Analytical model for measurement of stresses using two-hole drilling

Abstract

Residual stresses have a significant effect on the strength, deformation, plasticity, and fatigue properties of materials. In general, tensile residual stresses are adverse to material performance and component life, while compressive residual stresses can improve material fatigue strength. In this study, an analytical model employing two-hole drilling (THD) is proposed for the measurement of interior stresses. Firstly, the analytical solution for the distortion of the reference hole induced by drilling an adjacent hole is derived using the complex variable method. Based on the analytical solution, the reverse procedure is established to determine the original stress state. Then, the comparative validations of the THD method with the deep hole drilling (DHD) method are performed in conjunction with the finite element (FE) simulations for the beam subjected to bending, the unloaded elastoplastic beam, and the shrink fitted assembly. Finally, parametric analysis is conducted and the results show that: the influence of drilling an adjacent hole on the reference hole rises with the increase of the hole diameters or the decrease of the hole spacing; the THD method is able to give good estimations for the stresses with linear, parabolic, and sinusoidal distributions, although the accuracy is reduced for the prediction of the longitudinal residual stress in the cold-formed section; the uncertainties in evaluated stresses ascend linearly with the increase of the measurement error in the diameter of the reference hole. Relative to the DHD method, the THD method has the merits of less damage and less equipment required and can provide an effective approach for the measurement of stresses inside materials.