Improved understanding of metal cutting based on slip-line field theory
This dissertation consists of three papers, which describe a new capability for deriving slip-line fields (SLFs) from results of finite element analyses, and its application to the problem of metal cutting. The first paper describes the new SLF generation capability, that uses the stress components obtained from FE analysis (which already satisfy the equations of equilibrium) to obtain the first and second directions of maximum shear stress, the streamlines of which are the slip-lines. This new capability for slip-line field generation has been validated using the problem of compression of a plate between rough platens and there is an exact match between the slip-lines generated from FEA results and the analytical slip-line solution.. This study also shows the importance of alignment of the mesh with the velocity discontinuities in order to capture them accurately, as pointed out by various researchers. In the next chapter, the reason the hydrostatic pressure around the cutting edge in machining is much lower than that under an indenter, has been investigated by comparing the machining process with flat punch indentation. Using finite element simulations of flat punch indentation, it is shown that for confinement ratios above the critical value, the field is that given by Prandtl for flat punch indentation. But for confinement ratios less than the critical value, the indentation field changes to a ‘S’ shaped shear plane field which is similar to that in machining. The analogy with machining is made clear using finite element simulation of the initial contact between the workpiece and a tool with a rake angle of 0.05°. It is found that the slip line field is initially an indentation field. As the contact length increases, the field switches over to the ‘S’ shaped shear plane field at the exact confinement ratio (8.59) given by Chakrabarty (1987), to within the resolution of the mesh. This makes it clear that the ratio of the depth of cut to the contact length between the tool and the chip is the confinement ratio in machining. As the length vii of contact increases further, the contact pressure is observed to decrease. In metal cutting, the contact length is typically larger than the uncut chip thickness, making the confinement ratio less than one. Since the confinement ratio is very small compared to that in indentation, the hydrostatic pressure observed at the cutting tool tip is much smaller compared to that under the indenter. The new slip-line field generation capability is then applied to metal cutting. A new slip-line field model is developed for machining with tools having a finite cutting edge radius. The slip-line field model is based on the results of finite element simulations carried out under different conditions of friction, rake angle, and the ratio of the uncut chip thickness to the cutting edge radius ratio. It is shown that there exists a Dead Metal Zone (DMZ) for all non-zero values of sticking friction coefficient (m>0). For m<1, it is clearly shown that the plastic deformation originating from the lower boundary of the DMZ reaches the free surface of the chip forming a Primary Shear Zone (PSZ). At point A on the free surface, the width of the PSZ is zero making it a pressure singularity.
Thesis (Ph.D.)--Wichita State University, College of Engineering, Dept. of Industrial Engineering