ИСТИНА

The qualitative features of rigid plastic solutions for multi-layer materials are affected by the properties of each layer and geometric parameters. For example, in the case of plane strain flow of three-layer material obeying rigid perfectly plastic models through an infinite channel, the solution may not exist under certain conditions, and the solution in the vicinity of bi-material interfaces may be singular [1]. In the case of plane strain compression of such material between parallel plates, some layers may remain rigid under certain conditions [2]. All these properties are important for the application of these solutions to practical problems. In particular, the solution for the process of compression between rotating plates is required for the application of Orowan’s method [3]. This method is widely used for the analysis of the process of rolling. In the present paper, a semi-analytical solution for the process of compression of three-layer material between rotating plates is found assuming that each layer obeys the classical model of rigid plasticity based on the von Mises yield criterion and its associated flow rule. It is assumed that no slipping occurs at the bi-material interfaces if such a solution exists. The conditions under which the solution does not exist are found. In this case, the second invariant of the strain rate tensor approaches infinity in the vicinity of the bi-material interface. Under certain conditions, one or two layers may become rigid. The procedure for using the solution found in conjunction with Orowan’s method is outlined. REFERENCE 1. Alexandrov S., Mishuris G. and Miszuris W. Planar flow of a three-layer plastic material through a converging wedge - shaped channel - Part 1 - Analytical solution. Europ. J. Mech. A/Solids, 2000, vol. 19(5), 811-825. 2. Alexandrov S., Tzou G.-Y. and Huang M.-N. Plane strain compression of rigid/perfectly plastic multi-layer strip between parallel platens, Acta Mech. 2006, vol.184(1-4), 103-120. 3. 3. E. Orowan, The calculation of roll pressure in hot and cold flat rolling. Proc. Inst. Mech. Eng, 1943, vol.150, 140–167.