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This research is motivated by numerous experimental observations that demonstrate that a narrow layer with drastically modified microstructure is generated near frictional interfaces. This layer is usually called white layer in papers devoted to machining processes and fine grain layer in papers devoted to metal forming processes. Two of the main contributory mechanisms responsible for the generation of such layers are: (a) the mechanism of rapid heating and quenching and (b) the mechanism of intensive plastic deformation. The latter can be described by means of the strain rate intensity factor. This factor is the coefficient of the leading singular term in a series expansion of the equivalent strain rate near maximum friction surfaces. This expansion shows that the equivalent strain rate is infinite at the friction surface. Therefore, the strain rate intensity factor controls the magnitude of the equivalent strain rate in its vicinity. A necessary condition for the existence of the strain rate intensity factor is the friction boundary condition in the form of the maximum friction law. This boundary condition is often adopted at the tool - chip interface (at least, over a portion of this interface) in machining processes. This zone is usually called the sticking zone. The existence of such zones has been reported in deformation processes as well. However, it is worthy of note that the actual seizure (the velocity vector is continuous across the interface) may or may not occur in theoretical solutions. It depends on the constitutive equations chosen. The present paper deals with an approach for using the strain intensity factor in constitutive modeling for predicting the evolution of material properties in a narrow layer in the vicinity of frictional interfaces. The theory developed is supported by experiment on extrusion of a magnesium alloy.