Stress fields in the surface region of pearlite

Recently we analyzed by X-ray diffraction the triaxial thermoelastic stresses in white cast iron. The transition to the biaxial stress field in the surface region of the polyphase specimen was now studied using synchrotron radiation. In order to understand better the experimental results, a theoretical investigation of the stress fields in the surface region of an idealized pearlitic stack was performed. The study is based on the continuum theory of elasticity applied to the case of inclusions in a half space. An important result is the observation that gradients of the stress components which drop to zero in the surface automatically induce gradients of remaining biaxial stresses. Quantitatively this effect was already demonstrated for triaxial sinusoidal distortions, and qualitatively it may be immediately deduced from the equilibrium conditions. It therefore does not seem generally justified to believe that X-rays detect in the surface layer of polyphase materials the biaxial stresses from the bulk material.