The numerical calculation of statically admissible slip-line field for plane strain compression of a three-layer symmetric strip between rigid plates

This paper present a method to build up statically admissible slip-line field (the field of characteristics) and, as a result, the field of statically admissible stresses of the compression of a three-layer symmetric strip consisting of two different rigid perfectly plastic materials between rough, parallel, rigid plates (for the case: the shear 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 simultaneously the stress boundary conditions as well as the regime of sticking on the bi-material interfaces

A Machining Program Employing a Slip Line Field Modelling Technique Over Other Constitutive Models

Machining involves complex plastic material flow at the chip separation site which makes it difficult to predict forces and other machining outputs to higher accuracy. Modelling is a common technique which facilitates incorporation of analytical and experimentally derived equations to visualize the process and analyses the mechanism. It saves time and machining factors can be optimized without any trial and error method. In this paper, the significance of slip line field model over other constitutive laws in defining the complex regions in machining are thoroughly reviewed and a slip line field model is chosen which incorporates build up edge (BUE) of a larger size than the other previously defined slip line models for machining. The modified model also incorporate a region of shear zone instead of a shear line, takes into account the chip curl effect and conform to the velocity discontinuity and stress equilibrium. The slip line fields are generated using MATLAB and employing Dewhurst-Collin's matrix technique.

Solution of the problem of sheet bending by the slip line field method

One of the limitations imposed on this process of bending is the possibility of cracking on the surface of the sheet during bending. To predict this type of metal destruction, information is needed on the plastic properties of the material and the stress state in the deformation zone during the bending process. The solution of the problem of sheet bending under conditions of a flat-strained state by graphical construction of the slip line field using a rigid cylindrical mandrel has been analyzed. The material model is a perfectly plastic body. The stresses in the deformation zone and accumulated strains have been determined. The bending process is characterized as unidirectional and monotonous. It has been determined that the mean stress on the outer surface of the sheet during bending equals to 1, and it does not depend on the sheet thickness and the radius of the rigid cylindrical mandrel. Verification of the accuracy of the graphical solution is made. The resulting solution can be used as the basis for an experimental method for testing the plastic properties of metals.