On the Propagation of the Plastic Deformation Produced by an Expanding Cylinder
PENNSYLVANIA UNIV PHILADELPHIA
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In the present paper it is assumed, in accord with Bethes model for armor penetration, that the plastic deformation produced during armor penetration is similar to that produced by an expanding cylinder. The paper deals with the deformation produced in a plate which is thick enough so that the plate does not get appreciably thicker near the expanding cylindrical hole. In the first portion of the paper the relations between the stresses and the strains are considered and the wave equations which govern the motion of the material when it is rapidly deformed are derived. It is found that in the case of the thick plate an elastic wave diverges radially from the expanding cylinder, that this is followed by a plastic wave and that the elastic and plastic wave velocities do not differ very much. In the second portion of the paper an approximate expression for the displacement is obtained for the case where the deformation is elastic. In the last section of the paper a method of numerically integrating the wave equations is given. The method is applied to a particular numerical example, amid the displacement and the shearing strain produced by a uniformly expanding cylinder are calculated and plotted at various times during the expansion. The calculation shows that the shearing strain in both the elastic and the plastic regions increases as we go towards smaller radii. A discontinuity in the shearing strain is found at the boundary between the elastic and plastic regions. The calculation indicates that the compressibility and the density play an important role in determining the magnitude of the stresses developed in a thick plate. A program for future investigation is suggested.
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