Numerical Modeling of the Ductile-Brittle Transition

Abstract

Abstract. Numerical studies of the ductile-brittle transition are described that are based on incorporating physically based models of the competing fracture mechanisms into the material's constitutive relation. An elastic-viscoplastic constitutive relation for a porous plastic solid is used to model ductile fracture by the nucleation and subsequent growth of voids to coalescence. Cleavage is modeled in terms of attaining a temperature and strain rate independent critical value of the maximum principal stress over a specified material region. Various analyses of ductilebrittle transitions carried out within this framework are discussed. The fracture mode transition emerges as a natural outcome of the initial/boundary value problem solution.

Weakly nonlinear fracture mechanics: experiments and theory

“…high-strength steels). Many attempts to model the near-tip region have been empirical in nature, assuming either cohesive-zone type models in which different criteria are used to artificially "bond" the crack faces immediately behind the crack tip (Falk et al 2001;Klein et al 2001;Lobkovsky and Langer 1998;Miller et al 1999;Siegmund et al 1997), criteria for material softening in the near vicinity of the tip (Bazant and Novak 2000;Bouchbinder et al 2006;Buehler et al 2003;Buehler and Gao 2006;Gao 1996;Gumbsch and Gao 1999;Lu and Ravi-Chandar 1999), void nucleation and damage surrounding the crack tip (Afek et al 2005;Bouchbinder et al 2004;Lu et al 2005;Needleman and Tvergaard 2000;Pardoen and Hutchinson 2000;RaviChandar and Yang 1997), or a "damage" type order parameter in phase-field models of fracture (Aranson et al 2000;Hakim and Karma 2005;Henry and Levine 2004;Karma et al 2001;Karma and Lobkovsky 2004;Spatschek et al 2006).…”

Earthquake swarms at Upptyppingar, north-east Iceland: A sign of magma intrusion?

“…Needleman and Tvergaard (2000) used numerical modelling to demonstrate that brittle fracturing can occur within a ductile zone because of high strain rates. A likely reason for straining beneath Upptyppingar is the injection of a magma, as implied by geodetic results.…”

Micromechanical modeling of crack propagation in nodular cast iron with competing ductile and cleavage failure

“…To the authors' knowledge the first models of this type were presented by Tvergaard, Needleman and co-workers [36,21,37,5,22]. These authors modeled the whole domain by the Gurson-Tvergaard-Needleman model (GTN-model) with the microstructure represented by finite regions of nucleable porosity (''islands'').…”