Stress field in metals at initial stage of plastic deformation

Abstract

The initial stage of plastic deformation of a fine grained aggregate with slip occurring only in the most favourably oriented crystals is studied. The elastic modulus of the individual crystals is taken to be isotropic. The sliding crystals are assumed to be cubical in shape and located at the interior of the aggregate. Work-hardening in the sliding crystal is considered. The analogy of plastic strain gradient and body force in producing stress field in an elastic medium is developed. This analogy is applied to calculate the slip and stress fields caused by (1) one sliding crystal and (2) two sliding crystals spaced at a clear distance of half the crystal width. This shows the interaction effect of slips in two nearby crystals. From these stress fields, the residual stress may be easily obtained and the Bauschinger effect is clearly shown.