PSI - Issue 28

2030 N.V. Mikhailova et al. / Procedia Structural Integrity 28 (2020) 2026–2031 / Structural Integrity Procedia 00 (2020) 000–000 5 After computing the stress-time profiles for each section, the time of fracture criterion fulfillment ∗ can be determined for each part of the sample. Fig. 3(a) and (b) show the results of calculations made for a part of sample with free surface and a part with loading surface, respectively. The zero value of the section corresponds to the free surface and the time ∗ is counted since the compression wave arrives at the free surface. The dotted line �∗ is the spall section. The minimum value of the time ∗ is achieved in the section where the fracture occurs. However, for the considered loading, the graph does not have only one minimum point that means there is an interval in the specimen where fracture can occur. The lower part of the graph (Fig. 3(c)) shows the results of tests for the spalling of concrete rods obtained in (Schuler et al., 2006). Rectangles depict samples whose length is 250 mm. On the rods, dashed lines show the fracture locations in the sample for a set of experiments SHB 16, SHB 17, SHB 25, SHB 26, carried out at the same impactor speed. It is seen that the spall sections in the samples fall into the region of minimum values of ∗ . Thus, the results obtained in modelling of multiple spalling coincide with the experimental data. 4. Conclusions The study considers the modeling of multiple spalling. The proposed model uses the solution of the elastic wave problem to calculate the time profiles of stress, and fracture is predicted by the incubation time criterion. This method allows us to determine the place and time of fracture in the material, as well as to consider the effect in the material after the first spalling. In the work spall fracture modelling was carried out for concrete rods. As calculation result the first spall section was determined. Further, the recalculation of the stress-time dependences was carried out considering the formed new surface. Based on the performed stress calculations, the fracture time was determined for each part of the sample. As a result of modeling, the interval of cross-sections was determined in which fracture can occur with the same probability. Comparisons with the experimental data showed that the spall sections in the concrete rods coincident with the fracture region predicted by the model. Thus, the proposed method has potential in strength analysis, which sets the direction for further research. Acknowledgements The reported study was funded by RFBR, projects number 19-31-90135 and 18-51-80008. N.V. Mikhailova acknowledges support from the Russian Science Foundation (No.17-11-01053) for creation of section 2. References Bie, B.X., Han, J.H., Lu, L., Zhou, X.M., Qi, M.L., Zhang, Z., Luo, S.N., 2015. Dynamic fracture of carbon nanotube/epoxy composites under high strain-rate loading. 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