A numerical analysis of plane strain drawing employing experimentally measured traction as boundary conditions.

Abstract

The uncertainty of boundary conditions along the interface in metal forming forced many researchers to assume unrealistic friction models such as a constant coefficient of friction or a constant shear stress factor. None of these models is truly representative of the actual physical conditions along the interface. The experimental part of my doctoral thesis is aimed at solving this problem by measuring the exact variation of the friction coefficient along the interface in a strip-drawing process. New sapphire dies are used to obtain the tractions along the interface using a photoelasticity technique. Most previous researchers used this technique with plastic models of the die and workpiece materials, thus the earlier work was not representative of commercial materials processing. By contrast synthetic sapphire is hard enough to form commercial materials such as steel, aluminum, and copper. It also makes the observations of the tribological features such as asperity flattening and lubricant entrapment at the die-workpiece interface possible. The normal and shear stress distributions in the die and along the contact region are determined from the isochromatic and isoclinic fringe patterns using the shear difference method and the model fringe constant. It is concluded that transparent sapphire seems to be the only practical material that exhibits birefringent properties suitable for photoelasticity and at the same time its mechanical properties are comparable to those of the conventional die materials such as tool steel and tungsten carbide. Conventional dies are opaque and this opacity make the photoelasticity technique impossible to study the frictional boundary conditions quantitatively. Another technique, Moire Interferometry, is used here and is directed toward the study of the industrial application where tool steel dies and steel workpiece are used in a strip-drawing operation. The interfacial tractions are measured along the die-strip interface by using the High-Sensitivity Moire Interferometry Technique. The normal and shear strains along the contact surface of the die are determined and converted into the corresponding contact stresses by using the constitutive equations for the die material. The theoretical part of the work involves modifying a finite-element code to incorporate the measured tractions as prescribed boundary conditions, rather than assuming them, to analyze strip drawing operations. The finite element analysis is based on the rate formulation of the constitutive equations for an elastic-plastic isotropic work-hardening material with von Mises yield condition. The updated Lagrangian formulation is adopted in this code. Numerical predictions such as mesh distortion, metal flow, velocity distribution, and local stress and strain distributions are studied and compared to those obtained by other researchers.