Tikhonov Regularization for the Fully Coupled Integral Method of Incremental Hole-Drilling

Abstract

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.