Controlling of shear deformation and its role in forming a stress-strain state

Basing on a common mathematical model the variants of compressing rectangular blank with different schemes of contact friction forces are generalized. With a method of minimizing discrepancy for solving overdetermined system of equations stress and velocity field is determined. Potential for effective control of stress-strain state by targeted control of scheme of contact friction action is shown, that may be useful for decreasing deformation forces, forming material structure, compressing non-compact materials and for solving some special applications. Torque of friction influence on character of stress-strain and deformed state in non-symmetrical compressing in blank volume is shown for the first time. Existence of hardened deformation zones and their displacement to the edges of a blank while increasing a non-symmetricity of scheme of external friction is determined. The fact that influence of torque on stress-strain state is growing with increase of friction constant and height to length ratio of a blank is shown. Comparative evaluation of deformation heterogeneity in symmetrical and non-symmetrical compression modes is made. It depends on size ratio of a blank and is not one-valued. Some recommendation is made on use of method of discrepancy minimization in solving overdetermined system of equations for stress-strain state in metal forming. Its effectiveness, simplicity and high accuracy in comparison to a variational method is shown.