# Numerical simulation and theoretical analysis of plane-strain compression between perfectly rough dies

#### Abstract

The plane-strain compression is one of the most basic operations in metal forming and serves as a useful model for analyzing many forming processes. In this thesis, a numerical simulation procedure using the slip line field (SLF) method has been developed and applied to the analysis of plane strain compression between perfectly rough, inclined dies and perfectly rough, parallel dies. While previous studies of compression between rough, parallel dies have resulted in a characterization of the stress state, this study has provided a complete analysis of the deformation also. In the analysis of compression between rough, inclined dies, the present numerical procedure has enabled the calculation of the SLF, hodograph and the billet deformation. A criterion has also been developed to determine the multiple direction flow point (MDFP). These have been combined to obtain the mean pressure on the die surfaces during deformation as well as the deformed billet shape. The deformation calculation uses an updated Lagrange method. A closed form, analytical solution has been obtained for this compression problem using the element method. The distribution properties of the shear stress $\tau\sb{\rho\theta}$ and the circumferential velocity $\upsilon\sb\theta$ have been exploited in constructing this solution along with the uniqueness theorems for rigid-plastic solids. The results of the numerical simulation are validated using the analytical solution. Finally, the numerical simulation procedure has been used to simulate the multiple-pass compression of multi-layered metals between perfectly rough, parallel dies. The analysis of the deformation textures developed during such processing provides insight into the damascening process--a process developed almost two thousand years ago to make one type of Damascus steels. Furthermore, the simulation output provides a means for characterizing and evaluating the quality of bonded interfaces formed during the forging of layered metals.

#### Degree

Ph.D.

Johnson, Purdue University.

#### Subject Area

Mechanics|Mechanical engineering|Industrial engineering

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