ORIGINAL ARTICLE A slip-line model for serrated chip formation in machining of stainless steel and validation Alper Uysal 1,2 & I. S. Jawahir 1 Received: 3 August 2018 /Accepted: 25 November 2018 # Springer-Verlag London Ltd., part of Springer Nature 2018 Abstract Machining of difficult-to-cut materials producing serrated chip formation has generated a significant interest among academic researchers and industry groups because of the need for understanding the fundamental mechanisms to model the process. Therefore, various analytical and numerical models have been developed in the recent past to investigate such machining operations. The slip-line theory is one of the established modeling methods, but slip-line modeling of serrated chip formation has not been investigated adequately. In this study, a new slip-line model for serrated chip formation in machining with rounded cutting edge tool is presented along with its associated hodograph. In addition, Oxley’ s theory was integrated to the proposed slip- line model for stainless steel material, and the model was validated by experimental results. A good agreement between the experimental and analytically predicted results was obtained. The proposed slip-line model offers predictions of cutting and thrust forces, ploughing force, maximum and minimum chip thickness values, tool–chip contact length, chip up-curl radius, thickness of the primary shear zone, angular position of the stagnation point, shear strain, shear strain rate at the shear plane, and the prevalent flow stress. Keywords Slip-line model . Serrated chip . Oxley’ s theory . Stainless steel Nomenclature c Column vector representing a unit circle C Constant D Diameter of workpiece material F Resultant force k Material shear flow stress K Cutting tool’ s thermal conductivity l BH Tool–chip contact length n Strain hardening index P Ploughing force P A Hydrostatic pressure at point A Q, Q*, P , P*, R, G Basic matrix operators r Cutting edge radius R T Non-dimensional thermal number R u Chip up-curl radius R ui Intermediate variable of chip up-curl radius S Specific heat SR Segment ratio T Material temperature T ave Average temperature along shear plane T mod Velocity modified temperature T W Initial work temperature t 1 Uncut chip thickness t 2max Maximum chip thickness t 2min Minimum chip thickness V Cutting speed V ch Chip velocity V S Shear velocity w Width of cut α 1 and α 2 Angles of vertices β Proportion of heat conducted into work γ Shear strain γ ˙ Shear strain rate at shear plane γ 1 Rake angle ε Uniaxial strain ε ˙ Uniaxial strain rate * Alper Uysal auy223@uky.edu; auysal@yildiz.edu.tr 1 Department of Mechanical Engineering, Institute for Sustainable Manufacturing, University of Kentucky, Lexington, KY 40506, USA 2 Department of Mechanical Engineering, Yildiz Technical University, 34349 Istanbul, Turkey The International Journal of Advanced Manufacturing Technology https://doi.org/10.1007/s00170-018-3136-x