A nonlocal model of fracture by crazing in polymers

• We derive scaling laws for the macroscopic fracture energy of crazing in polymers.
• Scaling relations are derived from a micromechanical model of damage.
• The model posits a local energy density and a nonlocal regularization.
• The nonlocal regularization is based on strain-gradient elasticity.
• We present finite-element calculations that bear out the heuristic scaling relations.

We derive and numerically verify scaling laws for the macroscopic fracture energy of polymers undergoing crazing from a micromechanical model of damage. The model posits a local energy density that generalizes the classical network theory of polymers so as to account for chain failure and a nonlocal regularization based on strain-gradient elasticity. We specifically consider periodic deformations of a slab subject to prescribed opening displacements on its surfaces. Based on the growth properties of the energy densities, scaling relations for the local and nonlocal energies and for the specific fracture energy are derived. We present finite-element calculations that bear out the heuristic scaling relations.