PSI - Issue 2_A

L.R. Botvina et al. / Procedia Structural Integrity 2 (2016) 373–380 L.R. Botvina/ Structural Integrity Procedia 00 (2016) 000–000

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accelerated power law growth the perimeter of fractal curve. If this does not happen, the fractal dimension is close to one and characteristic size of the segment measured is missing. At describing the Schuhmann distribution, Grady (2010) identified two scales of fragment average length λ e and λ c (designated by us λ 1 и λ 3 ) limiting the power law region of the distribution, and proposed the dimensionless criterion of fragmentation, equal to the ratio of these lengths: F = λ c / λ e (or F = λ 3 / λ 1 according to our notation). To assess the initial length of the fragment according to the proposed model, he used the ratio: � � ~3�� � � ��� � � � , (3) where K c is the material fracture toughness, σ hel is the Hugoniot dynamical elastic limit, believing apparently that the ratio in parentheses characterizes the size of plastic deformation zone. For boron carbide ( K c = 5 MPa √ m, σ hel = 15 GPa) he received λ e = 0.3 μm. Evaluation of the length λ 1 for fragments of steel 60 with the fracture toughness ranging from 60 to 100 MPa √ m, depending on heat treatment, and the yield strength of Hugoniot σ hel = 1.44 GPa gives values λ 1 = 5.1 and 14.5 mm, respectively, which is in good agreement with the values of the length of the fragments presented in the table 3. 5. Conclusion Dynamic fragmentation diagrams for the shells of the three structural steels of various diameters are plotted. These diagrams, described by power-law relations in the middle section, allow to connect the fracture mechanisms with fragmentation regimes. Exponents in these relations were estimated, and it was shown that there is the influence on them of the diameter and the mechanical properties of shell material. The values of the characteristic mass of fragments was estimated and found their reduction with an increase in the diameter of the shells. Thus, it was shown that the scale effect is clearly pronounced despite the geometric similarity of shells of different diameters. References Banks, E.E., 1968.The ductility of metals under explosive loading conditions. Journal Inst. of Metals 96, 375 - 370. Botvina, L.R., Odintsov, V.A., 2006. Mechanisms of fragmentation of steel cylinders under impact loading. Deformation and fracture of materials 9, 11-17. Grady, D.E., 2010. Length scales and size distributions in dynamic fragmentation. International Journal Fracture 163, 85-99. Ivanov, A.G., Novikov, S.A. Sinitsyn, V.A., 1972. The scale effect in explosive fracture of the closed steel vessels, Physics of Combustion and Explosion 8, N1. Odintsov, V.A., 2002. In “Explosion Physics”. Orlenko, L.P. (Ed.) 3rd, revised, in 2 volumes, 2. Fizmatlit, Moscow, pp.656. Ritchie, R. O, Knott, J., 1973. Mechanism of fatigue crack growth in low alloy steel. Acta Metallurgica, 21, 639-648. Schuhmann, R. ,1940. Principles of comminution. I. Size distribution and surface calculation. AIME Tech. Publ. 1189. Mining Technology, 1-11. Slate, P.M., Billings, M.J. Fuller, P.J., 1967. The rupture behavior of metals at high strain rates. Journal Inst. Metals 95. N7, 244-251. Turcotte, D.L., 1986. Fractals and fragmentation. Journal Geophysical Research 1986 91, 1921-1926. Zhang, H., Ravi-Chandar, K., 2008. On the dynamics of necking and fragmentation II. Effect of material properties, geometrical constraints and absolute size. International Journal Fracture 150, 1–36.