Numerical calculation of statically admissible slip-line field for compression of a three-layer symmetric strip between rigid plates

Abstract

This paper presents a method to build up statically admissible slip-line field and, as a result, the field of statically admissible stresses of planc-strain compression of a three-layer symmetric strip consisting of two different rigid perfectly plastic materials between rough, parallel, rigid plates The case is considered when the shcar yield stress of the inner layer is greater than that of the outer layer. Under the conditions of sticking regime at bi-material interfaces and sliding occurs at rigid surfaces with maximum friction, the appropriate singularities on the boundary between the two materials have been assumed, then a standard numerical slip-line technique is supplemented with iterative procedure to calculate characteristic and stress fields that satisfy simultancously the stress boundary conditions as well as the regime of sticking on the bi-material interfaces. The correctness of this admissible slip-line field model is confirmed by comparison with an analytical solution. It is shown that the singularities built at the end points of the line of separation of the materials are necessary to ensure the sticking regime on the interface of the strip layers.