Solid-state batteries represent a transformative advancement in energy storage technology, offering enhanced safety, higher energy density, and superior thermal stability compared to conventional liquid lithium-ion batteries. These attributes make solid-state batteries a promising candidate for powering electric vehicles with ranges exceeding 1,000 km. Central to the performance of solid-state batteries are solid electrolytes, which separate the electrodes and facilitate ion transport. Among these, polymer electrolytes, such as polyimide (PI), are widely used due to their flexibility and processability. However, polymer materials exhibit distinct mechanical behaviors under prolonged loading, particularly in high-temperature and high-humidity environments, where creep deformation can lead to issues like increased interfacial resistance, reduced efficiency, and potential failure. Understanding the creep behavior of polymer electrolytes in solid-state batteries is crucial for improving battery reliability and longevity. In this study, we investigate the creep characteristics of PI polymer under high-temperature and high-humidity conditions through experimental testing and numerical simulation, employing a modified Burgers model implemented in ABAQUS via user-defined subroutines.
Creep in polymers involves time-dependent deformation under constant stress, which is exacerbated by elevated temperatures and humidity. Unlike metals, polymers can exhibit significant creep even at room temperature, but under high-temperature and high-humidity conditions, molecular mobility increases, leading to accelerated deformation. This behavior is critical in solid-state batteries, where dimensional stability of the electrolyte affects ion transport and interfacial contact. Our experimental setup involved a computer-controlled tensile testing machine capable of simulating environments from -40°C to 150°C and 0% to 100% relative humidity (RH). We designed specimens according to standardized dimensions, with a gauge length of 50 mm, and conducted creep tests under two environmental conditions: ambient (approximately 20°C, 50% RH) and high-temperature high-humidity (60°C, 90% RH). Stress levels of 40 MPa, 100 MPa, and 120 MPa were applied, with a loading rate of 200 N/min, and each test lasted 14,000 seconds, repeated three times for consistency.
The experimental results, as summarized in Table 1, demonstrate that high-temperature and high-humidity conditions significantly enhance creep strain in PI polymer compared to ambient conditions. For instance, at 120 MPa stress, the total creep strain under high-temperature high-humidity reached approximately 0.08, whereas it was only about 0.02 under ambient conditions. This increase is attributed to the heightened molecular vibration and reduced intermolecular forces in polymers at elevated temperatures, which lower the Young’s modulus and promote viscous flow. Humidity further plasticizes the polymer, facilitating chain slippage and irreversible deformation. These findings underscore the importance of accounting for environmental factors in the design of solid-state batteries to prevent performance degradation.
| Stress (MPa) | Environment | Total Creep Strain | Time to Stabilization (s) |
|---|---|---|---|
| 40 | Ambient (20°C, 50% RH) | 0.005 | 8,000 |
| 40 | High-Temperature High-Humidity (60°C, 90% RH) | 0.025 | 6,000 |
| 100 | Ambient (20°C, 50% RH) | 0.015 | 7,000 |
| 100 | High-Temperature High-Humidity (60°C, 90% RH) | 0.055 | 5,000 |
| 120 | Ambient (20°C, 50% RH) | 0.020 | 6,500 |
| 120 | High-Temperature High-Humidity (60°C, 90% RH) | 0.080 | 4,500 |
To model this creep behavior, we adopted a modified Burgers model, which combines elastic, viscoelastic, and viscous components to capture both recoverable and irreversible deformations. The Burgers model consists of two spring elements and two dashpot elements, as described by the following constitutive equations. The ideal springs represent elastic behavior governed by Hooke’s law: $$\sigma = E \epsilon$$ where $\sigma$ is stress, $E$ is the Young’s modulus, and $\epsilon$ is strain. The dashpots represent viscous behavior following Newton’s law: $$\sigma = \eta \frac{d\epsilon}{dt}$$ where $\eta$ is the viscosity. In the modified version, one dashpot has a time-dependent viscosity to account for nonlinear creep.
The total strain in the Burgers model can be decomposed into three parts: instantaneous elastic strain ($\epsilon_1$), viscoelastic strain ($\epsilon_2$), and viscous strain ($\epsilon_3$). The differential equation for the model is given by: $$\sigma + \eta_1 \left( \frac{1}{E_1} + \frac{1}{E_2} \right) \dot{\sigma} = \eta_1 \left( 1 + \frac{E_2}{E_1} \right) \dot{\epsilon}_e + \left( \frac{1}{E_1} + \frac{1}{E_2} \right) \epsilon_e$$ where $E_1$ and $E_2$ are the moduli of the springs, $\eta_1$ is the viscosity of the first dashpot, and $\epsilon_e$ is the viscoelastic strain. For finite element implementation, this is extended to three dimensions using the Jacobian matrix to compute stress increments.
We developed a user material subroutine (UMAT) in ABAQUS to incorporate the modified Burgers model. The UMAT algorithm involves four analysis steps: loading, creep under constant stress, unloading, and recovery. During the creep step, the strain increment is split into viscoelastic and viscous parts. The viscous strain increment is computed as: $$\Delta \epsilon_{c}^{(n+1)} = \int_{t}^{t+\Delta t} \frac{3}{2} \frac{\dot{\bar{\epsilon}}_{c}^{(n+1)}}{\bar{\tau}} \mathbf{S}^{(n+1)} d\tau$$ where $\mathbf{S}$ is the deviatoric stress, and $\bar{\tau}$ is the equivalent stress. The stress update follows: $$\Delta \sigma^{(n+1)} = \mathbf{D}^e (\Delta \epsilon^{(n+1)} – \Delta \epsilon_{c}^{(n+1)})$$ with $\mathbf{D}^e$ being the elastic stiffness matrix. The UMAT ensures accurate simulation of creep and recovery by tracking state variables like accumulated viscous strain.
For finite element modeling, we created a 3D representation of the specimen using C3D8R elements, with a mesh size of 0.5 mm after convergence studies. Boundary conditions included fixed support on one end and applied stress on the other. The material parameters for the Burgers model were derived from experimental data: $E_1$ and $E_2$ were obtained from uniaxial tensile tests under corresponding environments, and the viscosities $\eta_1$ and $\eta_2$ were fitted from creep curves using nonlinear regression. Table 2 lists the fitted parameters for high-temperature high-humidity conditions.
| Parameter | Value | Unit |
|---|---|---|
| $E_1$ | 2.5 | GPa |
| $E_2$ | 1.0 | GPa |
| $\eta_1$ | 500 | GPa·s |
| $\eta_2$ | 100 · e^{-0.001t} | GPa·s |
The simulation results closely matched the experimental data, as shown in Figure 1, which plots strain versus time for different stress levels. Under high-temperature high-humidity conditions, the model accurately captured the rapid initial creep and the steady-state phase, though minor discrepancies occurred in the high strain-rate region due to limitations in the Burgers model for nonlinear viscoelasticity. The complete creep and recovery process, illustrated in Figure 2, demonstrates the irreversible strain remaining after unloading, which is critical for assessing long-term deformation in solid-state batteries. The strain contours from the simulation, as in Figure 3, visualize the progression from elastic deformation to creep and recovery, highlighting the regions of maximum strain.
Further analysis using the time-temperature superposition principle could extend this model to predict long-term behavior, but our focus here is on the acute effects of high-temperature and high-humidity environments. The creep strain rate can be described by a power-law equation: $$\dot{\epsilon}_c = A \sigma^n e^{-Q/RT}$$ where $A$ is a pre-exponential factor, $n$ is the stress exponent, $Q$ is the activation energy, $R$ is the gas constant, and $T$ is temperature. For PI polymer, we found $n \approx 1.5$ and $Q \approx 50$ kJ/mol under high-humidity conditions, indicating diffusion-controlled creep mechanisms. This aligns with observations in solid-state batteries where humidity accelerates aging.
In solid-state batteries, the implications of polymer creep are profound. For instance, creep-induced thinning of the electrolyte can lead to short circuits or increased ionic resistance, reducing the cycle life. Our model provides a tool for optimizing polymer selection and battery design to mitigate these issues. Future work could explore other polymers like PVDF or composites under varying humidity levels to enhance the performance of solid-state batteries.
In conclusion, our study demonstrates that high-temperature and high-humidity conditions exacerbate creep in polymer electrolytes for solid-state batteries, necessitating robust material models. The modified Burgers model, implemented via UMAT in ABAQUS, reliably simulates this behavior, aiding in the development of more durable solid-state batteries. This approach can be extended to other components, such as electrodes, to comprehensively address mechanical challenges in next-generation energy storage systems.
The integration of experimental data and numerical simulation underscores the importance of environmental factors in the mechanical behavior of polymers. As solid-state batteries evolve, accounting for creep under realistic operating conditions will be essential for achieving commercial viability. Our work contributes to this goal by providing a validated framework for predicting and mitigating creep-related failures in solid-state batteries.