A Multiscale Ccomputational Framework to Predict Deformation and Failure in Polymer Matrix Composites
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Composite materials are made by combining different materials with distinct properties to create a more unique and superior material. Nowadays, composites such as polymer matrix composites (PMCs) are extensively used in aerospace applications due to their excellent thermal stability, high strength, and light weight. Perhaps, the greatest advantage of using composite materials over metals is the ability to tailor the properties of the material by properly choosing the resin, and reinforcement materials. Epoxy polymers are often used as the matrix of advanced PMCs. The failure in PMCs occur mainly in the matrix. Therefore, manipulating the properties of PMCs requires a deep understanding of properties of the matrix. However, despite the excellent service record of PMCs, especially in aerospace applications, in many cases there remains a considerable lack of basic understanding of the microstructure and mechanisms that control their properties. Thus, there is a strong need to develop a better understanding of the role of the microstructure and the dominant deformation mechanisms to improve upon the properties of PMCs for more advanced applications. In this thesis, a coarse-grained molecular dynamics model for modeling a highly cross-linked bisphenol a diglycidyl ether (DGEBA) system are developed to study the effects of microstructural variations on the behavior of PMCs. First, a coarse-grained molecular dynamics model is developed to simulate the thermomechanical properties of large scale epoxy systems. The interactions between particles in the coarse-grained structure are formulated by the inversion of the Boltzmann distribution of the coordinates associated with each interaction. The Boltzmann distributions are calculated from a large set of random walk simulations of the conformation of the atomic structure of the polymers using quantum mechanics simulations. In addition, a new algorithm is developed for simulating the curing process of highly cross-linked polymers. This algorithm is used to create a uniformly cross-linked epoxy system with a very high degree of cross-linkings not attainable by other algorithms in the literature. These new algorithms are available for public use as an open-source code for LAMMPS. Furthermore, a new algorithm is developed to characterize the free-volume hole distributions inside the network of epoxies. A free-volume hole is defined here as the volume between polymer chains in the network of the system. The distributions calculated from coarse-grained simulations are compared with the free-volume distribution measured from positron annihilation lifetime spectroscopy (PALS) at different temperatures, pressures, and during deformation. The predicted free-volume holes are in excellent agreement with those measured experimentally. The algorithms developed here are publicly available as an open-source software. To investigate the effect of structural features on predicted properties of epoxy systems, several cross-linked epoxy systems are created by varying the length of cross-linking, and the degree of cross-linking of the system. It is shown that there are strong correlations between the free-volume hole average radius size and the strength and glass transition temperature of these epoxies. Based on these simulations, a new model is developed to predict the glass transition temperature of a polymeric system based on the experimentally or computational measured initial distribution of free-volume holes. Finally, to investigate the effect of structural variation of the matrix on strength and damage evolution of PMCs, a highly cross-linked epoxy is created in the presence of two fibers. The free-volume hole distribution along the direction normal to the fibers shows a variation of matrix structure as a function of distance from the fibers. A multi-scale finite element model has been developed to better investigate the effects of localized matrix properties on the PMCs.