**Abstract**

The hole-drilling Strain-Gage method is a widely used and cost-effective technique for the evaluation of residual stresses. The test method is standardized by ASTM E837-13a, which defines the scope, measurement range, minimum requirements of instrumentation, test procedure, and algorithms and coefficients for the computation of uniform and non-uniform stress distribution. However, the standardized test method presents some limitations regarding the scope and measurement range; moreover, some typical errors involved in the measurements are not taken into account, i.e., errors due to the hole eccentricity, the local plasticity, the intermediate thickness, and the hole-bottom chamfer, which can affect the results in some cases. Also, the standard does not provide the user with a complete guide regarding the evaluation of the uncertainty connected with this type of measurement. The paper presents a more general approach that allows the correction of some errors and overcomes and some limitations of the ASTM E837-13a test method, contributing to greater accuracy of the test results.

**Keywords:** residual stress, hole-drilling method, ASTM E837, eccentricity error, local plasticity effect, intermediate thickness, hole-bottom chamfer, uncertainty evaluation

## **1. Introduction**

The hole-drilling method is one of the most cost-effective and simple methods to evaluate the residual stresses present in typical industrial workpieces. Those stresses are induced in the material whenever it is subjected to mechanical or thermal treatments and their effect is often a requirement for the best working condition of the workpiece. Therefore, in most industrial applications, it is very important to have an accurate estimation of the magnitude of the residual stresses particularly where they could represent a critical aspect for the integrity of a component. Nowadays, different methods can be adopted in order to measure the residual stresses in a specimen, and they differ in many features, such as, the depth of investigation or the type of material.

The hole-drilling method represents an interesting solution for the measurement of residual stress. Following the instructions reported in the ASTM E837-13a standard [1], a small hole is made in the center of a strain gage composed of a minimum of three grids. The method requires a sequence of drilling steps to be performed, at the end of which the relaxed strains are acquired from the rosette. The data are then used to calculate the magnitude and the direction of the residual stresses using the calibration coefficients supplied by the standard.

Sometimes, the hole-drilling method is used on components that have high residual stress values, comparable with the yield stress of the material. Drilling a hole locally modifies the geometry of the specimen and the stresses around the hole increase by the concentration factor of the discontinuity. It is possible to adopt a stress correction methodology for a uniform stress field and the blind

*Recent Advancements in the Hole-Drilling Strain-Gage Method for Determining Residual Stresses*

Evaluation of measurement-related uncertainties is also analyzed. Although the ASTM E837 standard does not include a detailed method for the uncertainty evaluation, some scientific works define the main sources of uncertainty and propose

Lastly, the paper shows an application of the hole-drilling method on a knownstress testing configuration obtained using a 4-point bending stress condition. The stresses are evaluated taking into account the effect of the correction of some of the errors described above, and then compared with the expected bending stress distribution. Finally, measurement uncertainty is evaluated with the same calculated

**2. Improvements in procedure and devices used to perform hole-drilling**

The ASTM E837 standard provides several details about the testing procedure for strain-gage hole-drilling measurements, including the requirements for the entire measurement chain used for performing the test. A typical hole-drilling measurement chain is composed of two parts: the device used for drilling the hole

The drilling sequence is performed using a drilling technology that minimizes the machining-induced residual stresses at the hole boundary. For this reason, the standard requires that drilling speed remains in the range of 20,000–400,000 rpm: this drilling speed can be obtained using either a high-speed air turbine or an

The hole can be made using center-hole drilling or the orbital drilling technique.

The orbital method has the advantages of adjusting the diameter of the hole by choosing the offset, of determining a more regular flow of chips and of reducing the

The ASTM standard defines some features of a hole-drilling device and the fundamental requirement that the drilling depth must be accurately controlled. The uncertainty of the depth increments, required by the standard, depends on the size of the strain gage rosette used during the measurement and needs to be lower than 0.004D. The depth accuracy requirement is essential in the case of a non-uniform stress profile where the hole is made using a step-by-step drilling sequence. For example, when using a rosette with a diameter D of approximately 2.56 mm, the depth uncertainty must be lower than 10 μm. This requirement can be difficult to

The use of an automatic drilling system instead of a manual system significantly increases the accuracy of the measurements. The automatic systems use an electronic device and dedicated acquisition and control software; they allow accurate control of the positioning of the end mill, necessary to meet the accuracy require-

When maximum accuracy is required in depth increments, it is advisable to use

an LVDT sensor, connected to the mechanical body of the drilling unit, which

geometric dimensions of the small chamfer at the bottom edge of the hole

ments of the standard and reducing the total testing time (**Figure 2**).

and the strain gage amplifier used for the acquisition of strains.

some approaches for expressing uncertainty in the case of uniform and

hole case [20–22].

stress distribution.

electric motor.

(**Figure 1b**).

**61**

non-uniform residual stresses [23–27].

*DOI: http://dx.doi.org/10.5772/intechopen.90392*

**residual stress measurements**

obtain using a manual drilling device.

The field of application of the method is wide-ranging and comprises typical mechanical engineering sectors, such as, metallurgy, automotive, aerospace and energy. Hole-drilling measurements can be performed in metal, composite and polymer materials [2]. The method also allows the test to be performed in different conditions, both in a laboratory and on field [3, 4].

According to the ASTM standard, the acquired strains are used for the calculation of residual stress applying the appropriate calibration coefficients depending on the thickness of the workpiece and the type of calculation (uniform or non-uniform). In the case of non-uniform distribution, the evaluation of residual stresses is based on the application of the integral method introduced by Schajer [5, 6].

Standard ASTM E837-13a reports the calibration coefficients for three types of standardized rosette (type A, type B and type C), specifying the related geometric dimensions. Unfortunately, the geometric dimensions of many commercial rosettes do not match those of standard rosettes, and in these cases, the calibration coefficients must be recalculated, taking into account the actual dimensions.

Beghini et al. [8, 9] introduced the influence function approach for a blind hole in a thick workpiece. The strain field was computed starting from a database of numerical solutions, implementing a specific geometric configuration in which the components of eccentricity are merely introduced as the geometry parameters rather than being considered as a source of error. This approach is more extensive with respect to the integral method and includes a parametric description of the strain gage rosette. Using the influence function approach, it is possible to include in the calculation different influence parameters such as the thickness of the specimen or a small bottom chamfer that could be present in the drilled hole.

The eccentricity is the possible error that can be made by the operator during the hole-drilling test, due to misalignment between the drilled hole and the strain gage circle. The ASTM standard sets the limit of 0.004 D (where D is the diameter of the gage circle) as the maximum error of eccentricity. If the actual eccentricity value is measured after drilling, the correction of the eccentricity error will increase the accuracy of the measurements. With this correction, the measurements could be acceptable even in cases where the limit set by the standard is exceeded. Over the years, several approaches have been proposed for the correction of this effect [8–14].

Regarding the thickness of the workpiece under testing, the ASTM standard does not include any instructions for residual stress evaluation for intermediate thickness values ranging from 0.2D to D, where D is the diameter of the strain gage circle. Nevertheless, industrial reality presents a lot of cases where this condition exists, such as with metal sheets or automotive parts. To solve this problem, Abraham and Schajer [15] and Beghini et al. [16] presented correction methods with related calibration coefficients.

The calibration coefficients provided by the ASTM E837-13a standard refer to a cylindrical hole with a flat bottom. Sometimes, end mills used in drilling have a small chamfer that produces a hole that is not perfectly cylindrical, with consequent errors in the measurement of relaxed deformations. To obtain measurements that are more accurate, it is therefore necessary to use calibration coefficients that consider the presence of the chamfer at the bottom of the hole. This source of error will be examined in greater detail, considering the proposed calibration coefficients to take this effect into account [17–19].

*Recent Advancements in the Hole-Drilling Strain-Gage Method for Determining Residual Stresses DOI: http://dx.doi.org/10.5772/intechopen.90392*

Sometimes, the hole-drilling method is used on components that have high residual stress values, comparable with the yield stress of the material. Drilling a hole locally modifies the geometry of the specimen and the stresses around the hole increase by the concentration factor of the discontinuity. It is possible to adopt a stress correction methodology for a uniform stress field and the blind hole case [20–22].

Evaluation of measurement-related uncertainties is also analyzed. Although the ASTM E837 standard does not include a detailed method for the uncertainty evaluation, some scientific works define the main sources of uncertainty and propose some approaches for expressing uncertainty in the case of uniform and non-uniform residual stresses [23–27].

Lastly, the paper shows an application of the hole-drilling method on a knownstress testing configuration obtained using a 4-point bending stress condition. The stresses are evaluated taking into account the effect of the correction of some of the errors described above, and then compared with the expected bending stress distribution. Finally, measurement uncertainty is evaluated with the same calculated stress distribution.
