Slip Distribution in a Thin Slice of a Crystal at a Free Surface

Abstract

The plastic deformation in a thin slice of a most-favorably-oriented crystal embedded at the free surface of a fine-grained aggregate is considered. The elastic moduli of the individual crystals are assumed to be isotropic and homogeneous. The analogy of plastic strain and applied force in an elastic medium is utilized. This equivalent force due to plastic strain is considered to be applied to a semi-infinite elastic medium under plane strain. Melan's results for the stress field caused by a force acting in a semi-infinite elastic plate modified for plane strain are used to calculate the plastic strain distribution. The slip near the free surface is greater than that at the interior end of the thin slice. This seems to explain the removal of some fatigue damage by electroplating the surface of a test specimen.