Full field methods and residual stress analysis in orthotropic material. I Linear approach

This work analyzes the problem of residual stress determination in an orthotropic material using the hole drilling technique combined with non-contact, full field optical methods. Due to the complex behavior of the material, first a solution algorithm for the isotropic case is analyzed, then the procedure is extended to solving the more complex problem. In the first part of the work, the simplified Smith–Schajer solution to the through-hole problem for an orthotropic material is analyzed, showing that the same linear least square approach used in the isotropic case applies to a large set of orthotropic materials; based on this analysis a simple residual stress measurement algorithm is developed using either analytical or numerically estimated calibration coefficients. In the second part of the work, the general solution is discussed: since in this case the simplified Smith–Schajer solution cannot be used, the Lekhnitskii’s analysis of the through-hole plate in tension is introduced and extended to handle residual stresses. On this basis a solution algorithm using the nonlinear fit of the theoretical displacement field capable of treating all the orthotropic materials at the cost of a more complex numerical procedure is proposed. The performances of both algorithms are tested against numerically generated noisy fields and experimental ones and show a good reliability and accuracy.