Analysis of the diffusion-induced stresses of a cylinder during carburization

The diffusion process of constant surface concentration of carbon from inner wall toward outer surface was studied based on the Fick's law. The formulas of the stresses induced by carbon diffusion in the cylindrical structure for the case of plain strain were derived using solid mechanics theory. The distribution of radial stress, circumferential stress and axial stress induced by carburization was investigated. The results show that for a given cylindrical structure the concentration increases with time extended. The radial stress component is compressive all the time. The circumferential stress has the maximum value at the inner surface of cylindrical structure at the initial. The state of circumferential stress is compressive in the region near inner surface and tensile near outer surface. The trend of the axial stress distribution is similar to the circumferential stress. The analysis also shows that the ratio of outer radius to inner radius of cylindrical structure has an effect on the distribution of carbon concentration and stresses.