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

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

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 electric motor.

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 geometric dimensions of the small chamfer at the bottom edge of the hole (**Figure 1b**).

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 obtain using a manual drilling device.

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

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

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 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

According to the ASTM standard, the acquired strains are used for the calculation of residual stress applying the appropriate calibration coefficients depending

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

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

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

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

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

non-uniform). In the case of non-uniform distribution, the evaluation of residual

on the thickness of the workpiece and the type of calculation (uniform or

stresses is based on the application of the integral method introduced by

do not match those of standard rosettes, and in these cases, the calibration coefficients must be recalculated, taking into account the actual dimensions.

or a small bottom chamfer that could be present in the drilled hole.

the calibration coefficients supplied by the standard.

*New Challenges in Residual Stress Measurements and Evaluation*

conditions, both in a laboratory and on field [3, 4].

Schajer [5, 6].

effect [8–14].

**60**

related calibration coefficients.

to take this effect into account [17–19].

between the tip and the surface of the workpiece. Alternatively, it is advisable to automatically measure the strain variation during the detection of the zero depth surface; when the end mill slowly touches the material surface, the strain gages detect the strain variation and the system immediately stops the drilling operation.

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

After acquisition of the relaxed strain values, the residual stresses need to be evaluated. First of all, it is necessary to choose between blind-hole and through-hole calculation and between uniform or non-uniform stress distribution along the depth. When the residual stress value is uniform along the depth, the ASTM E837-13a standard specifies that the formulas described in Section 8 of the standard be used. The standard suggests assuming the stress to be uniform only when prior information about the expected stress field is available or if a representative size of

Typical applications generally exhibit a non-uniform state of residual stresses. In this case, it is necessary to follow the instructions reported in Section 9 of ASTM E837-13a for the calculation of residual stresses along the depth. The standard provides the calibration matrices, derived by the integral method, that must be multiplied with the acquired strains to derive the stress values. The matrix coefficients, corresponding to each calculation depth, are dimensionless and almost independent

For the sake of simplicity, only the equation for the calculation of the

*aTa* <sup>þ</sup> *<sup>α</sup>PcTc* � *<sup>P</sup>* <sup>¼</sup> *<sup>E</sup>*

It is important to point out that dependence of the stresses on the Poisson's ratio,

All the coefficients reported in the calibration matrices A and B, for a nonuniform stress field, are strictly related to the nominal hole diameter (DN) of 2 mm.

If the diameter of the drilled hole (D0) differs from the nominal value, each matrix coefficient reported in the standard needs to be corrected using Eq. 2

*aj*,*kNEW* <sup>¼</sup> *<sup>D</sup>*<sup>0</sup>

drilled hole (D0) can vary from 1.88 to 2.12 mm. The ratio ð Þ *D*0*=DN*

*DN* <sup>2</sup>

The dependency of the coefficients of the calibration matrix on the drilled hole diameter, as expressed in Eq. 2, is approximated as explained by Alegre et al. [7]. For example, using a rosette with a strain gage circle diameter (D) of 5.13 mm, the nominal hole diameter (DN) is equal to 2 mm and the allowed diameter of the

Recently, some developments have been carried out to overcome the limits of the ASTM E837 standard previously described and to take into account other parameters affecting the results that are not considered in the standard.

Beghini et al. [8, 9] of the University of Pisa introduced a generalized integral method based on the analytical definition of influence functions. The method is substantially an evolution of the Integral Method and it also overcomes the limitation of the ASTM E837 standard regarding the maximum allowable value of

1 þ ν

*aTp* (1)

*aj*,*<sup>k</sup>* (2)

2 ranges

**3. Advancements in residual stress calculation**

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

the magnitude of the residual stress is required.

combination stress P is shown below.

as shown in Eq. 1, is simplified [13].

of the material [1].

reported below:

between 0.88 and 1.12.

**63**

**Figure 1.** *(a) LVDT sensor installed on the drilling device and (b) orbital drilling slide.*

#### **Figure 2.**

*Hole drilling measurements: typical automatic measuring device (MTS3000-Restan system—SINT Technology).*

allows an accuracy of few microns (**Figure 1a**). An automatic system allows a higher number of drilling steps, a uniform feed rate and a fixed stabilization time. Moreover, it can be controlled remotely, minimizing operator presence near the drilling unit [2]; this is particularly important in the case of hole-drilling measurements on polymeric or composite materials.

To obtain accurate measurements, it is very important to establish the point that corresponds to the "zero" cutter depth. The standard identifies it as the point at which the end mill begins to lightly scratch the surface of the workpiece, during slow advance drilling. It is clear that the quality of the results of this process greatly depends on the skill of the operator who carries out the measurements and may not be very accurate.

In the case of tests on conductive materials, it is possible to use the electrical contact technique that identifies the contact when the electrical connection occurs between the tip and the surface of the workpiece. Alternatively, it is advisable to automatically measure the strain variation during the detection of the zero depth surface; when the end mill slowly touches the material surface, the strain gages detect the strain variation and the system immediately stops the drilling operation.
