ABOUT THE CALCULATION OF INTERNAL STRESSES FROM MESODEFECTS ACCUMULATING AT THE BOUNDARIES DURING PLASTIC DEFORMATION OF SOLIDS

Abstract

A new method of calculation of elastic stress fields from internal interfaces (intergranular and interphase boundaries) of plastically deformed polycrystals is proposed. As elementary sources of stress fields, rectangular boundary segments containing uniformly distributed segments of dislocation families accumulating on these segments during plastic deformation are considered. It is shown that the elastic stresses field from a segment with arbitrary geometry of plastic flow and segment orientation can be represented as a superposition of fields from four families of continually distributed dislocation segments with tangential and normal components of the Burgers vector. Analytical expressions for the elastic stress tensor components from each of the four families are obtained. In the limiting case, when the length of dislocation segments tends to infinity, the resulting expressions for the components of the elastic stress field transform known expressions for rotational and shear mesodefects. If dislocation segments have a normal burgers vector, then the stress field is equivalent to the stress field from the biaxial dipole of wedge disclinations. In the case of tangential components of the burgers vector, the field is equivalent to the stress field of the planar mesodefect. As an example of the method application, the calculation of internal stress fields in the plastically deformed crystal containing uniformly distributed cubic particles of the second phase is given. It is shown that the intensity of internal stresses at a given value of strain increases with increasing volume fraction of particles. It is found that for a given volume fraction of the second phase, the internal stresses does not depend on their size.