Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
in January 1966
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IssuesArchive of Issues2008-5pp.798-807

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Yu. K. Bivin, "Strain and fracture of circular plates under static and dynamical loading by a spherical body," Mech. Solids. 43 (5), 798-807 (2008)
Year 2008 Volume 43 Number 5 Pages 798-807
DOI 10.3103/S0025654408050154
Title Strain and fracture of circular plates under static and dynamical loading by a spherical body
Author(s) Yu. K. Bivin (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526, Russia)
Abstract The strain and fracture of plates under the action of a load normal to their planes was studied in numerous papers. A review of publications in this field in the case of impact by a freely flying body is given in [1-3]. At first, researchersí attention was mainly paid to the so-called ideal version of collision in which the normal impact of a rigid body on the plate center was considered and the boundary conditions did not affect the results of impact. The plate strains were studied near and in the region of impact, the minimal velocities were determined for a body of some specific shape for which the plate is punched through (the so-called ballistic limit); the shapes of fractured punched plates and the residual velocity of the body if its initial velocity exceeds the ballistic limit were also determined. In the last years, the more complicated cases of collision have been studied, namely, the case in which the impact is not directed along the normal to the plate plane and the impact velocity vector does not coincide with the body symmetry axis as well as the case of impacts on shells. The research in this field was represented in [2, 3]. But in this case the influence of the boundary conditions is still considered insufficiently. This gap was indicated in [2].

In the present paper, we study the normal impacts of spherical bodies and deformable cylindrical bodies with spherical heads on circular plates for various boundary conditions and mechanical characteristics of their material. We consider the plate strains, determine the impact velocity at which the plate is punched through, and clarify the mechanism and the sequence of the plate fracture and break-though depending on their mechanical characteristics and boundary conditions. We make an attempt to perform numerical studies of the dynamic deflection at the center of a plate fixed on the boundary using its experimentally determined quasistatic rigidity and taking into account the boundary conditions for determining the associated mass. We estimate the influence of the body mass on the ballistic limit. The use of rigid spherical bodies permits treating any variations in the results of impacts as a characteristic reaction of the plates themselves, because in this case it is unnecessary to deal with the body orientation with respect to the velocity vector. For impacts with such bodies, we used plates made of aluminum alloys and of lead. We studied how the strength of cylindrical bodies with spherical heads made of plasticine or lead affects the strain of plates made of AMTsM alloy.
Received 01 November 2005
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