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

Abstract

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...

Homogenization of size-dependent multiphysics behavior of nanostructured piezoelectric composites with energetic surfaces

“…The cohesive interface model originally proposed by Barenblatt (1959;1962) and Dugdale (1960) is generally accepted, which has been further extended by Needleman and coworkers (Needleman, J o u r n a l P r e -p r o o f 4 1987; Xu and Needleman, 1994). The latter works have been extensively adopted in the literature to track interface separation in heterogeneous materials (Bormann et al, 2019;Elices et al, 2002;Tu and Chen, 2020a, b;Tu and Pindera, 2014;van den Bosch et al, 2007). The general interface model unifies all the aforementioned interface models, allowing for both traction and displacement discontinuities across the interface.…”