Titanium alloys are well-known as hard-to-machine materials with a low thermal conductivity which gives rise to heat and thermal stress localization near the tool-chip interface during machining. The constitutive model that describes material behavior during severe deformation is fundamental to the fidelity of numerical simulations that offer a cost-effective method to study the machining process. However, the lack of understanding on the coupled temperature effects involved in the evolution of chip morphology, the constitutive model, which is essential for optimizing a machining process, is underexploited. This paper presents an improved Johnson-Cook material constitutive model (JCM-IM) to account the temperature-dependent factor, and its coupled effects between the critical strain and temperature on flow-softening of Ti-6Al-4V alloy during machining. Along with the procedure for implementing and calibrating the JCM-IM in a machining FEA software, the best-fit parametric values of the JCM-IM for characterizing orthogonal cutting of Ti-6Al-4V alloy are presented. The calibrated JCM-IM, which has been verified by comparing the simulated forces, chip morphology and overall/critical shear strains in the primary shear band over a wide range of cutting speeds and feed-rates, is capable of predicting different deformation mechanisms around the dynamic recrystallization onset temperature for machining of Ti-6Al-4V alloy. Several sets of simulation results, which agree well with experimental data, illustrate the effects of cutting speed on temperature distribution around friction/shear zones, chip morphology evolution, and shear strains in the primary shear zone. The numerical findings offer intuitive insights into the transition from a continuously smooth flow to a periodically serrated flow as the cutting speed increases. © 2018, Springer-Verlag London Ltd., part of Springer Nature.