The aim of the paper is the modeling of chip formation in metal cutting in order to describe the thermomechanical interactions at the tool-chip interface (TCI). A particular attention is paid for the fully sticking case to complete previous modeling works which were more focused on the sliding regime or mixed sliding/sticking regime. The fully sticking contact is dominating due to the combined effects of high magnitudes of the normal stress, the average friction coefficient and the temperature. This case is also well adapted for cutting of titanium alloy. In the present model, these local parameters are macroscopically expressed through the average friction coefficient , and the velocity field on the secondary shear zone is modeled using a new approach. The ratio between real area of contact A (r) and the apparent area A (n) is taken into consideration. The developed approach is also fully thermomechanically coupled with heat transfer consideration. In this way, it was possible to predict normal and shear stress according to the variation of cutting velocities, feed and rake angle. The model was supported by the experimental trends from Ti6Al4V alloy cutting tests and worn tools analysis. It was shown that the distribution of the ratio A (r) /A (n) may be considered as a good indicator to describe the spreading of the adhesion marks on the contact. The model also highlights how the influence of the apparent friction coefficient, the rake angle, the feed and the cutting speed acts on the tool-chip contact length.