Abstract

Background

The unit pulse integral method is used extensively with the incremental hole-drilling residual stress measurement technique. The ASTM E837 standard, which applies only to isotropic materials, recommends the use of Tikhonov regularization to reduce instability when many depth increments are used. In its current formulation, Tikhonov regularization requires the decoupling of stress, as is possible for isotropic materials. The fully coupled integral method is needed for residual stress determination in layered composite laminates and is currently employed without Tikhonov regularization. This causes greater sensitivity to measurement errors and consequently large stress uncertainties. An approximate method of applying Tikhonov regularization exists for biaxial composites, but is not applicable to more complex laminates.

Objective

Extend Tikhonov regularization to the fully coupled integral method to improve residual stress determination in composite laminates.

Methods

This work investigates the use of the approximate and fully coupled regularization approaches in an angle ply composite laminate of [+45/-45/0/90]_s construction. Experimental validation in a [0/+45/90/-45]_s laminate is also presented where the regularized fully coupled integral method is compared to the series expansion method that includes all in-plane stress and strain directions simultaneously in a least-squares solution.

Results

The regularized integral method produces comparable results to those of series expansion while requiring twelve times less FE computation to calculate the compliances. The optimal degree of regularization is also more convenient to determine than the optimal combination of series order required by series expansion.

Conclusions

The new method is easily applied and should find wide application in the measurement of residual stresses in composite laminates.

中文翻译：

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增量钻孔全耦合积分法的吉洪诺夫正则化

摘要

背景

单位脉冲积分法广泛应用于增量式钻孔残余应力测量技术。ASTM E837 标准仅适用于各向同性材料，建议使用 Tikhonov 正则化来减少使用许多深度增量时的不稳定性。在当前的公式中，吉洪诺夫正则化需要应力解耦，这对于各向同性材料来说是可能的。确定层状复合材料层合板中的残余应力需要完全耦合积分方法，并且目前在没有吉洪诺夫正则化的情况下使用。这会导致对测量误差更加敏感，从而导致较大的应力不确定性。对于双轴复合材料存在应用吉洪诺夫正则化的近似方法，但不适用于更复杂的层压板。

客观的

将吉洪诺夫正则化扩展到全耦合积分方法，以改进复合材料层合板中残余应力的确定。

方法

_{这项工作研究了近似和完全耦合正则化方法在 [+45/-45/0/90]结构}的角层复合层压板中的使用。_{还介绍了 [0/+45/90/-45] s}层压板中的实验验证，其中将正则化全耦合积分方法与级数展开方法进行比较，级数展开方法同时以最小二乘法包含所有面内应力和应变方向解决方案。

结果

正则化积分方法可产生与级数展开相当的结果，同时计算合规性所需的 FE 计算量减少 12 倍。正则化的最优程度也比级数展开所需的级数最优组合更容易确定。

结论

新方法易于应用，应该在复合材料层压板残余应力的测量中得到广泛应用。