Finite element-based model for crack propagation in polycrystalline materials

Abstract

Abstract.In this paper, we use an extended form of the finite element method to study failure in polycrystalline microstructures. Quasi-static crack propagation is conducted using the extended finite element method (X-FEM) and microstructures are simulated using a kinetic Monte Carlo Potts algorithm. In the X-FEM, the framework of partition of unity is used to enrich the classical finite element approximation with a discontinuous function and the two-dimensional asymptotic crack-tip fields. This enables the domain to be modeled by finite elements without explicitly meshing the crack surfaces, and hence crack growth simulations can be carried out without the need for remeshing. First, the convergence of the method for crack problems is studied and its rate of convergence is established. Microstructural calculations are carried out on a regular lattice and a constrained Delaunay triangulation algorithm is used to mesh the microstructure. Fracture properties of the grain boundaries are assumed to be distinct from that of the grain interior, and the maximum energy release rate criterion is invoked to study the competition between intergranular and transgranular modes of crack growth.Mathematical subject classification: 74R10.

The criterion for determining the direction of crack propagation in a random pattern composites

“…Cracking analyses of geomaterials with random structures fit naturally in this group. The CrackPath3 computer code uses the new criterion for prediction of the crack propagation direction which is simpler than suggested for polycrystalline materials by Sukumar and Srolovitz [21].…”

“…There may be mentioned, for example, the approach proposed by Honein and Herrmann [7] and Sukumar and Srolovitz [21], where considered materials similar to that described in this work.…”

“…A number of different approaches to this problem can be found in the papers of Brighenti et al [4] Carpinteria et al [5] Honein and Herrmann [7], Kitagawa et al [8] Murakami [12]. The use different criteria for the propagation of the polycrystalline material presents Sukumar and Srolovitz [21]. Application in the analysis of the material models in mesoscale can be found in the works of Wriggers and Moftah [25] and Mishnaevsky [10].…”

Generalized Gaussian quadrature rules for discontinuities and crack singularities in the extended finite element method

“…This problem is considered in Sukumar and Srolovitz. [72]. The material is assumed to be homogeneous and isotropic with E = 1 and ν = 0.3.…”

Integrated experiment and modelling of microstructurally-sensitive crack growth

“…However most of these packages require extensive continuous re-meshing to capture geometric discontinuity during subsequent crack advancements which can be computationally expensive. There are some techniques which do not require the need for remeshing including the extended finite element method (X-FEM) which has been demonstrated by Sukumar et al [9][10][11][12][13] in their 2D and 3D models.…”