relation: http://eprints.imtlucca.it/2306/ title: A multi-scale numerical method for the study of size-Scale effects in ductile fracture creator: Corrado, Mauro creator: Paggi, Marco creator: Carpinteri, Alberto subject: TJ Mechanical engineering and machinery description: The use of a stress-strain constitutive relation for the undamaged material and a traction-separation cohesive crack model with softening for cracking has been demonstrated to be an effective strategy to predict and explain the size-scale effects on the mechanical response of quasi-brittle materials. In metals, where ductile fracture takes place, the situation is more complex due to the interplay between plasticity and fracture. In the present study, we propose a multi-scale numerical method where the shape of a global constitutive relation used at the macro-scale, the so-called hardening cohesive zone model, can be deduced from meso-scale numerical simulations of polycrystalline metals in tension. The shape of this constitutive relation, characterized by an almost linear initial branch followed by a plastic plateau with hardening and finally by softening, is in fact the result of the interplay between two basic forms of nonlinearities: elasto-plasticity inside the grains and classic cohesive cracking for the grain boundaries. publisher: MDPI date: 2014-08-27 type: Article type: PeerReviewed format: application/pdf language: en rights: cc_by_nd identifier: http://eprints.imtlucca.it/2306/1/metals-04-00428.pdf identifier: Corrado, Mauro and Paggi, Marco and Carpinteri, Alberto A multi-scale numerical method for the study of size-Scale effects in ductile fracture. Metals, 4 (3). pp. 428-444. ISSN 2075-4701 (2014) relation: http://dx.doi.org/10.3390/met4030428 relation: 10.3390/met4030428