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Simulation of Infinite Boundaries When Evaluating Hole-Drilling Calibration Data

  • Sp Iss: Advances in Residual Stress Technology
  • Published:
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Abstract

Background

Effective use of the hole-drilling method for measuring residual stresses depends on the availability of accurate calibration data. A challenge arises when doing finite element modeling because the hole is conceptually drilled into an "infinite" material, while any practical model must have a finite far boundary. The use of a very distant far boundary provides a better simulation, but makes the required finite element model large and computationally burdensome.

Objective

The objective is to develop the practical use of an outer ring surrounding the target area of interest that can simulate an infinite far boundary and so allow the use of a more compact and computationally efficient finite element model.

Methods

Mathematical formulas were developed that specify the material properties of the needed outer ring. These apply to calibration calculations using both the hole loading and thermal loading methods.

Results

Isotropic loading models work directly for all finite element types and reproduce theoretical expectations to within 0.05%. Deviatoric loading models require some adjustment to fit the finite element model used, after which they can reproduce theoretical expectations to within 0.4%.

Conlusions

The use of a boundary ring is effective in simulating an “infinite” boundary when modeling the deformations around a stressed hole. This is useful when computing the calibration coefficients required when making hole-drilling residual stress measurements.

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Notes

  1. Equation (1) is a general equation that describes the deformations around a circular hole in a stressed infinite material. For a hole-drilling measurement R would refer to the radius R1 of the drilled hole. This is the source of the “Theory” lines that subsequently appear in Figs. 4 and 5. Alternatively, R could refer to the radius of the "hole" formed when the "Area of Interest" shown in Fig. 1 is removed so as to focus on the properties of the surrounding material that extends to infinity. This latter interpretation of R is used when evaluating the elastic properties of the boundary ring that will make it elastically equivalent to the "infinite" surrounding material.

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Acknowledgements

Thanks are due to Prof. Antonio Baldi for his insightful discussions and for his interest and support in the pursuit of this topic. The work was financially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).

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  1. Dept. Mechanical Engineering, University of British Columbia, Vancouver, Canada

    G. S. Schajer & L. To

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  1. G. S. Schajer
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Correspondence to G. S. Schajer.

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Schajer, G.S., To, L. Simulation of Infinite Boundaries When Evaluating Hole-Drilling Calibration Data. Exp Mech 62, 1247–1255 (2022). https://doi.org/10.1007/s11340-022-00834-w

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  • DOI: https://doi.org/10.1007/s11340-022-00834-w

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