Titanium and its alloys are often used in aerospace, power and biomedical applications due to their low density, high tensile strength, resistance to corrosion and high temperatures. However, these materials are well known to be difficult-to-cut materials and require to follow some special techniques to improve their machinability. It should be also noticed that some phenomena like segmentation and recrystallization can occur during the chip formation process. Therefore, fine grains are observed in the adiabatic shear bands located in the chip segments. The machined surface also presents fine grains because of the recrystallization of the microstructure. In the present work, a 2D finite element model based on Lagrangian formulation was developed in Abaqus/Explicit to simulate the orthogonal cutting process of the Ti6Al4V alloy. To take into account the recrystallization phenomenon, a new material constitutive model denoted 'Multi-Branch Model' (MB) was developed. The MB model is based on the Johnson-Cook (JC) flow stress model and its modified formulation, known as the tangent hyperbolic model (TANH), to introduce the softening effect due to the recrystallization process. This new model is coupled to a microstructural criterion in order to simulate the workmaterial microstructure evolution during the machining process. The recrystallized grains size field, cutting forces and chips morphology are compared to those obtained with the TANH model. Based on these results, a relationship between recrystallization and chip segmentation has been found and deeply discussed.