PSI - Issue 13

106 3 where is normal vector of the m -th plane, is local stress intensity factor of the -th mode and ( ) is a function expressing the stress tensor near crack-tip in linear elastic solid (Anderson, 2005) and is angle of the m th plane relative to macroscopic crack plane. Because the grains are assumed as columnar cells, cleavage crack extension is treated in a discrete and step-wise manner, see Fig.2. A crack may extend across a grain boundary (Active front) but it may not at a different grain boundary (Arrest front), depending on the criterion Eq. (1). Taiko Aikawa et al. / Procedia Structural Integrity 13 (2018) 104–109 Aikawa/ Structural Integrity Procedia 00 (2018) 000 – 000

Fig.1 Determination of cleavage crack plane in front of crack front, numerical model.

Fig.2 Schematic of cleavage crack extension, top view, numerical model.

Their model has been extended to macroscopic fracture process, in the present study. Because of this, the cells in the present model has a size much larger than grain size, typically, 1mm. Therefore, the cells in the present model are “pseudo” crystal grain s. We employ further assumptions for simulating macroscopic fracture: − in Eq. (1) should be regarded as crack propagation resistance of the material. We then assume that − is related to macroscopic crack arrest toughness, : − = (3) where, is a constant. may be determined by crack arrest test using wide-plate specimens (WES 2815, 2014) but we assume that is expressed by an empirical formula, as a function of Charpy impact test absorbed energy transition temperature, , plate thickness, t , and temperature, T , (Nakai et al. 2014). Figure 3 shows the calculated result of for = 30mm and = -20, -40 and -60deg.C based on the formula.

Fig. 3 Crack arrest toughness assumed in the simulation.

Fig. 4 Distributions of local fracture toughness and stress intensity factor along crack front, schematic.

As has been mentioned previously, uncracked ligaments and shear-lips are formed near the plate surfaces on fracture surface. Reason for this is understood as that the plane strain condition is lost near the plate surfaces and brittle fracture no more takes place. It might be assumed that a depth of the zone where the plane strain condition is lost is proportional to (1⁄3 )( ⁄ ) 2 , where is stress intensity factor and is yield stress. The suppression of brittle