(山东大学 机械工程学院，济南 250061)
摘 要: 采用裂纹柔度法测试残余应力时，柔度函数的计算和插值函数阶数的合理选择对计算结果的精确性有着较大影响。采用有限元法计算得到测试试样的裂纹柔度函数；考虑应力计算不确定度两个主要的来源：应变测量数据的随机误差以及模型误差，基于应力总不确定度的最小化目标，确定最优的插值函数阶数，进而计算得到铝合金预拉伸板7050-T7451内部残余应力的分布规律。结果表明：采用9阶勒让德多项式能较好地拟合此铝合金板材内部残余应力的分布，不确定度的均方根值为2.797 MPa，预拉伸板内部残余应力呈明显的外压内拉的“M型曲线”分布规律。
关键字: 级数扩展；残余应力；裂纹柔度法；预拉伸铝合金板；不确定度
pre-stretched aluminum alloy plate using crack
compliance method
（School of Mechanical Engineering, Shandong University, Ji’nan 250061, China）
Abstract:In the evaluation of the residual stresses by the crack compliance method, the calculation of compliance functions and the choice of the order of interpolation function are important to calculation results. The compliance functions were calculated by using finite element method. An optimal expansion order was obtained based on minimizing the total stress uncertainty which was evaluated by considering the two main sources in the calculation of stress uncertainty: the random errors in strain data and model error. Then the residual stress depth profiles in pre-stretched aluminum alloy plate 7050-T7451 were determined. The results reveal that Legendre polynomials that the fit order is 9 can evaluate accurately through-thickness residual stresses of thick plate, and the root-mean-square average over uncertainty is only 2.797 MPa. It is also shown that the residual stresses distribution in pre-stretched aluminum alloy plate can be revealed by “M type curves”, that is, the exteriors are residual compressive stress and the interiors are residual tensile stress.
Key words: series expansion; residual stresses; crack compliance method; pre-stretched aluminum alloy plate; uncertainty
