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The finite element modeling is significantly dependent on the accurate prediction of the material behavior. In order to increase the accuracy of numerical simulations, a new phenomenological model is proposed in this study. Its mathematical formulation allows suitable predictions of the Ti6Al4V sensitivity to strain rates and temperatures, while maintaining a low identification cost of its constitutive coefficients. A subroutine VUMAT is developed, and its reliability is investigated in the case of the modeling of uniaxial tensile and impact tests. In addition, the 3D numerical analysis of the machining process is investigated 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. The significant sensitivity of the chip serration, the segments geometry, and the cutting forces to the feed rate is pointed out. Comparisons of the numerical results corresponding to different constitutive models are carried out. High-correlation levels with the experimental results are reached with the definition of the proposed phenomenological model, which is not the case of the Johnson-Cook empirical law. Moreover, intuitive insights about the effect of cutting conditions on the material flow towards the workpiece edges are provided with the 3D modeling. A pronounced increase of the width of side burrs with the feed rate rise was underlined. The results presented in this study point out the inability of 2D numerical simulations to accurately predict the phenomena induced during the machining process, even in the case of an orthogonal machining. [ABSTRACT FROM AUTHOR]