**ESPI HOLE DRILLING**

## Hole-drilling is a residual stress measurement technique, where stressed material is removed by drilling a small blind hole in the area of interest.

The remaining material around the hole spontaneously finds a new stress equilibrium. This re-arrangement of stresses leads to a slight distortion of the surface near the hole. Though the displacements are small, they are measurable with ESPI and allow the calculation of the stresses that were present in the part prior to drilling.

##### Electronic Speckle Pattern Interferometry (ESPI)

The sample is illuminated with coherent
laser light. Due to optical surface roughness, which exists on many sample
surfaces naturally, the image the camera receives is not sharp but shows a
speckle pattern. Diffuse light scattering lets each camera pixel receive light
from multiple locations, which interferes constructively or destructively,
creating bright and dark spots in the image. This speckle pattern is characteristic
of the surface topography and changes with surface shifts.

The camera image is created by the interference of the object beam with the reference beam. The latter is phase shifted in ¼-wavelength increments and an image is taken for each shift, so that the surface condition is characterized by four images, before and after each drilling increment. The four images allow calculating a phase angle for each pixel, which then is translated into a surface displacement.

##### Measurement

The typical procedure starts with
determining the sample surface position relative to the drilling tool tip. In
the standard method, the user moves the drill towards the sample using software
commands and assesses the live camera images. Alternatively, zero may be
determined for electrically conducting materials with an optional attachment.
The user then selects the desired drilling depths and other drilling parameters
and starts data acquisition.

The software’s user interface makes it easy-to-use while providing a variety of options for adjusting measurement and calculation settings. The user can activate each drilling increment separately and take laser and white-light images manually. But the measurement can also be performed fully automatically for the whole depth list or by any combination of the two methods since the measurement can be interrupted at any time. Each drilling increment can be subdivided into multiple steps to control contact time between tool and part. Data analysis is performed after completion of a measurement. A measurement can be appended to as long as the sample hasn’t moved.

##### Data analysis

The basis for the stress calculation is a
set of coefficients for a cylindrical hole in a semi-infinite body and a plane
stress state. Stress depth profiles are calculated using the Integral Method.
Tikhonov regularization (a form of smoothing) is optional. The stress
calculation is equivalent to that described in ASTM E837 for strain gage
hole-drilling, yet correlates displacements directly with stresses. Strains are
not evaluated. The software allows the user to set the ring-shaped analysis
area and apply an optional pixel correction that replaces values of
poor-quality pixels through interpolation. The stress calculation assesses the
changes occurring in each individual drilling step – rather than changes
relative to the starting condition. This means that errors do not accumulate
and that the measurement is less sensitive to disturbances.

The software is designed to calculate stress depth profiles for multiple scenarios, such as different analysis areas, depth increment and image set selections, and regularization factors. It provides automatic graphing for comparing the results. Multiple measurements also can be compared easily. Graphs are generated for stresses in the sample coordinate system – horizontal and vertical directions, and shear stress – and for the principal stress directions. Data from any and all calculations and measurements can be copied with a single command for use in spreadsheets.

##### References related to Prism

- M. Steinzig and E. Ponslet, "Residual Stress Measurement using the hole drilling method and laser speckle interferometry, Parts I-IV”, Experimental Techniques, Vol.27, Issues 3,4,5,&6, 2003
- G. S. Schajer and M. Steinzig, “Full-Field Calculation of Hole-Drilling Residual Stresses from ESPI Data”, Experimental Mechanics, Vol.45, No.6, pp.526-532, 2005
- G.S. Schajer and M.B. Prime, “Use of Inverse Solutions for Residual Stress Measurements”, J. Eng. Mater. Technol., 125(3), pp.375-382, 2006
- Y. An and G. S. Schajer, “Pixel Quality Evaluation and Correction Procedures in ESPI”, Experimental Techniques, Vol.105, pp.106-112, 2010
- G.S. Schajer and T.J. Rickert, “Incremental Computation Technique for Residual Stress Calculations Using the Integral Method”, Experimental Mechanics, Vol.51, No.7, pp.1217-1222, 2011
- T.J. Rickert, “Stress Measurement Repeatability in ESPI Hole Drilling", in "Residual Stress, Thermomechanics & Infrared Imaging, Hybrid Techniques and Inverse Problems", Vol 9: Proceedings of the 2015 Annual Conference on Experimental and Applied Mechanics, Proceedings of the 2015 Annual Conference on Experimental and Applied Mechanics, pp 363-369
- T.J. Rickert, and W.L. Gubbels, “ESPI Hole Drilling of Rings and Holes Using Cylindrical Hole Analysis", to be published in the Proceedings of the 2016 Annual Conference on Experimental and Applied Mechanics

##### References for hole-drilling in general

- ASTM E837 - 08e2 Standard Test Method for Determining Residual Stresses by the Hole-Drilling Strain-Gage Method
- Good Practice Guide No. 53 - The Measurement of Residual Stresses by the Incremental Hole-Drilling Technique, P V Grant, J D Lord and P S Whitehead, The National Physical Laboratory, UK