Field-theoretical description of the formation of a crack tip process zone

Abstract

The crack tip process zone is regarded as a region where the solid physical properties are altered due to high stress. They are controlled by the solid degrees of freedom existing within the zone and vanishing outside, and can be divided into two classes: (1) zones always existing at the tip and (2) those emerging as soon as certain conditions are met. We focus on the zones of the second kind and argue that they can be described analogously to phase transitions taking place locally. We report both a numerical and an analytical solution for the process zone. We find that the zone can only exist within a limited domain of the dynamic phase diagram, at one side of the phase transition line. We describe this domain and establish its dependence on the crack velocity. We show the existence of a critical crack velocity above which the zone cannot exist.

Phase transformations, fracture, and other structural changes in inelastic materials

“…Besides, stresses produced in the course of a PT may cause fracture, in particular during cyclic loading of SMAs [156]. PFA has been widely used for modeling fracture (see Section 19.5) and PTs (see Sections 11.4,11.6 and 16), and their interaction [34,35,48,73,329,397,473]. However, only several papers [73,177,338,397,473] study both fracture and PT within the PFA.…”

Phase-field modelling: effect of an interface crack on precipitation kinetics in a multi-phase microstructure

“…A number of models related to second-phase formation at a flaw tip in various crystalline materials have been developed in the past years (Varias and Massih 2002;Deschamps and Bréchet 1998;Gómez-Ramírez and Pound 1973;Boulbitch and Korzhenevskii 2016b;Léonard and Desai 1998;Hin et al 2008;Massih 2011;Bjerkén and Massih 2014;Jernkvist and Massih 2014;Jernkvist 2014;Nigro et al 2018). The phasefield method (Provatas and Elder 2010), based on the Ginzburg-Landau theory and employed in some of the cited works, has been not only extensively used within the magnetic field (Cyrot 1973;Berger 2005;Barba-Ortega et al 2009;Cao et al 2013;Gonçalves et al 2014) but also and particularly to predict microstructure evolutions in material.…”

Shape transformation of a wake following the process zone at the tip of a propagating crack

“…This often generates a process zone, a nano-to micro-scale region possessing specific properties. Such a zone can often be regarded as a phase of the solid, different from the one in the bulk [1,2]. It will be referred to here as the transfromational process zone (TPZ).…”

“…The behavior of the crack is controled by the elastic energy flux to its tip, the TPZ as well as to the energy dissipation additionally contributing to it [1,16,17] affecting both crack equilibrium and dynamics.…”

“…We develop an alternative approach within which the zone is described not only by the strain field, ε, but also by an internal variable, referred to as the order parameter, η, describing the difference between the zone and the matrix [1,2,24,30,31]. So far, the formation and dynamics of the wake have not been addressed.…”