A nonlocal model of fracture by crazing in polymers
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.
© 2015 Elsevier Ltd. Received 9 November 2014; Received in revised form 30 January 2015; Available online 26 February 2015. The work of SC was partially supported by the Deutsche Forschungsgemeinschaft through the Forschergruppe 797 Analysis and computation of microstructure in finite plasticity, project CO 304/4-2. MO gratefully acknowledges support from the Office of Naval Research through Grant N00014-11-1-0547, from the U. S. National Science Foundation through the Partnership for International Research and Education (PIRE) on Science at the Triple Point Between Mathematics, Mechanics and Materials Science, Award Number 0967140 and from the Institute for Applied Mathematics (IAM), University of Bonn, Germany.