Engineering Transactions, 44, 2, pp. 207-228, 1996

Three-Dimensional Slip-Line Field Theory With Rotational Continuity

R. L. Bish
Aeronautical and Maritime Research Laboratorty, Melbourne
Australia

For cold-worked metal bodies undergoing plastic deformation along well-defined loading paths, a three-dimensional slip-line field theory is developed, taking into account the new principle of rotation-rate continuity. It is shown that the slip-line network is always confined to one of the three families of principal stress surfaces and that the strain rate normal to those surfaces vanishes. Further, the ratio of the radii of curvature of the slip-lines in the plane tangent to the net remains constant. This condition, in tum, imposes restrictions on the geometric configurations that are allowed for the net boundary. The velocity hodograph always has one of these configurations.

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