Transition from multi-center fracture to fragmentation statistics under intensive loading

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Statistics of transition from multi-center fracture to fragmentation is studied analyzing multi-scale mechanisms of nucleation and growth of cracks in hollow cylindrical (tubular) samples made of Al2O3 ceramics due to underwater electrical wire explosion [1]. This study is a development of results [2-4] and focuses on the description of mechanisms of tube fracture operating at different stages of crack formation: in the course of spall crack formation in tubular samples, nucleation and growth the main cracks leading to the generation of coarse (2D) fragments and crack branching leading to 3D fragment formation. The fragments size distribution of 2D and 3D objects have been investigated for different types of cracks under the conditions of their nucleation and branching. The analysis of the fragment geometry allows us to determine the mechanisms responsible for the formation of 2D and 3D fragments. The 2D fragment are formed by the Mott mechanisms [5, 6], i.e. as a result of tube extension in the radial direction. The mechanisms of fracture and formation of 2D fragments is specified by the amplitude of the applied stress. The 3D objects are formed in the course of fragmentation of 2D object as a result of multiple spall fracture, which is manifested by the second peak on the profile of compression wave recorded by the VISAR interference system [4]. The 3D fragments size distribution is governed by the power law, which is typical of fracture of the “dynamic branch” under spall failure [7] where it has been shown that the time to spall failure in different spall cross-sections depends on the amplitude of loading pulse produced by dynamic loading of cylindrical PMMA samples. It has been found that the development of multiple fractures at increasing stress corresponds to a transition from the exponential kinetics (that is typical of quasi-static loading) to the “dynamic branch” characterized by a weak dependence of the time to fracture on the applied stresses. The results [7] are in the correspondence with the present study, in which fracture accompanied by the formation 2D fragments follows to the exponential distribution and the formation of 3D fragments is consistent with the power law distribution. Study of the influence of initial porosity of samples indicates that the distribution of pores’ is described by the power function, which, however, falls apart from the distribution of 3D fragments. This allows us to conclude that porosity does not exert essential effect on the formation of 3D fragments. [1] Bannikova I.A., Uvarov S.V., Bayandin Yu.V. and Naimark O.B. An experimental study of non-Newtonian properties of water under electroexplosive loading // Technical Physics Letters, Pleiades Publishing, Ltd., 2014. – Vol. 40, No.9. – P. 766-768. [2] Bannikova I., Uvarov S, Davydova M., Naimark O. Study of ceramic tube fragmentation under shock wave loading // 20th ECF, Norway. – Proc. Materials Sc., 2014. – Vol. 3. – P. 592-597. [3] Bannikova I., Uvarov S., Naimark О. Analysis of fragmentation statistics of alumina tubular specimens // AIP Publishing LLC. 2014. – Vol. 1623. – P. 59-62. [4] Bannikova I.A., Uvarov S.V., Naimark O.B. Experimental research of the self-regularities of ceramics fracture under shock wave loading // PNRPU Mechanics Bulletin, 2015. - No.3. – P. 25-37. [5] Mott N.F. Fragmentation of Shell Cases // Proc. Royal Soc., 1947. – Vol. 189, No.1018. – P. 300-308. [6] Fragmentation of rings and shells / Grady D. – Springer – Verlag Berlin Heidelberg, 2006. Printed in Germany. – 374 pp. [7] Bellendir E. N. , Belyaev V.V., Naimark O.B. Kinetics of multicenter rupture under the scabbing // Pisma v zhurnal tekhnicheskoi fiziki, 1989.- V. 15, No.13.- P. 90-93. (in Russian).