Crack velocity jumps engendered by a transformational process zone

Abstract

We study a concerted propagation of a fast crack with the process zone where a rearrangement of the solid structure takes place. The latter is treated as a second-order local phase transformation. We demonstrate that the propagation of such a zone gives rise to a nonlinear frictionlike force exerted on the crack tip, resisting its propagation. Depending on the temperature, it produces three regimes of crack motion, which differ in the behavior of the crack tip process zone: (i) always existing, (ii) only emerging at a high crack speed, and (iii) flickering. We show that the latter regime exhibits crack velocity jumps.

Molecular dynamics simulations of liquid crystalline phases of dodecyltrimethylammonium chloride

“…Bair et al (2017), Ma et al (2006), Thuinet et al (2013). Here, an analytical solution for the mechanical equilibrium in plane strain for an elastic structure containing a crack is found through the use of the Irwin's analytical solutions and is directly incorporated into the TDGL equation as in Boulbitch and Korzhenevskii (2016) in order to account for the presence of a fixed crack-induced stress. Thus, only one equation has to be solved rendering the model time-efficient.…”

“…Over the years, numerous models have been developed to describe the formation of a second phase at a flaw tip in a variety of crystalline materials (Varias and Massih 2002;Deschamps and Bréchet 1998;Gómez-Ramírez and Pound 1973;Boulbitch and Korzhenevskii 2016;Léonard and Desai 1998;Hin et al 2008;Massih 2011a;Bjerkén and Massih 2014;Jernkvist and Massih 2014;Jernkvist 2014). Among those are the models resting on the phase-field approach based on Ginzburg-Landau theory, see e.g.…”

Phase structural ordering kinetics of second-phase formation in the vicinity of a crack

“…Over the years, numerous models have been developed to describe the formation of a second phase at a flaw tip in a variety of crystalline materials (Varias and Massih 2002;Deschamps and Bréchet 1998;Gómez-Ramírez and Pound 1973;Boulbitch and Korzhenevskii 2016;Léonard and Desai 1998;Hin et al 2008;Massih 2011a;Bjerkén and Massih 2014;Jernkvist and Massih 2014;Jernkvist 2014). Among those are the models resting on the phase-field approach based on Ginzburg-Landau theory, see e.g.…”

“…One such study was reported by Massih (2011a), who presented a general set-up with coupled conserved and non-conserved field variables in the presence of cracks and dislocations in an elastic solid. Further, in a paper by Boulbitch and Korzhenevskii (2016), a nonconserved order parameter is used to study quasi-static phase transformation in the process zone of a propagating crack. These works constitute a suitable base reference to study the second-phase formation in presence of a crack.…”

“…To include the effect of the crack to the modeling, a mechanical equilibrium condition is added to the free energy formulation for the system at hand. The mechanical equilibrium is solved analytically reducing the number of equations to be solved to one, the TDGL equation, as in Boulbitch and Korzhenevskii (2016). To this end, a small perturbation from a stressed reference configuration under known stress conditions due to the presence of the crack is assumed.…”