Large Plastic Flow and the Collapse of Hollow Cylinders

Abstract

The collapse of heavy steel cylinders under external pressures running up to 412,000 p.s.i. was studied during the war under contract with the Watertown Arsenal. The distortions are so large that the conventional small strain analysis is not adequate. The presence of large strains is recognized in the analysis by writing the stress equations of equilibrium in terms of the final displaced positions of the particles instead of in terms of the initial positions. The conventional assumption of negligible volume change is retained. Attention is called to a purely geometrical condition on the strains. In the experiments the cylinders showed no change of length. The generality of the conditions under which this may be expected is examined. A linear relation was found experimentally between collapsing pressure and log (rext/rint). Furthermore, P/log(rext/rint) is not constant but rises continually with increasing collapsing pressure. These results indicate that the strain hardening increases continually with increasing distortion, but at a rate two- or threefold less than would be given by experiments in simple tension. The collapse was pushed experimentally to such extremes that the geometrical symmetry was lost because of the grain structure. This limits the region of applicability of any simple theory.