elements, and homogenized continuum shell elements.

**Figure 9.**The axial displacement at the extremity of the back dome vs. the internal pressure for different numbers of plies using the conventional shell element model.

**Figure 10.**Response simulation using the conventional shell element model at failure for a stacking of 24 plies: (

**a**) magnitude of the displacement, (

**b**) yield response in the polymeric liner, (

**c**) axial strain in the liner, (

**d**) compression damage of the matrix in the first ply, (

**e**) tensile damage of the matrix in the first ply, (

**f**) damage of the matrix in tension at the third ply, (

**g**) damage of the fiber in tension at the first ply, and (

**h**) damage of the fiber in compression at the first ply.

**Table 1.**Elastic properties and stress limits of glass-fiber-reinforced epoxy-based composites and elastic-plastic properties of the steel liner.

Symbol | Description | Unit | Value |
---|---|---|---|

Glass fiber/epoxy composite | |||

${E}_{1}$ | Longitudinal (fiber-dominated) modulus | MPa | 38,500 |

${E}_{2}={E}_{3}$ | Transverse (matrix-dominated) modulus | MPa | 16,500 |

${\nu}_{12}$ | Poisson’s ratio (in-plane) | - | 0.27 |

${\nu}_{23}$ | Poisson’s ratio (planes 2–3) | - | 0.28 |

${G}_{12}={G}_{13}$ | In-plane shear modulus | MPa | 4700 |

${G}_{23}$ | Shear modulus (planes 2–3) | MPa | 5000 |

${X}_{T}$ | Longitudinal (fiber-dominated) tensile strength | MPa | 1250 |

${X}_{C}$ | Longitudinal (fiber-dominated) compressive strength | MPa | −650 |

${Y}_{T}$ | Transverse (matrix-dominated) tensile strength | MPa | 36 |

${Y}_{C}$ | Transverse (matrix-dominated) compressive strength | MPa | −165 |

${S}_{L}$ | In-plane shear strength | MPa | 86 |

${G}_{f}$ | Fracture energy of the fiber | N/mm | 12.5 |

${G}_{m}$ | Fracture energy of the matrix | N/mm | 1 |

Steel liner (SL) | |||

${E}_{\mathrm{SL}}$ | Young’s modulus | MPa | 205,000 |

${\nu}_{\mathrm{SL}}$ | Poisson’s ratio | - | 0.3 |

${\sigma}_{y,\mathrm{SL}}$ | Yield strength | MPa | 743 |

${E}_{\mathrm{tan},\mathrm{SL}}$ | Bilinear isotropic hardening tangent modulus | MPa | 2600 |

**Table 2.**Three-dimensional effective properties corresponding to the solid-to-solid homogenization scenario.

${E}_{1}$ (MPa) | ${E}_{2}$ (MPa) | ${E}_{3}$ (MPa) | ${\mathit{\nu}}_{12}$ (-) | ${\mathit{\nu}}_{13}$ (-) | ${\mathit{\nu}}_{23}$ (-) | ${G}_{12}$ (MPa) | ${G}_{13}$ (MPa) | ${G}_{23}$ (MPa) |
---|---|---|---|---|---|---|---|---|

26,548.24 | 27,347.34 | 17,343.40 | 0.180 | 0.344 | 0.339 | 5204.77 | 4700 | 4700 |

Symbol | Description | Unit | Value | ||||
---|---|---|---|---|---|---|---|

Carbon fiber/epoxy composite | |||||||

${E}_{1}$ | Longitudinal (fiber-dominated) modulus | MPa | 141,000 | ||||

${E}_{2}={E}_{3}$ | Transverse (matrix-dominated) modulus | MPa | 11,400 | ||||

${\nu}_{12}$ | Poisson’s ratio (in-plane) | - | 0.28 | ||||

${\nu}_{23}$ | Poisson’s ratio (planes 2–3) | - | 0.40 | ||||

${G}_{12}={G}_{13}$ | In-plane shear modulus | MPa | 5000 | ||||

${G}_{23}$ | Shear modulus (planes 2–3) | MPa | 3080 | ||||

${X}_{T}$ | Longitudinal (fiber-dominated) tensile strength | MPa | 2080 | ||||

${X}_{C}$ | Longitudinal (fiber-dominated) compressive strength | MPa | −1250 | ||||

${Y}_{T}$ | Transverse (matrix-dominated) tensile strength | MPa | 60 | ||||

${Y}_{C}$ | Transverse (matrix-dominated) compressive strength | MPa | −290 | ||||

${S}_{L}$ | In-plane shear strength | MPa | 110 | ||||

${G}_{f}$ | Fracture energy of the fiber | N/mm | 78 | ||||

${G}_{m}$ | Fracture energy of the matrix | N/mm | 1 | ||||

Isotropic elastic properties for the high-density polyethylene liner (HDPE) [32] | |||||||

${E}_{\mathrm{HDPE}}$ | Young’s modulus | MPa | 903.114 | ||||

${\nu}_{\mathrm{HDPE}}$ | Poisson’s ratio | - | 0.39 | ||||

Isotropic plastic hardening data for the HDPE liner material [32] | |||||||

Yield stress (MPa) | 8.618 | 13.064 | 16.787 | 18.476 | 20.337 | 24.543 | 26.887 |

Plastic strain (-) | 0 | 0.007 | 0.025 | 0.044 | 0.081 | 0.28 | 0.59 |

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**MDPI and ACS Style**

Bouhala, L.; Koutsawa, Y.; Karatrantos, A.; Bayreuther, C.
Design of Type-IV Composite Pressure Vessel Based on Comparative Analysis of Numerical Methods for Modeling Type-III Vessels. *J. Compos. Sci.* **2024**, *8*, 40.
https://doi.org/10.3390/jcs8020040

**AMA Style**

Bouhala L, Koutsawa Y, Karatrantos A, Bayreuther C.
Design of Type-IV Composite Pressure Vessel Based on Comparative Analysis of Numerical Methods for Modeling Type-III Vessels. *Journal of Composites Science*. 2024; 8(2):40.
https://doi.org/10.3390/jcs8020040

**Chicago/Turabian Style**

Bouhala, Lyazid, Yao Koutsawa, Argyrios Karatrantos, and Claus Bayreuther.
2024. "Design of Type-IV Composite Pressure Vessel Based on Comparative Analysis of Numerical Methods for Modeling Type-III Vessels" *Journal of Composites Science* 8, no. 2: 40.
https://doi.org/10.3390/jcs8020040