PSI - Issue 42

Michal Vyhlídal et al. / Procedia Structural Integrity 42 (2022) 1000–1007 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 4. Isosurfaces of the first principal stress (left), and a graph describing the dependence of the F crit on the value of d (right).

3.4. Crack propagation in the left corner of the inclusion The distribution of average tangential stress ̅ in dependence on the polar coordinate  and the distance d , for the crack with its tip at the left corner of steel inclusion can be seen in Fig. 5 (right). The polar coordinate  between 0 ° and 90 ° represents the area of the steel inclusion which means, that the direction  = 0° is oriented in the edge of the inclusion (crack face) and positive values are counted counterclockwise. The graph clearly describes the maximum ̅ in the direction about 135°, which goes to the matrix (almost vertically). This is also in the agreement with the distribution of the first principal stress (Fig. 5, left).

Fig. 5. Isosurfaces of the first principal stress (left), Average opening stress ̅ (right). Nevertheless, to determine the crack propagation direction, critical applied forces must be determined separately for each material region. Of course, propagation to the steel inclusion is not possible, and only the matrix or the ITZ can be considered as potential crack propagation regions. These two regions are characterized by the values of fracture toughness K Ic,MTX , and K Ic, ITZ . The graph of F crit is shown in Fig. 6 in dependence on the material regions and on the distance d . We can see that the minimum value of critical force is in the ITZ, because we have chosen the fracture toughness of ITZ as 0.7 × K Ic,MTX . If fracture toughness of ITZ is greater, crack propagates vertically to the matrix, if it is less than or equal to 0.7  K Ic,MTX , crack propagates along the interface between steel inclusion and the matrix. Note that also the distance d plays a role in the competition between the crack propagation direction into MTX or ITZ. The comparison of critical forces of specimen with the inclusion and the reference specimen is not easy here, because the crack propagates in a straight line in homogeneous material. For this reason, the values of F crit (REF) are calculated for the crack tip in the center of the specimen. Due to the lower values of the fracture toughness of the ITZ K Ic, ITZ , the F crit (STE) also reaches lower values in comparison to the F crit (REF).