A new constitutive relation has been established by modifying Zerilli-Armstrong formulation whose performance is investigated in simulating continuous-shear and shear-localisation during orthogonal machining of a super alloy. Two different procedures in consonance with strains, strain rates, temperatures and thermo-mechanical-coupling encountered during metal cutting were adopted to identify material-constants for continuous-shear and shear-localisation. The constitutive data for continuous-shear is generated by using the distributed- primary-zone-deformation model. In contrast, an inverse methodology is followed to calibrate material-constants for shear-localisation where values were adjusted iteratively until predicted cutting force and chip morphology matched experimental values. The iterative procedure was also used to investigate sensitivity of shear-localisation to constitutive parameters. The constitutive relation was later implemented in two different finite element models to separately simulate serrated- and continuous-chip formation. The proposed constitutive relation successfully captured the underlying physics of continuous-shear and shear-localisation with finite element predictions of cutting force and chip morphology being in good agreement with experimental results over the range of conditions encompassing the two deformation mechanisms. The proposed law was further validated against split-Hopkinson-pressure-bar test-data. Moreover, the proposed relation gave better physics-based predictions when compared to those from the Johnson-Cook model. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.