The finite element modeling is significantly depended on the accurate prediction of the thermomechanical material behavior. In order to increase the accuracy of numerical simulations, a new phenomenological model is proposed in this study. Its mathematical formulation allows accurate predictions of the Ti6Al4V sensitivity to the strain rate and the temperature, while maintaining a low identification cost of its constitutive coefficients. Its implementation in the Abaqus® software is carried out based on the developed VUMAT. The subroutine robustness is investigated in the case of the modeling of uniaxial tensile and impact tests. A 3D numerical analysis of the Ti6Al4V machining is set up based on the definition of the rheological Johnson-Cook model and the proposed one. Experimental orthogonal machining tests are also established for several cutting conditions. An important sensitivity of the chip serration, segments geometry and the cutting forces to the feed rate is pointed out. Comparisons of the numerical results obtained with both models are carried out. Interesting agreements with the experimental results are guaranteed with the new phenomenological model, which is not the case of the Johnson-Cook empirical law. In addition, intuitive insights about the effect of the cutting conditions on the material flow towards the workpiece edges and the side burr geometry are provided with the 3D numerical modeling. The results presented in this study point out the inability of the 2D numerical simulations to accurately predict the phenomena induced during the machining process, even in the case of an orthogonal machining.