Challenges in Continuum Modelling of Intergranular Fracture

Abstract

Intergranular fracture in polycrystals is often simulated by finite elements coupled to a cohesive zone model for the interfaces, requiring cohesive laws for grain boundaries as a function of their geometry. We discuss three challenges in understanding intergranular fracture in polycrystals. First, 3D grain boundary geometries comprise a five-dimensional space. Second, the energy and peak stress of grain boundaries have singularities for all commensurate grain boundaries, especially those with short repeat distances. Thirdly, fracture nucleation and growth depend not only upon the properties of grain boundaries, but also in crucial ways on edges, corners and triple junctions of even greater geometrical complexity. To address the first two challenges, we explore the physical underpinnings for creating functional forms to capture the hierarchical commensurability structure in the grain boundary properties. To address the last challenge, we demonstrate a method for atomistically extracting the fracture properties of geometrically complex local regions on the fly from within a finite element simulation.

Fracture toughness and bond trapping of grain boundary cracks

“…Currently, GB fracture is typically modeled on the meso-and continuum scale using a cohesive zone approach [20][21][22][23][24][25][26][27][28][29][30][31][32]. Commonly used CZMs [20,75,76] require as parameters the ultimate/maximum tensile strength of the GB and the work of fracture needed to separate the cohesive zone.…”

“…However, the crack is often not directly modeled in these approaches, and instead these values are derived from tensile straining of GBs [25,77]. Such simulations are averaging over the atomic structure of GBs, and continuum simulations with CZM parameters derived that way failed to reproduce the atomistic simulation results [29]. By their very nature, simple CZMs are furthermore not able to properly describe the direction dependence of the fracture toughness of GBs.…”

“…Knowledge about the fracture toughness of GBs is of particular importance for continuum models of intergranular fracture [20][21][22][23][24][25][26][27][28][29][30][31][32], which allow to investigate failure of polycrystalline materials at the macroscale as well as for grain boundary engineering of structural materials [33,34]. The experimental determination of the fracture toughness of individual GBs is however challenging, as it requires the preparation of notched flat and defect-free GBs with defined misorientation.…”

Fracture ab initio: A force-based scaling law for atomistically informed continuum models

“…TS laws derived from atomistic simulations of homogeneous deformation of a single crystal, a bicrystal, or even model sections of polycrystalline microstructures can produce a stress-strain curve which reflects both elastic and dissipative processes during fracture. [15][16][17][18][19][20][21] However, dissipating the energy which is released during crack initiation and growth can be severely constrained in microstructures 22 so that the fracture toughness becomes dependent on length scale and geometry. This means that the TS law would have to be adapted for each specific microstructure.…”