Residual Stress Measurement by the Hole-Drilling Method

SINT Technology is an Italian firm located in Florence, Italy. The company, in partnership with HBM, produces and develops the MTS3000, an automatic system for measuring residual stresses by the hole-drilling method.

Residual stresses can be present in any mechanical structure because of many causes. They may be due to the technological process, such as plastic deformation or welding, non-uniform cooling of cast components, forging process or surface treatments like shot peening or surface hardening.

Residual stresses have the same role in a structure’s strength as common mechanical stresses. However, while stress due to external loads can be calculated with a degree of accuracy, residual stresses are difficult to foresee. It is, therefore, very important to have a reliable method able to measure them directly with minimum damage to the surface.

This is why the hole-drilling method has been developed. Basically, the method consists in drilling a small hole in the component at the centre of a strain gauge rosette. The residual stresses, in way of the removed material, are released enabling the surface strains to be measured by the strain gauges. A suitable mathematical model is then used to evaluate the reduced residual stress from the deformation measurements.


The MTS3000 system consists of:

  • An optical-mechanical system (to physically make the hole)
  • An electronic control unit (to control the optical-mechanical system and the measurements made by HBM’s QuantumX amplifier)
  • Hole drilling operating and control software (to enable automatic hole drilling)
  • Reprocessing software (to reprocess of data using different valuation methods).

The hole is made using an air turbine that rotates at about 350,000 RPM so that no residual stresses are added during the drilling process.

The reprocessing software allows the residual stresses in the material to be calculated from the measured strains.

The choice of back calculation method is very important in producing the most accurate representation of the real stress state. Many researchers have contributed, and continue to contribute, to the extensive literature describing the hole drilling method.

Currently, four different back calculation methods exist in the reprocessing software: the Uniform Stress Method according to ASTM E837-13 standard, the Non-Uniform Method according to ASTM E837-13 standard, the Schwarz- Kockelmann’s Method and the Integral Method.

Uniform Stress Method [Standard ASTM E 837-13]

This method, described in the ASTM E 837-13 standard, is based on the assumption that stresses do not vary with distance from the specimen’s surface. For this reason, the method does not consider spatial resolution. Nevertheless, when measured residual stresses are close to uniform stress field, this is the best method to choose, because it is the least sensitive to the effects of test errors.

It provides also a fast estimate of the average residual stress level into the specimen; that’s why this type of calculation is universally used and accepted.

Non-Uniform Stress Method [Standard ASTM E 837-13]

This method, described in the ASTM E 837-13 standard, introduces the computation of non-uniform stresses. Calculation steps and depth are fixed by this standard, and the calculation process refers to the Integral Method (see below for further details) with Tikhonov regularization to reduce the random errors in the calculated stresses.

The ASTM E 837-13 is the only complete standard on residual stresses available at world level.

Schwarz-Kockelmann’s method

Kockelmann’s method is based on the theory that there is a correlation function between the strain derivative and the stress distribution, expressed as a function of the hole’s depth. The bond is formed by a pair of coefficients (Kx and Ky), calculated on a simulation model, that relate stress and strain.

From these stress values it is possible to calculate the principal stresses and angle by using Mohr’s Circle.

Integral Method

This method, proposed by G. S. Schajer, provides a separate residual stress analysis at every hole-drilling depth increment. In this method, the contributions to the total measured strain relaxations of the stresses at all depths are considered simultaneously giving a higher spatial resolution than the other methods.

To simplify the problem of residual stress evaluation, Schajer proposed that the stress field could be described by means of step-wise functions whose value is constant through the partial hole depths. Using this hypothesis, Schajer established the numerical coefficients that are used for the calculation. The maximum depth that the method can be used for is 0.5 times the mean radius of the strain rosette used for the test.

The integral method should be chosen when residual stresses are expected to vary significantly with depth; however, it also has the highest sensitivity to test errors.

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