3. Summary The patterns of multiple fractures in carbon steel specimens at different stages of tension, cyclic and dynamic loading were studied; characteristics of damage accumulation were estimated and the cumulative distributions of microcracks and shell fragments were plotted. Analysis of damage accumulation process with the use of mechanical and physical methods allows us to establish some general laws characterizing this process on different stages. They include, in particular, the following. • Distributions of microcracks under static and cyclic loading and amplitude distributions of acoustic emission signals measured during static loading are described by an exponential function at the initial stage of fracture and a power –law one at the final stage of fracture. • Cumulative number-mass distributions of the shell fragments obey the exponential relations with the slope coefficients, which decrease for the brittle materials. • There is a quantitative relationships of the exponents of functions approximating the distributions with material properties and loading parameters. • Parameters of the cumulative distributions of microcracks and amplitude distributions of acoustic emission signals, as well as the concentration criterion are reduced at the stage of prefracture and can serve as diagnostic signs of the approaching fracture. Acknowledgements This study was partially supported by the Russian Foundation for Basic Research, project no. 1208-13182 and 11-08-00983. References [1] L.R. Botvina, N.A. Zharkova, Self - similarity of the radiation defects accumulation process, Scripta metall. 38 (1998) 1829 – 1833. [2] N.H. Paskan, Fluence and dependence of void formation in pure aluminum, J. of Nucl. Mater., 40 (1971) 11 – 17. [3] K. Bethge, D. Munz, J. Neumann, Crack initiation and crack propagation under thermal cyclic loading, High Temp. Techn., 8 (1990) 98 – 104, [4] L.R. Botvina, G.I.Barenblatt, Self–similarity of damage accumulation, Problems of Strength, 12 (1985)17 – 24, [5] M.R. Tyutin, L.R. Botvina, N.A. Zharkova, T.B. Petersen, J.A. Hudson, Evolution of damage in low - carbon steel in tension condition, Strength, Fract. and Compl., 3 (2005) 73 – 80. [6] L.R. Botvina, Fracture: kinetics, mechanisms, common regularities, Nauka, Moscow, 2008. [7] C.M. Suh, R.Yuuki, H. Kitagawa, Fatigue microcracks in low carbon steel, Fatigue Fract. Eng. Mater. Struct., 8 (1985) 193 – 203. [8] L.R. Botvina, V.N. Mochov, On parameters determining a character of dynamic fragmentation of steel shells, Deform. and Fract. of Mater., 12 (2006)19 – 25. [9] L.R. Botvina. Dynamic fragmentation that reflects the effect of composition and mechanical properties of a material and loading conditions, Russian Metallurgy (Metally), 10(2011) 973 – 980. [10] S.N. Zhurkov, V.S. Kuksenko, A.I. Sluzker, Formation of submicroscopic cracks in polymers under load, Physics of solid, 11 (1969) 296 – 302. [11] S.N. Zhurkov, Kinetic concept of the strength of solids, Intern J. of Fracture Mechanics 1 (1965) 311–323. [12] S. B. Ratner, Yu. I. Brochin, Temperature-time dependence of the limit stress of induced
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