PSI - Issue 13

Kazuki Shibanuma et al. / Procedia Structural Integrity 13 (2018) 1238–1243 Author name / Structural Integrity Procedia 00 (2018) 000–000

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reported that the nonhomogeneous distributions of grain size and orientation in the thickness direction has a possibility to macroscopically enhance the arrestability of steel (Tsuyama et al., (2012)). However, the detail of the theoretical mechanism has been scarcely clarified.

Fig. 1 3D image of cleavage crack surface measured by the laser micrography

The major reason of the insufficient theoretical understanding is geometrical complexity of the fracture morphology as shown in Fig. 1, which is a typical 3D image of cleavage fracture surface measured by a leaser micrography. One of the latest attempt to simulate the cleavage crack propagation may be the model proposed by Aihara and Tanaka (2011). However, their proposal was a simplified quasi-3D model where a polycrystal was modelled by rectangular unit cells of same size. Therefore, any models to evaluate quantitative and universal relationship between microstructure and crack arrest toughness based on physical model of cleavage crack propagation has not been established. As above-mentioned facts, the cleavage fracture crack propagation is geometrically complicated (see Fig. 1). On the other hand, its it accompanies with small deformation. That is, material and geometrical non-linearities of the deformation may be neglected. In the present study, we propose a model for cleavage crack propagation in steel based on the extended finite element method (XFEM) (Moës et al. (2002)). In addition, we conduct a qualitative validation by comparing the proposed model simulation results with the actual fracture surface observation results by fractography. 2. Modeling of cleavage crack propagation 2.1. Modeling outline Although the cleavage crack propagation is a geometrically complicated phenomenon, it does not accompany with large plastic deformation. This feature indicates that the linear fracture mechanics modeling using XFEM is suitable to simulate the phenomenon. In the proposed model, the polycrystal including geometries and spatial distribution of grains is defined independently from finite element mesh, as well as the crack, as shown in Fig. 2. The polycrystal in the calculation domain was constructed by Neper developed by Quey et al. (2011). The details about the XFEM approximation and the fracture criterion are shown in following Section 2.2 and Section 2.3, respectively. 2.2. XFEM approximation The XFEM is a finite element method where a crack shape can be modeled independently from the finite element mesh and theref ore a crack propagation analysis can be carried out without remeshing procedure. The XFEM approximation � � is defined to add the enrichment terms to the ordinary finite element approximation, as � � � �� � � � � ��� ��� � � � � � � ��� ��� � � ��� � � � �� � ��� ��� (1)