A Displacement Based Analytical Model to Determine Residual Stress Components in a Finite Elastic Thin Plate with Hole-Drilling Method

Abstract

In order to measure the residual stress components in an elastic thin plate, the hole-drilling strain-gage method has been used. This method enables to determine the relation between the magnitudes and directions of the principal stresses and the strain relaxation about the hole. In the existing analytical models based on stress field, the formulations associated with the hole-drilling method are based on the assumption of an infinite plate, this may cause some errors for a finite plate and it’s difficult to validate these solutions by FE methods. Furthermore, in the composite, the displacement field is continuous but the stress field is not necessarily continuous, the displacement field based method has to be used. In the present paper an analyt-ical model based on a displacement field described by a function with coefficients to determine for a finite round thin plate is presented. The coefficients used in the displacement field are independent on the three residual stress components, and they are determined by minimization of the internal strain energy during the hole-drilling process. Once the coefficients in the dis-placement field are determined, three strains measured in three radial directions are utilized to determine the three residual stress components. The proposed analytical model can be also adapted to infinite plate by assuming that the diameter of the round plate tends to infinite.