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.

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The interaction of dislocations with phase boundaries is a complex phenomenon, that is far from being fully understood. A 2D Peierls-Nabarro finite element (PN-FE) model for studying edge dislocation transmission across fully coherent and non-damaging phase boundaries was recently proposed. This paper brings a new dimension to the complexity by extending the PN-FE model with a dedicated cohesive zone model for the phase boundary. With the proposed model, a natural interplay between dislocations, external boundaries and the phase boundary, including decohesion of that boundary, is provided. It allows one to study the competition between dislocation transmission and phase boundary decohesion. Commonly, the interface potentials required for glide plane behaviour and phase boundary decohesion are established through atomistic simulations.They are corresponding to the misfit energy intrinsic to a system of two bulks of atoms that are translated rigidly with respect to each other. It is shown that the blind utilisation of these potentials in zero-thickness interfaces (as used in the proposed model) may lead to a large quantitative error. Accordingly, for physical consistency, the potentials need to be reduced towards zero-thickness potentials. In this paper a linear elastic reduction is adopted. With the reduced potentials for the glide plane and the phase boundary, the competition between dislocation transmission and phase boundary decohesion is studied for This article was presented at the IUTAM Symposium on Size-Effects in Microstructure and an 8-dislocation pile-up system. Results reveal a strong influence of the phase contrast in material properties as well as the phase boundary toughness on the outcome of this competition. In the case of crack nucleation, the crack length shows an equally strong dependency on these properties.Dislocation interactions with grain and phase boundaries are known to be complex phenomena. Depending on the geometrical properties (e.g. grain misorientation) and the material properties (intra-and interphase), a variety of events may occur. To gain a more profound insight in the interplay between dislocations and internal boundaries, atomistic studies on various grain and phase boundaries have been performed [1][2][3][4][5][6][7][8][9][10][11]. Reported events are dislocation obstruction, dislocation reflection, dislocation nucleation, dislocation transmission across the boundary, dislocation absorption into the boundary and dislocation induced decohesion. However, the underlying mechanisms controlling these phenomena are not properly understood -let alone their interplay and/or competition. To acquire a better understanding of the mechanics of these events, each isolated event needs to be scrutinised. Atomistic models generally are not suitable for this because they do not allow one to "switch off" certain mechanisms. Several alternative modelling approaches have been proposed to capture the local dislocation behaviour. The most common approaches are the Peierls-Nabarro (PN) model [12][13...

Lattice models are often used to analyze materials with discrete micro-structures mainly due to their ability to accurately reflect behaviour of individual fibres or struts and capture macroscopic phenomena such as crack initiation, propagation, or branching. Due to the excessive number of discrete interactions, however, such models are often computationally expensive or even intractable for realistic problem dimensions. Simplifications therefore need to be adopted, which allow for efficient yet accurate modelling of engineering applications. For crack propagation modelling, the underlying discrete microstructure is typically replaced with an effective continuum, whereas the crack is inserted as an infinitely thin cohesive zone with a specific traction-separation law. In this work, the accuracy and efficiency of such an effective cohesive zone model is evaluated against the full lattice representation for an example of crack propagation in a three-point bending test. The variational formulation of both models is provided, and obtained results are compared for brittle and ductile behaviour of the underlying lattice in terms of force-displacement curves, crack opening diagrams, and crack length evolutions. The influence of the thickness of the process zone, which is present in the full lattice model but neglected in the effective cohesive zone model, is studied in detail.

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