A Study on an Improved Fatigue Life Prediction Method for Type IV Cylinders

Abstract

With the rapid development of the hydrogen economy, Type IV composite pressure vessels have emerged as the core components of on-board hydrogen storage systems. However, accurate fatigue life prediction remains a critical bottleneck limiting their design optimization and safe operation. Existing methods often exhibit prediction errors exceeding ±50% due to the inherent scatter, anisotropy, and complex service environments of composites. This study proposes an improved simulation method for fatigue life prediction of Type IV cylinders. Systematic tension–tension fatigue tests were conducted on carbon fiber-reinforced polymer (CFRP) laminates at four ply angles (0°, ±15°, ±30°, ±45°) and PA6 liner at three temperatures (−30 °C, 25 °C, 82 °C) to establish comprehensive S-N curve databases. The results reveal that ply angle is the predominant factor governing CFRP fatigue performance, while temperature significantly influences PA6 behavior, and failure mode transitions from fiber fracture to matrix-dominated damage as ply angle increases. A fatigue analysis model was developed in nCode, incorporating the ply fatigue Algorithm to characterize the anisotropic fatigue behavior of CFRP overwraps. Full-scale validation on Type IV cylinders under cyclic pressure (2–87.5 MPa) confirmed the method’s effectiveness, achieving prediction errors of 11.5% and 35.3% for the two failed specimens, with failure locations well predicted. This study provides a rapid and reliable engineering calculation method and data support for the anti-fatigue design, safety assessment, and life management of Type IV cylinders.

1. Introduction

Driven by the global imperatives of energy transition and carbon emission reduction, hydrogen energy has attracted significant attention as a clean and efficient secondary energy source, with its associated industries developing rapidly [1]. Fuel cell vehicles represent a major application avenue for hydrogen energy, for which high-performance on-board hydrogen storage systems are a prerequisite for large-scale commercialization. The Type IV cylinder—a pressure vessel featuring a polymer liner (e.g., Polyamide 6, PA6) and a carbon fiber composite (e.g., T700/Epoxy CFRP) overwrap—has become the dominant technology for 70 MPa on-board storage due to its advantages of light weight and high hydrogen storage density, and is poised for large-scale industrial application [2,3,4,5,6,7]. However, Type IV cylinders undergo frequent hydrogen charge–discharge pressure cycles during service. Fatigue damage accumulation and ultimate failure within the CFRP overwrap are primary failure modes [2,6,8,9]. The fatigue life directly governs the vessel’s safety and service life, making it a critical focus of current research and development [10,11,12,13].

Accurate prediction of the fatigue life of Type IV cylinders is crucial. Currently, fatigue life prediction methods for composite structures can be broadly categorized into three types: the empirical S-N curve method, residual strength models based on damage accumulation theory, and progressive damage models based on continuum damage mechanics [14,15,16]. Among these, the S-N curve method is the most widely applied due to its simplicity and strong engineering applicability. This method establishes the relationship between stress amplitude (S) and fatigue life (N) through standard fatigue tests on materials or structures, and life prediction is typically performed using linear damage accumulation rules (e.g., Miner’s rule). However, the direct application of this method to complex wound structures like Type IV cylinders faces significant challenges. Firstly, CFRP exhibits pronounced anisotropy; its fatigue performance is highly dependent on the fiber orientation. The cylinder overwrap comprises plies with various winding angles (e.g., helical, hoop), making it difficult to accurately characterize the fatigue performance and define an equivalent stress for plies in different orientations [17,18]. Secondly, the actual stress state within the vessel structure is complex and involves significant mean stresses. Since baseline S-N curves are usually generated at a specific stress ratio (e.g., R = 0.1), accurate correction for the mean stress effect is critical [19,20,21,22]. Thirdly, Type IV cylinders operate over a wide temperature range (e.g., −40 °C to 85 °C, as stipulated in standards ISO 19881:2025), and the influence of temperature on the fatigue performance of both the CFRP and the liner material cannot be neglected [23,24,25,26,27,28].

The existing S-N curve method encounters significant errors in predicting the fatigue life of Type IV cylinders. These errors primarily stem from three sources. First, there is an inherent scatter in the fatigue data of composite materials. The intrinsic heterogeneity of composites, coupled with minor manufacturing process variations and the stochastic nature of defect distribution, leads to significant statistical scatter in fatigue test data, even under strictly controlled conditions. This introduces an inherent and difficult-to-eliminate background uncertainty into any prediction method reliant on such experimental data [29,30,31]. Second, there is an inadequate characterization of anisotropic fatigue behavior. The fatigue performance of CFRP is highly dependent on the fiber orientation. Traditional prediction methods often employ an S-N curve from a single ply angle (e.g., 0°) to represent structures with complex winding patterns (e.g., hoop and helical), or they account for the contribution of plies at different orientations through overly simplified rules. This approach fails to accurately capture the physical damage mechanism, wherein stress induces failure via distinct modes—such as fiber-dominated tensile failure versus matrix/interface-dominated shear failure—in plies of different orientations, thereby introducing a fundamental model error [4,32,33,34]. Third, there is insufficient consideration of, and a lack of data support for, the influence of key environmental factors, particularly temperature. Type IV cylinders operate over a wide temperature range, where temperature exerts a very significant influence on the fatigue performance of both the CFRP and the PA6 liner. However, traditional design approaches often lack systematic, multi-temperature fatigue property databases. Consequently, prediction models struggle to accurately assess the life attenuation caused by temperature variations, leading to further increased prediction errors under non-isothermal service conditions [25].

These three error sources are coupled, resulting in life predictions for complex structures like Type IV cylinders that often exhibit high scatter, low reliability, and error ranges frequently exceeding ±50%. Such performance is inadequate for directly guiding high-reliability design optimization and precise life assessment [35,36,37]. Although employing larger safety factors is a common engineering practice to compensate for uncertainties, this approach often leads to overly conservative and costly designs, and may still mask underlying risks [36,38,39].

To overcome these limitations, this study proposes an improved simulation-based method for fatigue life prediction. The method establishes a systematic workflow from material performance characterization to structural life prediction. Its core advancement addresses two key technical challenges: (1) The first lies in establishing a comprehensive S-N curve database for T700/Epoxy CFRP and PA6 liner materials through material-level fatigue tests conducted at multiple ply angles (0°, ±15°, ±30°, ±45°) and temperatures (−30 °C, 25 °C, 82 °C), thereby providing direct, high-fidelity input for subsequent simulations. (2) The second lies in developing an algorithm within the nCode simulation platform that can accurately characterize the anisotropic fatigue behavior of the CFRP overwrap. The algorithm operates by first extracting the fiber-direction stresses at the element level via coordinate transformation. It then determines an equivalent stress based on the difference in failure modes (employing maximum principal stress for hoop-dominant plies and shear stress for helical-dominant plies), incorporates an angle symmetry function to ensure ply continuity, and finally computes the fatigue life for a ply at any winding angle through linear interpolation based on the experimental database.

This study proposes an improved fatigue life prediction method for Type IV cylinders. The key contributions that differentiate this work from existing methods are as follows: (1) Literature gap addressed: Previous studies on Type IV cylinder fatigue either neglect the effect of varying fiber winding angles along the meridian, or require expensive experimental testing for each specific angle. This study fills this gap by developing an angular interpolation algorithm that enables S-N prediction at arbitrary angles based on a limited set of experimental data points. (2) Algorithm novelty: The proposed angular interpolation scheme is mathematically distinct from conventional approaches. Unlike simple linear interpolation between discrete S-N curves, this method fits basis functions to the angle-dependent S-N coefficients, enables extrapolation for winding angles not directly tested, and accounts for the physical constraint that ±θ angles exhibit equivalent fatigue behavior. This approach significantly reduces testing costs while maintaining prediction accuracy. (3) Integrated workflow: While individual components (FEM analysis, S-N curves, Miner’s rule) are well-established, their integration into an automated FEM-nCode coupling framework with material coordinate transformation is novel for Type IV cylinder applications. This integrated approach enables efficient design optimization that was not previously achievable. (4) Multi-factor database: The combined temperature-angle S-N database represents a systematic characterization that exceeds the scope of existing studies on Type IV cylinders. The 4 unique ply angles (0°, ±15°, ±30°, ±45°) correspond to the winding angles used in practice, as the helical winding process creates symmetric ±θ layers that share the same fatigue properties.

The theoretical basis, experimental methodology, and simulation framework are comprehensively presented, and the prediction accuracy is rigorously validated through full-scale cylinder fatigue tests, providing a reliable engineering tool for anti-fatigue design and safety assessment of Type IV hydrogen storage cylinders.

2. Experimental Section

2.1. Test Materials and Equipment

This study focuses on the CFRP and PA6 materials used in 70 MPa on-board Type IV hydrogen storage cylinders. The CFRP was based on a domestic T700-grade carbon fiber-reinforced epoxy resin system (SYT49S, Zhongfu Shenying Carbon Fiber, Lianyungang, China). Its density, measured via ASTM D792 drainage method, was 1.56 ± 0.06 g·cm⁻³ [40]. The mass fraction of carbon fiber, determined by the combustion method in accordance with ASTM D3171-22 (the most widely recognized method for determining fiber content in polymer matrix composites, with Procedure G—matrix burn-off in muffle furnace—well-suited to the T700/Epoxy system), was 69.8 ± 1.12%, corresponding to a volume fraction of approximately 60.49 ± 3.33% [41,42,43,44]. The volume fraction was calculated from the measured mass fraction using the density method specified in ASTM D3171-22: $V_{\mathrm{f}}=\left(m_{\mathrm{f}}/m_{\mathrm{f}}\right)\times 100\times {\rho }_c/{\rho }_{\mathrm{r}}$, where $m_{\mathrm{f}}$ and $m_{\mathrm{f}}$ are the final fiber mass (after matrix burn-off) and the initial specimen mass, respectively, and ${\rho }_c$ and ${\rho }_{\mathrm{r}}$ are the densities of the composite specimen and the T700 carbon fiber (as specified by the manufacturer: 1.8 g/cm³), respectively. The specimens for mechanical and fatigue testing were straight CFRP laminate specimens manufactured by filament winding. These specimens were designed with ply angles of 0°, ±15°, ±30°, and ±45° to simulate the stress states in the cylinder barrel associated with different winding angles (hoop and helical), and their dimensions conformed to the ASTM D3039/D3039M-17 standard [45]. The PA6 (Akulon^® F223-D, Royal DSM, Heerlen, Netherlands) specimens for mechanical and fatigue testing were dumbbell-shaped sheets produced by injection molding, with dimensions following the Type 1A specimen specification of ISO 527-2:2025 [46].

All fatigue tests were conducted on a microcomputer-controlled electro-hydraulic servo dynamic fatigue testing machine (PLW-100kN, Shenli Testing Machine, Shanghai, China). The machine was equipped with an environmental chamber (GDW-150-40, Jinan Wenteng Testing Instrument, Jinan, China), providing a controllable temperature range from −70 °C to 150 °C, as shown in Figure 1, to accommodate testing at the required temperatures [47,48].

2.2. Test Methods and Conditions

The testing procedure followed the ISO 13003:2003 standard [49]. A tension–tension fatigue test method was employed with a sinusoidal load waveform, a stress ratio (R) of 0.1, and a cyclic frequency controlled between 5 and 15 Hz to prevent significant specimen self-heating at higher frequencies [27,50]. The three testing temperatures (−30 °C, 25 °C, and 82 °C) were selected based on the service temperature envelope defined in ISO 19881:2025 and SAE J2579:2018, representing cold-climate, ambient, and elevated-temperature conditions, respectively [23,24]. For CFRP specimens, S-N curves were obtained at four ply angles with 5–9 stress levels per angle, ultimately yielding 1–10 valid specimens per stress level. For PA6 specimens, S-N curves were obtained at three temperatures with 5–6 stress levels per temperature, ultimately yielding 1–7 valid specimens per stress level. The S-N data were fitted to establish the fatigue curves for subsequent fatigue analysis.

The failure criterion for CFRP specimens was the occurrence of visible macroscopic failure modes, such as fiber breakage, delamination, and interlaminar shear failure [45]. PA6 specimens exhibited three failure modes: necking, fracture, and cumulative plastic deformation. The cumulative plastic deformation mode could lead to continuous (runaway) elongation of the specimen. In such cases, the number of cycles at which the specimen elongation reached 5% was defined as the fatigue life. The applied load, number of cycles to failure, and failure mode for each test were recorded [51].

2.3. Test Results

2.3.1. Fatigue Performance of Carbon Fiber-Reinforced Polymer (CFRP)

Figure 2 presents the S-N curves for 0° ply CFRP specimens at different temperatures. The fatigue life of CFRP decreases in a power-law manner with increasing fiber axial stress amplitude, ${\sigma }_{\mathrm{a},1}$. Temperature significantly influences the fatigue performance. At the low temperature of −30 °C, the fatigue resistance of the material is enhanced, with a pronounced improvement observed in the high-stress region. In contrast, at the elevated temperature of 82 °C, the performance of the resin matrix degrades, which may lead to a reduction in interface strength and, consequently, a slight decrease in fatigue life [52,53].

The test results for plies with different orientations were systematically compared. Figure 3 compares the S-N curves of specimens with different ply angles at room temperature. The results indicate that the fiber ply angle is one of the most critical factors governing the fatigue performance of CFRP. The 0° ply, where the fibers are aligned with the loading direction, exhibits superior fatigue resistance because the load is primarily carried by the high-strength carbon fibers. As the ply angle deviates from 0° to ±15°, ±30°, and ±45°, the fatigue performance declines rapidly. This decline occurs because an increasing proportion of the load is transferred to the matrix and the fiber–matrix interface, which constitute the weak links. Owing to the higher shear stress components, the ±45° ply exhibits the lowest fatigue life, with failure modes predominantly being matrix cracking and interlaminar shear failure [54]. The fiber-direction normal stress ${\sigma }_1$ and the in-plane shear stress ${\tau }_{12}$ can be derived from the applied stress ${\sigma }_{\mathrm{x}}$ through the stress transformation formula:

$$\left\{\begin{array}{l}{\sigma }_1={\sigma }_{\mathrm{x}}{\cos }^2(\alpha )\\ {\tau }_{12}=-{\sigma }_{\mathrm{x}}\sin \alpha \cos \alpha \end{array}\right.$$

(1)

where ${\sigma }_1$ is the fiber-direction normal stress (normal stress acting along the fiber axis); ${\sigma }_{\mathrm{x}}$ is the applied stress in the loading direction (far-field tensile stress); α is the ply angle (angle between fiber direction and loading direction); ${\tau }_{12}$ is the in-plane shear stress (shear stress resulting from the angled fiber orientation). Subscripts 1 and 2 denote the axes of the material (fiber) coordinate system aligned with the fiber direction, while subscript x denotes the axis of the laminate (specimen) coordinate system aligned with the loading direction. For a 0° ply (α = 0), the material and laminate coordinate systems are aligned, yielding ${\sigma }_1={\sigma }_{\mathrm{x}}$ and ${\tau }_{12}$ = 0. For plies at other angles, stresses must be transformed between these coordinate systems using Equation (1) to obtain the fiber-direction stresses required for S-N curve application.

The scatter in the fatigue test data was analyzed. Even with strict control over specimen preparation and testing conditions, CFRP fatigue life data exhibit inherent scatter. This scatter originates from the material’s intrinsic heterogeneity, the stochastic nature of defect distribution, and minor manufacturing process variations [55]. To ensure data validity, outliers with significant scatter were identified and removed using the Grubbs criterion [56].

Data screening confirmed a log-linear relationship between the fiber-direction stress amplitude ${\sigma }_{\mathrm{a},1}$ and the number of cycles to failure $N_{\mathrm{f}}$. Therefore, the experimental data were fitted using the two-parameter Basquin equation, a common model in fatigue and fracture mechanics, to derive the S-N curves for CFRP at different ply angles under room temperature conditions. The fitted curves are presented in

Table 1. Basquin coefficients (${\sigma }_{\mathrm{a},1}=a{\left(N_{\mathrm{f}}\right)}^b$) for CFRP laminates with different ply angles at room temperature.

Ply Angle	Fitting Parameters a	Fitting Parameters b	Correlation Coefficient ${\mathit{R}}^2$
0°	773.36	−0.06378	0.72
±15°	141.56	−0.06975	0.80
±30°	86.71	−0.10071	0.88
±45°	20.72	−0.08229	0.81

. The Basquin equation is given by:

$${\sigma }_{\mathrm{a},1}=a{\left(N_{\mathrm{f}}\right)}^b$$

(2)

2.3.2. Fatigue Performance of the Liner Material (PA6)

Figure 4 presents the S-N curves for the PA6 liner material at different temperatures. The results indicate that temperature exerts a profound influence on the fatigue performance of PA6. At the low temperature of −30 °C, the PA6 material exhibits its greatest fatigue resistance. In contrast, at the elevated temperature of 82 °C, material softening occurs, creep effects are intensified, and the fatigue life is significantly reduced. The cumulative plastic deformation of the polymer liner is a potential driver of fatigue failure in Type IV cylinders; therefore, its performance data are critical for accurate overall life prediction.

As the relationship between the stress amplitude ${\sigma }_{\mathrm{a}}$ and the cycle number $N_{\mathrm{f}}$ is log-nonlinear, the experimental data for PA6 were fitted using the three-parameter Equation (3) to derive the S-N fatigue curves at the different test temperatures, as summarized in

Table 2. Three-parameter exponential model coefficients (${\sigma }_a=A{\left(1-e^{-B{N}_{\mathrm{f}}}\right)}^C$) for PA6 at different temperatures.

Environmental Temperature	Fitting Parameters A	Fitting Parameters B	Fitting Parameters C	Correlation Coefficient ${\mathit{R}}^2$
−30 °C	20.07	6.83 × 10−10	−0.01181	0.82
Room temp	12.75	9.51 × 10−5	−0.02118	0.78
82 °C	5.56	2.47 × 10−4	−0.04553	0.73

.

$${\sigma }_{\mathrm{a}}=A{\left(1-e^{-B{N}_{\mathrm{f}}}\right)}^C$$

(3)

2.3.3. CFRP Failure Mode Analysis

The fatigue fracture surfaces were observed and the failure modes were classified with reference to the ASTM D3039/D3039M-17 standard. The dominant failure mode for the 0° ply specimens was longitudinal splitting and explosive failure, indicative of brittle fracture characteristics. In contrast, specimens with off-axis plies exhibited fracture surfaces with more complex morphologies, showing clear evidence of matrix cracking, fiber pull-out, delamination, and interlaminar shear failure (as shown in Figure 5). This indicates a transition in the fatigue damage mechanism: as the ply angle increases, damage accumulation shifts from being primarily fiber-dominated to being governed by the matrix and the fiber–matrix interface. Understanding these failure modes is crucial for informing the selection of appropriate damage parameters in life prediction models.

3. Simulation Model Construction

3.1. Framework of the Fatigue Life Prediction Method

The simulation-based fatigue life prediction method for Type IV cylinders proposed in this study is founded on the S-N curve method and ply fatigue algorithm. Its core framework is illustrated in Figure 6. The workflow consists of the following key steps: (1) Systematic material-level testing is conducted to obtain the fundamental S-N curves for CFRP at various ply angles and temperatures. (2) A finite element model of the Type IV cylinder is developed, and a static analysis is performed to determine the stress field under cyclic pressure loading. (3) The resulting stress field is imported into the specialized fatigue analysis software nCode(ver 2022.1). Within nCode, the fatigue damage and life for each element in the composite layer are calculated by integrating the material S-N curve database, a mean stress correction model, and the ply fatigue algorithm. (4) Finally, the life of the composite overwrap is predicted based on Miner’s linear cumulative damage rule, and the prediction is validated against full-scale cylinder fatigue tests.

3.2. Finite Element Static Model

A finite element model of the Type IV cylinder was developed using the commercial software Abaqus(ver 2021). The model comprises the CFRP overwrap, the PA6 liner, and the Al6061-T6 metal boss. The mesh was composed of axisymmetric elements (CAX4). The fiber direction, thickness, and material properties for each layer were defined using the ply property functionality in Abaqus [57,58,59]. CAX4 axisymmetric elements were selected for the finite element model based on the rotational symmetry of the Type IV cylinder. This approach reduces computational cost by representing the full 3D structure with a single cross-sectional model. Mesh sensitivity analysis with five mesh densities confirmed that the third (162,791 nodes) mesh level provides converged results within 1% of the finer meshes, ensuring solution accuracy while maintaining computational efficiency.

The ply angle α varies along the meridian direction of the cylinder. This angle represents the orientation of the fibers relative to the meridian and ranges from 0° to 90°. In the finite element model, this continuous variation in fiber orientation was accurately represented by defining appropriate local coordinate systems and ply sequences [60].

The constitutive model for the CFRP was an orthotropic linear elastic model. Its engineering constants—including the elastic moduli ($E_1$, $E_2$, $E_3$), Poisson’s ratios (${\nu }_{12}$, ${\nu }_{13}$, ${\nu }_{23}$), and shear moduli ($G_{12}$, $G_{13}$, $G_{23}$)—were determined from tensile tests on unidirectional laminates. The PA6 liner was modeled using a bilinear elastic-plastic constitutive model, with its engineering constants obtained from standard tensile tests. The engineering constants for the Al6061-T6 boss material were taken from the Ref [61]. All material constants used as input for the static finite element analysis are listed in

Table 3. Material engineering constants used as input for the finite element model.

Component	Materials	Parameter	Sample	Unit	Value
Fiber layer	T700/Epoxy CFRP	1-direction tensile modulus	E1	MPa	151,500
		2-direction tensile modulus	E2	MPa	8830
		3-direction tensile modulus	E3	MPa	8830
		12-direction Poisson’s ratio	υ12		0.307
		13-direction Poisson’s ratio	υ13		0.307
		23-direction Poisson’s ratio	υ23		0.45
		12-direction shear modulus	G12	MPa	5070
		13-direction shear modulus	G13	MPa	5070
		23-direction shear modulus	G23	MPa	3050
Liner	PA6	Tensile modulus	E	MPa	1010.635
		Poisson’s ratio	υ		0.4
		Yield strength	Rp0.2	MPa	30.187
		Elongation	εf	%	108.1
Boss	Al6061-T6 [61]	Tensile modulus	E	MPa	68,000
		Poisson’s ratio	υ		0.33
		Yield strength	Rp0.2	MPa	270
		Elongation	εf	%	14.8

.

The finite element model was validated at two complementary levels prior to fatigue life prediction.

• Material-level validation. For the PA6 material, an FEM model of the standardized tensile coupon (ISO 527-2 Type 1A) was built using the elastic–plastic bilinear constitutive model. The simulated stress–strain curve showed good agreement with the experimental data across the elastic region, yield transition, and plastic plateau, confirming that the extracted parameters ($E$ = 1010.635 MPa, $R_{p0.2}$ = 30.187 MPa) are consistent with the constitutive model used in the cylinder FEM. For the CFRP overwrap, the nine orthotropic elastic constants were directly adopted from standardized tensile tests (ASTM D3039/D3039M-17) and used as the input of a linear-elastic constitutive model, where the fatigue behavior is handled through the ply fatigue algorithm on top of the linear-elastic stress field.
• Structural-level validation. The cylinder FEM was validated against the experimentally measured burst pressure of 181 MPa. The CFRP tensile strength exhibits a 95% confidence interval of [2142, 2811] MPa. The lower bound of the predicted burst pressure corresponds to the internal pressure at which the maximum principal stress in the fiber layer first reaches 2142 MPa, and the upper bound corresponds to the pressure at which it first reaches 2811 MPa. Two pressure levels were evaluated: at 175 MPa, the peak fiber stress reached 2229.708 MPa (exceeding the lower bound), indicating that the minimum predicted burst pressure is below 175 MPa; at 234 MPa, the peak fiber stress reached 3808.129 MPa at the dome/polar boss interface (exceeding the upper bound), indicating that the maximum predicted burst pressure is 234 MPa. The predicted burst range of [175, 234) MPa encloses the experimental value of 181 MPa, providing a direct verification of the cylinder-level load-bearing capacity.

The loading and boundary conditions were configured to simulate the cylinder undergoing a pressure cycle between its minimum (2 MPa)- and maximum-rated working pressures (70 MPa/87.5 MPa). A pressure load was applied to the model’s inner surface, while rigid body displacements were constrained. A nonlinear static analysis, which accounted for geometric nonlinearities, was performed to obtain the stress and strain fields at both the maximum and minimum pressure levels. These results served as the input for the subsequent fatigue analysis in nCode.

3.3. nCode Fatigue Analysis Model

The stress results from the finite element static analysis (in OP2 file format) were imported into the fatigue analysis module of nCode software.

Material Property Definition and S-N Curve Library: Custom fatigue material definitions for CFRP and PA6 were created within the nCode material library. For the CFRP, rather than assigning a single S-N curve, a family of S-N curves was defined, with the curves parameterized by both ply angle and temperature. The S-N curve data—specifically, the fitted parameters of the Basquin equation—obtained from the experimental tests for the 0°, ±15°, ±30°, and ±45° plies at the three temperatures were all entered into this database. Each curve in the library corresponds to a unique set of test conditions (ply angle and temperature).

Mean Stress Correction: In service, the cylinder experiences a pulsating pressure cycle, resulting in a complex stress state where the stress ratio R varies spatially and significant mean stresses are present. The nCode software incorporates several established models for mean stress correction, such as the Goodman, Gerber, and Soderberg models. Based on the material behavior and a comparative assessment, the Gerber model was selected for this study due to its satisfactory correction performance. This model was applied to adjust the baseline S-N curves (typically generated at R = 0.1 or R = −1) to account for the effect of the actual mean stress on the predicted fatigue life.

Ply fatigue Algorithm: This constitutes the core innovation of the simulation model. Within the CFRP overwrap, the fiber orientation varies from one finite element to another. Consequently, the fatigue life $N_{\mathrm{f}}$ for a given ply depends on both its local winding angle α and the local equivalent stress $\sigma$, i.e., $N_{\mathrm{f}}=N_{\mathrm{f}}\left(\alpha ,\sigma \right)$. Determining this functional relationship is essential. In the nCode workflow, the fiber direction for each element is automatically retrieved from the finite element model. The choice of the equivalent stress parameter $\sigma$ is based on the dominant failure mode associated with the fiber direction. For hoop-oriented plies, where failure is primarily driven by fiber tensile fracture, the fiber-direction normal stress ${\sigma }_1$ is employed as the equivalent stress. In contrast, for helically oriented plies, where interlaminar shear failure is predominant, the in-plane shear stress ${\tau }_{12}$ is used as the equivalent stress. This approach ensures that the stress metric driving the fatigue calculation is physically consistent with the expected damage mechanism.

The stresses in the material coordinate system (${\sigma }_1$, ${\sigma }_2$, ${\tau }_{12}$) are obtained from the finite element output stresses ($S_{11}$, $S_{33}$, $S_{13}$) in the elemental coordinate system using the coordinate transformation formula:

$$\left\{\begin{array}{c}{\sigma }_1\\ {\sigma }_2\\ {\tau }_{12}\end{array}\right\}=\left[\begin{array}{ccc}{\cos }^2\alpha & {\sin }^2\alpha & 2\sin \alpha \cos \alpha \\ {\sin }^2\alpha & {\cos }^2\alpha & -2\sin \alpha \cos \alpha \\ -\sin \alpha \cos \alpha & \sin \alpha \cos \alpha & {\cos }^2\alpha -{\sin }^2\alpha \end{array}\right]\left\{\begin{array}{c}{S}_{11}\\ S_{33}\\ S_{13}\end{array}\right\}$$

(4)

where ${\sigma }_1$ and ${\sigma }_2$ are the normal stresses in the material (fiber) coordinate system; ${\tau }_{12}$ is the shear stress in the material coordinate system; $S_{11}$ and $S_{33}$ are the normal stress components output from the CAX4 element in the elemental coordinate system; $S_{13}$ is the shear stress component output from the CAX4 element in the elemental coordinate system; and α is the ply angle (rotation angle between elemental and material coordinate systems). This transformation matrix enables stress components to be expressed in the material coordinate system aligned with the fiber direction, which is essential for applying the ply-angle-specific S-N curves in the fatigue analysis.

Furthermore, the algorithm accounts for the symmetry in the fatigue response of helical plies. For instance, a 75° helical ply and a 15° helical ply, when subjected to the same elemental stress state, should experience the same equivalent stress magnitude. This is because the 75° ply (winding angle close to 90° with respect to the cylinder axis) primarily carries hoop stress (the circumferential stress acting perpendicular to the cylinder’s longitudinal axis, which tends to expand the cylinder radially under internal pressure), while the 15° ply (winding angle close to 0° with respect to the cylinder axis) primarily carries axial stress (the longitudinal stress acting along the cylinder’s axis, which tends to elongate the cylinder under internal pressure). However, both plies are oriented symmetrically with respect to the 45° direction. This symmetry arises from the fact that both 0° (axial) and 90° (hoop) fibers carry load along their respective directions. To enforce this physical symmetry in the fatigue calculation, a symmetry function about 45° was defined. The symmetry function is given by:

$$\beta =\beta \left(\alpha \right)=\left\{\begin{array}{l}\alpha ,\alpha \in \left[0,{45}^{°}\right]\\ -\alpha +{90}^{°},\alpha \in \left({45}^{°},{90}^{°}\right]\end{array}\right.$$

(5)

where $\beta$ is the symmetrized ply angle (effective ply angle after symmetry transformation, ranging from 0° to 45°); α is the original ply angle (angle between fiber direction and cylinder axis); and $\beta \left(\alpha \right)$ is the symmetry function that maps any original ply angle to its equivalent angle in the [0°, 45°] range.

For plies with $\alpha$ $\in$ [0°, 45°], $\beta$ equals $\alpha$ directly. For plies with $\alpha$ $\in$ (45°, 90°], the function $\beta =-\alpha +90°$ ensures symmetry about the 45° direction. This transformation ensures that helical plies with angles $\alpha$ and $(90°-\alpha )$ are treated equivalently in terms of their fatigue life contribution.

The S-N curve for an intermediate winding angle $\beta$ is then determined through bilinear interpolation using the S-N curve parameters (e.g., the Basquin parameters $a$ and $b$) from two adjacent, experimentally characterized angles (e.g., ±15° and ±30°). In this way, the fatigue life $N_{\mathrm{f}}(\beta ,\sigma )$ for CFRP at any winding angle $\beta$ under a given equivalent stress $\sigma$ can be established. This completes the mathematical characterization of the material’s anisotropic fatigue behavior with the algorithm, as illustrated in Figure 7.

Damage Accumulation and Life Calculation: Fatigue life prediction was based on Miner’s linear cumulative damage rule. Failure is assumed to occur when the accumulated damage index $D$ reaches or exceeds 1, where $D$ is defined as:

$$D={\displaystyle \sum \left(N_{\mathrm{i}}/N_{\mathrm{fi}}\right)}\ge 1$$

(6)

where $N_{\mathrm{i}}$ is the number of cycles experienced at the i-th stress level, and $N_{\mathrm{f}\mathrm{i}}$ is the fatigue life (number of cycles to failure) at that stress level, as determined from the appropriate S-N curve.

Within the nCode workflow, the entire post-processing sequence—including stress cycle counting via the rainflow method, application of the mean stress correction, S-N curve lookup and interpolation, damage calculation, and damage summation—is performed automatically. The software finally outputs the predicted fatigue life (in cycles) and a logarithmic damage contour plot for each element in the model.

3.4. Full-Scale Cylinder Fatigue Test Validation Model

To validate the accuracy of the simulation method, full-scale fatigue tests were performed on Type IV cylinders. The tests were conducted in accordance with ISO 19881:2018 standards [23]. The cylinders underwent cyclic pressure loading from 2 MPa to the maximum working pressure at room temperature until leakage or rupture occurred. The number of cycles to failure (fatigue life) for each cylinder was recorded. Subsequently, post-test dissection analysis was carried out to identify the primary fatigue damage locations and failure modes.

4. Analysis and Discussion

4.1. Simulation Stress Analysis and Life Prediction Results

A simulation model based on the actual geometry and service conditions of cylinder vessel-1 was established, as shown in Figure 8. Fatigue life prediction was then conducted for this specific Type IV cylinder design.

Figure 9 presents the stress contour of vessel-1 under the maximum working pressure. The high-stress regions within the fiber layer are primarily located in the transition zone between the cylinder barrel and the dome, as well as near the port opening. The liner exhibits high stresses predominantly at its interface with the metal boss, whereas the boss itself shows high-stress concentrations at its connection to the composite overwrap. As evident from Figure 9, the fiber layer is primarily subjected to tensile stresses, the liner to compressive stresses, and the boss experiences a combination of both tensile and compressive stresses. The fibers in the region near the equator of the barrel and dome are subjected to simultaneous hoop and axial stresses, making this area a critical focus for potential fatigue failure.

Figure 10 presents the logarithmic fatigue life contour obtained from the nCode calculation. The prediction results indicate that the region with the minimum predicted fatigue life is located near the equator of the dome. This location correlates with the region experiencing the maximum hoop stress and where the principal stress direction in the CFRP layer deviates from the local fiber orientation. The predicted minimum life is 24,699 cycles.

4.2. Comparison and Validation with Full-Scale Test Results

A direct comparison was made between the simulation predictions and the experimental fatigue test results for three full-scale Type IV cylinders with different ply sequences, as summarized in

Table 4. Comparison of simulated predicted life and experimental life from full-scale cylinder tests.

Cylinder Number	Condition/MPa	Experimental Results		Simulation Results		Relative Error/%
		Number of Cycles	Failure Location	Number of Cycles	Failure Location
vessel-1	2~87.5	21,859	Dome	24,699	Near equator of dome	11.5
vessel-2	2~70	64,572	No failure	420,512	Cylinder barrel	-
vessel-3	2~87.5	22,793	Dome	16,850	Near equator of dome	35.3

. The experimentally measured fatigue lives (number of cycles to failure) for the three cylinders were 21,859, 64,572, and 22,793 cycles, respectively. The location of the minimum predicted life from the simulation model showed good agreement with the crack initiation sites observed in the tests. The relative error was calculated by comparing the predicted fatigue life with the measured life for each cylinder.

The calculated relative errors between the simulated and experimentally measured fatigue lives are within 35.3% for the cases where failure was observed. This level of prediction accuracy represents a significant improvement over traditional simplified S-N curve methods, which typically do not incorporate angle interpolation or mean stress correction and often report errors exceeding 50%. This comparison substantiates the effectiveness of the proposed simulation framework. Potential sources of the remaining prediction error include the inherent scatter in material fatigue properties, simplifications in the finite element model boundary conditions, residual stresses arising from manufacturing processes (e.g., non-uniform fiber tension during winding), and slight variations in test conditions (e.g., minor temperature fluctuations).

As shown in Table 4, the full-scale fatigue test for vessel-2 under the 2~70 MPa condition was suspended at 64,572 cycles, and the cylinder had not failed. The simulation model predicted a fatigue life of 420,512 cycles for this vessel. Although a quantitative error could not be calculated due to the absence of a true failure life, this prediction, when considered together with the result for vessel-1 (2~87.5 MPa), clearly demonstrates that the simulation model successfully captured the key trend that reducing the working pressure can significantly extend the fatigue life. Furthermore, an examination of the two cases with complete failure data—vessel-1 (error of +11.5%) and vessel-3 (error of −35.3%)—reveals that the method did not produce predictions that were systematically and significantly non-conservative (i.e., unconservatively high) compared to the measured failure lives. In fact, for vessel-3, the prediction was on the conservative side. This indicates that, within the framework of the current method, the prediction results possess acceptable reliability for engineering design assessment and tend to provide a conservative safety margin.

4.3. Parameter Influence and Sensitivity Analysis

Influence of Ply Angle on Fatigue Life: To assess the effect of fiber ply angle on the fatigue performance of CFRP, a comparative analysis of simulation models with different ply angles (0°, ±15°, ±30°, ±45°) was performed, leveraging the material test data. The results confirm that the ply angle is the predominant factor governing the fatigue performance of CFRP. The 0° ply exhibits optimal fatigue resistance because the applied load is primarily carried by the high-strength carbon fibers. As the ply angle deviates from the 0° direction, an increasing proportion of the load is transferred to the polymer matrix and the fiber–matrix interface. This shift in load-carrying mechanism leads to a significant decline in fatigue performance. The ±45° ply, subjected to the highest levels of in-plane shear stress, demonstrates the shortest fatigue life. These findings provide a quantitative basis for optimizing the winding sequence of the cylinder overwrap to enhance its fatigue resistance.

Comparison of Different Pressure Conditions: A comparison was performed between simulation predictions and experimental validation for the cylinder under two typical working pressure conditions: Condition 1 (2~87.5 MPa) and Condition 2 (2~70 MPa). Under Condition 1, the measured fatigue life was 21,859 cycles. Under Condition 2, the measured fatigue life exceeded 64,572 cycles with no failure occurring. The simulation predictions were highly consistent with the trend observed experimentally: reducing the working pressure significantly extends the cylinder’s fatigue life. Specifically, the predicted life under Condition 2 was approximately 20 times greater than that under Condition 1. These results demonstrate that a rational selection of the operating pressure range is an effective technical approach for enhancing the fatigue life of Type IV cylinders.

4.4. Method Discussion and Limitations

The fatigue life prediction simulation framework developed in this study offers several advantages: (1) Systematic approach: It forms a complete workflow from material-level characterization to structural-level simulation. (2) Improved accuracy: The incorporation of key techniques, including multi-angle interpolation and mean stress correction, has significantly enhanced prediction accuracy, as validated by full-scale tests. (3) Engineering practicality: Being implemented on commercial finite element and fatigue analysis software platforms, the method is readily applicable in industrial research and development.

The sample size for the full-scale cylinder fatigue validation (n = 3) is consistent with that reported in comparable studies. While the high cost and extended duration of such tests inherently limit the sample size, the three cylinders tested cover two distinct pressure ranges (2~87.5 MPa and 2~70 MPa), which is sufficient to demonstrate the predictive capability of the method across different loading conditions. Although material-level tests adequately characterized the influence of temperature (−30 °C to 82 °C) on the fatigue performance of CFRP and PA6, full-scale tests under temperature variations were not conducted due to budgetary constraints. Nevertheless, the proposed methodological framework is inherently extensible to such conditions.

The method, however, has certain limitations: (1) Simplified damage mechanics: The S-N curve approach coupled with Miner’s rule is an empirical, phenomenological methodology. It does not explicitly model the evolution of progressive damage mechanisms within the CFRP, such as matrix cracking, delamination, fiber breakage, and fiber–matrix interfacial damage. The accuracy is therefore limited by inherent S-N assumptions: constant amplitude loading; linear damage accumulation; self-similarity of S-N curves. For applications requiring detailed damage evolution modeling, progressive damage methods may be more appropriate. (2) Environmental factors: The current model primarily addresses temperature effects. It does not sufficiently account for other complex environmental couplings, such as humidity, exposure to hydrogen, or long-term creep. (3) The prediction accuracy is inherently limited by the scatter present in the underlying material S-N curve database. The moderate R² values observed in the S-N curve fitting (CFRP: 0.72–0.88; PA6: 0.73–0.82) reflect the inherent variability in composite and polymer fatigue data. For CFRP, this scatter originates from microstructural heterogeneity, stochastic defect distribution, and processing-induced imperfections. PA6, as a semi-crystalline polymer, exhibits temperature-dependent viscoelastic behavior that contributes additional scatter across test temperatures. The three-parameter exponential model was selected for PA6 to capture this sigmoidal fatigue behavior, though the moderate R² values indicate that temperature effects on polymer fatigue remain complex. The establishment of a comprehensive S-N database requires substantial experimental investment, and prediction accuracy is highly dependent on the completeness and quality of this database. (4) Failure criterion: The failure criterion is currently defined by a cumulative damage index of D = 1. Since actual failure in CFRP structures can be diverse and complex, determining a more physically precise failure threshold warrants further investigation.

5. Conclusions

This study addressed the engineering challenge of low accuracy in fatigue life prediction for filament-wound Type IV pressure vessels. A systematic investigation was conducted, encompassing material fatigue testing, development of an improved simulation model, and full-scale validation. The main conclusions are as follows:

• A comprehensive S-N curve database was established through tension–tension fatigue tests on CFRP at various ply angles (0°, ±15°, ±30°, ±45°) and temperatures (−30 °C, 25 °C, 82 °C). The results reveal that the ply angle is the predominant factor governing the fatigue performance of CFRP, while temperature significantly influences the behavior of the PA6 liner material. Analysis of failure modes indicates a transition in the dominant damage mechanism from fiber fracture to matrix- and interface-driven damage accumulation as the ply angle increases.
• A simulation-based method for predicting the fatigue life of Type IV cylinders was developed. Its core innovation is the integration of a multi-angle anisotropic fatigue algorithm for the fiber layers. Implemented within the Abaqus and nCode software environment, this method enables accurate characterization of the anisotropic fatigue behavior of CFRP, overcoming the limitation of oversimplified angle treatment inherent in traditional approaches.
• Validation against full-scale Type IV cylinder fatigue tests demonstrated the method’s effectiveness. The location of the minimum predicted fatigue life correlated well with the experimentally observed failure sites. The prediction error was below 35.3%, which represents a significant improvement in accuracy over conventional simplified methods.
• Parameter studies confirmed that the fiber ply angle is the key parameter controlling CFRP layer fatigue. Furthermore, the simulation model successfully captured the important trend that reducing the operational pressure substantially extends the fatigue life.