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

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Abstract

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.

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Notes

  1. It is worth noting that the same formulas are used in the ring-core method; thus the following discussion also applies to the evaluation of calibration coefficients for this technique.

  2. Note that infinite elements are not always available in commercial codes.

  3. Gary S. Schajer, personal communication.

  4. Actually, quite satisfactory results are obtained using the same width as in the hydrostatic case.

  5. In principle, the ring could be radially free, because load is self-balanced, but this assumption leads to physically inconsistent results (either a negative Young’s modulus or c<b is obtained)

  6. Note that if a semi-analytical solution is used (i.e. an axial-symmetric computation expanded in Fourier series), the \(\cos (2\theta )\) and \(\sin (2\theta )\) terms are implicit in the expansion, thus u r has to be evaluated at 𝜃=0 whereas u 𝜃 has to be computed assuming 𝜃 = π/4.

References

  1. ASTM E837-08e1 (2008) Standard test method for determining residual stresses by the hole-drilling strain-gage method. American Society for Testing and Materials, West Conshohocken, PA

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Acknowledgments

I am grateful to Prof. G. S. Schajer with whom I discussed some of the topics investigated in this paper. He provided me insightful comments and constructive criticisms at different stages of my work. Any error contained herein, naturally, remain my responsibility.

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  1. Dipartimento di Ingegneria Meccanica, Chimica e dei Materiali, Università degli Studi di Cagliari, Via Marengo, 2, I-09123, Cagliari, Italy

    Antonio Baldi

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Correspondence to Antonio Baldi.

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Baldi, A. Far-Field Boundary Conditions for Calculation of Hole-Drilling Residual Stress Calibration Coefficients. Exp Mech 57, 659–664 (2017). https://doi.org/10.1007/s11340-016-0235-1

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