⚡ electrical engineering

Interlaminar Shear Degradation and Cohesive Zone Modelling of Thermally Aged CFRP Laminates

This study establishes a quantitative framework linking thermal aging history to interlaminar shear degradation in T700/epoxy CFRP laminates by combining experimental short beam shear tests with Bayesian-inferred cohesive zone parameters and temperature-dependent evolution models to accurately predict long-term interface behavior and mechanical response.

Original authors: Zhizhong Tan, Jinsheng Xu, Qixuan Song, Yixue Yin, Shuwen Wang, Zongtao Guo

Published 2026-09-24

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CC BY 4.0

Original authors: Zhizhong Tan, Jinsheng Xu, Qixuan Song, Yixue Yin, Shuwen Wang, Zongtao Guo

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Modern aircraft, wind turbines, and high-performance cars increasingly rely on a material that is as strong as steel but light as a feather: carbon fiber reinforced polymer. This material is made by layering thin sheets of carbon fibers embedded in a sticky plastic resin, much like a sandwich. While the fibers provide the strength, the resin holds them together and transfers the load from one layer to the next. However, these structures often face a silent enemy: heat. Over years of storage or service, exposure to warm air can slowly change the chemistry of the resin, making it brittle or causing the bond between the fibers and the plastic to weaken. This damage is often invisible to the naked eye, yet it can lead to layers peeling apart, a failure known as delamination, which can compromise the entire structure. Understanding exactly how heat ages this material is critical for predicting how long these machines can safely fly or operate.

A team of researchers at Nanjing University of Science and Technology set out to map this invisible decay. They focused on a specific type of carbon fiber composite, using a standard test where a short, thick block of the material is bent until it breaks. By heating samples to temperatures of 150, 180, and 200 degrees Celsius for periods ranging from one day to over a year, they watched how the material's ability to resist shearing forces changed. They did not just measure how much weight the samples could hold before breaking; they also looked at the broken surfaces under a powerful microscope and used advanced computer simulations to reverse-engineer the hidden properties of the material's internal layers. The goal was to create a mathematical model that could predict how the material would behave after years of aging, based on just a few weeks of testing.

The results revealed that heat does not simply make the material weaker in a straight line. At the lower temperature of 150 degrees Celsius, the material actually held slightly more weight after a few months of aging, suggesting that the heat might have helped the resin harden or settle further, a process known as post-curing. However, as the temperature rose to 180 and 200 degrees, or as the exposure time stretched toward 1,000 hours, the material began to degrade. After a full year at 200 degrees, the material retained about 91 percent of its original strength, a significant drop that signaled the onset of serious internal damage.

Looking closely at the broken pieces, the researchers saw a clear shift in how the material failed. Fresh samples broke in a messy mix of cracked resin and separated fibers. But the samples that had been baked at high temperatures for long periods showed a different story: the fibers were stripped clean of resin, and the layers had peeled apart cleanly along the interface. This indicated that the heat had weakened the glue-like bond between the fiber and the plastic, causing the layers to slide apart rather than the resin itself to shatter.

To understand the mechanics behind this, the team built a detailed computer model of the bending test. They used a sophisticated mathematical approach, similar to a highly efficient trial-and-error system, to guess the hidden properties of the interface between the layers. They adjusted three key numbers in their simulation: how stiff the bond was before it broke, how strong the bond was at the moment of failure, and how much energy it took to pull the layers apart once the damage started. By matching the computer's output to the real-world test data, they identified exactly how these three properties changed with time and temperature.

The study found that the strength of the bond was the primary factor controlling how much weight the material could hold, while the stiffness of the bond determined how the material behaved before it started to fail. The energy required to pull the layers apart governed how the damage spread after the peak load. Using the data from the shorter aging periods, the researchers created a set of equations that described how these properties evolved over time. When they used these equations to predict the behavior of the material after 1,000 hours of aging, their predictions were remarkably accurate, missing the actual experimental results by only about 1.5 percent on average.

This work provides a new way to look at the aging of composite materials. Instead of just measuring how much weight a sample can hold, the researchers have linked the visible performance to the invisible changes happening at the microscopic level. They have shown that by understanding the specific way heat alters the bond between layers, engineers can build models that accurately forecast the remaining life of a structure. This means that in the future, the safety and longevity of aircraft and other critical components could be assessed not just by how they look, but by a precise calculation of how their internal bonds have changed over time.

Technical Summary: Interlaminar Shear Degradation and Cohesive Zone Modelling of Thermally Aged CFRP Laminates

Problem Statement
Carbon fibre reinforced polymer (CFRP) laminates are critical for aerospace and automotive structures, yet their long-term reliability is threatened by thermal aging. Under high-temperature or thermo-oxidative environments, the epoxy matrix may undergo post-curing, oxidation, and embrittlement, while the fibre-matrix interface may debond. While previous studies have established that thermal aging reduces interlaminar mechanical properties, the quantitative relationship between macroscopic interlaminar shear strength (ILSS) degradation and the evolution of equivalent cohesive zone model (CZM) interface parameters remains insufficiently established. Conventional experimental approaches typically focus on strength retention or fracture morphology but fail to directly reveal how key interface quantities—such as stiffness, characteristic displacement, and fracture energy—evolve under coupled aging temperature and exposure time.

Methodology
This study integrates experimental characterization, finite element (FE) inversion, and evolutionary modelling to map thermal aging history to interlaminar shear response.

Experimental Protocol: T700/epoxy symmetric $[0^\circ]_{20}$ laminates were subjected to accelerated thermal aging at 150, 180, and 200 °C for durations ranging from 24 to 1000 hours. Interlaminar shear properties were evaluated using short beam shear tests (ASTM D2344/D2344M-22). Fracture surfaces were characterized via scanning electron microscopy (SEM) to observe damage morphology.
Finite Element Modelling: A 3D FE model of the short beam shear specimen was developed in Abaqus/Explicit. The model utilized an intralaminar orthotropic elastic constitutive law and a surface-based cohesive contact formulation with a bilinear traction-separation law to simulate interlaminar delamination.
Parameter Inversion: To identify the equivalent cohesive parameters (interface penalty stiffness $K$ , tangential nominal strength $t_{s0}$ , and mode II critical fracture energy $G_{IIc}$ ), a Bayesian optimization approach using the Tree-structured Parzen Estimator (TPE) algorithm (via the Optuna framework) was employed. This method minimized a multi-response objective function comprising normalized root mean square error (NRMSE) of the load-displacement curve, peak load/displacement errors, initial stiffness errors, and quasi-static energy penalties.
Evolution Modelling: Discrete equivalent parameters obtained from the inversion were fitted to temperature-dependent empirical models (exponential and stretched exponential functions) to describe parameter evolution over time. These models were calibrated using data from 24 to 500 hours and validated retrospectively against 1000-hour conditions.
Sensitivity Analysis: A perturbation analysis was conducted to determine the specific influence of each inverted parameter on peak load, displacement, stiffness, and energy absorption.

Key Results

Degradation Behavior: The interlaminar shear response exhibited non-monotonic behavior. At 150 °C, short and intermediate exposure times resulted in a slight increase in ILSS (up to 104.9% at 100 h), attributed to post-curing or structural stabilization. However, at 180 and 200 °C, ILSS decreased progressively with time. After 1000 hours at 200 °C, the strength retention was 91.4%. Notably, energy absorption before the peak load decreased earlier than ILSS in some conditions, suggesting that peak strength alone may underestimate early-stage aging damage.
Fracture Morphology: SEM analysis revealed a shift in failure mechanisms. Unaged and mildly aged specimens showed mixed matrix and interface failure. With prolonged high-temperature aging, the failure mode shifted toward delamination dominated by the interface, characterized by continuous exposed fibres and reduced matrix residue.
Parameter Evolution: The Bayesian inversion successfully identified distinct evolution trends for the cohesive parameters. $K$ and $t_{s0}$ at 150 °C showed an initial increase followed by degradation, whereas at 180 and 200 °C, they degraded exponentially. $G_{IIc}$ consistently decreased toward a residual value across all temperatures.
Model Accuracy: The temperature-dependent evolution models, calibrated on 24–500 h data, predicted the 1000 h conditions with a mean absolute percentage error (MAPE) of 1.45% for the equivalent interface parameters. The corresponding FE simulations using these predicted parameters reproduced the experimental load-displacement responses with an average normalized root mean square error (NRMSE) of 7.01%.
Optimization Efficiency: Comparative analysis demonstrated that the Bayesian TPE algorithm outperformed random search and Hooke-Jeeves methods in finding low-objective function regions with fewer finite element evaluations, particularly under limited computational budgets.

Key Contributions

Quantitative Linkage: The study establishes a quantitative route connecting thermal aging history (temperature and time) to equivalent interface degradation parameters ( $K$ , $t_{s0}$ , $G_{IIc}$ ) and macroscopic shear response.
Inverse Framework: It validates a Bayesian TPE-based inversion workflow capable of extracting physically meaningful interface parameters from macroscopic short beam shear data, overcoming the non-uniqueness issues of simple curve fitting.
Mechanism Clarification: Sensitivity analysis clarified the distinct roles of the identified parameters: $t_{s0}$ governs peak load and damage initiation; $K$ controls pre-peak elastic response; and $G_{IIc}$ regulates post-peak softening and energy dissipation.
Predictive Capability: The proposed empirical evolution models enable the retrospective extrapolation of interface properties to long-term aging conditions (1000 h) based on shorter-term data, providing a tool for service life assessment.

Significance and Claims
The paper claims to provide a "quantitative route" for mapping thermal aging to interlaminar shear response and equivalent interface degradation. It emphasizes that while the framework successfully links aging conditions to macroscopic responses and damage parameters within the tested range (150–200 °C, 24–1000 h), the proposed evolution models are empirical and limited to this specific experimental domain. The authors note that the Bayesian TPE method demonstrated superior search efficiency for this specific inverse problem but do not claim general statistical superiority over other algorithms in all contexts. The study concludes that evaluating ILSS alongside pre-peak energy absorption and using inverse modelling offers a more complete picture of thermal aging damage than relying solely on peak strength retention.

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