13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- considered in the cohesive finite element method (CFEM) framework developed. This framework also provides a means for evaluating fracture toughness through explicit simulation of 3D fracture processes in microstructures by calculating the J-integral. 2. Model structure Our proposed framework consists of two length scales. At the microscopic scale, 3D cohesive elements with 6-node zero thickness (COH3D6) permeate the whole microstructure as an intrinsic part of material characterization. Constitutive relations for the grains and grain boundaries are specified separately. The cohesive relation allows damage and crack surface separation to be considered. Fracture emerges as a natural outcome of the deformation process without the use of any failure criterion. The macroscopic region is homogenized by using the Mori-Tanaka method. Structural response, such as fracture toughness IC K , is evaluated by calculating the J-integral along an arbitrary contour in the homogenized region. 2.1. Generation of 3D polycrystal samples Voronoi tessellation has been one of the most popular techniques for generating polycrystalline microstructures due to its simplicity, space-filling nature and the availability of theoretical results on the topological properties [7-8]. However, microstructures generated in this way are not always consistent with experimental results [9]. To realistically capture the topological and statistical properties of microstructures, a method for generating a 3D polycrystalline microstructure from a series of 2D images is developed. This capability extends the source of 2D images from computer generated microstructures to realistic section images obtained by Electron Back Scatter Diffraction (EBSD) or Focused Ion Beam (FIB) diffraction. In this paper, the 2D microstructure images are generated by an ellipsoidal packing algorithm [10]. Ellipsoidal grains are randomly placed with the aspect ratios and grain sizes fitted to pre-defined distributions. In order to obtain good delineation of grain boundary and potential crack trajectory, unstructured tetrahedral meshes are generated by iso2mesh [11] as illustrated in Fig. 1. Fig.1 3D microstructure reconstruction and meshing.
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