Abstract
The two theories gave a nearly satisfactory solution for a problem about the mysterious flexibility shown in high-energy-rate-forming of a hard metal. The one is the deformation theory of zero-thickness-plate under lateral impact, and the other that of strain-wave-stracture which states about the thickness-criterion indicating the limit of application of the zero-thickness-theory, using the strain-wave which is deduced from the same theory. But it was found afterwards that the theoretical wave form differed a little from the observed one. And to clean up discrepancy and related conflicts, New Deformation Theory has been developed, under the consideration of the plate thickness δ0. The main results are summarized as follows:
1. If we consider merely the changing profile of a thin plate, its deformation is well explained by the theory of zero-thickness-plate.
2. If the strain of plate comes into question, there must be considered the longitudinal elongation infront of the material point where the maximum curvature K0 occurs. The strain e is given by: ε=1/2K0δ0(δc/γc-γ)2(γt/ξ-γ/γc)2, where : the velocity of propagation of the maximum curvature K0 along the plate, γc: that of sound, ξ the original coordinate of the specific particle-point on the material-plate, and t: the time measured from the instant when the impact begins.
3. In the portion by where the maximum curvature has past, the strain ε increases from 1/2K0δ0 to 1/2(U/c)2, where c: the horizontal velocity of propagation of the maximum curvatureK0 relative to the space-fixed-coordinate-system, and there the deforming motion occurs almost entirely in accordance with the theory of zero-thickness-plate.
