Determining a material constitutive law that is representative of the extreme conditions found in the cutting zone during machining operations is a very challenging problem. In this study, dynamic shear tests, which reproduce, as faithfully as possible, these conditions in terms of strain, strain rate, and temperature, have been developed using hat-shaped specimens. The objective was to identify the parameters of a Johnson–Cook material behavior model by an inverse method for two titanium alloys: Ti6Al4V and Ti555-3. In order to be as representative as possible of the experimental results, the parameters of the Johnson–Cook model were not considered to be constant over the total range of the strain rate and temperature investigated. This reflects a change in the mechanisms governing the deformation. The shear zones observed in hat-shaped specimens were analyzed and compared to those produced in chips during conventional machining for both materials. It is concluded that the observed shear bands can be classified as white-etching bands only for the Ti555-3 alloy. These white bands are assumed to form more easily in the Ti555-3 alloy due to its predominately β phase microstructure compared to the Ti6Al4V alloy with a α + β microstructure.