ORIGINAL ARTICLE Numerical assessment of residual stresses induced by combining turning-burnishing (CoTuB) process of AISI 4140 steel using 3D simulation based on a mixed approach Anis Rami 1,2 & Achref Kallel 1 & Syrine Djemaa 2 & Tarek Mabrouki 3 & Salem Sghaier 2 & Hedi Hamdi 1 Received: 14 January 2018 /Accepted: 25 April 2018 # Springer-Verlag London Ltd., part of Springer Nature 2018 Abstract The “combined turning-burnishing” (“CoTuB”) process is a new methodology to perform both machining and finishing operations simultaneously. The improved surface integrity and reduction in manufacturing time and cost are the main advantages of this technique. The purpose of this paper is to develop a numerical model for combined cutting and burnishing operation, thus explaining the underlying physical phenomenon. The cutting operation is modelled using a new concept named as the “mixed approach”. It consists of replacing the cutting tool by an equivalent thermo- mechanical loading applied on the external surface of the workpiece. It is possible to simulate the CoTuB process using the mixed approach combined with the burnishing ball. The residual stress from the numerical simulation was compared with the experimental results measured by the X-ray diffraction. The 2D model gave a better prediction of the residual stress in the feed direction than in the burnishing direction, whereas the 3D configuration provided a good prediction of the residual stress in both feed and burnishing directions. The developed numerical models gave qualitatively good results of the residual stress for different conditions of burnishing force and feed rate. Keywords Residual stress . Combined turning-burnishing . 3D numerical modelling . AISI 4140 steel Nomenclature A Initial yield stress (MPa) B Hardening modulus (MPa) C Dependent strain rate coefficient (MPa) m Thermal softening coefficient n Work-hardening exponent η Ratio of mean stress to effective stress σ Equivalent stress ε Equivalent strain ε ˙ Plastic strain rate ε ˙ 0 Reference strain rate (10 -3 s -1 ) T room Room temperature (°C) T melt Melting temperature (°C) f Feed rate a p Depth of cut (mm) μ Coulomb’ s friction coefficient t CoTuB Turning-burnishing time (s) t cool Cooling time (s) d C Cylinder radius (mm) d a Axial offset between the centre of the burnishing- ball and the application point of the equivalent load- ings (mm) d r Radial offset between the centre of the burnishing- ball and the application point of the equivalent load- ings (mm) F Burnishing force (N) R The reduced radius of curvature (mm) a The radius of the contact area between the burnishing-ball and the external surface of the work- piece (mm) * Anis Rami anis.rami@outlook.com 1 LTDS, ENISE, Université de Lyon, 58 rue Jean parot, 42023 Saint-Étienne, France 2 ENIM, LGM, Université de Monastir, Avenue Ibn Eljazzar, 5000 Monastir, Tunisia 3 ENIT, Université de Tunis El Manar, 1002 Tunis, Tunisia The International Journal of Advanced Manufacturing Technology https://doi.org/10.1007/s00170-018-2086-7