A finite element model has been developed with Abaqus/Explicit to model the orthogonal cutting of Ti6Al4V. Experiments were carried out to validate its results. The experimental cutting conditions are the same as those used in the finite element model. They lead to the production of a saw-toothed chip, either numerically or experimentally. The comparison of the model results shows that the difference with the experimental RMS cutting force value is quite large (about 40%). Both chips morphologies are similar although the teeth of the simulated one have smaller valleys and lengths. The numerical model could therefore be improved. The aim of this paper is to study the influence of the material behavior law and the damage value on the model results, in order to get closer to the experimental results. It shows that the difference between numerical and experimental cutting forces reduces drastically (it becomes of the order of 2%) for stresses obtained with the modified behavior law similar to those observed in the literature. The teeth of the chip have a larger valley and are therefore closer to the experimental chip. These improvements do not interfere with the physics of the saw-toothed chip formation, which is still the same as the experimental one. An important point is that it turns out that the influence of the material behavior law and of the damage value are almost decoupled within the limits of the variations selected. Indeed, the material behavior law controls the level of the cutting force while the damage value acts mostly on the morphology.