Modeling Interfaces through an Extension of Continuum Mechanics to the Nanoscale with Application to Fracture, Debonding and Composites.

摘要

This report summarizes the progress made in developing the theoretical underpinnings for two new theories of brittle fracture. One is based upon an extension of continuum mechanics to the nano-scale while the second is based upon a strain limited constitutive relation. In contrast to classical fracture theories, the new theories predict bounded crack tip stresses and strains. The first theory is implemented by including classical bulk properties with a novel boundary condition arising from the jump momentum balance enforced on fracture surfaces which are modeled as dividing surfaces with excess physical properties including surface free energy, surface tension and surface entropy. In the second, classical boundary conditions are applied to novel bulk constitutive relations. As a result of the bounded crack tip stresses and strains, it was necessary to introduce a new notion of crack tip Energy Release Rate (ERR) and a new fracture criterion.