Machining of metals is an essential operation in the manufacturing industry. Chip formation in metal cutting is associated with large plastic strains, large deformations, high strain rates and high temperatures, mainly located in the primary and in the secondary shear zones. During the last decades, there has been significant progress in numerical methods and constitutive modeling for machining operations. In this work, the Particle Finite Element Method (PFEM) together with a dislocation density (DD) constitutive model are introduced to simulate the machining of Ti-6Al-4V. The work includes a study of two constitutive models for the titanium material, the physically based plasticity DD model and the phenomenology based Johnson-Cook model. Both constitutive models were implemented into an in-house PFEM software and setup to simulate deformation behaviour of titanium Ti6Al4V during an orthogonal cutting process. Validation show that numerical and experimental results are in agreement for different cutting speeds and feeds. The dislocation density model, although it needs more thorough calibration, shows an excellent match with the results. This paper shows that the combination of PFEM together with a dislocation density constitutive model is an excellent candidate for future numerical simulations of mechanical cutting.