PSI - Issue 33

Naoya Oie et al. / Procedia Structural Integrity 33 (2021) 586–597 Oie, N. / Structural Integrity Procedia 00 (2019) 000–000

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3.3. Comparison of the variation of critical Weibull stress In Fig. 5(a), the vertical axis represents ���� and the horizontal axis represents B . After calculating ���� for five specimens of each of the eight models, the average values of the five specimens are plotted on the graph. The Bordet and Yoshizu models tend to have smaller values of ���� than the Beremin model. In both models, it is clear from equations (9)-(11) that this is due to the addition of � to the term, which is often less than 100%, i.e., less than 1. As described in Chapter 1, there is a need for an index that can uniformly evaluate the fracture toughness or critical conditions of materials. For each of the three models shown in Fig. 5(a), the distributions of the critical Weibull stresses for eight different specimens are compared. The standard deviations for each model are shown in Fig. 5(b). The left vertical axis is the value of the standard deviation of ���� for each model, shown as a bar graph. The right vertical axis is the standard deviation divided by the mean value of the critical Weibull stress of the models (%) and is shown as a line graph. Fig. 14 shows that compared to the Beremin model, the Bordet and Yoshizu models, especially the Yoshizu model, have less variation and are more uniform in evaluating fracture toughness. In the next chapter, we will discuss the validity of the modified Weibull stress model and reverse optimization of the fracture conditions based on consistency with the initiation point using fracture probability.

Fig. 5. Comparison of the critical Weibull stress (a) for different thicknesses and (b) variation.

4. Discussion 4.1. Definition of fracture probability

To evaluate the validity of the existing Weibull stress models and to consider the reformulation of the local approach, the fracture probability is defined based on the consistency with the actual fracture initiation position. The fracture probability of a small reference volume V 0 is considered from previous studies, as shown in Fig. 6. The Beremin model assumes an initial defect and considers only stress-induced crack propagation. Initial defects begin to propagate under load stress, leading to brittle fracture. The probability of crack propagation from the initial defect is expressed as shown in equation (12). On the other hand, the Bordet model considers the probability of microcracks in the brittle phase due to plastic deformation. Microcracks are nucleated in the brittle phase, and they propagate to the matrix. The fracture probability of V 0 , including the probability of microcrack nucleation, is expressed as equation (13). In the Bordet model, the cumulative probability of crack initiation is linearly related to the equivalent plastic strain, but this is modified in the Yoshizu model by considering it as an exponent of β . In this study, the probability density function that brittle fracture is initiated at a position f was defined to have the same factor as in the Yoshizu model, as shown in equation (14). This function was also obtained from the FE analysis.