The Johnson–Cook constitutive equation is very widely used for simulating cutting processes. Different methods are applied for establishing parameters of the constitutive equation. Based on the methods analysed in this study, two algorithms were worked out to determine the constitutive parameters for the prevailing conditions during cutting processes. In the first algorithm, all constitutive parameters were established simultaneously with standardized test methods. In the second algorithm, the constitutive parameters were established separately in accordance with the cutting conditions prevailing in machining processes. The developed methodology was verified with AISI 1045 heat-treatable steel and Ti10V2Fe3Al (Ti-1023) titanium alloy. The two materials were examined in standardized tensile and compression tests with varying strain rates and temperatures. In addition, the kinetic characteristics of the orthogonal cutting process were established. Based on the results obtained by experiment and the algorithms developed, the constitutive parameters for the cutting conditions were calculated. The parameters were used to determine the material model for simulating the orthogonal cutting process. The algorithms developed were verified by comparing the simulated and experimentally determined kinetic cutting characteristics, which confirmed their good quality.

The thermomechanical interaction of the tool with the chip in the most loaded secondary cutting zone depends on the contact length of the tool rake face with the chip. Experimental studies of the dependency of the contact length on the cutting speed, the undeformed chip thickness, and the tool rake angle, performed by the optical method, are used for comparison with the contact length obtained by the FE modeling of the orthogonal cutting process. To determine the parameters of the constitutive Johnson–Cook equation, which serves as a material model of the FE cutting model that has a predominant influence on the contact length, a software-implemented algorithm was developed. This algorithm is based on determining the generalized parameters of the constitutive equation through finding the intersection of these parameter sets. The plurality intersection of the parameter sets of the constitutive equation is determined by means of the design of experiments and refined by subsequent multiple iterations. The comparison of the contact length values, obtained by simulating the cutting process using the generalized parameters of the constitutive equation as a material model with their experimental values, does not exceed 12% for a wide range of cutting speeds and depths of cut, as well as for the tool rake angle.