Molecular Dynamics Simulation for Evaluating Fracture Entropy of a Polymer Material under Various Combined Stress States

Numerical Simulations for Damage and Failure of a Polymer Material Subjected to Thermal Fatigue Loading

This study proposes a novel numerical approach to simulate damage accumulation and failure in polymer materials under thermal fatigue, using an entropy-based damage criterion. Unlike the many experimental studies in this area, few numerical simulations exist due to the complexity of modeling thermal fatigue. In our method, thermal and mechanical stresses arising from thermal expansion mismatches and temperature gradients are modeled through a coupled simulation approach. A viscoelastic constitutive equation is implemented in ABAQUS via a user-defined subroutine to capture damage progression. The method includes surface and internal thermal conduction, thermal deformation, and time-temperature superposition using reduced viscosity, enabling accurate simulation under varying thermal conditions. The results show that localized thermal stresses induced by temperature gradients lead to progressive damage and failure. This study demonstrates the first successful numerical simulation of thermal fatigue-induced damage in polymer materials. The proposed framework reduces the need for extensive experiments and offers insights into residual stress prediction and durability evaluation, contributing to polymer design and application in high-performance environments.

Change in Thermodynamic Entropy and Free Volume of Epoxy Resin During Tensile Deformation

The relationship between thermodynamic entropy generation and free volume changes during the tensile deformation of epoxy resin was investigated. Thermodynamic entropy generation was evaluated using differential scanning calorimetry (DSC) for samples at various strain levels, while free volume changes were measured with positron annihilation lifetime spectroscopy (PALS). Volumetric strain was assessed through the digital image correlation (DIC) method. The results showed that both thermodynamic entropy and free volume increase during tensile deformation, and the average free volume radius becomes more uniform. It was observed that thermodynamic entropy generation and free volume each exhibit a linear relationship with volumetric strain. Additionally, thermodynamic entropy generation increased linearly with free volume. These findings suggest that the increase in thermodynamic entropy during tensile deformation is attributed to irreversible changes, such as the expansion of free volume within the material.

Efficient Prediction of Fatigue Damage Analysis of Carbon Fiber Composites Using Multi-Timescale Analysis and Machine Learning

Carbon fiber reinforced plastic (CFRP) possesses numerous advantages, such as a light weight and high strength; however, its complex damage mechanisms make the evaluation of fatigue damage particularly challenging. Therefore, this study proposed and demonstrated an entropy-based damage evaluation model for CFRP that leverages the entropy derived from heat capacity measurements and does not require knowledge of the loading history. This entropy-based fatigue degradation model, though accurate, is computationally intensive and impractical for high-cycle analysis. To address this, we reduce computational cost through multi-timescale analysis, replacing cyclic loading with constant displacement loading. Characteristic variables are optimized using the machine learning model LightGBM and the response surface method (RSM), with LightGBM achieving a 75% lower root mean squared error than RSM by increasing features from 3 to 21. This approach cuts analysis time by over 90% while retaining predictive accuracy, showing that LightGBM outperforms RSM and that multi-timescale analysis effectively reduces computational demands.

Numerical Simulation for Durability of a Viscoelastic Polymer Material Subjected to Variable Loadings Fatigue Based on Entropy Damage Criterion

This study aims to explore the impact of load history on the premature failure of the viscoelastic polymer matrix in carbon-fiber-reinforced plastics (CFRPs) using a method based on the concept of fracture fatigue entropy (FFE). A user-defined subroutine (UMAT) developed by the authors in previous studies was incorporated to apply the FFE damage criterion using ABAQUS software. Several variable-amplitude load modes, including frequent load amplitude changes and intermittent interruptions, were designed based on the conventional linear damage accumulation method (Palmgren-Miner rule), and the fatigue life under these loadings was obtained via numerical simulations. The results show that both frequent amplitude changes and even brief pauses in loading can accelerate damage accumulation, leading to premature failure of the polymer matrix. In these scenarios, the fatigue life ranged from 33.6% to 91.9% of the predictions made using the Palmgren-Miner rule, which shows significant variation and highlights cases in which the predicted fatigue life falls far short of expectations. This study offers a more practical and reliable approach for predicting fatigue life under complex loading conditions. Since the accuracy of the FFE criterion has been comprehensively validated in previous studies, this research focuses on its application to predict failure under variable loading conditions.

Molecular Dynamics Simulation of Cumulative Microscopic Damage in a Thermosetting Polymer under Cyclic Loading

To develop durable composite materials, it is crucial to elucidate the correlation between nanoscale damage in thermosetting resins and the degradation of their mechanical properties. This study aims to investigate this correlation by performing cyclic loading tests on the cross-linked structure of diglycidyl ether bisphenol A (DGEBA) and 4,4'-diaminodiphenyl sulfone (44-DDS) using all-atom molecular dynamics (MD) simulations. To accurately represent the nanoscale damage in MD simulations, a bond dissociation algorithm based on interatomic distance criteria is applied, and three characteristics are used to quantify the microscopic damage: stress-strain curves, entropy generation, and the formation of voids. As a result, the number of covalent bond dissociations increases with both the cyclic loading and its amplitude, resulting in higher entropy generation and void formation, causing the material to exhibit inelastic behavior. Furthermore, our findings indicate the occurrence of a microscopic degradation process in the cross-linked polymer: Initially, covalent bonds align with the direction of the applied load. Subsequently, tensioned covalent bonds sequentially break, resulting in significant void formation. Consequently, the stress-strain curves exhibit nonlinear and inelastic behavior. Although our MD simulations employ straightforward criteria for covalent bond dissociation, they unveil a distinct correlation between the number of bond dissociations and microscale damage. Enhancing the algorithm holds promise for yielding more precise predictions of material degradation processes.

Durability Analysis of CFRP Adhesive Joints: A Study Based on Entropy Damage Modeling Using FEM

Experimental methodologies for fatigue lifetime prediction are time-intensive and susceptible to environmental variables. Although the cohesive zone model is popular for predicting adhesive fatigue lifetime, entropy-based methods have also displayed potential. This study aims to (1) provide an understanding of the durability characteristics of carbon fiber-reinforced plastic (CFRP) adhesive joints by incorporating an entropy damage model within the context of the finite element method and (2) examine the effects of different adhesive layer thicknesses on single-lap shear models. As the thickness of the adhesive layer increases, damage variables initially increase and then decrease. These peak at 0.3 mm. This observation provides a crucial understanding of the stress behavior at the resin-CFRP interface and the fatigue mechanisms of the resin.

A Molecular Dynamics Simulation for Thermal Activation Process in Covalent Bond Dissociation of a Crosslinked Thermosetting Polymer

A novel algorithm for covalent bond dissociation is developed to accurately predict fracture behavior of thermosetting polymers via molecular dynamics simulation. This algorithm is based on the Monte Carlo method that considers the difference in local strain and bond-dissociation energies to reproduce a thermally activated process in a covalent bond dissociation. This study demonstrates the effectiveness of this algorithm in predicting the stress-strain relationship of fully crosslinked thermosetting polymers under uniaxial tensile conditions. Our results indicate that the bond-dissociation energy plays an important role in reproducing the brittle fracture behavior of a thermosetting polymer by affecting the number of covalent bonds that are dissociated simultaneously.

Numerical and Experimental Studies for Fatigue Damage Accumulation of CFRP Cross-Ply Laminates Based on Entropy Failure Criterion

The transverse cracking behavior of a carbon-fiber-reinforced plastic (CFRP) cross-ply laminate is investigated using a fatigue test and an entropy-based failure criterion in this study. The results of fatigue experiments show that the crack accumulation behavior depends on the cyclic number level and frequency, in which two obvious transverse cracks are observed after 10⁴ cyclic loads and 37 transverse cracks occur after 10⁵ cycles. The final numbers of transverse cracks decrease from 29 to 11 when the load frequency increases from 5 Hz to 10 Hz. An entropy-based failure criterion is proposed to predict the long-term lifetime of laminates under cyclic loadings. The transverse strength of 90° ply is approximated by the Weibull distribution for a realistic simulation. Progressive damage and transverse cracking behavior in CFRP ply can be reproduced due to entropy generation and strength degradation. The effects of stress level and load frequency on the transverse cracking behavior are investigated. It is discovered that, at the edge, the stress σ₂₂ + σ₃₃ that is a dominant factor for matrix tensile failure mode is greater than the interior at the first cycle load, and as stress levels rise, a transverse initial crack forms sooner. However, the initial transverse crack initiation is delayed as load frequencies increase. In addition, transverse crack density increases quickly after initial crack formation and then increases slowly with the number of load cycles. The proposed method's results agree well with those of the existing experimental method qualitatively. In addition, the proposed entropy-based failure criterion can account for the effect of load frequency on transverse crack growth rate, which cannot be addressed by the well-known Paris law.

Evaluation of Microscopic Damage of PEEK Polymers under Cyclic Loadings Using Molecular Dynamics Simulations

Full-atomic molecular dynamics simulations were conducted to investigate the time evolution of microscopic damage in polyetheretherketone (PEEK) polymers under cyclic loading conditions. Three characteristics were used to quantify microscopic damage: entropy, distribution of the end-to-end distance of polymers, and the volume fraction of voids. Our results show that the degree of disentanglement of polymers and the volume fraction of voids increase with cyclic loading, which may lead to entropy generation. Uniaxial tensile strength simulations of the polymer system before and after cyclic loading were performed. The tensile strength after cyclic loading was lower than that before loading. Furthermore, two systems with the same entropy and different loading histories showed almost the same strength. These results imply that entropy generation is expressed as the total microscopic damage and can potentially be employed for effective evaluation of the degradation of material characteristics.

Effect of Electrostatic Interactions on the Interfacial Energy between Thermoplastic Polymers and Graphene Oxide: A Molecular Dynamics Study

In this study, the atomistic-scale mechanisms affecting the interfacial stability of a thermoplastic polymer/graphene oxide interface are investigated using molecular dynamics simulations. Different combinations of thermoplastic polymers (polyethersulfone (PES) and polyetherimide (PEI)) and graphene oxides modified with -O-, -OH, and -COOH are prepared. PES is found to be more strongly stabilized with modified/functionalized graphene oxide in the order of -COOH, -OH, -O-, which is opposite to the stability order of PEI. Our results suggest that these orders of stability are governed by a balance between the following two factors resulting from electrostatic interactions: (1) atoms with a strong charge bias attract each other, thereby stabilizing the interface; (2) the excluded-volume effect of the functional groups on graphene oxide destabilizes the interface by preventing π-π stacking of aromatic rings.

A Possibility for Quantitative Detection of Mechanically-Induced Invisible Damage by Thermal Property Measurement via Entropy Generation for a Polymer Material

Entropy generation from a mechanical and thermal perspective are quantitatively compared via molecular dynamic (MD) simulations and mechanical and thermal experiments. The entropy generation values regarding mechanical tensile loading—which causes invisible damage—of the Polyamide 6 (PA6) material are discussed in this study. The entropy values measured mechanically and thermally in the MD simulation were similar. To verify this consistency, mechanical and thermal experiments for measuring entropy generation were conducted. The experimentally obtained mechanical entropy was slightly less than that calculated by MD simulation. The thermal capacity is estimated based on the specific heat capacity measured by differential scanning calorimetry (DSC), applying the assumed extrapolation methods. The estimated entropy generation was higher than the aforementioned values. There is a possibility that the entropy-estimating method used in this study was inappropriate, resulting in overestimations. In any case, it is verified that entropy increases with mechanical loading and material invisible damage can be qualitatively detected via thermal property measurements.