Current constraints on aeronautical parts have led to the introduction of materials like titanium alloys as well as new part geometries featuring large dimensions and reduced thickness. Inappropriate cutting forces during turning operations could lead to high deflections and damage to the machine. In order to ensure the respect of final part geometry and the optimal use of resources, cutting forces have to be known, to anticipate the deformed shape during and after machining operations on thin parts. Current models are offering a solution which can be optimised by the modelling influence of the ploughing effect on cutting forces. Therefore, a mechanistic model is developed in order to improve the prediction of cutting forces during turning operations on titanium alloy Ti6Al4V: this model includes the effect of the clearance face contact radius and comprises two main steps. First, the effect of the clearance contact radius and the effect of the cutting edge lead angle are determined independently, via a direct identification method based on elementary cutting tests. Secondly, this analysis is extended to cutting trials in boring, cylindrical turning and face turning. Then, based on a mechanistic approach, a model is defined according to the previous results and the coefficients are identified thanks to cutting trials in real conditions. The results of the proposed model are then compared to a commonly used model which takes into account mostly the uncut chip thickness effect. It is demonstrated that the proposed cutting force model provides a more accurate prediction of cutting forces.