Plastic Flows of Tubes and Blocks.

Expansion of thick-walled tubes and compression of rectangular blocks to produce plastic deformations in them are treated as flow problems. These plastic flows are analyzed by a variational formulation of the limit analysis. To treat realistically the contact condition in the both cases, the hydrostatic pressure distribution and the friction effect have been studied. The expansion is accomplished by forcing a m and rel through the tube. A frictional contact condition is assumed. M and rel profile is optimized among a class of shapes including spheres, cones and paraboloids for the least forming pressure. A specific paraboloid is found to be optimal for a given set of geometric and friction conditions. The block compression is also analyzed with a realistic contact condition. The effects of friction and aspect ratio of the block are studied. A critical friction coefficient is found for each aspect ratio of the block. Numerical results are presented for a wide range of parameter variation. These results provide new interpretations for some experimental phenomena understood before only from an empirical point of view.Ph.D.MechanicsUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/159590/1/8324227.pd