圆筒中渗碳诱发的扩散应力分析

以菲克第2定律为基础,研究了表面碳浓度恒定时碳由圆筒内表面向外表面扩散的浓度分布情况.运用固体力学理论推导在平面应变条件下圆筒中各扩散应力分量的表达式,分析了圆筒中渗碳诱发的径向应力、周向应力和轴向应力沿壁厚的分布规律,并讨论了圆筒内、外半径比对碳浓度及其扩散应力分布的影响.结果表明,圆筒的内、外半径比对其渗碳表面的碳浓度和扩散应力分布的影响不同.当圆筒的内、外径一定时,其渗碳表面的碳浓度随着渗碳时间增加而增大;径向应力始终表现为压应力;周向和轴向的应力分布相似,并在渗碳初期,处于圆筒内表面周向、轴向的应力达到最大值;随着渗碳时间的延长,从内表面向外表面渗透的过程中,其应力状态逐渐由压应力转变为拉应力.

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.