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.

Evaluation of True Bonding Strength for Adhesive Bonded Carbon Fiber-Reinforced Plastics.

Carbon fiber-reinforced thermoplastics (CFRTPs) have attracted attention in aerospace because of their superior specific strength and stiffness. It can be assembled by adhesive bonding; however, the existing evaluation of bonding strength is inadequate. For example, in a single-lap shear test, the weld zone fails in a combined stress state because of the bending moment. Therefore, the strength obtained experimentally is only the apparent strength. The true bonding strength was obtained via numerical analysis by outputting the local stress state at the initiation point of failure. In this study, the apparent and true bonding strengths were compared with respect to three types of strength evaluation tests to comprehensively evaluate bonding strength. Consequently, the single-lap shear test underestimates the apparent bonding strength by less than 14% of the true bonding strength. This indicates that care should be taken when determining the adhesion properties for use in numerical analyses based on experimental results. We also discussed the thickness dependence of the adhesive on the stress state and found that the developed shear test by compression reduced the discrepancy between apparent and true strength compared with the single-lap shear test and reduced the thickness dependence compared with the flatwise tensile test.

Enhanced Estimation of Axial Compressive Strength for CFRP Based on Microscale Numerical Simulation and the Response Surface Method.

Compressive strength is one of the most important properties of carbon fiber reinforced plastics (CFRP). In this study, a new method for predicting the axial compressive strength of CFRP using the response surface method is developed. We focused on a microbuckling model to predict the compressive strength of unidirectional fiber composites. For the microbuckling model, axial shear properties are required. To obtain the compressive strength for various material properties, we perform individual shear tests and numerical simulations, but these require enormous computational costs and extended time. To address the issue of computational cost, in this study, we propose a new method to predict compressive strength using the response surface method. First, we perform shear simulation in a microscale fracture model for unidirectional CFRP with various parameters of the fiber and resin properties. Based on the results of the shear simulation, the response surface method is used to evaluate and develop prediction equations for the shear properties. This method allows for the study of the objective values of the parameters, without significant computational effort. By comparing both the results predicted from the response surface method (RSM) and the simulation results, we verify the reliability of the prediction equation. As a result, the coefficient of determination was higher than 94%, and the validity of the prediction method for the compressive strength of CFRP using the response surface method (RSM) developed in this study was confirmed. Additionally, we discuss the material properties that affect the compressive strength of composites comprised of fibers and resin. As a result, we rank the parameters as follows: fiber content, elastic modulus after resin yield, yield stress, and initial elastic modulus.

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.

Micro-Scale Numerical Simulation of Fatigue Failure for CFRP Subjected to Multiple-Amplitude Cyclic Loadings Based on Entropy Damage Criterion.

Fatigue failure of carbon fiber-reinforced plastics (CFRPs) under cyclic loadings has attracted the attention of researchers recently. In this study, the entropy-based failure criterion is proposed to investigate the fatigue lifetime of unidirectional CFRPs subjected to multiple-amplitude cyclic loadings. Due to the heterogeneity of CFRPs, a micro-finite element model considering matrix resin and fibers independently is developed, and the entropy-based damage criterion is implemented into a user-subroutine of Abaqus to model the progressive damage of matrix resin. The fatigue lifetime of CFRPs under typical loading sequences consisting of two stages, such as varying from low to high (L-H) or from high to low (H-L) loading sequence, is estimated with the proposed failure criterion. Numerical results show that the initial damage occurs near the area between two fibers, and a transverse crack propagates progressively under the cyclic loading. The difference in predicted lifetime to final failure in L-H and H-L stress levels is 6.3%. Thus, the effect of loading sequence on the fatigue lifetime can be revealed via the proposed entropy-based damage criterion. Comparisons with the conventional linear cumulative damage (LCD) and kinetic crack growth (KCG) theories are also conducted to demonstrate the validity of the proposed method. The entropy-based failure criterion is a promising method to predict the residual strength and fatigue lifetime of CFRP components.

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.

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.

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.

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

Herein, the stress-state dependence of fracture entropy for a polyamide 6 material is investigated through molecular dynamics simulations. Although previous research suggests that a constant entropy increase can be universally applied for the definition of material fracture, the dependence of stress triaxiality has not yet been discussed. In this study, entropy values are evaluated by molecular dynamics simulations with varied combined stress states. The calculation is implemented using the 570,000 all-atom model. Similar entropy values are obtained independently of stress triaxiality. This study also reveals the relationship between material damage, which is correlated with void size, and the entropy value.

Formulation of non-linear viscoelastic-viscoplastic constitutive equation for polyamide 6 resin.

In this study, a non-linear viscoelastic-viscoplastic constitutive equation for polyamide 6 (PA6) is formulated and a new model is suggested for the viscoplastic part of the equation. The suggested model is empirical but can accurately predict the viscoplastic strain. In this study, creep and recovery tests are conducted to evaluate the viscoplastic strain. Using a non-linear dashpot, a viscoplastic strain is formulated and its parameters are identified for PA6. In addition, a stress relaxation test is conducted, and the relationship between the viscoelastic strain and stress is identified when considering the viscoplastic strain. In this study, the time-temperature superposition principle is thoroughly applied to include the effect of elevated temperature on the viscoelastic-viscoplastic behavior. All material constants in the non-linear viscoelastic-viscoplastic constitutive equation including the time-temperature superposition principle for PA6 are presented in this study.

Analysis of Three-Phase Structure of Epoxy Resin/CNT/Graphene by Molecular Simulation.

In this study, the three-phase structure consisting of epoxy resin, carbon nanotubes (CNTs), and graphene, which is assumed to be the surface of carbon fiber, was simulated using molecular dynamics. Models in which the CNT number and initial position of CNT are varied were prepared in this study. Relaxation calculation for each three-phase model was implemented, and the movement of molecules was investigated. When CNTs are located between the graphene and epoxy at initial, how the epoxy approaches to graphene was discussed. Besides, interaction energies between CNT/graphene, CNT/epoxy, and graphene/epoxy were evaluated after relaxations. The value of the interaction energy between two individual molecules (epoxy resin and graphene, CNTs and graphene, epoxy resin and CNTs) among three-phase structure were obtained, respectively, and those mechanisms were discussed in this study.