基于弹性理论的残余应力反演和变形计算

Residual Stress Inversion and Deformation Calculation Based on Theory of Elasticity

毛坯在制造过程中,材料力学性能的非均匀性导致其内部产生残余应力.残余应力会造成结构破坏,在工件的切削去除过程中,残余应力会逐渐释放并引起变形.采用有限元的“生死单元”技术模拟材料的切削去除过程,并转化为残余应力的释放,基于板壳理论、小变形理论、弹性理论和叠加原理,将径向基函数插值法与几何方程、物理方程相结合,开发出一种新的解析方法,反演残余应力场并计算变形.结果表明解析方法的理论解与有限元解高度吻合,能够用于判断残余应力分布并计算残余应力弹性释放引起的变形.

During the manufacturing process of a rough workpiece,the non-uniformity of material mechanical properties can result in the generation of residual stresses within the workpiece.The residual stresses can lead to structural failure.During the cutting removal process of the workpiece,the residual stresses will gradually release and then cause deformation.The"birth-death element"technique of finite element analysis was used to simulate the material's cutting removal process.And then we transformed this process into the release of residual stresses.This study proposed a novel analytical method that combined radial basis function interpolation with geometric and physical equations.It was based on the plate shell theory,small deformation theory,elasticity theory,and the superposition principle.The method aimed to invert the residual stress field and calculate the resulting deformation.The paper was divided into two parts.In the first part,the influence of stress equilibrium equations was neglected.We used the radial basis function interpolation method to invert the release of residual stresses in thin plates according to the initial residual stress field and the residual stress field after material removal.Next,the stresses were substituted into the physical equations to calculate the strain.The strain was substituted into the geometric equations and then the plane displacement was calculated by strain integration from geometric equations.Based on plate shell theory equations,the buckling deformation was inverted according to the plane displacement.In the second part,the reverse process of the first part was performed.Firstly.we inverted the buckling deformation caused by material removal in the thin plate.Then,the buckling deformation was substituted into the plate shell theory equations.We used them to invert the release of residual stress and the reconstructed residual stress field.The results demonstrated the reversibility of these two processes.Furthermore,the analytical solutions showed high agreement with the finite element solutions.This suggested that the analytical method of this paper is applicable to thin plate structures under elastic conditions.It is expected to estimate the residual stress distribution and predict the deformation in the thin plate cutting removal process.