Simulation of Mechanical Properties: Strain Rate Dependence of Epoxies

In recent years, many have sought to understand the modes of fracture in epoxy systems to further improve their applications in aerospace technology as adhesives and composites. The fracture patterns of epoxies and other thermosets differ from those of their thermoplastic counterparts due to the inherent differences in how the materials are formed. Thermoplastic materials exposed to tension exhibit hydrogen bond cleavage as polymer chains slide past one another, whereas thermoset materials fracture under tension due to broken covalent bonds. Thermosets are valued particularly for their toughness and their properties as part of polymer matrix composites (PMCs). Epoxies in particular have been studied extensively both experimentally and computationally, and this project looks to combine the two strategies to understand how epoxies fracture when exposed to differing strain conditions.

            Simulations completed thus far have studied diglycidyl ether of bisphenol A (DGEBA) with 4,4’-diaminodiphenylmethane (MDA) without diluents present. The DGEBA monomers have varying molecular weights, accomplished by varying the chain length of the prepolymers. Multiple distinct configurations of the epoxies of interest were constructed as 70 Å cubic systems composed of stoichiometric ratios of DGEBA and MDA. A computer program cross-linked each configuration to a minimum 88% degree of cure, calculated as the ratio of “reacted” end groups to those present at the beginning of the simulation. This method uses an isothermal-isobaric ensemble to relax the system between molecular dynamics cross-link steps and assumes equal reactivity of primary and secondary amine groups.

            Five independent cross-linked configurations for each system were created and subjected to uniaxial strain using LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator), a molecular dynamics simulation program. Stress-strain relationships for each individual system were examined for strain rates varying from 10⁶ s^-1 to 10¹¹ s^-1. Properties examined during the project included Young’s modulus and strength at yield, which enabled analysis of the effects of molecular weight (chain length) and strain rate on epoxy fracture. The stress-strain curves will be used as inputs for a continuum-level theory in order to calculate the stress integral ahead of the crack tip, ultimately allowing the calculation of the J_IC integral.

            Experimental results will be used to validate the computational method. The first goal will be to develop a process to construct  highly cross-linked epoxy systems using DGEBA resins of varying molecular weight with both 4,4’-diaminodiphenyl sulfone (DDS) and 3,3’ DDS. Thermogravimetric analysis (TGA) will be used to determine the degradation points of the uncured and cured samples. Differential scanning calorimetry (DSC) will be used to provide the degree of cure for each epoxy system created. Further plans for experiments include combination of materials characterizations including varieties of spectroscopy, microscopy and mechanical testing to understand morphology (amorphous/crystalline), chemical composition and bonding mechanism within matrix, at fiber/matrix interfaces/interphases, and micro-failure features (like micro-voids, matrix and interfacial cracks).