The integral method of incremental hole-drilling is used extensively to determine the residual stress distribution in isotropic materials. When used with Tikhonov regularization, the method is robust and produces accurate results with minimal uncertainty. Alternatively, an optimal hole depth distribution can be found using the method of Zuccarello to improve the conditioning of the calibration matrices. If substantial measurement noise or a steep variation in stress exists, however, considerable uncertainty in, or distortion of, the calculated residual stress distribution can occur. Series expansion offers an alternative solution, but it has been reported to become unstable before meaningful accuracy can be achieved. Investigate the use of series expansion to determine a rapidly changing throughthickness residual stress distribution in an aluminium alloy 7075 plate subjected to laser shock peening treatment. Power series expansion of eigenstrains is used in finite element modelling to calculate the calibration coefficients. Monte Carlo simulation is used to determine robust uncertainties in the residual stress distributions. This allows the series order with the lowest RMS uncertainty in stress to be selected from those series orders that have converged. The best estimate of the residual stress distribution is thereby obtained. Series expansion is shown to be stable up to 8th order and convergence to a stress solution can be found before instability dominates. The method is insensitive to measurement errors due to the least-squares approach employed by the inverse solution. The use of series expansion reduces the RMS uncertainty in stress when compared to the regularized integral and Zuccarello methods.

中文翻译：

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幂级数展开法在增量钻孔法测定残余应力中的应用

增量钻孔的积分方法被广泛用于确定各向同性材料的残余应力分布。当与 Tikhonov 正则化一起使用时，该方法是稳健的，并以最小的不确定性产生准确的结果。或者，可以使用 Zuccarello 方法找到最佳孔深度分布，以改进校准矩阵的条件。但是，如果存在大量的测量噪声或应力的急剧变化，则计算出的残余应力分布可能会出现相当大的不确定性或失真。系列扩展提供了一种替代解决方案，但据报道，在达到有意义的精度之前，它会变得不稳定。研究使用系列扩展来确定经过激光冲击强化处理的 7075 铝合金板中快速变化的全厚度残余应力分布。在有限元建模中使用本征应变的幂级数展开来计算校准系数。Monte Carlo 模拟用于确定残余应力分布中的稳健不确定性。这允许从已经收敛的那些级数中选择具有最低应力 RMS 不确定性的级数。从而获得残余应力分布的最佳估计。级数展开被证明在 8 阶之前是稳定的，并且在不稳定性占主导地位之前可以找到应力解的收敛。由于逆解采用最小二乘法，该方法对测量误差不敏感。与正则化积分和 Zuccarello 方法相比，级数展开的使用降低了应力的 RMS 不确定性。