Application of slip line field theory and finite element method for analysis of micro indentation of a rigid conical wedge into a semi infinite plate and to estimate grinding force using single grit

Abstract

This work aims at studying of plastic flow of metal around a wedge when the wedge is newlineindented to a semi-infinite block by numerical slip-line field, finite element analysis and newlineexperimentations. Previous researchers in this field considered the free surface of bulged up newlinematerial, called lip, to be linear, but the present work assumes that lip profile is actually newlineparabolic and tends to become linear with the increase of the value of coefficient of friction newlinebetween the wedge and the block and also the wedge angle. The proposition in this work has newlinebeen verified by both experimentation and finite element analysis, and corresponding new slipline newlinefield has been generated in this work. The results obtained from slip-line field analysis, newlinefinite element analysis and the experiments were compared. As the hardness is an intrinsic newlineproperty of a material, the hardness of metals should bear the nearly same values irrespective of newlinethe shapes of lips around wedge whether it is linear or parabolic. The author also calculates and newlinecompares the hardness values from the results obtained by slip-line field method. The nonlinear newlinenature of lip was also verified by hardness point of view. The trajectory of any particle in newlinedeformed plastic zone around the wedge is analyzed by deformation of square grids in slip-line newlinefield. The present work develops a new mathematical formulation for square grid deformation newlineas the lip becomes parabolic. The new slip-line field model developed in this work has been newlineapplied to the field of grinding. The grits which take part in grinding has generally high value of newlinesemi-wedge angle, usually greater than 45°. The present work is applied to calculate the forces newlineassociated in metal ploughing for a single grit using numerical slip-line field technique. newline newline