Bridging length scales from micro to mesoscale through rate-dependent traction-separation law predictions

Mesoscale models are useful for modeling dynamic impact on fiber reinforced polymer composites. Mesoscale damage can be modeled using cohesive zones, but determining the governing traction-separation laws is a challenge. We developed finite element models with a stochastic fiber-matrix microstructure embedded within a larger mesoscale continuum to study transverse tension and shear loading of unidirectional S-glass/epoxy composite. We included rate-dependent matrix constitutive behavior and failure and rate-dependent fiber-matrix interface debonding, which are important microscale damage mechanisms that comprise mesoscale fracture. With these multiscale models, we simulated mode I and II crack initiation and propagation. We determined mesoscale, mode I and II, rate-dependent cohesive laws from the models using a domain J-integral approach to calculate the fracture energy as a function of crack opening displacement. We explored the effects of loading rate, matrix failure strain, and fiber-matrix interface debonding properties on the traction laws and crack morphologies. Finally, consistent bridging between length scales is demonstrated by comparing energy dissipation of microstructurally-resolved fracture to mesoscale continuum cohesive zone fracture. This work provides a methodology for determining rate-dependent traction-separation laws, derived from accurate micro-mechanics and experimental input, for bridging lengths scales and use in mesoscale models to evaluate ballistic performance of composites.