A Multiscale Model for the Quasi-Static Thermo-Plastic Behavior of Highly Cross-Linked Glassy Polymers (original) (raw)
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Composites Part B-engineering, 2018
We propose an efficient simulation-based methodology to characterize the quasi-static (experimental low strain rate) yield stress of an amorphous thermoset polymer, which has generally been considered a limitation of molecular dynamics (MD) simulations owing to the extremely short time steps involved. In an effort to overcome this limitation, the temperature-accelerated methodin which temperature is treated as being equivalent to time in deformation kineticsis employed to explore the experimental strain rate conditions. The mechanical tensile behavior of a highly crosslinked polymer is then investigated with MD simulations by considering different strain rates and temperatures below the glass transition temperature. The derived yield stress represents the time-and temperature-dependent characteristics, showing that the yield stress decreases with increasing temperature and decreasing strain rate. Changeable vertical and horizontal shift factors are introduced for the first time to reflect nonlinear characteristics of the yield stress across a broad range of strain rates and to quantify the correlation between increasing temperatures and decreasing strain rates. With the proposed method, the Eyring plot, which describes the rate effect on yield from quasi-static to high-rate conditions, is predicted from MD simulations, and agrees well with macroscopic experimental results. From the constructed Eyring plot, the experimentally validated quasi-static stress-strain response is also estimated by using linear elastic model and Ludwick's hardening model. The proposed method provides new avenues for the design of glassy polymers using only fully atomistic MD simulations, thus overcoming the existing temporal scale limitations.
Molecular dynamics predictions of thermomechanical properties of an epoxy thermosetting polymer
Polymer, 2020
This paper reports the thermomechanical properties of a thermosetting polymer formed by curing a DGEBA resin with a Jeffamine D230 agent predicted by molecular dynamics (MD) simulations. A multistep crosslinking approach is used to form the crosslinked network of the thermosetting polymer. The radial distribution function and X-ray diffraction pattern of the MD predicted crosslinked structure are calculated and compared with experimental results to validate the epoxy network system. Thermomechanical properties such as mass density, gel point, glass transition temperature (g), elastic moduli (Young's modulus and shear modulus), and yield strength in shear and tension are calculated at different temperatures and crosslinking conversions by employing the DREIDING and AMBER force fields. The MD predicted results are in good agreement with theoretical studies and existing experimental data. We find a significant increase in g and yield strength with crosslinking conversion. The elastic modulus is less sensitive to the strain rate, but the yield strength is significantly strain-rate dependent. The high-quality digital epoxy configurations developed in this work are available in LAMMPS data format from the journal website.
Atomistic molecular simulations of structure and dynamics of crosslinked epoxy resin
Polymer, 2007
Many excellent thermal and mechanical performances of cured epoxy resin products can be related to their specific network structure. In this work, a typical crosslinked epoxy resin was investigated using detailed molecular dynamics (MD) simulations, in a wide temperature range from 250 K to 600 K. A general constant-NPT MD procedure widely used for linear polymers failed to identify the glass transition temperature (T g ) of this crosslinked polymer. This can be attributed to the bigger difference in the time scales and cooling rates between the experiments and simulations, and specially to the highly crosslinked infinite network feature. However, by adopting experimental densities appropriate for the corresponding temperatures, some important structural and dynamic features both below and above T g were revealed using constant-NVT MD simulations. The polymer system exhibited more local structural features in case of below T g than above T g , as suggested by some typical radial distribution functions and torsion angle distributions. Non-bond energy, not any other energy components in the used COMPASS forcefield, played the most important role in glass transition. An abrupt change occurring in the vicinity of T g was also observed in the plots of the mean squared displacements (MSDs) of the crosslinks against the temperature, indicating the great importance of crosslinks to glass transition. Rotational dynamics of some bonds in epoxy segments were also investigated, which exhibited great diversity along the chains between crosslinks. The reorientation functions of these bond vectors at higher temperatures can be well fitted by KohlrauscheWilliamseWatts (KWW) function.
Atomistic Modeling of Cross-linked Epoxy Polymer
52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 2011
Molecular Dynamics simulations are used to study cross-linking of an epoxy polymer. OPLS force field parameters are used for modeling a 2:1 stoichiometric mixture of epoxy resin and the cross-linking agent. The model has 17,928 united atoms and a static cross-linking method is used along with molecular minimization and molecular dynamics techniques to achieve two different cross-link densities. The crosslinked models can be used for understanding various phenomenon occurring in cross-linked epoxy resins at the atomic scale. Glass-transition temperature ranges of two differently cross-linked samples have been predicted using the models. These models will be used for studying aging behavior at the atomic level in epoxy materials and understanding the influence of aging on mechanical properties. I. Introduction poxy Resins are prime constituents in adhesives, sealants, and aircraft composite structural components. A wide range of studies have focused on epoxy-based materials to establish physical and mechanical properties. 1-3 The excellent specific-stiffness and specific-strength properties of epoxy-based composite materials are due to the complex microstructure of their constituent materials. There is significant interest in understanding the aging response of these material systems due to their widespread use in commercial aircraft. A. Computational Studies on Epoxy Polymers Epoxy resins are formed when epoxy monomers react with compounds known as cross-linking or curing agents with active hydrogens such as amines and anhydrides. 4 A trial-and-error approach to experimentally optimize the processing conditions of epoxy materials can become time-consuming and expensive. With the advancement of computational technology, computational modeling has provided an efficient route to study these polymer resins. 5-14,4,15 Molecular dynamics (MD) simulations based on the bead-spring model 10,11 and Monte-Carlo simulations based on the bond-fluctuation model 16,8,9 have been used in the last two decades for studying epoxy materials. The beadspring models did not take into account the details of the molecular structures and thus cannot predict the influence of specific groups of atoms on the physical properties. In the last few years, MD at the atomic scale has been quite successful in exploring different phenomena occurring at pico-to nano-second time scales in epoxy resins. 14 Many researchers have studied the formation of cross-linked epoxy resins using different approaches of simulated cross-linking. Doherty et al. 5 modeled PMA networks using lattice-based simulations in a polymerization MD scheme. Yarovsky and Evans 15 discussed a cross-linking technique which they used to crosslink low molecularweight, water-soluble, phosphate-modified epoxy resins (CYMEL 1158). The cross-linking reactions were carried out simultaneously (static cross-linking process). Dynamic cross-linking of epoxy resins was performed by Xu et al. 4
Molecular dynamics simulations are performed to study compressive yielding behavior of epoxy-amine cross-linked polymer networks in the low temperature glassy state. The mechanism of yielding is identified to be activation of wedge disclinations through visualization of atomic chains. For the first time in literature, both the chemistry and geometry (critical segment length, angles, bond torsions) involved in the molecular mechanism of compressive yielding have been measured. We analyze these results in the context of the ...
Polymer, 2011
In this study, the glass transition and thermoelastic properties of cross-linked epoxy-based nanocomposites and their filler-size dependency are investigated through molecular dynamics simulations. In order to verify the size effect of nanoparticles, five different unit cells with different-sized silicon carbide (SiC) nanoparticles are considered under the same volume fraction. By considering a wide range of temperatures in isobaric ensemble simulations, the glass transition temperature is obtained from the specific volumeetemperature relationship from the cooling-down simulation. In addition, the coefficient of thermal expansion (CTE) and the elastic stiffness of the nanocomposites at each temperature are predicted and compared with one another. As a result, the glass transition and thermoelastic properties of pure epoxy are found to be improved by embedding the SiC nanoparticles. Especially regarding the CTE and elastic moduli of nanocomposites, the particle-size dependency is clearly observed below and above the glass transition temperature.
Macromolecules, 2012
Molecular dynamics and molecular mechanics simulations have been used to study thermo-mechanical response of highly cross-linked polymers composed of epoxy resin DGEBA and hardener DETDA. The effective cross-linking approach used in this work allowed construction of a set of stress-free molecular models with high conversion degree containing up to 35000 atoms. The generated structures were used to investigate the influence of model size, length of epoxy strands, and degree of cure on thermo-mechanical properties. The calculated densities, coefficients of thermal expansion, and glass transition temperatures of the systems are found to be in good agreement with experimental data. The computationally efficient static deformation approach we used to calculate elastic constants of the systems successfully compensated for the large scattering of the mechanical properties data due to nanoscopically small volume of simulation cells and allowed comparison of properties of similar polymeric networks having minor differences in structure or chemistry. However, some of the elastic constants obtained using this approach were found to be higher than in real macroscopic samples. This can be attributed to both finite-size effect and to the limitations of the static deformation approach to account for dynamic effects. The observed dependence of properties on system size, in this work, can be used to estimate the contribution of large-scale defects and relaxation events into macroscopic properties of the thermosetting materials.
Atomistic prediction of plane stress behavior of glassy thermosets
Computational Materials Science, 2017
When any covalent bond energy reached a threshold indicative of incipient bond scission, the simulation was stopped. This method was used to examine the responses of three highlycrosslinked epoxy systems. Systems were large enough to include 110 to 480 crosslink sites. Both elastic and yield properties show good agreement with the experiments of others. Continuum yield theories commonly applied to polymers are compared with the data. A Drucker-Prager pressure-dependent yield function applied best in the second and third quadrants of the domain. In the first quadrant, however, data more closely match a normal-stress-yielding criterion. In biaxial tension and simple tension, plastic behavior and large growth in nanoporosity were observed. Ductility was lowest in simple tension and biaxial compression. In simple tension, the bonds at crosslink sites and in ether linkages were the most highly strained whereas carbon-carbon backbone bonds between phenyl groups were highly strained in other cases. When system energy at imminent bond rupture was divided on a per-atom basis, consistency with Peterlin's theory for molecular rupture was found.
High strain rate mechanical properties of a cross-linked epoxy across the glass transition
Polymer, 2013
Molecular dynamics simulations were used to study the high strain rate mechanical properties of a crosslinked epoxy system comprised of diglycidyl ether of bisphenol A (DGEBA) that is cross-linked by a poly(oxypropylene) diamine with three propylene oxide moieties per diamine. Atomistic network structures were characterized using volume-temperature behavior and their response to mechanical deformation. The Young's modulus was determined as a function of temperature across strain rates spanning three decades in magnitude, and collapsed onto a single "master curve" using the time etemperature superposition principle (TTSP). The master curve obtained from molecular dynamics simulation data shows good agreement with a similar master curve of the reduced storage modulus as a function of frequency, which was obtained using experiments. At higher strain rates, the simulation master curve deviated from the experimental master curve. This deviation could be attributed to the lack of occurrence of sub-T g motions on the time scale of simulations due to the use of higher strain rates in simulations compared to experiments. Our work demonstrates the utility of TTSP in connecting the thermo-mechanical behavior of polymers at high strain rates and high temperatures to experiments performed at much different conditions. To the best of our knowledge, the use of the timeetemperature superposition to compare mechanical properties determined from molecular simulation and experiments is the first reported effort of its kind.