ИСТИНА

Ideal flows have been defined elsewhere as solenoidal smooth deformations in which an eigenvector field associated everywhere with the greatest principal strain rate is fixed in the material. Under such conditions all material elements undergo paths of minimum plastic work, a condition which is advantageous for metal forming processes. The ideal flow theory has been used as the basis of a procedure for the preliminary design of such processes. In particular, the distribution of strain and material properties is uniform in the final product of steady processes. The ideal flow theory has been long associated with the Tresca yield criterion and its associated flow rule. The objective of the present paper is to extend this theory to the double shearing model and the double slip and rotation model that are widely adopted in pressure – dependent plasticity. Both steady and nonsteady processes under splane strain and axial symmetry conditions are considered. Efficient numerical approaches for design of metal forming processes are developed. The approaches are based on the method of characteristics. In the case of plane strain problems, the original system of equations reduces to the equation of telegraphy and subsequent numerical integration.