A computational approach towards modelling dislocation transmission across phase boundaries

Abstract

To study the nanoscopic interaction between edge dislocations and a phase boundary within a two-phase microstructure the effect of the phase contrast on the internal stress field due to the dislocations needs to be taken into account. For this purpose a 2D semi-discrete model is proposed in this paper. It consists of two distinct phases, each with its specific material properties, separated by a fully coherent and non-damaging phase boundary. Each phase is modelled as a continuum enriched with a Peierls-Nabarro (PN) dislocation region, confining dislocation motion to a discrete plane, the glide plane. In this paper, a single glide plane perpendicular to and continuous across the phase boundary is considered. Along the glide plane bulk induced shear tractions are balanced by glide plane shear tractions based on the classical PN model. The model's ability to capture dislocation obstruction at phase boundaries, dislocation pile-ups and dislocation transmission is studied. Results show that the phase contrast in material properties (e.g. elastic stiffness, glide plane properties) alone creates a barrier to the motion of dislocations from a soft to a hard phase. The proposed model accounts for the interplay between dislocations, external boundaries and phase boundary and thus represents a suitable tool for studying edge dislocation-phase boundary interaction in two-phase microstructures.

On the competition between dislocation transmission and crack nucleation at phase boundaries

“…In this paper, a previously proposed Peierls-Nabarro finite element model [24] was complemented with a model that accounts for decohesion of a phase boundary, resulting in a Peierls-Nabarro cohesive zone (PN-CZ) model. Its total free energy is formulated on the basis of linear elastic strain energy density, a glide plane potential for dislocation behaviour and the cohesive phase boundary potential.…”

“…To nucleate dislocations, i.e. no annihilation of the dipole occurs, the methodology outlined in [24] is followed.…”

“…Note that the difference in model response strongly depends on the phase contrast k m and the toughness factor k pb . While a higher value of k m leads to enhanced dislocation obstruction [24], k pb sets the compliance of the phase boundary. Thus, with increasing k pb (lower compliance) the influence of the potential reduction diminishes.…”

“…al [27] proposed the exclusion of this linear elastic response from the atom-istically calculated potentials and its reduction towards a non-linear potentials that correspond to zero-thickness interfaces. In later studies, Xu et al [28,29] showed that the linear elastic potential reduction has a significant influence on the Peierls stress and on the activation energy for dislocation nucleation from a crack tip, and it hence may not be neglected -as is commonly done in the literature -including our earlier work in Reference [24].…”

“…The most common approaches are the Peierls-Nabarro (PN) model [12][13][14], phase-field based models [15][16][17] and Field Dislocation Mechanics [18][19][20]. Using these models, dislocation transmission across simple grain and phase boundary structures was recently studied [21][22][23][24].Here we add a novel dimension to the problem beyond transmission, by extending the recently proposed 2D Peierls-Nabarro finite element (PN-FE) model [24] to incorporate decohesion. This extension enables us to study how the local stresses due to a dislocation or a pile-up of dislocations may result…”