Hierarchical Multiscale Approach for Modeling the Deformation and Failure of Epoxy-Based Polymer Matrix Composites.

Coarse-grained molecular dynamics (CG-MD) simulations were conducted to characterize the molecular structure and mechanical properties in the epoxy matrix around fibers in polymer matrix composites (PMCs). From these simulations, the molecular structure was quantified by measuring the free-volume hole radius distribution as a function of position from the matrix-fiber interface. Additionally, correlations between the epoxy mechanical properties and the average free-volume hole radius were established for different degrees of cross-linking. These results were then upscaled into a finite element model (FEM) of a PMC representative volume. The results from the CG-MD-informed FEM model were compared to conventional FEM simulations that assume uniform epoxy mechanical properties, and the results indicate that conventional FEM simulations overestimate the strength of PMCs and predict a symmetric damage evolution in the matrix. On the other hand, the CG-MD-informed FEM simulations predict a more realistic localization of damage around the fiber-matrix interface.

Correlating Free-Volume Hole Distribution to the Glass Transition Temperature of Epoxy Polymers.

A new algorithm is developed to quantify the free-volume hole distribution and its evolution in coarse-grained molecular dynamics simulations of polymeric networks. This is achieved by analyzing the geometry of the network rather than a voxelized image of the structure to accurately and efficiently find and quantify free-volume hole distributions within large scale simulations of polymer networks. The free-volume holes are quantified by fitting the largest ellipsoids and spheres in the free-volumes between polymer chains. The free-volume hole distributions calculated from this algorithm are shown to be in excellent agreement with those measured from positron annihilation lifetime spectroscopy (PALS) experiments at different temperature and pressures. Based on the results predicted using this algorithm, an evolution model is proposed for the thermal behavior of an individual free-volume hole. This model is calibrated such that the average radius of free-volumes holes mimics the one predicted from the simulations. The model is then employed to predict the glass-transition temperature of epoxy polymers with different degrees of cross-linking and lengths of prepolymers. Comparison between the predicted glass-transition temperatures and those measured from simulations or experiments implies that this model is capable of successfully predicting the glass-transition temperature of the material using only a PDF of the initial free-volume holes radii of each microstructure. This provides an effective approach for the optimized design of polymeric systems on the basis of the glass-transition temperature, degree of cross-linking, and average length of prepolymers.

Coarse-Grained Molecular Dynamics Study of the Curing and Properties of Highly Cross-Linked Epoxy Polymers.

In this work, a coarse-grained model is developed for highly cross-linked bisphenol A diglycidyl ether epoxy resin with diaminobutane hardener. In this model, all conformationally relevant coarse-grained degrees of freedom are accounted for by sampling over the free-energy surfaces of the atomic structures using quantum mechanical simulations. The interaction potentials between nonbonded coarse-grained particles are optimized to accurately predict the experimentally measured density and glass-transition temperature of the system. In addition, a new curing algorithm is also developed to model the creation of highly cross-linked epoxy networks. In this algorithm, to create a highly cross-linked network, the reactants are redistributed from regions with an excessive number of reactive molecules to regions with a lower number of reactants to increase the chances of cross-linking. This new algorithm also dynamically controls the rate of cross-linking at each local region to ensure uniformity of the resulting network. The curing simulation conducted using this algorithm is able to develop polymeric networks having a higher average degree of cross-linking, which is more uniform throughout the simulation cell as compared to that in the networks cured using other curing algorithms. The predicted gel point from the current curing algorithm is in the acceptable theoretical and experimental range of measured values. Also, the resulting cross-linked microstructure shows a volume shrinkage of 5%, which is close to the experimentally measured volume shrinkage of the cured epoxy. Finally, the thermal expansion coefficients of materials in the glassy and rubbery states show good agreement with the experimental values.