## Abstract

Type III accumulator is widely used in hydrogen stations. A high-cost pressure cycle test is mandatory to ensure the safety of the accumulator in present regulations. To reduce the high cost, the aim is to develop a methodology of numerical fatigue life prediction, where an axisymmetric finite element model for the Type III accumulator is created precisely and actual loading process including autofrettage pressure is simulated. The alternating stress intensity is evaluated based on the instructions in KD-3 of 2015 ASME Boiler & Pressure Vessel Code, Section VIII, Division 3. By comparing stress amplitude distributions with the leak positions after the pressure cycle test, and plotting the results in the design fatigue curve, it could be shown that fatigue life prediction of Type III accumulator can be done by precise finite element analysis of the liner including dome part, where the principal axes of stress change in pressure cycle.

## Introduction

Reducing carbon dioxide emission challenge leads to an increase in electric vehicles all over the world [1]. There has been growing interest in fuel cell vehicles (FCV) for their merit of running distance for one filling among the electric vehicles. There are commercial FCVs in the market, such as “MIRAI” from TOYOTA [2]. Aiming at popularization of FCVs, more hydrogen fueling stations has been planned to be built [3]. To accelerate the speed of expanding station numbers, reducing its construction cost is strongly desired. This research focuses on Type III composite reinforced accumulator, which is main component of the station and enhances the construction cost. Type III accumulator is made by filament winding method, which is good at manufacturing thick carbon fiber reinforced plastic (CFRP) layers and automated [4] for cylindrical members. The construction of CFRP layers of Type III accumulator becomes very complicated, since various fiber orientations are employed in helical layers to avoid excessively thick CFRP at dome part. The fiber angle and layer thickness continuously change from the equator to the pole boss in dome part, so that, the material properties in global coordinate should be set according to the angle of fiber direction to the meridian [5–10]. It has made finite element (FE) modeling and analysis very difficult and unreliable. Therefore, the high-cost pressure cycle tests have been obligated to estimate fatigue life of Type III accumulator [11,12]. To exempt costly pressure cycle tests, the applicability of fatigue life evaluations by FE analysis must be established. In this research, FE modeling software, which is named as FrontCOMP_tank, is developed. It includes fiber reinforced plastic (FRP) layer's thickness limit setting and shape approximation with sine and cosine function which enables us to create nearly same smooth dome and boss shape compared with the actual shape [13]. Fatigue life evaluations with the created models are done and compared with pressure cycle test results using 111 L and 76 L accumulators. The results show that the number of cycles to leak in pressure cycle tests are reasonably predicted by the ASME *S*–*N* curve.

### Pressure Cycle Tests.

Three hydrostatic pressure cycle tests were carried out by changing pressure ranges for three identical Type III accumulators with both 111 L and 76 L internal volume, respectively. For 111 L accumulators, the design pressure is set to 95 MPa. The dimensions of the liner are shown in Fig. 1(a). There are 57 CFRP layers, which consist of 11 hoop layers, 41 high-angle helical layers, and 5 helical layers that are wound on the liner by filament winding method. Total thickness of CFRP layers in cylindrical part is about 52 mm. Autofrettage pressure of 163 MPa was applied before the cyclic load to give the residual compressive stress in the inner surface of the liner, respectively. So that, it improves fatigue life [14,15]. The pressure ranges of three tests are 0–85.5 MPa, 9.5–95 MPa, and 28.5–85.5 MPa. They are set to assume the real situation in hydrogen charging process at the station. For 76 L accumulators, the design pressure is set to 99 MPa. The dimensions of the liner are shown in Fig. 1(b). There are 78 CFRP layers that consist of 2 hoop layers, 46 high-angle helical layers and 30 helical layers, and 3 glass fiber reinforced plastic layers that consist of 2 hoop layers and 1 helical layer, which are also wound on the liner by filament winding method. Total thickness of CFRP and glass fiber reinforced plastic layers in cylindrical part is about 70 mm. Autofrettage pressure of 197 MPa was applied. The pressure ranges of three tests are 0–90 MPa, 50–90 MPa, and 70–90 MPa. They are also set to assume the real situation in hydrogen charging process at the station. The pressure cycle test equipment consists of hydraulic pressure system, pressure transducer, hydraulic temperature control system, hydraulic PLC, and temperature transmitter. During the tests, temperatures were controlled without exceeding 50 °C, so the material properties change during tests were not considered. The cycling rate during the pressure cycle was 3 cycles/min for pressure range of 0–85.5 MPa and 9.5–95 MPa and 4 cycles/min for the pressure range of 28.5–85.5 MPa for 111 L accumulators. For all the 76 L accumulators, the cycling rate during the pressure cycle was 10 cycles/minute. After the tests, the leakage positions were carefully investigated. The pressure ranges and leakage positions are listed in Table 1 for 111 L accumulators and Table 2 for 76 L accumulators. For each case, more specific leakage positions could be found in Figs. 2 and 3, respectively.

### Axisymmetric Finite Element Modeling Method.

where *t* is the thickness at the desired point and suffix *c* denotes the value at the cylinder part. The thickness *t* never increases to infinity even though near the turn-around point, where *α* becomes 90 deg. Its upper limit exists and the thickness decreases near the turn-around point, since fiber bundles slip. In hoop layers, the end position and the attenuation length will be set to adjust the outer surface at equator to fit the actual shape of the accumulator. In high angle helical and helical layer, attenuation length and maximum thickness are set to adjust the outer surface of dome part to fit the actual shape of the accumulator. The definitions of the parameters are illustrated in Fig. 4. FE models are created using the developed software, frontcomp_tank in accordance with the method explained above, and the FE analyses are conducted using commercial software, ansys with APDL [17]. The inner and outer surfaces of the liner and the outer surface of FRP layer are adjusted to the real shape by changing shape parameters such as maximum thickness and attenuation length parameters. FE models using axisymmetric second order triangular elements are shown in Fig. 5(a) for 111 L accumulator and Fig. 5(b) for 76 L accumulator. For considering symmetry, only a quarter of the accumulator is modeled. The number of elements and number of nodes are 177,820 and 357,259 for the 111 L accumulator and 420,562 and 843,309 for the 76 L accumulator, respectively. The plug is not modeled, so the axial load in *z* direction is applied at the top of the liner as shown in Figs. 5(a) and 5(b). The liner is modeled as elastic-plastic continuum using the A6061-T6's material properties listed in Tables 3 and 4, respectively. CFRP layers are modeled as orthogonal elastic continuum, the material properties of which are calculated based on the rule of mixture [18,19]. The volume fraction of fiber is 0.65 for both cases. All material properties in Tables 3 and 4 are provided from the manufacturers.

Materials | Properties | Values |
---|---|---|

A6061-T6 | Young's modulus | 69 GPa |

Poisson's ratio | 0.33 | |

Yield strength | 279 MPa | |

Tangential modulus | 924 MPa | |

Carbon fiber | Young's modulus | 290 GPa |

Poisson's ratio | 0.2 | |

Epoxy resin | Young's modulus | 2.7 GPa |

Poisson's ratio | 0.35 |

Materials | Properties | Values |
---|---|---|

A6061-T6 | Young's modulus | 69 GPa |

Poisson's ratio | 0.33 | |

Yield strength | 279 MPa | |

Tangential modulus | 924 MPa | |

Carbon fiber | Young's modulus | 290 GPa |

Poisson's ratio | 0.2 | |

Epoxy resin | Young's modulus | 2.7 GPa |

Poisson's ratio | 0.35 |

Materials | Properties | Values |
---|---|---|

A6061-T6 | Young's modulus | 69 GPa |

Poisson's ratio | 0.33 | |

Yield strength | 349 MPa | |

Tangential modulus | 2018 MPa | |

Carbon fiber | Young's modulus | 258 GPa |

Poisson's ratio | 0.28 | |

Epoxy resin | Young's modulus | 3.1 GPa |

Poisson's ratio | 0.35 |

Materials | Properties | Values |
---|---|---|

A6061-T6 | Young's modulus | 69 GPa |

Poisson's ratio | 0.33 | |

Yield strength | 349 MPa | |

Tangential modulus | 2018 MPa | |

Carbon fiber | Young's modulus | 258 GPa |

Poisson's ratio | 0.28 | |

Epoxy resin | Young's modulus | 3.1 GPa |

Poisson's ratio | 0.35 |

### Fatigue Design Code by American Society of Mechanical Engineers Code.

In this paper, fatigue life prediction is conducted based on the concept that the fatigue life of Type III accumulator is governed by the fatigue life of the liner. Its fatigue life is estimated on the basis of ASME B&PV Code, Section VIII, Division 3, article KD-3 [12] since leak-before-burst is found in the pressure cycle test. In the article, the S–N curve for the liner material A6061-T6 is given from the fatigue test of the specimen with safety factors, which are 2 on stress amplitude and 20 on number of cycles. The maximum mean stress effect is considered for getting the design fatigue curve [19], assuming tensile mean stress shortens the fatigue life.

In the calculation method of stress amplitude for fatigue life prediction, there are two important factors. One is that the fatigue life is governed by the maximum shear stress represented by the difference of the principal stresses. The other is that the maximum shear stress plane must be identified when the principal axes change during the loading cycle.

The procedure to calculate stress amplitudes (equivalent alternating stress intensities) is as follows:

Case 1. When principal axes do not change during the loading cycle

- Calculate stress differenceswhere $\sigma i$ is a principal stress.$Sij=\sigma i\u2212\sigma j\u2009(i=1,2,3)$(3)
Identify maximum and minimum stress differences during the loading cycle without changing directions during the pressurization process

- Calculate alternating stress intensity$Salt\u2009ij=0.5(Sij\u2009max\u2212Sij\u2009min)\u2009(i,j=1,2,3)$(4)
- For the nonwelded aluminum alloy, alternating stress intensity value of Eq. (4) becomes equivalent alternating stress intensity$Seq\u2009ij=Salt\u2009ij\u2009(i,j=1,2,3)$(5)

Case 2. When principal axes change during the loading cycle

Calculating alternating stress intensity by following Case. 1 for the plane parallel to the inner surface

Change axes to calculate alternating stress intensity

Calculate alternating stress intensity assuming the axes are principal axes.

Search for the maximum equivalent alternating stress by repeating process (2) and (3)

Identify the maximum equivalent alternating stress intensity and the axes to give it.

### Calculation of Equivalent Alternating Stress Intensities.

It has been known that maximum shear stress is a better criterion than maximum principal stress for the estimation of fatigue life of the pressure vessel [14]. In ASME code of pressure vessel, the maximum shear stress is regarded as the criterion of the fatigue life. However, the way to calculate the value is not so easy task especially when the direction of the principal stress changes during the loading cycles. That is partly because of the autofrettage pressure effect. After the autofrettage pressure is applied, the yielding region is investigated. As shown in Fig. 6(a) for 111 L accumulator and Fig. 6(b) for 76 L accumulator, except near the boss part, almost all region of liner is yielded. When the direction of the maximum principal stress changes during the pressurizing process, the plane yielding the maximum shear stress must be defined. Determining the plane can be done by following the procedure mentioned in the previous chapter. In Fig. 7, principal stress changes at cylinder parts and dome parts in both 111 L and 76 L accumulators are shown. As shown in Fig. 7(a) for 111 L accumulator and Fig. 7(c) for 76 L accumulator, at the cylinder part, the three principal stresses linearly change during pressurizing process because reyielding did not take place during the cyclic pressure was applied. The stresses at 0 Pa mean residual stresses after autofrettage pressure is relieved. $\sigma rr$ are the same as internal pressures. $\sigma zz$ are quite different for both accumulators because the yield strength of liner in 76 L accumulator is 17% larger than that in 111 L accumulator. As shown in Fig. 7(b) for 111 L accumulator and Fig. 7(d) for 76 L accumulator, at the upper dome part, the three principal stresses also linearly change during pressurizing pressure: *P *=* *0.0 Pa, and when the design pressure of 95.0 MPa is applied the maximum principal stress changes to $\sigma hp$. However, the principal plane remains the same all along with the pressurizing process. In Figs. 7(b) and 7(d), $\sigma \u22a5$ means the stress component in perpendicular direction. At dome part indicated by circle in Fig. 6(a) for 111 L accumulator and Fig. 6(b) for 76 L accumulator, the plane of maximum principal stress changes as internal pressure increases. Therefore, the axes which yield the maximum equivalent alternating stress are searched for with an increment of 1.0 deg in *r*–*z* plane. The axes deviate 40 and 29 deg from *r*–*z* axes in counterclockwise direction for 111 L case and 76 L case as shown in Figs. 7(b) and 7(d).

The principal axes change at the upper dome part is illustrated in Fig. 8 during the pressurizing process in the 111 L accumulator. After depressurizing of the autofrettage, the direction of the maximum stress is perpendicular to liner surface (See Fig. 8(a)). However, the direction starts to change to the counterclockwise while the internal pressure *P* increases (See Fig. 8(c)). Finally, in some elements, the direction of the maximum principal stress is found to be in hoop direction or in the direction along the surface at the design pressure. This occurs only upper dome part or boss part. At cylinder part and lower dome part, the principal stress axes never change during the pressurizing process.

### Results and Discussion.

As the three cyclic pressure tests for both 111 L and 76 L accumulators were conducted with different pressure ranges, FE analysis according to the loading history, which consists of autofrettage, depressurizing, and pressurizing was carried out. During pressurizing process, the equivalent alternating stress intensities based on the ASME code is calculated. The results for the 111 L accumulators with the pressure range of 0–85.5 MPa, 9.5–95 MPa, and 28.5–85.5 MPa are shown in Fig. 2. For all the cases, the maximum values appear in upper dome part. The leak position with the pressure range of 28.5–85.5 MPa is in dome part, and the analyzed equivalent alternating stress intensity is the maximum at the position. For the pressure range of 0–85.5 MPa and 9.5–95 MPa, leak positions are in cylinder part; however, the alternating stress intensity in cylinder part is lower than those in dome or boss part. Mean stresses were calculated according to ASME code [12]. However, the mean stresses in dome or boss part were higher than those in cylinder part, so mean stress effect was not the reason why cylinder parts were the leak positions for the pressure range of 0–85.5 MPa, and 9.5–95 MPa.

The results for the 76 L accumulators with the pressure range of 0–90 MPa, 50–90 MPa, and 70–90 MPa are shown in Fig. 3. For all the cases, the maximum values appear in cylinder parts, and the analyzed equivalent alternating stress intensity is the maximum at the cylinder.

Considering that the leak positions for the various pressure ranges in 76 L accumulators are the maximum alternating stress intensity positions, cylinder part leaks for the 111 L seem to be irregular cases. Probably, there were initial defects in cylinder part for a couple of 111 L accumulators.

With the calculated equivalent alternating stress intensities in leak positions and cycle test results, the points were plotted in the *S*–*N* curve of the liner material, A6061-T6 in Fig. 9. There are three curves [20]. One is the best fit curve from specimen fatigue test results, the second is design fatigue curve with consideration of safety factor and maximum mean stress. The *S*–*N* curve, which is in ASME code, is the same as the red curve in Fig. 9. The plotted *S*–*N* relations for the 111 L accumulators are settled between two curves of best fit curve and design fatigue curve of zero mean stress even for 28.5–85 MPa case. For 76 L accumulator's results, one plotted point is over the best fit curve. The result should be caused by the differences of each liner's ultimate strength and yield strength. Liner's yield strength for 76 L accumulator is about 33% larger than the value for pressure vessels used for ASME curves [21]. As shown in Fig. 7, the absolute values of residual stresses in 76 L accumulator are much larger than those in 111 L accumulator. That is why the slope of plotted data of 76 L accumulator and 111 L accumulator is quite different as shown in Fig. 9. However, all the plotted data show that the fatigue life of Type III accumulator by the design fatigue curve can still be predicted conservatively.

### Conclusions.

Fatigue design methodology by FE analysis based on the ASME code for Type3 CFRP accumulators has been proposed in this research.

FE model is created for FE analysis by following basic equations with a few adjustment parameters which can be determined by comparison with the actual shape of the accumulators.

Based on the design code, ASME Boiler & Pressure Vessel Code, Sec. VIII, Division 3, article KD-3, leak-before-burst CFRP accumulator's fatigue analysis have been carried out.

Three pressure cycle tests for 111 L and 76 L accumulators have been conducted, and investigation for leak positions and number of cycles to leak have been done. Except a couple of cases, the leak positions have good agreement with maximum alternating stress intensity positions.

With the test results as well as analysis results, it is found that number of cycles to leak in cyclic pressurizing test is reasonably predicted by the ASME

*S*–*N*curve.

## Acknowledgment

This paper was based on results obtained from a project, JPNP18011, commissioned by the New Energy and Industrial Technology Development Organization (NEDO).

## Data Availability Statement

The authors attest that all data for this study are included in the paper.