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General Calibration Formulas for Incremental Hole Drilling Optical Measurement

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Abstract

Residual stress measurement has significant practical implications in the service, security and reliability of components. The hole-drilling method is one of the most popular techniques used to measure residual stress. With hole drilling calibration matrices, it is possible to deduce the variation in stress with depth by incrementally deepening the hole. Calibration matrices for each type rosette of strain gauges contain a large number of discrete redundancy data and the drilling depth must be specified and spaced evenly throughout. Thus, it greatly limits the flexibility of optical measurement methods. For this reason, it is important to have more compact and continuous formulas for the measurement of residual stress. In this paper, the discrete redundancy coefficients have been simplified through formulations. The modified calibration formulas, the error of which is less than 1 %, can improve the performance and flexibility of residual stress distribution measurement across thickness. Meanwhile, it allows us to obtain some special data for any arbitrary depth that are not contained in the hole-drilling strain-gage method.

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Acknowledgments

The authors are grateful for the financial support from the National Natural Science Foundation of China (Grant Nos.11072151, 11372182).

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Authors and Affiliations

  1. Department of Engineering Mechanics, Shanghai Jiao Tong University, 800 Dongchuan RD. Minhang District, Shanghai, 200240, China

    K. Zhang, M. Yuan & J. Chen

  2. MOE Key Laboratory of Hydrodynamics, Shanghai Jiao Tong University, Shanghai, 200240, China

    J. Chen

Authors
  1. K. Zhang
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  2. M. Yuan
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  3. J. Chen
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Corresponding author

Correspondence to J. Chen.

Appendix A Symbols

Appendix A Symbols

E :

Young’s modulus

μ :

Poisson’s ratio

θ :

angle of measuring point from the x-axis

r :

radius of the measuring point

r o :

radius of the drilled hole

j :

number of hole depth steps so far

k :

sequence number for hole depth steps

H :

hole depth so far corresponding to j

H :

stress depth corresponding to k

ε j :

relieved strain measured after j hole depth steps have been drilled

ε r :

radial relieved strain for uniform stress case

σ r :

uniform normal r-stress

σ θ :

uniform normal θ-stress

σ 1 :

maximum principal stress

σ 2 :

minimum principal stress

D :

diameter of the measuring point

D o :

diameter of the drilled hole

σ x :

uniform normal x-stress

σ y :

uniform normal y-stress

a jk :

calibration matrix for isotropic stresses

b jk :

calibration matrix for shear stresses

A jk :

cumulative calibration matrix for isotropic stresses

B jk :

cumulative calibration matrix for shear stresses

A l j-k :

normalized accumulated release formula for isotropic stresses

B l j-k :

normalized accumulated release formula for shear stresses

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Zhang, K., Yuan, M. & Chen, J. General Calibration Formulas for Incremental Hole Drilling Optical Measurement. Exp Tech 41, 1–8 (2017). https://doi.org/10.1007/s40799-016-0008-x

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  • DOI: https://doi.org/10.1007/s40799-016-0008-x

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