Discontinuous deformation as a phenomenon of plastic deformation instability, observes for a variety ductile materials in some range of strain rates and temperature. It is known fact that the tem- perature and strain rate are the most important parameters of the inelastic deformation. For the majority of polycrystalline materials, in the absence of phase transitions, temperature increase and decrease of strain rate leads to a reduction in plastic deformation resistance. At the same time for the majority of alloys in some ranges of temperatures and strain rates observed inverse dependence of the flow stress. Most researchers considered that the main cause of the anomalous behavior is a diffusion process and dislocation-impurity interaction. Portevin-Le Chatelier effect is the best known manifestation of the influ- ence of diffusion processes on the behavior of deformable material. Establishing the ranges of impacts which implement discontinuous yielding and eliminate them from the technological regimes is a very urgent problem today.Various methods and approaches based on mathematical modeling, are most preferred for the analysis of discontinuous yielding, determine the effective processing conditions and design of new materials. Experimental methods for studying this phenomenon resource intensive and applicable only for existing materials. Construction of mathematical models which accurately reproduce investigated processes is impossible without studying the available empirical information to establish the leading physical mechanisms.In the first part of the review considered the works devoted the description of the physical mechanisms and experimental studies of serrated yielding. The main mechanism is considered the interactions between mobile dislocations and diffusing solute atoms. Three main types of Portevin-Le Chatelier effects has been allocated based on the experimental data of uniaxial loading, in real experi- ments could experience different combination of these three types. Different approaches and models (macro phenomenological, structure-mechanical, physical) used for the theoretical description of the discontinuous deformation, in the present review we analyze only phenomenological models.

review, models, Portevin-Le Chatelier effect, serrated yielding, strain aging, nega- tive strain-rate sensitivity, instability, constitutive model, elasto-viscoplastic model, phenomenological model.