INSTABILITY IN A DISLOCATION ENSEMBLE AT PLASTIC DEFORMATION IN METALS

A problem related to the development of instability of a homogeneous state in an ensemble of screw dislocations under plastic deformation of metals is considered . The study of the development of instability and structure formation in the dislocation ensemble is carried out on the basis of the method developed for charged particles in plasma and associated with the correlation interaction of electrons and positively charged ions. Accordingly, the screw dislocation ensemble is represented as a system of dislocations with an opposite Burgers vector, i.e., as a plasma-like medium with opposite dislocation charges. The total dislocation charge of the dislocation ensemble is equal to zero due to the law of conservation of the Burgers vector. In this situation, the elastic field of dislocations is “cut off”. The stress field of a single dislocation is shielded by a uniformly distributed dislocation “background” and is characterized by a certain effective potential. It is found that at long distances it decreases exponentially. Therefore, the value in the argument of the falling potential can be considered as the radius of screening of the elastic field of dislocations. It is shown that the screening radius is equal to the correlation radius, which makes it possible to construct a two-particle correlation function and find the energy of the correlation interaction of dislocations. A system of kinetic equations for a dislocation ensemble is formulated, taking into account the elastic and correlation interaction of dislocations, as well as the processes of their generation and annihilation. The criterion of instability of the homogeneous distribution of dislocations for the formulated system of equations is established. The instability criterion is met under the condition that the dislocation density exceeds a certain critical value that depends on the square of the flow stress and material constants (such as the Burgers vector modulus and shear modulus, as well as indirectly, the packing defect energy). In the framework of linear analysis, it is shown that when one system of sliding screw dislocations is taken into account, a one – dimensional periodic dislocation dissipative structure is formed at the moment of instability occurrence, and when multiple sliding is taken into account, solutions appear in the form of various variants of polyhedral lattices (cellular structures). It is established that the characteristic size of the cellular structure coincides with the experimental dependence both qualitatively and quantitatively ( the cell size is proportional to the square root of the dislocation density, and the proportionality coefficient is about ten). It is shown that the origin of spatially inhomogeneous dislocation structures, based on correlation instability, depends mainly on the features of the elastic interaction of dislocations and is not critical to the choice of the mechanisms of their kinetics (i.e., the mechanisms of generation, annihilation, and runoff of dislocations).