Far-Field Boundary Conditions for Calculation of Hole-Drilling Residual Stress Calibration Coefficients

The Hole-Drilling method for residual stress measurement, both in its standard version based on strain gauge rosettes (ASTM E837-08e1 2008) and its derivative using optical methods for estimating the displacement field around the hole (Baldi (2005) J Eng Mater Technol 127(2):165–169; Schajer and Steinzig (2005) Exp Mech 45(6):526–532; Schajer (2010) Exp Mech 50(2):159–168), relies on numerical calibrated coefficients (A and B) to correlate the experimentally acquired strains (displacements) with residual stress components. To estimate the A and B coefficients, two FEM (Finite Element Method) computations are required, the former related to a hydrostatic stress state, the latter to a pure shear case. Both can be implemented using either a semi-analytical approach (i.e. an axis-symmetric mesh expanded in the tangential direction using a Fourier series) or a tri-dimensional mesh, usually exploiting the double symmetry of the problem. Whatever the approach selected, the definition of constraints to be applied to the outer boundary is critical because the hole-drilling method assumes an infinite plate, thus both the usual solutions—fully constrained or free boundaries—are unable to correctly describe the theoretical situation. In the following, the problem of correct simulation of the infinite domain will be discussed and two simple and effective solutions will be proposed.