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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2.3. Fracture criterion and cleavage plane formation A criterion proposed by Aihara and Tanaka (2011) is employed as fracture condition of cleavage crack propagation across a grain boundary. In the criterion, one of the three {1 0 0} planes in a grain located in front of a crack front where the normal stress acting on the plane is maximum is selected as the cleavage plane. In the actual calculation, the normal stress of the - th {1 0 0} plane of the -th grain is evaluated as the corresponding stress intensity factor � �� from the mixed mode local stress intensity factors � ( � �� �� 3 ), as � �� � � � T ∙ �� � � 3 �� � ∙ (2) where �� is a unit normal vector of the -th {100} plane of the -th grain ahead of the crack front. �� is the local kinked angle between the exist cleavage plane and the -th {100} plane. � � � is coefficient tensor functions of corresponding to the -th fracture mode ( � �� �� 3 ), used in the expression of asymptotic solution of stress tensor near the crack tip (Anderson (2017)). The cleavage plane is assumed to be formed on the {1 0 0} plane where the maximum normal stress, i.e., the highest � �� , is applied. A schematic of the modeling of the cleavage plane formation is shown in Fig. 3. The evaluation points are defined at the center of crack front segments in the respective finite elements. The mixed mode stress intensity factors are evaluated by the interaction integral method with the implementation scheme proposed by González-Albuixech et al. (2013). In addition, only one cleavage facet is assumed to be formed in each grain for simplification. 3. Comparison with observation results In order to evaluate the validity of the developed model, we compared the model simulation results with the SEM observation results for the actual fracture surface. We employed an ordinary ferrite-pearlite steel which is the most widely used as a structural steel. The chemical compositions of the employed steel are shown in Table 1. In addition, the micrograph and grain size distribution of the employed steel are shown in Fig. 5. A double cantilever beam (DCB) test was conducted at ���� , which was sufficiently lower than the brittle-ductile transition temperature of the Charpy impact test, to obtain the cleavage fracture surface. A numerical simulation was carried out using the same grain size distribution data with the employed steel. The calculation domain was set as a cube whose side length was 200 μm. The number of finite elements was 12,167.

Local crack propagation direction

Grain ahead of crack front

Existing cleavage plane

� ��

Newly formed cleavage plane (Maxmum applied)

Evaluation point

{1 0 0} planes

Fig. 4 Modeling of cleavage plane formation