In recent years, solid-state batteries have emerged as a promising alternative to conventional liquid lithium-ion batteries due to their enhanced safety, higher energy density, and superior thermal stability. These attributes position solid-state batteries as key enablers for electric vehicles targeting ranges exceeding 1,000 km. Companies like CATL, Quantum Scape, Solid Power, and Samsung SDI have developed solid-state batteries based on oxide and sulfide electrolyte systems. However, interfacial challenges such as high contact resistance, low ion mobility, creep, delamination, and fracture persist, particularly under extreme environmental conditions. Among the core components, solid polymer electrolytes play a critical role in isolating electrodes and facilitating ion transport. Understanding the creep behavior of these polymers under high-temperature and high-humidity conditions is essential for ensuring the long-term reliability and performance of solid-state batteries. Unlike metallic materials, polymers exhibit significant creep even at room temperature, but this behavior is exacerbated in harsh environments, leading to dimensional changes, increased internal resistance, and potential failure. This study focuses on the creep characteristics of polyimide (PI), a commonly used polymer electrolyte in solid-state batteries, under elevated temperature and humidity. Through experimental analysis and finite element simulation using a modified Burgers model, we aim to provide insights into material behavior that can guide optimization strategies for solid-state battery design.
The importance of studying creep in solid-state batteries cannot be overstated, as it directly impacts the mechanical integrity of the electrolyte layer. In high-temperature and high-humidity environments, polymer materials like PI undergo molecular chain mobility increases, leading to accelerated deformation under sustained stress. This can result in uneven electrode contact, elevated resistance, and reduced efficiency in solid-state batteries. Moreover, prolonged exposure may cause irreversible viscous flow, compromising the battery’s lifespan. To address this, we conducted creep experiments on PI samples under controlled conditions, comparing behavior at room temperature (approximately 20°C and 50% RH) with high-temperature and high-humidity settings (60°C and 90% RH). The experiments were performed using a microcomputer-controlled tension testing machine capable of simulating environments from -40°C to 150°C and 0% to 100% RH. Samples were designed according to modified standards, with dimensions of 100 mm × 10 mm and a gauge length of 50 mm, to fit the testing chamber. Creep tests were carried out at stress levels of 40 MPa, 100 MPa, and 120 MPa, each lasting 14,000 seconds, with three repetitions per condition to ensure statistical reliability.
The experimental results revealed that PI exhibits substantially higher creep strain under high-temperature and high-humidity conditions compared to room environments. For instance, at 120 MPa stress, the total strain after 14,000 seconds was approximately 0.08 in high-temperature and high-humidity settings, whereas it was only about 0.02 at room conditions. This disparity arises from increased molecular thermal energy and reduced intermolecular forces in polymers at elevated temperatures, which lower the Young’s modulus and enhance viscous flow. Humidity further plasticizes the material by absorbing moisture, facilitating chain slippage. Such behavior underscores the need for accurate constitutive models to predict long-term performance in solid-state batteries. To quantify this, we employed a modified Burgers model, which combines elastic, viscoelastic, and viscous elements to capture both recoverable and permanent deformations. The model consists of two spring elements and two dashpot elements, with one dashpot being time-dependent to account for nonlinear creep. The constitutive equations are derived as follows:
The stress-strain relationship for the Burgers model can be expressed as a differential equation. For the elastic part, Hooke’s law applies: $$ \sigma = E \epsilon $$, where \( E \) is the Young’s modulus. For the viscous elements, Newton’s law is used: $$ \sigma = \eta \frac{d\epsilon}{dt} $$, with \( \eta \) representing viscosity. The overall model behavior is described by:
$$ \sigma + \left( \frac{\eta_1}{E_1} + \frac{\eta_1}{E_2} \right) \dot{\sigma} = \frac{\eta_1}{1 + \frac{E_2}{E_1}} \dot{\epsilon}_e + \frac{1}{\frac{1}{E_1} + \frac{1}{E_2}} \epsilon_e $$
where \( \epsilon_e \) denotes the viscoelastic strain, and the parameters \( E_1 \), \( E_2 \), \( \eta_1 \), and \( \eta_2 \) are determined experimentally. For finite element implementation, this was extended to three dimensions using the Jacobian matrix in ABAQUS via a user-defined material subroutine (UMAT). The UMAT routine calculates stress increments based on strain increments, considering both the viscoelastic and viscous flow components. In the simulation, we defined four analysis steps: loading, creep holding, unloading, and recovery, to replicate the experimental process. The mesh sensitivity was verified, with a grid size of 0.5 mm selected for accuracy after convergence tests showed less than 1% variation compared to finer meshes.
To parameterize the model, we conducted uniaxial tensile tests under identical environmental conditions to determine the elastic modulus, while the other parameters were fitted from creep curves using nonlinear regression. The table below summarizes the fitted parameters for PI under high-temperature and high-humidity conditions (60°C, 90% RH):
| Parameter | Symbol | Value (High-Temp/High-Humidity) | Value (Room Temp/Room Humidity) |
|---|---|---|---|
| Elastic Modulus 1 | \( E_1 \) (MPa) | 1500 | 3000 |
| Elastic Modulus 2 | \( E_2 \) (MPa) | 500 | 1000 |
| Viscosity 1 | \( \eta_1 \) (MPa·s) | 1.5 × 105 | 3.0 × 105 |
| Viscosity 2 | \( \eta_2 \) (MPa·s) | 2.0 × 106 | 5.0 × 106 |
The simulation results demonstrated good agreement with experimental data, particularly in the steady-state creep phase. For example, at 100 MPa stress under high-temperature and high-humidity conditions, the simulated strain after 14,000 seconds was within 5% of the experimental value. However, discrepancies were noted in the initial rapid creep stage, where the model underestimated strain rates due to limitations in capturing high strain-rate sensitivity. The full creep and recovery curve, as predicted by the Burgers model, showed that upon unloading, the elastic and viscoelastic strains recovered, leaving a residual strain from the viscous flow. This behavior is critical for assessing the long-term deformation in solid-state batteries, as irreversible strain could lead to permanent damage in the electrolyte layer.
Further analysis involved comparing the creep strain evolution across different stress levels. The table below provides a summary of the maximum creep strain observed in experiments and simulations for PI under high-temperature and high-humidity conditions:
| Stress (MPa) | Experimental Strain | Simulated Strain | Relative Error (%) |
|---|---|---|---|
| 40 | 0.040 | 0.038 | 5.0 |
| 100 | 0.075 | 0.072 | 4.0 |
| 120 | 0.088 | 0.085 | 3.4 |
The finite element simulations also allowed for visualization of strain distribution throughout the sample. During the loading phase, elastic strain was uniformly distributed, while the creep phase showed progressive accumulation, particularly in the central gauge region. After unloading, the strain cloud indicated partial recovery, consistent with the Burgers model predictions. This comprehensive approach highlights the effectiveness of the modified Burgers model in simulating creep behavior for solid-state battery applications, though improvements are needed for high strain-rate regimes.
In conclusion, this study underscores the significant impact of high-temperature and high-humidity conditions on the creep behavior of polymer electrolytes in solid-state batteries. The experimental and numerical analyses confirm that PI undergoes enhanced creep deformation under such environments, which could compromise the performance and durability of solid-state batteries. The modified Burgers model, implemented via UMAT in ABAQUS, provides a robust framework for predicting creep strain, with simulations closely matching experimental results in the steady-state region. Future work should focus on refining the model for transient creep stages and exploring other polymer systems to broaden the applicability in solid-state battery design. By addressing these challenges, we can advance the development of reliable solid-state batteries capable of withstanding harsh operational conditions, ultimately contributing to the evolution of next-generation energy storage solutions.
The implications of this research extend to the optimization of solid-state batteries, where controlling creep-induced deformations is crucial for maintaining interfacial integrity. For instance, in solid-state batteries, even minor strains can lead to contact loss between electrodes and electrolytes, increasing resistance and reducing cycle life. Our findings suggest that material selection for solid-state batteries should account for environmental factors, and the Burgers model can serve as a tool for virtual prototyping. Additionally, the methodology developed here can be applied to other polymers used in solid-state batteries, such as polyethylene oxide (PEO) or poly(vinylidene fluoride) (PVDF), to assess their suitability under similar conditions. As the demand for high-performance solid-state batteries grows, understanding and mitigating creep behavior will be pivotal in achieving commercial viability and widespread adoption in electric vehicles and portable electronics.
To further elaborate on the model’s mathematical foundation, the total strain in the Burgers model can be decomposed into three components: instantaneous elastic strain \( \epsilon_1 \), viscoelastic strain \( \epsilon_2 \), and viscous strain \( \epsilon_3 \). The governing equations are:
$$ \epsilon = \epsilon_1 + \epsilon_2 + \epsilon_3 $$
$$ \epsilon_1 = \frac{\sigma}{E_1} $$
$$ \frac{d\epsilon_2}{dt} = \frac{\sigma}{\eta_1} – \frac{E_2}{\eta_1} \epsilon_2 $$
$$ \frac{d\epsilon_3}{dt} = \frac{\sigma}{\eta_2(t)} $$
where \( \eta_2(t) = A e^{Bt} \) is a time-dependent viscosity for the generalized dashpot, with \( A \) and \( B \) as fitting parameters. This formulation allows the model to capture nonlinear creep, which is common in polymers under high stress. In the finite element implementation, the incremental strain update in UMAT follows:
$$ \Delta \epsilon_{c}^{(n+1)} = \int_{t}^{t+\Delta t} \frac{3}{2} \frac{\tau}{\bar{\sigma}} \dot{\bar{\epsilon}}_{c}^{(n+1)} d\tau $$
$$ \Delta \sigma^{(n+1)} = \mathbf{D}^e \left( \Delta \epsilon^{(n+1)} – \Delta \epsilon_{c}^{(n+1)} \right) $$
where \( \mathbf{D}^e \) is the elastic stiffness matrix, and \( \Delta \epsilon_{c} \) is the creep strain increment. This approach ensures numerical stability and accuracy in simulating long-term behavior for solid-state battery components.
In summary, the integration of experimental data and advanced modeling provides a pathway for improving the reliability of solid-state batteries. As research progresses, addressing creep in solid-state batteries will remain a key focus, enabling the development of safer and more efficient energy storage systems. The insights gained from this work contribute to the broader goal of enhancing solid-state battery technology, paving the way for innovations that meet the demands of modern applications.